TSTP Solution File: ALG146+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG146+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:37:37 EDT 2023
% Result : Unsatisfiable 16.55s 3.82s
% Output : Proof 160.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ALG146+1 : TPTP v8.1.2. Released v2.7.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 02:55:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.25/1.56 Prover 1: Preprocessing ...
% 4.25/1.56 Prover 4: Preprocessing ...
% 4.42/1.61 Prover 0: Preprocessing ...
% 4.42/1.61 Prover 2: Preprocessing ...
% 4.42/1.61 Prover 5: Preprocessing ...
% 4.42/1.61 Prover 6: Preprocessing ...
% 4.42/1.61 Prover 3: Preprocessing ...
% 7.22/2.18 Prover 2: Constructing countermodel ...
% 7.22/2.18 Prover 3: Constructing countermodel ...
% 8.07/2.30 Prover 0: Constructing countermodel ...
% 8.07/2.30 Prover 4: Constructing countermodel ...
% 8.07/2.30 Prover 6: Constructing countermodel ...
% 8.56/2.34 Prover 1: Constructing countermodel ...
% 10.17/2.71 Prover 5: Constructing countermodel ...
% 16.55/3.82 Prover 6: proved (3140ms)
% 16.55/3.82
% 16.55/3.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.55/3.82
% 16.55/3.82 Prover 5: stopped
% 16.55/3.83 Prover 2: stopped
% 16.55/3.84 Prover 3: stopped
% 16.55/3.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.55/3.86 Prover 0: proved (3183ms)
% 16.55/3.86
% 16.55/3.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.55/3.86
% 16.55/3.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.55/3.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.55/3.87 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.06/3.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.97/4.11 Prover 11: Preprocessing ...
% 17.97/4.15 Prover 8: Preprocessing ...
% 17.97/4.17 Prover 7: Preprocessing ...
% 17.97/4.18 Prover 10: Preprocessing ...
% 18.83/4.19 Prover 13: Preprocessing ...
% 19.65/4.29 Prover 11: Constructing countermodel ...
% 19.78/4.32 Prover 8: Constructing countermodel ...
% 19.87/4.37 Prover 10: Constructing countermodel ...
% 19.87/4.39 Prover 7: Constructing countermodel ...
% 20.46/4.46 Prover 13: Constructing countermodel ...
% 52.16/9.41 Prover 13: stopped
% 52.16/9.43 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 52.66/9.54 Prover 16: Preprocessing ...
% 52.66/9.69 Prover 16: Constructing countermodel ...
% 89.16/15.31 Prover 16: stopped
% 89.16/15.32 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 90.32/15.45 Prover 19: Preprocessing ...
% 90.32/15.58 Prover 19: Constructing countermodel ...
% 93.96/15.99 Prover 1: stopped
% 116.77/19.09 Prover 19: stopped
% 147.64/24.45 Prover 10: Found proof (size 134376426)
% 147.64/24.45 Prover 10: proved (20612ms)
% 147.64/24.46 Prover 11: stopped
% 147.64/24.46 Prover 4: stopped
% 147.64/24.46 Prover 8: stopped
% 147.64/24.46 Prover 7: stopped
% 147.64/24.46
% 147.64/24.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 147.64/24.46
% 149.82/25.32 % SZS output start Proof for theBenchmark
% 150.14/25.37 Assumptions after simplification:
% 150.14/25.37 ---------------------------------
% 150.14/25.37
% 150.14/25.37 (ax1)
% 150.14/25.42 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.14/25.42 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 150.14/25.42 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 150.14/25.42 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 150.14/25.42 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 150.14/25.42 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 150.14/25.42 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 150.14/25.42 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 150.14/25.42 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 150.14/25.42 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 150.14/25.42 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 150.14/25.42 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 150.14/25.42 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 150.14/25.42 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 150.14/25.42 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 150.14/25.42 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 150.14/25.42 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 150.14/25.42 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 150.14/25.42 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 150.14/25.42
% 150.14/25.42 (ax10)
% 150.14/25.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.14/25.43 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 150.14/25.43 op(e0, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e0) = v1 &
% 150.14/25.43 $i(v1))))
% 150.14/25.43
% 150.14/25.43 (ax11)
% 150.14/25.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.14/25.43 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 150.14/25.43 op(e0, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e0) = v1 &
% 150.14/25.43 $i(v1))))
% 150.14/25.43
% 150.14/25.43 (ax12)
% 150.14/25.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.14/25.43 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 150.14/25.43 op(e1, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e1) = v1 &
% 150.14/25.43 $i(v1))))
% 150.14/25.43
% 150.14/25.43 (ax13)
% 150.14/25.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.14/25.43 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 150.14/25.43 op(e1, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e1) = v1 &
% 150.14/25.43 $i(v1))))
% 150.14/25.43
% 150.14/25.43 (ax14)
% 150.14/25.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.14/25.44 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 150.14/25.44 op(e1, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e1) = v1 &
% 150.14/25.44 $i(v1))))
% 150.14/25.44
% 150.14/25.44 (ax15)
% 150.14/25.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.14/25.44 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 150.14/25.44 op(e1, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e1) = v1 &
% 150.14/25.44 $i(v1))))
% 150.14/25.44
% 150.14/25.44 (ax16)
% 150.48/25.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.44 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 150.48/25.44 op(e1, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e1) = v1 &
% 150.48/25.44 $i(v1))))
% 150.48/25.44
% 150.48/25.44 (ax17)
% 150.48/25.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.44 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 150.48/25.44 op(e1, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e1) = v1 &
% 150.48/25.44 $i(v1))))
% 150.48/25.44
% 150.48/25.44 (ax18)
% 150.48/25.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.44 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 150.48/25.44 op(e2, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e2) = v1 &
% 150.48/25.44 $i(v1))))
% 150.48/25.44
% 150.48/25.44 (ax19)
% 150.48/25.45 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.45 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 150.48/25.45 op(e2, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e2) = v1 &
% 150.48/25.45 $i(v1))))
% 150.48/25.45
% 150.48/25.45 (ax2)
% 150.48/25.47 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.47 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 150.48/25.47 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 150.48/25.47 $i] : ? [v14: $i] : ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 =
% 150.48/25.47 e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3,
% 150.48/25.47 e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 150.48/25.47 e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15
% 150.48/25.47 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 &
% 150.48/25.47 op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3,
% 150.48/25.47 e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2)
% 150.48/25.47 | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1
% 150.48/25.47 & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3,
% 150.48/25.47 e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) =
% 150.48/25.47 e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15
% 150.48/25.47 = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 150.48/25.47 op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3,
% 150.48/25.47 e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0)
% 150.48/25.47 | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3
% 150.48/25.47 & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2)
% 150.48/25.47 = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 150.48/25.47 (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 150.48/25.47 op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2)
% 150.48/25.47 = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) |
% 150.48/25.47 (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 150.48/25.47 op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2,
% 150.48/25.47 e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) =
% 150.48/25.47 e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 150.48/25.47 (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 150.48/25.47 op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1)
% 150.48/25.47 = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) |
% 150.48/25.47 (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 &
% 150.48/25.47 op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2,
% 150.48/25.47 e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3))
% 150.48/25.47 & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 150.48/25.47 op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3,
% 150.48/25.47 e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1)
% 150.48/25.47 | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0
% 150.48/25.47 & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1)
% 150.48/25.47 = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) |
% 150.48/25.47 (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 150.48/25.47 op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) =
% 150.48/25.47 e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8
% 150.48/25.47 = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 &
% 150.48/25.47 op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2)
% 150.48/25.47 = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) &
% 150.48/25.47 ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 150.48/25.47 op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0)
% 150.48/25.47 = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0
% 150.48/25.47 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 &
% 150.48/25.47 op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) =
% 150.48/25.47 e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 150.48/25.47 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 150.48/25.47 op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) =
% 150.48/25.47 e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2
% 150.48/25.47 = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 &
% 150.48/25.47 op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3,
% 150.48/25.47 e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) =
% 150.48/25.47 e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) |
% 150.48/25.47 (v1 = e0 & op(e0, e1) = e0)))))
% 150.48/25.47
% 150.48/25.47 (ax20)
% 150.48/25.47 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.47 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 150.48/25.47 op(e2, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e2) = v1 &
% 150.48/25.47 $i(v1))))
% 150.48/25.47
% 150.48/25.47 (ax21)
% 150.48/25.47 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.47 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 150.48/25.47 op(e2, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e2) = v1 &
% 150.48/25.47 $i(v1))))
% 150.48/25.47
% 150.48/25.47 (ax22)
% 150.48/25.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.48 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 150.48/25.48 op(e2, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e2) = v1 &
% 150.48/25.48 $i(v1))))
% 150.48/25.48
% 150.48/25.48 (ax23)
% 150.48/25.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.48 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 150.48/25.48 op(e2, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e2) = v1 &
% 150.48/25.48 $i(v1))))
% 150.48/25.48
% 150.48/25.48 (ax24)
% 150.48/25.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.48 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 150.48/25.48 op(e3, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e3) = v1 &
% 150.48/25.48 $i(v1))))
% 150.48/25.48
% 150.48/25.48 (ax25)
% 150.48/25.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.48 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 150.48/25.48 op(e3, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e3) = v1 &
% 150.48/25.48 $i(v1))))
% 150.48/25.48
% 150.48/25.48 (ax26)
% 150.48/25.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.48 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 150.48/25.48 op(e3, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e3) = v1 &
% 150.48/25.48 $i(v1))))
% 150.48/25.48
% 150.48/25.48 (ax27)
% 150.48/25.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.48/25.48 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 150.48/25.48 op(e3, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e3) = v1 &
% 150.48/25.48 $i(v1))))
% 150.48/25.48
% 150.48/25.48 (ax28)
% 150.71/25.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.71/25.49 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 150.71/25.49 op(e3, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e3) = v1 &
% 150.71/25.49 $i(v1))))
% 150.71/25.49
% 150.71/25.49 (ax29)
% 150.71/25.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.71/25.49 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 150.71/25.49 op(e3, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e3) = v1 &
% 150.71/25.49 $i(v1))))
% 150.71/25.49
% 150.71/25.49 (ax3)
% 150.71/25.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.71/25.49 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 150.71/25.49 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 150.71/25.49 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 150.71/25.49 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 150.71/25.49 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 150.71/25.49 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 150.71/25.49 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 150.71/25.49 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 150.71/25.49 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 150.71/25.49 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 150.71/25.49 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 150.71/25.49 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 150.71/25.49 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 150.71/25.49 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 150.71/25.49 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 150.71/25.49 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 150.71/25.49 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 150.71/25.49 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 150.71/25.49 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 150.71/25.49
% 150.71/25.49 (ax4)
% 150.71/25.49 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~
% 150.71/25.49 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 150.71/25.49
% 150.71/25.49 (ax5)
% 150.71/25.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.71/25.50 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 150.71/25.50 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 150.71/25.50 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v3 & op(e2, e2) = v2 &
% 150.71/25.50 op(e1, e1) = v1 & op(e0, e0) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~
% 150.71/25.50 (v3 = e2) | (v15 = e3 & op(e3, e2) = e3)) & ( ~ (v3 = e1) | (v14 = e3 &
% 150.71/25.50 op(e3, e1) = e3)) & ( ~ (v3 = e0) | (v13 = e3 & op(e3, e0) = e3)) & ( ~
% 150.71/25.50 (v2 = e3) | (v12 = e2 & op(e2, e3) = e2)) & ( ~ (v2 = e1) | (v11 = e2 &
% 150.71/25.50 op(e2, e1) = e2)) & ( ~ (v2 = e0) | (v10 = e2 & op(e2, e0) = e2)) & ( ~
% 150.71/25.50 (v1 = e3) | (v9 = e1 & op(e1, e3) = e1)) & ( ~ (v1 = e2) | (v8 = e1 &
% 150.71/25.50 op(e1, e2) = e1)) & ( ~ (v1 = e0) | (v7 = e1 & op(e1, e0) = e1)) & ( ~
% 150.71/25.50 (v0 = e3) | (v6 = e0 & op(e0, e3) = e0)) & ( ~ (v0 = e2) | (v5 = e0 &
% 150.71/25.50 op(e0, e2) = e0)) & ( ~ (v0 = e1) | (v4 = e0 & op(e0, e1) = e0)) & (v3 =
% 150.71/25.50 e3 | v2 = e2 | v1 = e1 | v0 = e0) & ((v15 = e3 & v12 = e3 & ~ (v2 = e2) &
% 150.71/25.50 op(e3, e2) = e3 & op(e2, e3) = e3) | (v15 = e2 & v12 = e2 & ~ (v3 = e3)
% 150.71/25.50 & op(e3, e2) = e2 & op(e2, e3) = e2) | (v14 = e3 & v9 = e3 & ~ (v1 =
% 150.71/25.50 e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (v14 = e1 & v9 = e1 & ~
% 150.71/25.50 (v3 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (v13 = e3 & v6 = e3 &
% 150.71/25.50 ~ (v0 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (v13 = e0 & v6 = e0 &
% 150.71/25.50 ~ (v3 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (v11 = e2 & v8 = e2
% 150.71/25.50 & ~ (v1 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (v11 = e1 & v8 =
% 150.71/25.50 e1 & ~ (v2 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (v10 = e2 & v5
% 150.71/25.50 = e2 & ~ (v0 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (v10 = e0 &
% 150.71/25.50 v5 = e0 & ~ (v2 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) | (v7 = e1 &
% 150.71/25.50 v4 = e1 & ~ (v0 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (v7 = e0 &
% 150.71/25.50 v4 = e0 & ~ (v1 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)))
% 150.71/25.50
% 150.71/25.50 (ax6)
% 150.71/25.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.71/25.50 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 150.71/25.50 op(e0, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e0) = v1 &
% 150.71/25.50 $i(v1))))
% 150.71/25.50
% 150.71/25.51 (ax7)
% 150.71/25.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.71/25.51 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 150.71/25.51 op(e0, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e0) = v1 &
% 150.71/25.51 $i(v1))))
% 150.71/25.51
% 150.71/25.51 (ax8)
% 150.71/25.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.71/25.51 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 150.71/25.51 op(e0, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e0) = v1 &
% 150.71/25.51 $i(v1))))
% 150.71/25.51
% 150.71/25.51 (ax9)
% 150.71/25.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 150.71/25.51 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 150.71/25.51 op(e0, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e0) = v1 &
% 150.71/25.51 $i(v1))))
% 150.71/25.51
% 150.71/25.51 (function-axioms)
% 150.71/25.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 150.71/25.51 v2) = v1) | ~ (op(v3, v2) = v0))
% 150.71/25.51
% 150.71/25.51 Those formulas are unsatisfiable:
% 150.71/25.51 ---------------------------------
% 150.71/25.51
% 150.71/25.51 Begin of proof
% 150.71/25.51 |
% 150.71/25.51 | ALPHA: (ax1) implies:
% 150.71/25.52 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 150.71/25.52 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 150.71/25.52 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 150.71/25.52 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 150.71/25.52 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 150.71/25.52 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 150.71/25.52 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 150.71/25.52 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 150.71/25.52 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 150.71/25.52 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 150.71/25.52 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 150.71/25.52 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 150.71/25.52 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 150.71/25.52 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 150.71/25.52 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 150.71/25.52 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 150.71/25.52 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 150.71/25.52 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 150.71/25.52 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 150.71/25.52 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 150.71/25.52 | = e0))
% 150.71/25.52 |
% 150.71/25.52 | ALPHA: (ax2) implies:
% 150.71/25.54 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 150.71/25.54 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 150.71/25.54 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 150.71/25.54 | ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2)
% 150.71/25.54 | = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) =
% 150.71/25.54 | e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 150.71/25.54 | e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3))
% 150.71/25.54 | & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11
% 150.71/25.54 | = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 =
% 150.71/25.54 | e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 150.71/25.54 | op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 &
% 150.71/25.54 | op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 &
% 150.71/25.54 | op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 &
% 150.71/25.54 | op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 &
% 150.71/25.54 | op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 &
% 150.71/25.54 | op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 150.71/25.54 | op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 &
% 150.71/25.54 | op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 &
% 150.71/25.54 | op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 &
% 150.71/25.54 | op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 &
% 150.71/25.54 | op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 &
% 150.71/25.54 | op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 &
% 150.71/25.54 | op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 150.71/25.54 | op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 &
% 150.71/25.54 | op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 &
% 150.71/25.54 | op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 &
% 150.71/25.54 | op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 &
% 150.71/25.54 | op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 150.71/25.54 | op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 &
% 150.71/25.54 | op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 &
% 150.71/25.54 | op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 150.71/25.54 | op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 150.71/25.54 | op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 &
% 150.71/25.54 | op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 &
% 150.71/25.54 | op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 &
% 150.71/25.54 | op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 &
% 150.71/25.54 | op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 &
% 150.71/25.54 | op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 150.71/25.54 | op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 &
% 150.71/25.54 | op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 &
% 150.71/25.54 | op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 &
% 150.71/25.54 | op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 &
% 150.71/25.54 | op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 &
% 150.71/25.54 | op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 &
% 150.71/25.54 | op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 150.71/25.54 | op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 &
% 150.71/25.54 | op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 &
% 150.71/25.54 | op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 &
% 150.71/25.54 | op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 &
% 150.71/25.54 | op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 &
% 150.71/25.54 | op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 &
% 150.71/25.54 | op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 150.71/25.54 | op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 &
% 150.71/25.54 | op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 &
% 150.71/25.54 | op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 &
% 150.71/25.54 | op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 &
% 150.71/25.54 | op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 &
% 150.71/25.54 | op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 150.71/25.54 | op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 150.71/25.54 | op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 &
% 150.71/25.54 | op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 &
% 150.71/25.54 | op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 150.71/25.54 | op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 150.71/25.54 | op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 &
% 150.71/25.54 | op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 &
% 150.71/25.54 | op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 150.71/25.54 | op(e0, e1) = e0)))))
% 150.71/25.54 |
% 150.71/25.54 | ALPHA: (ax3) implies:
% 150.71/25.54 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 150.71/25.54 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 150.71/25.54 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 150.71/25.54 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 150.71/25.54 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 150.99/25.54 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 150.99/25.54 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 150.99/25.54 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 150.99/25.54 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 150.99/25.54 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 150.99/25.54 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 150.99/25.54 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 150.99/25.54 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 150.99/25.54 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 150.99/25.54 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 150.99/25.54 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 150.99/25.54 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 150.99/25.54 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 150.99/25.54 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 150.99/25.54 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 150.99/25.54 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 150.99/25.54 |
% 150.99/25.54 | ALPHA: (ax4) implies:
% 150.99/25.54 | (4) ~ (e1 = e0)
% 150.99/25.54 | (5) ~ (e2 = e0)
% 150.99/25.54 | (6) ~ (e2 = e1)
% 150.99/25.54 | (7) ~ (e3 = e0)
% 150.99/25.54 | (8) ~ (e3 = e1)
% 150.99/25.54 | (9) ~ (e3 = e2)
% 150.99/25.54 |
% 150.99/25.54 | ALPHA: (ax5) implies:
% 150.99/25.55 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 150.99/25.55 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 150.99/25.55 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 150.99/25.55 | $i] : ? [v15: $i] : (op(e3, e3) = v3 & op(e2, e2) = v2 & op(e1, e1)
% 150.99/25.55 | = v1 & op(e0, e0) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3
% 150.99/25.55 | = e2) | (v15 = e3 & op(e3, e2) = e3)) & ( ~ (v3 = e1) | (v14 =
% 150.99/25.55 | e3 & op(e3, e1) = e3)) & ( ~ (v3 = e0) | (v13 = e3 & op(e3, e0)
% 150.99/25.55 | = e3)) & ( ~ (v2 = e3) | (v12 = e2 & op(e2, e3) = e2)) & ( ~ (v2
% 150.99/25.55 | = e1) | (v11 = e2 & op(e2, e1) = e2)) & ( ~ (v2 = e0) | (v10 =
% 150.99/25.55 | e2 & op(e2, e0) = e2)) & ( ~ (v1 = e3) | (v9 = e1 & op(e1, e3) =
% 150.99/25.55 | e1)) & ( ~ (v1 = e2) | (v8 = e1 & op(e1, e2) = e1)) & ( ~ (v1 =
% 150.99/25.55 | e0) | (v7 = e1 & op(e1, e0) = e1)) & ( ~ (v0 = e3) | (v6 = e0 &
% 150.99/25.55 | op(e0, e3) = e0)) & ( ~ (v0 = e2) | (v5 = e0 & op(e0, e2) = e0))
% 150.99/25.55 | & ( ~ (v0 = e1) | (v4 = e0 & op(e0, e1) = e0)) & (v3 = e3 | v2 = e2
% 150.99/25.55 | | v1 = e1 | v0 = e0) & ((v15 = e3 & v12 = e3 & ~ (v2 = e2) &
% 150.99/25.55 | op(e3, e2) = e3 & op(e2, e3) = e3) | (v15 = e2 & v12 = e2 & ~
% 150.99/25.55 | (v3 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (v14 = e3 & v9
% 150.99/25.55 | = e3 & ~ (v1 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (v14
% 150.99/25.55 | = e1 & v9 = e1 & ~ (v3 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 150.99/25.55 | e1) | (v13 = e3 & v6 = e3 & ~ (v0 = e0) & op(e3, e0) = e3 &
% 150.99/25.55 | op(e0, e3) = e3) | (v13 = e0 & v6 = e0 & ~ (v3 = e3) & op(e3,
% 150.99/25.55 | e0) = e0 & op(e0, e3) = e0) | (v11 = e2 & v8 = e2 & ~ (v1 =
% 150.99/25.55 | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (v11 = e1 & v8 = e1
% 150.99/25.55 | & ~ (v2 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (v10 = e2
% 150.99/25.55 | & v5 = e2 & ~ (v0 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 150.99/25.55 | (v10 = e0 & v5 = e0 & ~ (v2 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 150.99/25.55 | = e0) | (v7 = e1 & v4 = e1 & ~ (v0 = e0) & op(e1, e0) = e1 &
% 150.99/25.55 | op(e0, e1) = e1) | (v7 = e0 & v4 = e0 & ~ (v1 = e1) & op(e1,
% 150.99/25.55 | e0) = e0 & op(e0, e1) = e0)))
% 150.99/25.55 |
% 150.99/25.55 | ALPHA: (ax6) implies:
% 150.99/25.55 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 150.99/25.55 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e0, e0) = v1 &
% 150.99/25.55 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1))))
% 150.99/25.55 |
% 150.99/25.55 | ALPHA: (ax7) implies:
% 150.99/25.55 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 150.99/25.55 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e0, e0) = v1 &
% 150.99/25.55 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1))))
% 150.99/25.55 |
% 150.99/25.55 | ALPHA: (ax8) implies:
% 150.99/25.55 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 150.99/25.55 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e0, e0) = v1 &
% 150.99/25.55 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1))))
% 150.99/25.55 |
% 150.99/25.55 | ALPHA: (ax9) implies:
% 150.99/25.55 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 150.99/25.55 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e0, e0) = v1 &
% 150.99/25.55 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1))))
% 150.99/25.55 |
% 150.99/25.55 | ALPHA: (ax10) implies:
% 150.99/25.56 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 150.99/25.56 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e0, e0) = v1 &
% 150.99/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1))))
% 150.99/25.56 |
% 150.99/25.56 | ALPHA: (ax11) implies:
% 151.04/25.56 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e0, e0) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax12) implies:
% 151.04/25.56 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e1, e1) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax13) implies:
% 151.04/25.56 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e1, e1) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax14) implies:
% 151.04/25.56 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e1, e1) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax15) implies:
% 151.04/25.56 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e1, e1) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax16) implies:
% 151.04/25.56 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e1, e1) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax17) implies:
% 151.04/25.56 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e1, e1) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax18) implies:
% 151.04/25.56 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e2, e2) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax19) implies:
% 151.04/25.56 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e2, e2) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax20) implies:
% 151.04/25.56 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e2, e2) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax21) implies:
% 151.04/25.56 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 151.04/25.56 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e2, e2) = v1 &
% 151.04/25.56 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1))))
% 151.04/25.56 |
% 151.04/25.56 | ALPHA: (ax22) implies:
% 151.04/25.57 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 151.04/25.57 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e2, e2) = v1 &
% 151.04/25.57 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1))))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (ax23) implies:
% 151.04/25.57 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 151.04/25.57 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e2, e2) = v1 &
% 151.04/25.57 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1))))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (ax24) implies:
% 151.04/25.57 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 151.04/25.57 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e3, e3) = v1 &
% 151.04/25.57 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1))))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (ax25) implies:
% 151.04/25.57 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 151.04/25.57 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e3, e3) = v1 &
% 151.04/25.57 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1))))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (ax26) implies:
% 151.04/25.57 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 151.04/25.57 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e3, e3) = v1 &
% 151.04/25.57 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1))))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (ax27) implies:
% 151.04/25.57 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 151.04/25.57 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e3, e3) = v1 &
% 151.04/25.57 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1))))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (ax28) implies:
% 151.04/25.57 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 151.04/25.57 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e3, e3) = v1 &
% 151.04/25.57 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1))))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (ax29) implies:
% 151.04/25.57 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 151.04/25.57 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e3, e3) = v1 &
% 151.04/25.57 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1))))
% 151.04/25.57 |
% 151.04/25.57 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 151.04/25.57 | (35) op(e0, e0) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e1) | ( ~ (all_4_0
% 151.04/25.57 | = e3) & op(all_4_1, e0) = all_4_0 & op(e1, e1) = all_4_1 &
% 151.04/25.57 | $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e2) & op(e1, e1) =
% 151.04/25.57 | all_4_1 & $i(all_4_1)))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (35) implies:
% 151.04/25.57 | (36) op(e0, e0) = all_4_2
% 151.04/25.57 | (37) ~ (all_4_2 = e1) | ( ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 151.04/25.57 | op(e1, e1) = all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 =
% 151.04/25.57 | e2) & op(e1, e1) = all_4_1 & $i(all_4_1))
% 151.04/25.57 |
% 151.04/25.57 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 151.04/25.57 | (38) op(e1, e1) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e2) | ( ~ (all_6_0
% 151.04/25.57 | = e0) & op(all_6_1, e1) = all_6_0 & op(e2, e2) = all_6_1 &
% 151.04/25.57 | $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e3) & op(e2, e2) =
% 151.04/25.57 | all_6_1 & $i(all_6_1)))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (38) implies:
% 151.04/25.57 | (39) op(e1, e1) = all_6_2
% 151.04/25.57 | (40) ~ (all_6_2 = e2) | ( ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 &
% 151.04/25.57 | op(e2, e2) = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 151.04/25.57 | e3) & op(e2, e2) = all_6_1 & $i(all_6_1))
% 151.04/25.57 |
% 151.04/25.57 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 151.04/25.57 | (41) op(e2, e2) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e1) | ( ~ (all_8_0
% 151.04/25.57 | = e0) & op(all_8_1, e2) = all_8_0 & op(e1, e1) = all_8_1 &
% 151.04/25.57 | $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e3) & op(e1, e1) =
% 151.04/25.57 | all_8_1 & $i(all_8_1)))
% 151.04/25.57 |
% 151.04/25.57 | ALPHA: (41) implies:
% 151.04/25.57 | (42) op(e2, e2) = all_8_2
% 151.04/25.58 | (43) ~ (all_8_2 = e1) | ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 &
% 151.04/25.58 | op(e1, e1) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 =
% 151.04/25.58 | e3) & op(e1, e1) = all_8_1 & $i(all_8_1))
% 151.04/25.58 |
% 151.04/25.58 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 151.04/25.58 | gives:
% 151.04/25.58 | (44) op(e3, e3) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e0) | ( ~
% 151.04/25.58 | (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e0, e0) =
% 151.04/25.58 | all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e1) &
% 151.04/25.58 | op(e0, e0) = all_10_1 & $i(all_10_1)))
% 151.04/25.58 |
% 151.04/25.58 | ALPHA: (44) implies:
% 151.04/25.58 | (45) op(e3, e3) = all_10_2
% 151.04/25.58 | (46) ~ (all_10_2 = e0) | ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0
% 151.04/25.58 | & op(e0, e0) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 151.04/25.58 | (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1))
% 151.04/25.58 |
% 151.04/25.58 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 151.04/25.58 | gives:
% 151.04/25.58 | (47) op(e0, e0) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e1) | ( ~
% 151.04/25.58 | (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e1, e1) =
% 151.04/25.58 | all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e3) &
% 151.04/25.58 | op(e1, e1) = all_12_1 & $i(all_12_1)))
% 151.04/25.58 |
% 151.04/25.58 | ALPHA: (47) implies:
% 151.04/25.58 | (48) op(e0, e0) = all_12_2
% 151.04/25.58 | (49) ~ (all_12_2 = e1) | ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0
% 151.04/25.58 | & op(e1, e1) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 151.04/25.58 | (all_12_1 = e3) & op(e1, e1) = all_12_1 & $i(all_12_1))
% 151.04/25.58 |
% 151.04/25.58 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 151.04/25.58 | gives:
% 151.04/25.58 | (50) op(e2, e2) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e3) | ( ~
% 151.04/25.58 | (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e3, e3) =
% 151.04/25.58 | all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e0) &
% 151.04/25.58 | op(e3, e3) = all_14_1 & $i(all_14_1)))
% 151.04/25.58 |
% 151.04/25.58 | ALPHA: (50) implies:
% 151.04/25.58 | (51) op(e2, e2) = all_14_2
% 151.04/25.58 | (52) ~ (all_14_2 = e3) | ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0
% 151.04/25.58 | & op(e3, e3) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 151.04/25.58 | (all_14_1 = e0) & op(e3, e3) = all_14_1 & $i(all_14_1))
% 151.04/25.58 |
% 151.04/25.58 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2
% 151.04/25.58 | gives:
% 151.04/25.58 | (53) op(e3, e3) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e2) | ( ~
% 151.04/25.58 | (all_16_0 = e1) & op(all_16_1, e3) = all_16_0 & op(e2, e2) =
% 151.04/25.58 | all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e0) &
% 151.04/25.58 | op(e2, e2) = all_16_1 & $i(all_16_1)))
% 151.04/25.58 |
% 151.04/25.58 | ALPHA: (53) implies:
% 151.04/25.58 | (54) op(e3, e3) = all_16_2
% 151.04/25.58 | (55) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0
% 151.04/25.58 | & op(e2, e2) = all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 151.04/25.58 | (all_16_1 = e0) & op(e2, e2) = all_16_1 & $i(all_16_1))
% 151.04/25.58 |
% 151.04/25.58 | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2
% 151.04/25.58 | gives:
% 151.04/25.58 | (56) op(e1, e1) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e2) | ( ~
% 151.04/25.58 | (all_18_0 = e3) & op(all_18_1, e1) = all_18_0 & op(e2, e2) =
% 151.04/25.58 | all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e0) &
% 151.04/25.58 | op(e2, e2) = all_18_1 & $i(all_18_1)))
% 151.04/25.58 |
% 151.04/25.58 | ALPHA: (56) implies:
% 151.04/25.58 | (57) op(e1, e1) = all_18_2
% 151.04/25.58 | (58) ~ (all_18_2 = e2) | ( ~ (all_18_0 = e3) & op(all_18_1, e1) = all_18_0
% 151.04/25.58 | & op(e2, e2) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 151.04/25.58 | (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1))
% 151.04/25.58 |
% 151.04/25.58 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2
% 151.04/25.58 | gives:
% 151.04/25.58 | (59) op(e0, e0) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e2) | ( ~
% 151.04/25.58 | (all_20_0 = e3) & op(all_20_1, e0) = all_20_0 & op(e2, e2) =
% 151.04/25.58 | all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e1) &
% 151.04/25.58 | op(e2, e2) = all_20_1 & $i(all_20_1)))
% 151.04/25.58 |
% 151.04/25.58 | ALPHA: (59) implies:
% 151.04/25.58 | (60) op(e0, e0) = all_20_2
% 151.04/25.58 | (61) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0
% 151.04/25.58 | & op(e2, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 151.04/25.58 | (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1))
% 151.04/25.58 |
% 151.04/25.58 | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2
% 151.04/25.58 | gives:
% 151.04/25.58 | (62) op(e2, e2) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e3) | ( ~
% 151.04/25.58 | (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 151.04/25.58 | all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) &
% 151.04/25.58 | op(e3, e3) = all_22_1 & $i(all_22_1)))
% 151.04/25.58 |
% 151.04/25.58 | ALPHA: (62) implies:
% 151.04/25.58 | (63) op(e2, e2) = all_22_2
% 151.04/25.58 | (64) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0
% 151.04/25.58 | & op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 151.04/25.58 | (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 151.04/25.58 |
% 151.04/25.58 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2
% 151.04/25.58 | gives:
% 151.04/25.58 | (65) op(e3, e3) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e0) | ( ~
% 151.04/25.58 | (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 & op(e0, e0) =
% 151.04/25.58 | all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e2) &
% 151.04/25.58 | op(e0, e0) = all_24_1 & $i(all_24_1)))
% 151.04/25.58 |
% 151.04/25.58 | ALPHA: (65) implies:
% 151.04/25.58 | (66) op(e3, e3) = all_24_2
% 151.04/25.59 | (67) ~ (all_24_2 = e0) | ( ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0
% 151.04/25.59 | & op(e0, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 151.04/25.59 | (all_24_1 = e2) & op(e0, e0) = all_24_1 & $i(all_24_1))
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2
% 151.04/25.59 | gives:
% 151.04/25.59 | (68) op(e0, e0) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e2) | ( ~
% 151.04/25.59 | (all_26_0 = e1) & op(all_26_1, e0) = all_26_0 & op(e2, e2) =
% 151.04/25.59 | all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e3) &
% 151.04/25.59 | op(e2, e2) = all_26_1 & $i(all_26_1)))
% 151.04/25.59 |
% 151.04/25.59 | ALPHA: (68) implies:
% 151.04/25.59 | (69) op(e0, e0) = all_26_2
% 151.04/25.59 | (70) ~ (all_26_2 = e2) | ( ~ (all_26_0 = e1) & op(all_26_1, e0) = all_26_0
% 151.04/25.59 | & op(e2, e2) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 151.04/25.59 | (all_26_1 = e3) & op(e2, e2) = all_26_1 & $i(all_26_1))
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2
% 151.04/25.59 | gives:
% 151.04/25.59 | (71) op(e1, e1) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e3) | ( ~
% 151.04/25.59 | (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 151.04/25.59 | all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e0) &
% 151.04/25.59 | op(e3, e3) = all_28_1 & $i(all_28_1)))
% 151.04/25.59 |
% 151.04/25.59 | ALPHA: (71) implies:
% 151.04/25.59 | (72) op(e1, e1) = all_28_2
% 151.04/25.59 | (73) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0
% 151.04/25.59 | & op(e3, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 151.04/25.59 | (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1))
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2
% 151.04/25.59 | gives:
% 151.04/25.59 | (74) op(e2, e2) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e0) | ( ~
% 151.04/25.59 | (all_30_0 = e3) & op(all_30_1, e2) = all_30_0 & op(e0, e0) =
% 151.04/25.59 | all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e1) &
% 151.04/25.59 | op(e0, e0) = all_30_1 & $i(all_30_1)))
% 151.04/25.59 |
% 151.04/25.59 | ALPHA: (74) implies:
% 151.04/25.59 | (75) op(e2, e2) = all_30_2
% 151.04/25.59 | (76) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0
% 151.04/25.59 | & op(e0, e0) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~
% 151.04/25.59 | (all_30_1 = e1) & op(e0, e0) = all_30_1 & $i(all_30_1))
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 151.04/25.59 | gives:
% 151.04/25.59 | (77) op(e3, e3) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e1) | ( ~
% 151.04/25.59 | (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 & op(e1, e1) =
% 151.04/25.59 | all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e2) &
% 151.04/25.59 | op(e1, e1) = all_32_1 & $i(all_32_1)))
% 151.04/25.59 |
% 151.04/25.59 | ALPHA: (77) implies:
% 151.04/25.59 | (78) op(e3, e3) = all_32_2
% 151.04/25.59 | (79) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0
% 151.04/25.59 | & op(e1, e1) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~
% 151.04/25.59 | (all_32_1 = e2) & op(e1, e1) = all_32_1 & $i(all_32_1))
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2
% 151.04/25.59 | gives:
% 151.04/25.59 | (80) op(e0, e0) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e3) | ( ~
% 151.04/25.59 | (all_34_0 = e2) & op(all_34_1, e0) = all_34_0 & op(e3, e3) =
% 151.04/25.59 | all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e1) &
% 151.04/25.59 | op(e3, e3) = all_34_1 & $i(all_34_1)))
% 151.04/25.59 |
% 151.04/25.59 | ALPHA: (80) implies:
% 151.04/25.59 | (81) op(e0, e0) = all_34_2
% 151.04/25.59 | (82) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e2) & op(all_34_1, e0) = all_34_0
% 151.04/25.59 | & op(e3, e3) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~
% 151.04/25.59 | (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1))
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2
% 151.04/25.59 | gives:
% 151.04/25.59 | (83) op(e1, e1) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e3) | ( ~
% 151.04/25.59 | (all_36_0 = e0) & op(all_36_1, e1) = all_36_0 & op(e3, e3) =
% 151.04/25.59 | all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e2) &
% 151.04/25.59 | op(e3, e3) = all_36_1 & $i(all_36_1)))
% 151.04/25.59 |
% 151.04/25.59 | ALPHA: (83) implies:
% 151.04/25.59 | (84) op(e1, e1) = all_36_2
% 151.04/25.59 | (85) ~ (all_36_2 = e3) | ( ~ (all_36_0 = e0) & op(all_36_1, e1) = all_36_0
% 151.04/25.59 | & op(e3, e3) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 151.04/25.59 | (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1))
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 151.04/25.59 | gives:
% 151.04/25.59 | (86) op(e3, e3) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e2) | ( ~
% 151.04/25.59 | (all_38_0 = e0) & op(all_38_1, e3) = all_38_0 & op(e2, e2) =
% 151.04/25.59 | all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e1) &
% 151.04/25.59 | op(e2, e2) = all_38_1 & $i(all_38_1)))
% 151.04/25.59 |
% 151.04/25.59 | ALPHA: (86) implies:
% 151.04/25.59 | (87) op(e3, e3) = all_38_2
% 151.04/25.59 | (88) ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e3) = all_38_0
% 151.04/25.59 | & op(e2, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 151.04/25.59 | (all_38_1 = e1) & op(e2, e2) = all_38_1 & $i(all_38_1))
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2
% 151.04/25.59 | gives:
% 151.04/25.59 | (89) op(e1, e1) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e0) | ( ~
% 151.04/25.59 | (all_40_0 = e3) & op(all_40_1, e1) = all_40_0 & op(e0, e0) =
% 151.04/25.59 | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e2) &
% 151.04/25.59 | op(e0, e0) = all_40_1 & $i(all_40_1)))
% 151.04/25.59 |
% 151.04/25.59 | ALPHA: (89) implies:
% 151.04/25.59 | (90) op(e1, e1) = all_40_2
% 151.04/25.59 |
% 151.04/25.59 | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2
% 151.04/25.59 | gives:
% 151.04/25.60 | (91) op(e2, e2) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e0) | ( ~
% 151.04/25.60 | (all_42_0 = e1) & op(all_42_1, e2) = all_42_0 & op(e0, e0) =
% 151.04/25.60 | all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e3) &
% 151.04/25.60 | op(e0, e0) = all_42_1 & $i(all_42_1)))
% 151.04/25.60 |
% 151.04/25.60 | ALPHA: (91) implies:
% 151.04/25.60 | (92) op(e2, e2) = all_42_2
% 151.04/25.60 | (93) ~ (all_42_2 = e0) | ( ~ (all_42_0 = e1) & op(all_42_1, e2) = all_42_0
% 151.04/25.60 | & op(e0, e0) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 151.04/25.60 | (all_42_1 = e3) & op(e0, e0) = all_42_1 & $i(all_42_1))
% 151.04/25.60 |
% 151.04/25.60 | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2
% 151.04/25.60 | gives:
% 151.04/25.60 | (94) op(e0, e0) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e3) | ( ~
% 151.04/25.60 | (all_44_0 = e1) & op(all_44_1, e0) = all_44_0 & op(e3, e3) =
% 151.04/25.60 | all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e2) &
% 151.04/25.60 | op(e3, e3) = all_44_1 & $i(all_44_1)))
% 151.04/25.60 |
% 151.04/25.60 | ALPHA: (94) implies:
% 151.04/25.60 | (95) op(e0, e0) = all_44_2
% 151.04/25.60 |
% 151.04/25.60 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 151.04/25.60 | gives:
% 151.04/25.60 | (96) op(e1, e1) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e0) | ( ~
% 151.04/25.60 | (all_46_0 = e2) & op(all_46_1, e1) = all_46_0 & op(e0, e0) =
% 151.04/25.60 | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e3) &
% 151.04/25.60 | op(e0, e0) = all_46_1 & $i(all_46_1)))
% 151.04/25.60 |
% 151.04/25.60 | ALPHA: (96) implies:
% 151.04/25.60 | (97) op(e1, e1) = all_46_2
% 151.04/25.60 | (98) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(all_46_1, e1) = all_46_0
% 151.04/25.60 | & op(e0, e0) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 151.04/25.60 | (all_46_1 = e3) & op(e0, e0) = all_46_1 & $i(all_46_1))
% 151.04/25.60 |
% 151.04/25.60 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2
% 151.04/25.60 | gives:
% 151.04/25.60 | (99) op(e2, e2) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e1) | ( ~
% 151.04/25.60 | (all_48_0 = e3) & op(all_48_1, e2) = all_48_0 & op(e1, e1) =
% 151.04/25.60 | all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e0) &
% 151.04/25.60 | op(e1, e1) = all_48_1 & $i(all_48_1)))
% 151.04/25.60 |
% 151.04/25.60 | ALPHA: (99) implies:
% 151.04/25.60 | (100) op(e2, e2) = all_48_2
% 151.04/25.60 | (101) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(all_48_1, e2) =
% 151.04/25.60 | all_48_0 & op(e1, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | (
% 151.04/25.60 | ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1))
% 151.04/25.60 |
% 151.04/25.60 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 151.04/25.60 | gives:
% 151.04/25.60 | (102) op(e3, e3) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e1) | ( ~
% 151.04/25.60 | (all_50_0 = e2) & op(all_50_1, e3) = all_50_0 & op(e1, e1) =
% 151.04/25.60 | all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e0) &
% 151.04/25.60 | op(e1, e1) = all_50_1 & $i(all_50_1)))
% 151.04/25.60 |
% 151.04/25.60 | ALPHA: (102) implies:
% 151.04/25.60 | (103) op(e3, e3) = all_50_2
% 151.04/25.60 | (104) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e2) & op(all_50_1, e3) =
% 151.04/25.60 | all_50_0 & op(e1, e1) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | (
% 151.04/25.60 | ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 & $i(all_50_1))
% 151.04/25.60 |
% 151.04/25.60 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 151.04/25.60 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 151.04/25.60 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 151.04/25.60 | (105) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 =
% 151.04/25.60 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) &
% 151.04/25.60 | ~ (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 =
% 151.04/25.60 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) &
% 151.04/25.60 | ~ (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 =
% 151.04/25.60 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) &
% 151.04/25.60 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 =
% 151.04/25.60 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) &
% 151.04/25.60 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 =
% 151.04/25.60 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) &
% 151.04/25.60 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 =
% 151.04/25.60 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) &
% 151.04/25.60 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8
% 151.04/25.60 | = all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11)
% 151.04/25.60 | & ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~
% 151.04/25.60 | (all_52_9 = all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 =
% 151.04/25.60 | all_52_11) & ~ (all_52_10 = all_52_14) & ~ (all_52_11 =
% 151.04/25.60 | all_52_15) & ~ (all_52_12 = all_52_13) & ~ (all_52_12 =
% 151.04/25.60 | all_52_14) & ~ (all_52_12 = all_52_15) & ~ (all_52_13 =
% 151.04/25.60 | all_52_14) & ~ (all_52_13 = all_52_15) & ~ (all_52_14 =
% 151.04/25.60 | all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3,
% 151.04/25.60 | e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 &
% 151.04/25.60 | op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) =
% 151.04/25.60 | all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1,
% 151.04/25.60 | e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 &
% 151.04/25.60 | op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) =
% 151.04/25.60 | all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 151.04/25.60 | & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) &
% 151.04/25.60 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) &
% 151.04/25.60 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15)
% 151.04/25.60 |
% 151.04/25.60 | ALPHA: (105) implies:
% 151.04/25.60 | (106) ~ (all_52_14 = all_52_15)
% 151.04/25.60 | (107) ~ (all_52_13 = all_52_15)
% 151.04/25.60 | (108) ~ (all_52_13 = all_52_14)
% 151.04/25.60 | (109) ~ (all_52_12 = all_52_15)
% 151.04/25.60 | (110) ~ (all_52_12 = all_52_14)
% 151.04/25.60 | (111) ~ (all_52_12 = all_52_13)
% 151.04/25.60 | (112) ~ (all_52_11 = all_52_15)
% 151.04/25.60 | (113) ~ (all_52_10 = all_52_14)
% 151.04/25.60 | (114) ~ (all_52_10 = all_52_11)
% 151.04/25.60 | (115) ~ (all_52_9 = all_52_13)
% 151.04/25.60 | (116) ~ (all_52_9 = all_52_11)
% 151.04/25.60 | (117) ~ (all_52_9 = all_52_10)
% 151.04/25.60 | (118) ~ (all_52_8 = all_52_12)
% 151.04/25.60 | (119) ~ (all_52_8 = all_52_11)
% 151.04/25.60 | (120) ~ (all_52_8 = all_52_10)
% 151.04/25.60 | (121) ~ (all_52_8 = all_52_9)
% 151.04/25.60 | (122) ~ (all_52_7 = all_52_15)
% 151.04/25.60 | (123) ~ (all_52_7 = all_52_11)
% 151.04/25.60 | (124) ~ (all_52_6 = all_52_14)
% 151.04/25.60 | (125) ~ (all_52_6 = all_52_10)
% 151.04/25.60 | (126) ~ (all_52_6 = all_52_7)
% 151.04/25.60 | (127) ~ (all_52_5 = all_52_13)
% 151.04/25.60 | (128) ~ (all_52_5 = all_52_9)
% 151.04/25.60 | (129) ~ (all_52_5 = all_52_7)
% 151.04/25.60 | (130) ~ (all_52_5 = all_52_6)
% 151.04/25.60 | (131) ~ (all_52_4 = all_52_12)
% 151.04/25.60 | (132) ~ (all_52_4 = all_52_8)
% 151.04/25.60 | (133) ~ (all_52_4 = all_52_7)
% 151.04/25.60 | (134) ~ (all_52_4 = all_52_6)
% 151.04/25.61 | (135) ~ (all_52_4 = all_52_5)
% 151.04/25.61 | (136) ~ (all_52_3 = all_52_15)
% 151.04/25.61 | (137) ~ (all_52_3 = all_52_11)
% 151.04/25.61 | (138) ~ (all_52_3 = all_52_7)
% 151.04/25.61 | (139) ~ (all_52_2 = all_52_14)
% 151.04/25.61 | (140) ~ (all_52_2 = all_52_10)
% 151.04/25.61 | (141) ~ (all_52_2 = all_52_6)
% 151.04/25.61 | (142) ~ (all_52_2 = all_52_3)
% 151.04/25.61 | (143) ~ (all_52_1 = all_52_13)
% 151.04/25.61 | (144) ~ (all_52_1 = all_52_9)
% 151.04/25.61 | (145) ~ (all_52_1 = all_52_5)
% 151.04/25.61 | (146) ~ (all_52_1 = all_52_3)
% 151.04/25.61 | (147) ~ (all_52_1 = all_52_2)
% 151.04/25.61 | (148) ~ (all_52_0 = all_52_12)
% 151.04/25.61 | (149) ~ (all_52_0 = all_52_8)
% 151.04/25.61 | (150) ~ (all_52_0 = all_52_4)
% 151.04/25.61 | (151) ~ (all_52_0 = all_52_3)
% 151.04/25.61 | (152) ~ (all_52_0 = all_52_2)
% 151.04/25.61 | (153) ~ (all_52_0 = all_52_1)
% 151.04/25.61 | (154) op(e0, e0) = all_52_15
% 151.04/25.61 | (155) op(e0, e1) = all_52_11
% 151.04/25.61 | (156) op(e0, e2) = all_52_7
% 151.04/25.61 | (157) op(e0, e3) = all_52_3
% 151.04/25.61 | (158) op(e1, e0) = all_52_14
% 151.04/25.61 | (159) op(e1, e1) = all_52_10
% 151.04/25.61 | (160) op(e1, e2) = all_52_6
% 151.04/25.61 | (161) op(e1, e3) = all_52_2
% 151.04/25.61 | (162) op(e2, e0) = all_52_13
% 151.04/25.61 | (163) op(e2, e1) = all_52_9
% 151.04/25.61 | (164) op(e2, e2) = all_52_5
% 151.04/25.61 | (165) op(e2, e3) = all_52_1
% 151.04/25.61 | (166) op(e3, e0) = all_52_12
% 151.04/25.61 | (167) op(e3, e1) = all_52_8
% 151.04/25.61 | (168) op(e3, e2) = all_52_4
% 151.04/25.61 | (169) op(e3, e3) = all_52_0
% 151.04/25.61 |
% 151.04/25.61 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 151.04/25.61 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 151.04/25.61 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 151.29/25.61 | (170) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 151.29/25.61 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 151.29/25.61 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 151.29/25.61 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 151.29/25.61 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 151.29/25.61 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 151.29/25.61 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 151.29/25.61 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 151.29/25.61 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 151.29/25.61 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 151.29/25.61 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 151.29/25.61 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 151.29/25.61 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 151.29/25.61 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 151.29/25.61 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 151.29/25.61 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 151.29/25.61 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 151.29/25.61 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 151.29/25.61 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 151.29/25.61 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 151.29/25.61 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 151.29/25.61 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 151.29/25.61 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 151.29/25.61 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 151.29/25.61 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 151.29/25.61 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 151.29/25.61 |
% 151.29/25.61 | ALPHA: (170) implies:
% 151.29/25.61 | (171) op(e0, e0) = all_54_15
% 151.29/25.61 | (172) op(e0, e1) = all_54_14
% 151.29/25.61 | (173) op(e0, e2) = all_54_13
% 151.29/25.61 | (174) op(e0, e3) = all_54_12
% 151.29/25.61 | (175) op(e1, e0) = all_54_11
% 151.29/25.61 | (176) op(e1, e1) = all_54_10
% 151.29/25.61 | (177) op(e1, e2) = all_54_9
% 151.29/25.61 | (178) op(e1, e3) = all_54_8
% 151.29/25.61 | (179) op(e2, e0) = all_54_7
% 151.29/25.61 | (180) op(e2, e1) = all_54_6
% 151.29/25.61 | (181) op(e2, e2) = all_54_5
% 151.29/25.61 | (182) op(e2, e3) = all_54_4
% 151.29/25.61 | (183) op(e3, e0) = all_54_3
% 151.29/25.61 | (184) op(e3, e1) = all_54_2
% 151.29/25.61 | (185) op(e3, e2) = all_54_1
% 151.29/25.61 | (186) op(e3, e3) = all_54_0
% 151.29/25.61 | (187) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 151.29/25.61 | (188) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.29/25.61 | (189) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 151.29/25.61 | (190) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 151.29/25.61 | (191) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 151.29/25.61 | (192) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 151.29/25.61 | (193) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.29/25.61 | (194) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 151.29/25.61 | (195) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 151.29/25.61 | (196) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 151.29/25.61 | (197) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 151.29/25.61 | (198) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 151.29/25.61 | (199) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.29/25.62 | (200) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 151.29/25.62 | (201) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 151.29/25.62 | (202) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 151.29/25.62 |
% 151.29/25.62 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2,
% 151.29/25.62 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 151.29/25.62 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 151.29/25.62 | (203) op(e3, e3) = all_56_12 & op(e2, e2) = all_56_13 & op(e1, e1) =
% 151.29/25.62 | all_56_14 & op(e0, e0) = all_56_15 & $i(all_56_12) & $i(all_56_13) &
% 151.29/25.62 | $i(all_56_14) & $i(all_56_15) & ( ~ (all_56_12 = e2) | (all_56_0 = e3
% 151.29/25.62 | & op(e3, e2) = e3)) & ( ~ (all_56_12 = e1) | (all_56_1 = e3 &
% 151.29/25.62 | op(e3, e1) = e3)) & ( ~ (all_56_12 = e0) | (all_56_2 = e3 &
% 151.29/25.62 | op(e3, e0) = e3)) & ( ~ (all_56_13 = e3) | (all_56_3 = e2 &
% 151.29/25.62 | op(e2, e3) = e2)) & ( ~ (all_56_13 = e1) | (all_56_4 = e2 &
% 151.29/25.62 | op(e2, e1) = e2)) & ( ~ (all_56_13 = e0) | (all_56_5 = e2 &
% 151.29/25.62 | op(e2, e0) = e2)) & ( ~ (all_56_14 = e3) | (all_56_6 = e1 &
% 151.29/25.62 | op(e1, e3) = e1)) & ( ~ (all_56_14 = e2) | (all_56_7 = e1 &
% 151.29/25.62 | op(e1, e2) = e1)) & ( ~ (all_56_14 = e0) | (all_56_8 = e1 &
% 151.29/25.62 | op(e1, e0) = e1)) & ( ~ (all_56_15 = e3) | (all_56_9 = e0 &
% 151.29/25.62 | op(e0, e3) = e0)) & ( ~ (all_56_15 = e2) | (all_56_10 = e0 &
% 151.29/25.62 | op(e0, e2) = e0)) & ( ~ (all_56_15 = e1) | (all_56_11 = e0 &
% 151.29/25.62 | op(e0, e1) = e0)) & (all_56_12 = e3 | all_56_13 = e2 | all_56_14
% 151.29/25.62 | = e1 | all_56_15 = e0) & ((all_56_0 = e3 & all_56_3 = e3 & ~
% 151.29/25.62 | (all_56_13 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0
% 151.29/25.62 | = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 &
% 151.29/25.62 | op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14
% 151.29/25.62 | = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_1 = e1 &
% 151.29/25.62 | all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 & op(e1,
% 151.29/25.62 | e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 151.29/25.62 | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 &
% 151.29/25.62 | all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0,
% 151.29/25.62 | e3) = e0) | (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 151.29/25.62 | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 &
% 151.29/25.62 | all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 & op(e1,
% 151.29/25.62 | e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 151.29/25.62 | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_5 = e0 &
% 151.29/25.62 | all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 & op(e0,
% 151.29/25.62 | e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 151.29/25.62 | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 &
% 151.29/25.62 | all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0,
% 151.29/25.62 | e1) = e0))
% 151.29/25.62 |
% 151.29/25.62 | ALPHA: (203) implies:
% 151.29/25.62 | (204) op(e0, e0) = all_56_15
% 151.29/25.62 | (205) op(e1, e1) = all_56_14
% 151.29/25.62 | (206) op(e2, e2) = all_56_13
% 151.29/25.62 | (207) op(e3, e3) = all_56_12
% 151.29/25.62 | (208) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) =
% 151.29/25.62 | e3 & op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~
% 151.29/25.62 | (all_56_12 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 =
% 151.29/25.62 | e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1,
% 151.29/25.62 | e3) = e3) | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3)
% 151.29/25.62 | & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 =
% 151.29/25.62 | e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 151.29/25.62 | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 151.29/25.62 | e0 & op(e0, e3) = e0) | (all_56_4 = e2 & all_56_7 = e2 & ~
% 151.29/25.62 | (all_56_14 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 =
% 151.29/25.62 | e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 & op(e1,
% 151.29/25.62 | e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0)
% 151.29/25.62 | & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_5 = e0 & all_56_10 =
% 151.29/25.62 | e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 151.29/25.62 | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) =
% 151.29/25.62 | e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~
% 151.29/25.62 | (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 151.29/25.62 | (209) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 151.29/25.62 | (210) ~ (all_56_15 = e1) | (all_56_11 = e0 & op(e0, e1) = e0)
% 151.29/25.62 | (211) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 151.29/25.62 | (212) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 151.29/25.62 | (213) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 151.29/25.62 | (214) ~ (all_56_14 = e2) | (all_56_7 = e1 & op(e1, e2) = e1)
% 151.29/25.62 | (215) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 151.29/25.62 | (216) ~ (all_56_13 = e0) | (all_56_5 = e2 & op(e2, e0) = e2)
% 151.29/25.62 | (217) ~ (all_56_13 = e1) | (all_56_4 = e2 & op(e2, e1) = e2)
% 151.29/25.62 | (218) ~ (all_56_13 = e3) | (all_56_3 = e2 & op(e2, e3) = e2)
% 151.29/25.62 | (219) ~ (all_56_12 = e0) | (all_56_2 = e3 & op(e3, e0) = e3)
% 151.29/25.62 | (220) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 151.29/25.62 | (221) ~ (all_56_12 = e2) | (all_56_0 = e3 & op(e3, e2) = e3)
% 151.29/25.62 |
% 151.29/25.62 | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2,
% 151.29/25.62 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9,
% 151.29/25.62 | all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives:
% 151.29/25.63 | (222) ((all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 151.29/25.63 | e3) | (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 151.29/25.63 | e0) = e3)) & ((all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 =
% 151.29/25.63 | e3 & op(e2, e3) = e3) | (all_58_6 = e3 & op(e1, e3) = e3) |
% 151.29/25.63 | (all_58_12 = e3 & op(e0, e3) = e3)) & ((all_58_0 = e2 & op(e3, e3)
% 151.29/25.63 | = e2) | (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_4 = e2 &
% 151.29/25.63 | op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)) &
% 151.29/25.63 | ((all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 151.29/25.63 | e2) | (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 151.29/25.63 | op(e0, e3) = e2)) & ((all_58_0 = e1 & op(e3, e3) = e1) |
% 151.29/25.63 | (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_4 = e1 & op(e3, e1) =
% 151.29/25.63 | e1) | (all_58_9 = e1 & op(e3, e0) = e1)) & ((all_58_0 = e1 &
% 151.29/25.63 | op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_6
% 151.29/25.63 | = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)) &
% 151.29/25.63 | ((all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 151.29/25.63 | e0) | (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 151.29/25.63 | e0) = e0)) & ((all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 =
% 151.29/25.63 | e0 & op(e2, e3) = e0) | (all_58_6 = e0 & op(e1, e3) = e0) |
% 151.29/25.63 | (all_58_12 = e0 & op(e0, e3) = e0)) & ((all_58_1 = e3 & op(e3, e2)
% 151.29/25.63 | = e3) | (all_58_3 = e3 & op(e2, e2) = e3) | (all_58_7 = e3 &
% 151.29/25.63 | op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)) &
% 151.29/25.63 | ((all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 151.29/25.63 | e2) | (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 151.29/25.63 | op(e0, e2) = e2)) & ((all_58_1 = e1 & op(e3, e2) = e1) |
% 151.29/25.63 | (all_58_3 = e1 & op(e2, e2) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 151.29/25.63 | e1) | (all_58_13 = e1 & op(e0, e2) = e1)) & ((all_58_1 = e0 &
% 151.29/25.63 | op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) | (all_58_7
% 151.29/25.63 | = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)) &
% 151.29/25.63 | ((all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 151.29/25.63 | e3) | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 151.29/25.63 | op(e2, e0) = e3)) & ((all_58_2 = e2 & op(e2, e3) = e2) |
% 151.29/25.63 | (all_58_3 = e2 & op(e2, e2) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 151.29/25.63 | e2) | (all_58_10 = e2 & op(e2, e0) = e2)) & ((all_58_2 = e1 &
% 151.29/25.63 | op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) | (all_58_5
% 151.29/25.63 | = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)) &
% 151.29/25.63 | ((all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 151.29/25.63 | e0) | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 151.29/25.63 | op(e2, e0) = e0)) & ((all_58_4 = e3 & op(e3, e1) = e3) |
% 151.29/25.63 | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_8 = e3 & op(e1, e1) =
% 151.29/25.63 | e3) | (all_58_14 = e3 & op(e0, e1) = e3)) & ((all_58_4 = e2 &
% 151.29/25.63 | op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_8
% 151.29/25.63 | = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)) &
% 151.29/25.63 | ((all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 151.29/25.63 | e1) | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 151.29/25.63 | op(e0, e1) = e1)) & ((all_58_4 = e0 & op(e3, e1) = e0) |
% 151.29/25.63 | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_8 = e0 & op(e1, e1) =
% 151.29/25.63 | e0) | (all_58_14 = e0 & op(e0, e1) = e0)) & ((all_58_6 = e3 &
% 151.29/25.63 | op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_8
% 151.29/25.63 | = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)) &
% 151.29/25.63 | ((all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 151.29/25.63 | e2) | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 151.29/25.63 | op(e1, e0) = e2)) & ((all_58_6 = e1 & op(e1, e3) = e1) |
% 151.29/25.63 | (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_8 = e1 & op(e1, e1) =
% 151.29/25.63 | e1) | (all_58_11 = e1 & op(e1, e0) = e1)) & ((all_58_6 = e0 &
% 151.29/25.63 | op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_8
% 151.29/25.63 | = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 151.29/25.63 | ((all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 151.29/25.63 | e3) | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 151.29/25.63 | op(e0, e0) = e3)) & ((all_58_9 = e2 & op(e3, e0) = e2) |
% 151.29/25.63 | (all_58_10 = e2 & op(e2, e0) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 151.29/25.63 | e2) | (all_58_15 = e2 & op(e0, e0) = e2)) & ((all_58_9 = e1 &
% 151.29/25.63 | op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 151.29/25.63 | (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 151.29/25.63 | e1)) & ((all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 151.29/25.63 | op(e0, e2) = e3) | (all_58_14 = e3 & op(e0, e1) = e3) |
% 151.29/25.63 | (all_58_15 = e3 & op(e0, e0) = e3)) & ((all_58_12 = e2 & op(e0, e3)
% 151.29/25.63 | = e2) | (all_58_13 = e2 & op(e0, e2) = e2) | (all_58_14 = e2 &
% 151.29/25.63 | op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)) &
% 151.29/25.63 | ((all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 151.29/25.63 | e1) | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 151.29/25.63 | op(e0, e0) = e1)) & ((all_58_15 = e0 & op(e0, e0) = e0) |
% 151.29/25.63 | (((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 151.29/25.63 | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 =
% 151.29/25.63 | e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 151.29/25.63 | (all_58_14 = e0 & op(e0, e1) = e0))))
% 151.29/25.63 |
% 151.29/25.63 | ALPHA: (222) implies:
% 151.29/25.63 | (223) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 151.29/25.63 | e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 151.29/25.63 | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 151.29/25.63 | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 151.29/25.63 | = e0)))
% 151.29/25.63 | (224) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 151.29/25.63 | e1) | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 151.29/25.63 | e0) = e1)
% 151.29/25.63 | (225) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 151.29/25.63 | e2) | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 151.29/25.63 | e0) = e2)
% 151.29/25.63 | (226) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 151.29/25.63 | e3) | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 151.29/25.63 | e0) = e3)
% 151.29/25.63 | (227) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 151.29/25.63 | e1) | (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 151.29/25.63 | e0) = e1)
% 151.29/25.63 | (228) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 151.29/25.63 | e2) | (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 151.29/25.63 | e0) = e2)
% 151.29/25.64 | (229) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 151.29/25.64 | e3) | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 151.29/25.64 | e0) = e3)
% 151.29/25.64 | (230) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 151.29/25.64 | | (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 151.29/25.64 | e0)
% 151.29/25.64 | (231) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 151.29/25.64 | | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 151.29/25.64 | e1)
% 151.29/25.64 | (232) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 151.29/25.64 | | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 151.29/25.64 | e2)
% 151.29/25.64 | (233) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 151.29/25.64 | | (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 151.29/25.64 | e3)
% 151.29/25.64 | (234) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 151.29/25.64 | | (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 151.29/25.64 | e0)
% 151.29/25.64 | (235) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 151.29/25.64 | | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 151.29/25.64 | e1)
% 151.29/25.64 | (236) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 151.29/25.64 | | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 151.29/25.64 | e2)
% 151.29/25.64 | (237) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 151.29/25.64 | | (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 151.29/25.64 | e3)
% 151.29/25.64 | (238) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 151.29/25.64 | | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 151.29/25.64 | e0)
% 151.29/25.64 | (239) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 151.29/25.64 | | (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 151.29/25.64 | e1)
% 151.29/25.64 | (240) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 151.29/25.64 | | (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 151.29/25.64 | e2)
% 151.29/25.64 | (241) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 151.29/25.64 | | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 151.29/25.64 | e3)
% 151.29/25.64 | (242) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 151.29/25.64 | | (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 151.29/25.64 | e0)
% 151.29/25.64 | (243) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 151.29/25.64 | | (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 151.29/25.64 | e1)
% 151.29/25.64 | (244) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 151.29/25.64 | | (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 151.29/25.64 | e2)
% 151.29/25.64 | (245) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 151.29/25.64 | | (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 151.29/25.64 | e3)
% 151.29/25.64 | (246) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 151.29/25.64 | | (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 151.29/25.64 | e0)
% 151.29/25.64 | (247) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 151.29/25.64 | | (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 151.29/25.64 | e0)
% 151.29/25.64 | (248) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 151.29/25.64 | | (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 151.29/25.64 | e1)
% 151.29/25.64 | (249) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 151.29/25.64 | | (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 151.29/25.64 | e1)
% 151.29/25.64 | (250) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 151.29/25.64 | | (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 151.29/25.64 | e2)
% 151.29/25.64 | (251) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 151.29/25.64 | | (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 151.29/25.64 | e2)
% 151.29/25.64 | (252) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 151.29/25.64 | | (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 151.29/25.64 | e3)
% 151.29/25.64 | (253) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 151.29/25.64 | | (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 151.29/25.64 | e3)
% 151.29/25.64 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_20_2, e0, e0,
% 151.29/25.65 | simplifying with (48), (60) gives:
% 151.29/25.65 | (254) all_20_2 = all_12_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_34_2, e0, e0,
% 151.29/25.65 | simplifying with (69), (81) gives:
% 151.29/25.65 | (255) all_34_2 = all_26_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_34_2, e0, e0,
% 151.29/25.65 | simplifying with (60), (81) gives:
% 151.29/25.65 | (256) all_34_2 = all_20_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_44_2, e0, e0,
% 151.29/25.65 | simplifying with (81), (95) gives:
% 151.29/25.65 | (257) all_44_2 = all_34_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_52_15, e0, e0,
% 151.29/25.65 | simplifying with (95), (154) gives:
% 151.29/25.65 | (258) all_52_15 = all_44_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0,
% 151.29/25.65 | e0, simplifying with (154), (171) gives:
% 151.29/25.65 | (259) all_54_15 = all_52_15
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_56_15, e0,
% 151.29/25.65 | e0, simplifying with (171), (204) gives:
% 151.29/25.65 | (260) all_56_15 = all_54_15
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_56_15, e0, e0,
% 151.29/25.65 | simplifying with (36), (204) gives:
% 151.29/25.65 | (261) all_56_15 = all_4_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1,
% 151.29/25.65 | e0, simplifying with (155), (172) gives:
% 151.29/25.65 | (262) all_54_14 = all_52_11
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_54_13, e2, e0,
% 151.29/25.65 | simplifying with (156), (173) gives:
% 151.29/25.65 | (263) all_54_13 = all_52_7
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_12, e3, e0,
% 151.29/25.65 | simplifying with (157), (174) gives:
% 151.29/25.65 | (264) all_54_12 = all_52_3
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_54_11, e0,
% 151.29/25.65 | e1, simplifying with (158), (175) gives:
% 151.29/25.65 | (265) all_54_11 = all_52_14
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_28_2, e1, e1,
% 151.29/25.65 | simplifying with (57), (72) gives:
% 151.29/25.65 | (266) all_28_2 = all_18_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_36_2, e1, e1,
% 151.29/25.65 | simplifying with (72), (84) gives:
% 151.29/25.65 | (267) all_36_2 = all_28_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_52_10, e1, e1,
% 151.29/25.65 | simplifying with (97), (159) gives:
% 151.29/25.65 | (268) all_52_10 = all_46_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_52_10, e1, e1,
% 151.29/25.65 | simplifying with (90), (159) gives:
% 151.29/25.65 | (269) all_52_10 = all_40_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_52_10, e1, e1,
% 151.29/25.65 | simplifying with (84), (159) gives:
% 151.29/25.65 | (270) all_52_10 = all_36_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_54_10, e1, e1,
% 151.29/25.65 | simplifying with (97), (176) gives:
% 151.29/25.65 | (271) all_54_10 = all_46_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_54_10, all_56_14, e1,
% 151.29/25.65 | e1, simplifying with (176), (205) gives:
% 151.29/25.65 | (272) all_56_14 = all_54_10
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_56_14, e1, e1,
% 151.29/25.65 | simplifying with (39), (205) gives:
% 151.29/25.65 | (273) all_56_14 = all_6_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1,
% 151.29/25.65 | simplifying with (160), (177) gives:
% 151.29/25.65 | (274) all_54_9 = all_52_6
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1,
% 151.29/25.65 | simplifying with (161), (178) gives:
% 151.29/25.65 | (275) all_54_8 = all_52_2
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_54_7, e0, e2,
% 151.29/25.65 | simplifying with (162), (179) gives:
% 151.29/25.65 | (276) all_54_7 = all_52_13
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2,
% 151.29/25.65 | simplifying with (163), (180) gives:
% 151.29/25.65 | (277) all_54_6 = all_52_9
% 151.29/25.65 |
% 151.29/25.65 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_30_2, e2, e2,
% 151.29/25.65 | simplifying with (63), (75) gives:
% 151.47/25.65 | (278) all_30_2 = all_22_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_30_2, e2, e2,
% 151.47/25.65 | simplifying with (51), (75) gives:
% 151.47/25.65 | (279) all_30_2 = all_14_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_42_2, e2, e2,
% 151.47/25.65 | simplifying with (63), (92) gives:
% 151.47/25.65 | (280) all_42_2 = all_22_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_54_5, e2, e2,
% 151.47/25.65 | simplifying with (164), (181) gives:
% 151.47/25.65 | (281) all_54_5 = all_52_5
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_54_5, e2, e2,
% 151.47/25.65 | simplifying with (42), (181) gives:
% 151.47/25.65 | (282) all_54_5 = all_8_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_56_13, e2, e2,
% 151.47/25.65 | simplifying with (164), (206) gives:
% 151.47/25.65 | (283) all_56_13 = all_52_5
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_56_13, e2, e2,
% 151.47/25.65 | simplifying with (100), (206) gives:
% 151.47/25.65 | (284) all_56_13 = all_48_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_56_13, e2, e2,
% 151.47/25.65 | simplifying with (92), (206) gives:
% 151.47/25.65 | (285) all_56_13 = all_42_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_54_4, e3, e2,
% 151.47/25.65 | simplifying with (165), (182) gives:
% 151.47/25.65 | (286) all_54_4 = all_52_1
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_54_3, e0, e3,
% 151.47/25.65 | simplifying with (166), (183) gives:
% 151.47/25.65 | (287) all_54_3 = all_52_12
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_54_2, e1, e3,
% 151.47/25.65 | simplifying with (167), (184) gives:
% 151.47/25.65 | (288) all_54_2 = all_52_8
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_54_1, e2, e3,
% 151.47/25.65 | simplifying with (168), (185) gives:
% 151.47/25.65 | (289) all_54_1 = all_52_4
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_32_2, e3, e3,
% 151.47/25.65 | simplifying with (66), (78) gives:
% 151.47/25.65 | (290) all_32_2 = all_24_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_38_2, e3, e3,
% 151.47/25.65 | simplifying with (78), (87) gives:
% 151.47/25.65 | (291) all_38_2 = all_32_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_50_2, e3, e3,
% 151.47/25.65 | simplifying with (87), (103) gives:
% 151.47/25.65 | (292) all_50_2 = all_38_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_52_0, e3, e3,
% 151.47/25.65 | simplifying with (103), (169) gives:
% 151.47/25.65 | (293) all_52_0 = all_50_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_52_0, e3, e3,
% 151.47/25.65 | simplifying with (54), (169) gives:
% 151.47/25.65 | (294) all_52_0 = all_16_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_54_0, e3, e3,
% 151.47/25.65 | simplifying with (66), (186) gives:
% 151.47/25.65 | (295) all_54_0 = all_24_2
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_12, e3, e3,
% 151.47/25.65 | simplifying with (186), (207) gives:
% 151.47/25.65 | (296) all_56_12 = all_54_0
% 151.47/25.65 |
% 151.47/25.65 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_56_12, e3, e3,
% 151.47/25.65 | simplifying with (45), (207) gives:
% 151.47/25.65 | (297) all_56_12 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (296), (297) imply:
% 151.47/25.66 | (298) all_54_0 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (298) implies:
% 151.47/25.66 | (299) all_54_0 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (283), (284) imply:
% 151.47/25.66 | (300) all_52_5 = all_48_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (300) implies:
% 151.47/25.66 | (301) all_52_5 = all_48_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (284), (285) imply:
% 151.47/25.66 | (302) all_48_2 = all_42_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (272), (273) imply:
% 151.47/25.66 | (303) all_54_10 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (303) implies:
% 151.47/25.66 | (304) all_54_10 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (260), (261) imply:
% 151.47/25.66 | (305) all_54_15 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (305) implies:
% 151.47/25.66 | (306) all_54_15 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (295), (299) imply:
% 151.47/25.66 | (307) all_24_2 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (307) implies:
% 151.47/25.66 | (308) all_24_2 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (281), (282) imply:
% 151.47/25.66 | (309) all_52_5 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (309) implies:
% 151.47/25.66 | (310) all_52_5 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (271), (304) imply:
% 151.47/25.66 | (311) all_46_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (311) implies:
% 151.47/25.66 | (312) all_46_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (259), (306) imply:
% 151.47/25.66 | (313) all_52_15 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (313) implies:
% 151.47/25.66 | (314) all_52_15 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (293), (294) imply:
% 151.47/25.66 | (315) all_50_2 = all_16_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (315) implies:
% 151.47/25.66 | (316) all_50_2 = all_16_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (301), (310) imply:
% 151.47/25.66 | (317) all_48_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (317) implies:
% 151.47/25.66 | (318) all_48_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (268), (269) imply:
% 151.47/25.66 | (319) all_46_2 = all_40_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (319) implies:
% 151.47/25.66 | (320) all_46_2 = all_40_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (269), (270) imply:
% 151.47/25.66 | (321) all_40_2 = all_36_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (258), (314) imply:
% 151.47/25.66 | (322) all_44_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (322) implies:
% 151.47/25.66 | (323) all_44_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (292), (316) imply:
% 151.47/25.66 | (324) all_38_2 = all_16_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (324) implies:
% 151.47/25.66 | (325) all_38_2 = all_16_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (302), (318) imply:
% 151.47/25.66 | (326) all_42_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (326) implies:
% 151.47/25.66 | (327) all_42_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (312), (320) imply:
% 151.47/25.66 | (328) all_40_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (328) implies:
% 151.47/25.66 | (329) all_40_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (257), (323) imply:
% 151.47/25.66 | (330) all_34_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (330) implies:
% 151.47/25.66 | (331) all_34_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (280), (327) imply:
% 151.47/25.66 | (332) all_22_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (332) implies:
% 151.47/25.66 | (333) all_22_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (321), (329) imply:
% 151.47/25.66 | (334) all_36_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (334) implies:
% 151.47/25.66 | (335) all_36_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (291), (325) imply:
% 151.47/25.66 | (336) all_32_2 = all_16_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (336) implies:
% 151.47/25.66 | (337) all_32_2 = all_16_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (267), (335) imply:
% 151.47/25.66 | (338) all_28_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (338) implies:
% 151.47/25.66 | (339) all_28_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (255), (256) imply:
% 151.47/25.66 | (340) all_26_2 = all_20_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (255), (331) imply:
% 151.47/25.66 | (341) all_26_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (290), (337) imply:
% 151.47/25.66 | (342) all_24_2 = all_16_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (342) implies:
% 151.47/25.66 | (343) all_24_2 = all_16_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (278), (279) imply:
% 151.47/25.66 | (344) all_22_2 = all_14_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (344) implies:
% 151.47/25.66 | (345) all_22_2 = all_14_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (266), (339) imply:
% 151.47/25.66 | (346) all_18_2 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (340), (341) imply:
% 151.47/25.66 | (347) all_20_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (347) implies:
% 151.47/25.66 | (348) all_20_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (308), (343) imply:
% 151.47/25.66 | (349) all_16_2 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (333), (345) imply:
% 151.47/25.66 | (350) all_14_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (350) implies:
% 151.47/25.66 | (351) all_14_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (254), (348) imply:
% 151.47/25.66 | (352) all_12_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (352) implies:
% 151.47/25.66 | (353) all_12_2 = all_4_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (279), (351) imply:
% 151.47/25.66 | (354) all_30_2 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (337), (349) imply:
% 151.47/25.66 | (355) all_32_2 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (325), (349) imply:
% 151.47/25.66 | (356) all_38_2 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (316), (349) imply:
% 151.47/25.66 | (357) all_50_2 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (269), (329) imply:
% 151.47/25.66 | (358) all_52_10 = all_6_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (294), (349) imply:
% 151.47/25.66 | (359) all_52_0 = all_10_2
% 151.47/25.66 |
% 151.47/25.66 | COMBINE_EQS: (284), (318) imply:
% 151.47/25.66 | (360) all_56_13 = all_8_2
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (153), (359) imply:
% 151.47/25.66 | (361) ~ (all_52_1 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (361) implies:
% 151.47/25.66 | (362) ~ (all_52_1 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (152), (359) imply:
% 151.47/25.66 | (363) ~ (all_52_2 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (363) implies:
% 151.47/25.66 | (364) ~ (all_52_2 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (151), (359) imply:
% 151.47/25.66 | (365) ~ (all_52_3 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (365) implies:
% 151.47/25.66 | (366) ~ (all_52_3 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (150), (359) imply:
% 151.47/25.66 | (367) ~ (all_52_4 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (367) implies:
% 151.47/25.66 | (368) ~ (all_52_4 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (149), (359) imply:
% 151.47/25.66 | (369) ~ (all_52_8 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (369) implies:
% 151.47/25.66 | (370) ~ (all_52_8 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (148), (359) imply:
% 151.47/25.66 | (371) ~ (all_52_12 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (371) implies:
% 151.47/25.66 | (372) ~ (all_52_12 = all_10_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (145), (310) imply:
% 151.47/25.66 | (373) ~ (all_52_1 = all_8_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (140), (358) imply:
% 151.47/25.66 | (374) ~ (all_52_2 = all_6_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (136), (314) imply:
% 151.47/25.66 | (375) ~ (all_52_3 = all_4_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (135), (310) imply:
% 151.47/25.66 | (376) ~ (all_52_4 = all_8_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (130), (310) imply:
% 151.47/25.66 | (377) ~ (all_52_6 = all_8_2)
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (377) implies:
% 151.47/25.66 | (378) ~ (all_52_6 = all_8_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (129), (310) imply:
% 151.47/25.66 | (379) ~ (all_52_7 = all_8_2)
% 151.47/25.66 |
% 151.47/25.66 | SIMP: (379) implies:
% 151.47/25.66 | (380) ~ (all_52_7 = all_8_2)
% 151.47/25.66 |
% 151.47/25.66 | REDUCE: (128), (310) imply:
% 151.47/25.67 | (381) ~ (all_52_9 = all_8_2)
% 151.47/25.67 |
% 151.47/25.67 | SIMP: (381) implies:
% 151.47/25.67 | (382) ~ (all_52_9 = all_8_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (127), (310) imply:
% 151.47/25.67 | (383) ~ (all_52_13 = all_8_2)
% 151.47/25.67 |
% 151.47/25.67 | SIMP: (383) implies:
% 151.47/25.67 | (384) ~ (all_52_13 = all_8_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (125), (358) imply:
% 151.47/25.67 | (385) ~ (all_52_6 = all_6_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (122), (314) imply:
% 151.47/25.67 | (386) ~ (all_52_7 = all_4_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (120), (358) imply:
% 151.47/25.67 | (387) ~ (all_52_8 = all_6_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (117), (358) imply:
% 151.47/25.67 | (388) ~ (all_52_9 = all_6_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (114), (358) imply:
% 151.47/25.67 | (389) ~ (all_52_11 = all_6_2)
% 151.47/25.67 |
% 151.47/25.67 | SIMP: (389) implies:
% 151.47/25.67 | (390) ~ (all_52_11 = all_6_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (113), (358) imply:
% 151.47/25.67 | (391) ~ (all_52_14 = all_6_2)
% 151.47/25.67 |
% 151.47/25.67 | SIMP: (391) implies:
% 151.47/25.67 | (392) ~ (all_52_14 = all_6_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (112), (314) imply:
% 151.47/25.67 | (393) ~ (all_52_11 = all_4_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (109), (314) imply:
% 151.47/25.67 | (394) ~ (all_52_12 = all_4_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (107), (314) imply:
% 151.47/25.67 | (395) ~ (all_52_13 = all_4_2)
% 151.47/25.67 |
% 151.47/25.67 | REDUCE: (106), (314) imply:
% 151.47/25.67 | (396) ~ (all_52_14 = all_4_2)
% 151.47/25.67 |
% 151.47/25.67 | BETA: splitting (37) gives:
% 151.47/25.67 |
% 151.47/25.67 | Case 1:
% 151.47/25.67 | |
% 151.47/25.67 | | (397) ~ (all_4_2 = e1)
% 151.47/25.67 | |
% 151.47/25.67 | | BETA: splitting (40) gives:
% 151.47/25.67 | |
% 151.47/25.67 | | Case 1:
% 151.47/25.67 | | |
% 151.47/25.67 | | | (398) ~ (all_6_2 = e2)
% 151.47/25.67 | | |
% 151.47/25.67 | | | BETA: splitting (43) gives:
% 151.47/25.67 | | |
% 151.47/25.67 | | | Case 1:
% 151.47/25.67 | | | |
% 151.47/25.67 | | | | (399) ~ (all_8_2 = e1)
% 151.47/25.67 | | | |
% 151.47/25.67 | | | | BETA: splitting (46) gives:
% 151.47/25.67 | | | |
% 151.47/25.67 | | | | Case 1:
% 151.47/25.67 | | | | |
% 151.47/25.67 | | | | | (400) ~ (all_10_2 = e0)
% 151.47/25.67 | | | | |
% 151.47/25.67 | | | | | BETA: splitting (52) gives:
% 151.47/25.67 | | | | |
% 151.47/25.67 | | | | | Case 1:
% 151.47/25.67 | | | | | |
% 151.47/25.67 | | | | | | (401) ~ (all_14_2 = e3)
% 151.47/25.67 | | | | | |
% 151.47/25.67 | | | | | | REDUCE: (351), (401) imply:
% 151.47/25.67 | | | | | | (402) ~ (all_8_2 = e3)
% 151.47/25.67 | | | | | |
% 151.47/25.67 | | | | | | BETA: splitting (55) gives:
% 151.47/25.67 | | | | | |
% 151.47/25.67 | | | | | | Case 1:
% 151.47/25.67 | | | | | | |
% 151.47/25.67 | | | | | | | (403) ~ (all_16_2 = e2)
% 151.47/25.67 | | | | | | |
% 151.47/25.67 | | | | | | | REDUCE: (349), (403) imply:
% 151.47/25.67 | | | | | | | (404) ~ (all_10_2 = e2)
% 151.47/25.67 | | | | | | |
% 151.47/25.67 | | | | | | | BETA: splitting (61) gives:
% 151.47/25.67 | | | | | | |
% 151.47/25.67 | | | | | | | Case 1:
% 151.47/25.67 | | | | | | | |
% 151.47/25.67 | | | | | | | | (405) ~ (all_20_2 = e2)
% 151.47/25.67 | | | | | | | |
% 151.47/25.67 | | | | | | | | REDUCE: (348), (405) imply:
% 151.47/25.67 | | | | | | | | (406) ~ (all_4_2 = e2)
% 151.47/25.67 | | | | | | | |
% 151.47/25.67 | | | | | | | | BETA: splitting (73) gives:
% 151.47/25.67 | | | | | | | |
% 151.47/25.67 | | | | | | | | Case 1:
% 151.47/25.67 | | | | | | | | |
% 151.47/25.67 | | | | | | | | | (407) ~ (all_28_2 = e3)
% 151.47/25.67 | | | | | | | | |
% 151.47/25.67 | | | | | | | | | REDUCE: (339), (407) imply:
% 151.47/25.67 | | | | | | | | | (408) ~ (all_6_2 = e3)
% 151.47/25.67 | | | | | | | | |
% 151.47/25.67 | | | | | | | | | BETA: splitting (76) gives:
% 151.47/25.67 | | | | | | | | |
% 151.47/25.67 | | | | | | | | | Case 1:
% 151.47/25.67 | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | (409) ~ (all_30_2 = e0)
% 151.47/25.67 | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | REDUCE: (354), (409) imply:
% 151.47/25.67 | | | | | | | | | | (410) ~ (all_8_2 = e0)
% 151.47/25.67 | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | BETA: splitting (197) gives:
% 151.47/25.67 | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | Case 1:
% 151.47/25.67 | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | (411) all_54_5 = e3
% 151.47/25.67 | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | COMBINE_EQS: (282), (411) imply:
% 151.47/25.67 | | | | | | | | | | | (412) all_8_2 = e3
% 151.47/25.67 | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | REDUCE: (402), (412) imply:
% 151.47/25.67 | | | | | | | | | | | (413) $false
% 151.47/25.67 | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | CLOSE: (413) is inconsistent.
% 151.47/25.67 | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | Case 2:
% 151.47/25.67 | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | (414) ~ (all_54_5 = e3)
% 151.47/25.67 | | | | | | | | | | | (415) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 151.47/25.67 | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | BETA: splitting (415) gives:
% 151.47/25.67 | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | Case 1:
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | (416) all_54_5 = e2
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | COMBINE_EQS: (282), (416) imply:
% 151.47/25.67 | | | | | | | | | | | | (417) all_8_2 = e2
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | COMBINE_EQS: (360), (417) imply:
% 151.47/25.67 | | | | | | | | | | | | (418) all_56_13 = e2
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | REDUCE: (373), (417) imply:
% 151.47/25.67 | | | | | | | | | | | | (419) ~ (all_52_1 = e2)
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | REDUCE: (376), (417) imply:
% 151.47/25.67 | | | | | | | | | | | | (420) ~ (all_52_4 = e2)
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | REDUCE: (378), (417) imply:
% 151.47/25.67 | | | | | | | | | | | | (421) ~ (all_52_6 = e2)
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | REDUCE: (380), (417) imply:
% 151.47/25.67 | | | | | | | | | | | | (422) ~ (all_52_7 = e2)
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | REDUCE: (382), (417) imply:
% 151.47/25.67 | | | | | | | | | | | | (423) ~ (all_52_9 = e2)
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | REDUCE: (384), (417) imply:
% 151.47/25.67 | | | | | | | | | | | | (424) ~ (all_52_13 = e2)
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | REDUCE: (402), (417) imply:
% 151.47/25.67 | | | | | | | | | | | | (425) ~ (e3 = e2)
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | BETA: splitting (240) gives:
% 151.47/25.67 | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | Case 1:
% 151.47/25.67 | | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | | (426) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 151.47/25.67 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 151.47/25.67 | | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | | BETA: splitting (426) gives:
% 151.47/25.67 | | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | | Case 1:
% 151.47/25.67 | | | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | | | (427) all_58_2 = e2 & op(e2, e3) = e2
% 151.47/25.67 | | | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | | | ALPHA: (427) implies:
% 151.47/25.67 | | | | | | | | | | | | | | (428) op(e2, e3) = e2
% 151.47/25.67 | | | | | | | | | | | | | |
% 151.47/25.67 | | | | | | | | | | | | | | REF_CLOSE: (165), (419), (428), (function-axioms) are
% 151.47/25.68 | | | | | | | | | | | | | | inconsistent by sub-proof #1544.
% 151.47/25.68 | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | Case 2:
% 151.47/25.68 | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | (429) all_58_3 = e2 & op(e2, e2) = e2
% 151.47/25.68 | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | ALPHA: (429) implies:
% 151.47/25.68 | | | | | | | | | | | | | | (430) all_58_3 = e2
% 151.47/25.68 | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 151.47/25.68 | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | Case 1:
% 151.47/25.68 | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | (431) ~ (all_32_2 = e1)
% 151.47/25.68 | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | REDUCE: (355), (431) imply:
% 151.47/25.68 | | | | | | | | | | | | | | | (432) ~ (all_10_2 = e1)
% 151.47/25.68 | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 151.47/25.68 | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | Case 1:
% 151.47/25.68 | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | (433) all_54_0 = e3
% 151.47/25.68 | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (433) imply:
% 151.47/25.68 | | | | | | | | | | | | | | | | (434) all_10_2 = e3
% 151.47/25.68 | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (434) imply:
% 151.47/25.68 | | | | | | | | | | | | | | | | (435) all_56_12 = e3
% 151.47/25.68 | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | REDUCE: (368), (434) imply:
% 151.47/25.68 | | | | | | | | | | | | | | | | (436) ~ (all_52_4 = e3)
% 151.47/25.68 | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | REDUCE: (370), (434) imply:
% 151.47/25.68 | | | | | | | | | | | | | | | | (437) ~ (all_52_8 = e3)
% 151.47/25.68 | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | REDUCE: (45), (434) imply:
% 151.47/25.68 | | | | | | | | | | | | | | | | (438) op(e3, e3) = e3
% 151.47/25.68 | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 151.47/25.68 | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.68 | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | (439) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 151.47/25.68 | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 151.47/25.68 | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | BETA: splitting (439) gives:
% 151.47/25.68 | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.68 | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (440) all_58_0 = e3 & op(e3, e3) = e3
% 151.47/25.68 | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | | ALPHA: (440) implies:
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (441) all_58_0 = e3
% 151.47/25.68 | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (39), (42), (45), (82),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (108), (115), (116), (121), (123), (124), (126),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (134), (137), (138), (139), (141), (142), (143),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (144), (146), (147), (155), (156), (157), (158),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (167), (168),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (187), (188), (189), (191), (192), (194), (195),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (198), (208), (212), (213), (220), (223), (224),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (225), (226), (227), (228), (229), (230), (232),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (233), (234), (235), (236), (237), (238), (239),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (241), (242), (243), (245), (246), (247), (248),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (249), (250), (251), (252), (253), (261), (262),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (263), (265), (273), (275), (276), (286), (304),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (306), (331), (374), (375), (386), (388), (392),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (395), (397), (398), (399), (402), (404), (406),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (408), (418), (419), (420), (421), (422), (423),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (424), (430), (435), (436), (437), (438), (441),
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.47/25.68 | | | | | | | | | | | | | | | | | | #1354.
% 151.47/25.68 | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.68 | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (442) all_58_2 = e3 & op(e2, e3) = e3
% 151.47/25.68 | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | | ALPHA: (442) implies:
% 151.47/25.68 | | | | | | | | | | | | | | | | | | (443) all_58_2 = e3
% 151.47/25.68 | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 151.47/25.68 | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.68 | | | | | | | | | | | | | | | | | | |
% 151.47/25.68 | | | | | | | | | | | | | | | | | | | (444) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 151.47/25.69 | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (445) all_58_0 = e3 & op(e3, e3) = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (446) all_58_0 = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (39), (42), (45), (82),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (108), (115), (116), (121), (123), (124), (126),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (134), (137), (138), (139), (141), (142), (143),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (144), (146), (147), (155), (156), (157), (158),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (167), (168),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (187), (188), (189), (191), (192), (194), (195),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (198), (208), (212), (213), (220), (223), (224),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (225), (226), (227), (228), (229), (230), (232),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (233), (234), (235), (236), (237), (238), (239),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (241), (242), (243), (245), (246), (247), (248),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (249), (250), (251), (252), (253), (261), (262),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (263), (265), (273), (275), (276), (286), (304),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (306), (331), (374), (375), (386), (388), (392),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (395), (397), (398), (399), (402), (404), (406),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (408), (418), (419), (420), (421), (422), (423),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (424), (430), (435), (436), (437), (438), (446),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | #1354.
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (447) all_58_1 = e3 & op(e3, e2) = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (448) op(e3, e2) = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (436), (448), (function-axioms) are
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1540.
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.69 | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | (449) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 151.47/25.69 | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (449) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (450) all_58_4 = e3 & op(e3, e1) = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | ALPHA: (450) implies:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (451) op(e3, e1) = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (437), (451), (function-axioms) are
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (452) all_58_9 = e3 & op(e3, e0) = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | ALPHA: (452) implies:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | (453) all_58_9 = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | (454) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (168), (404), (420), (454),
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | #1503.
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | (455) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | (456) all_58_4 = e2 & op(e3, e1) = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | (457) all_58_4 = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | (458) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | (459) all_58_9 = e2 & op(e3, e0) = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (453), (459) are inconsistent by sub-proof
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | #1353.
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | (460) all_58_10 = e2 & op(e2, e0) = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | (461) op(e2, e0) = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (424), (461), (function-axioms) are
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1535.
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | (462) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | (463) all_58_11 = e2 & op(e1, e0) = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (463) implies:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | (464) all_58_11 = e2
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | (465) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (465) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_58_0 = e1 & op(e3, e3) = e1
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_58_6 = e3 & op(e1, e3) = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (468) implies:
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_58_6 = e3
% 151.47/25.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (155), (160), (162), (163), (165), (168),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (224), (227), (228), (230), (231), (232),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (235), (236), (239), (241), (245), (246),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247), (248), (249), (250), (251), (252), (253),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (398), (399), (402), (404), (406), (419),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420), (421), (423), (424), (435), (436), (438),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469), (function-axioms) are inconsistent by
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1320.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_58_7 = e3 & op(e1, e2) = e3
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (470) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_58_7 = e3
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (472) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_58_0 = e0 & op(e3, e3) = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (473) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) op(e3, e3) = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (438), (474), (function-axioms) are
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1521.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_58_1 = e0 & op(e3, e2) = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (475) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_58_1 = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (477) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_58_1 = e1 & op(e3, e2) = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (476), (478) are inconsistent by sub-proof
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1424.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_58_3 = e1 & op(e2, e2) = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (399), (479), (function-axioms) are
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (480) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_58_7 = e1 & op(e1, e2) = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (481) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_58_7 = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (482) imply:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) e3 = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (45), (168), (220), (251), (404), (420),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435), (453), (483), (function-axioms) are
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1322.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_58_13 = e1 & op(e0, e2) = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_58_13 = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) op(e0, e2) = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (487) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_58_12 = e3 & op(e0, e3) = e3
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_58_12 = e3
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155), (156), (162), (165), (168), (223), (225),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (230), (233), (235), (237), (246),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247), (248), (250), (251), (252), (253), (404),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406), (408), (419), (420), (422), (424), (436),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438), (489), (function-axioms) are inconsistent
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1450.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) all_58_13 = e3 & op(e0, e2) = e3
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (490) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_58_13 = e3
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (485), (491) imply:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) e3 = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (492) imply:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_58_7 = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (168), (245), (402), (436), (485),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (function-axioms) are inconsistent by
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1419.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (494) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_58_14 = e3 & op(e0, e1) = e3
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (495) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_58_14 = e3
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (497) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_58_12 = e2 & op(e0, e3) = e2
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (498) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_58_12 = e2
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_58_0 = e0 & op(e3, e3) = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (501) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) op(e3, e3) = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (438), (502), (function-axioms) are
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1521.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_58_2 = e0 & op(e2, e3) = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (503) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_58_2 = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (443), (504) are inconsistent by sub-proof
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1485.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (505) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (466) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) op(e3, e3) = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e3,
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (438), (506) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) e3 = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (507) imply:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_58_7 = e1
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (168), (245), (402), (436), (485),
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508), (function-axioms) are inconsistent by
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1419.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_58_12 = e0 & op(e0, e3) = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (509) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_58_12 = e0
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (499), (510) are inconsistent by sub-proof
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1482.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_58_13 = e2 & op(e0, e2) = e2
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (511) implies:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) op(e0, e2) = e2
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (156), (486), (512), (function-axioms) are
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1319.
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (513) gives:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) all_58_14 = e2 & op(e0, e1) = e2
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (514) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_58_14 = e2
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (496), (515) are inconsistent by sub-proof
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1405.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_58_15 = e2 & op(e0, e0) = e2
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (516) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_58_15 = e2
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (223), (227), (453),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464), (517) are inconsistent by sub-proof #1453.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_58_15 = e3 & op(e0, e0) = e3
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (518) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_58_15 = e3
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (223), (227), (453),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464), (519) are inconsistent by sub-proof #1316.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (453), (457), (520) are inconsistent by
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1314.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (521) gives:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_58_8 = e3 & op(e1, e1) = e3
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (408), (522), (function-axioms) are
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1469.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_58_11 = e3 & op(e1, e0) = e3
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (464), (523) are inconsistent by sub-proof
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1313.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_58_1 = e1 & op(e3, e2) = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (524) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_58_1 = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (247), (438), (453), (457), (525),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | #1312.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | (526) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_58_4 = e1 & op(e3, e1) = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (527) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_58_4 = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (457), (528) are inconsistent by sub-proof
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | #1311.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_58_9 = e1 & op(e3, e0) = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (529) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_9 = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (530) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (531) e3 = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (531) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_56_12 = e1
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (45), (168), (220), (251), (404), (420),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (530), (532), (function-axioms) are inconsistent
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1323.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | (533) all_58_15 = e2 & op(e0, e0) = e2
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (406), (533), (function-axioms) are
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1452.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | (534) all_58_9 = e2 & op(e3, e0) = e2
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (453), (534) are inconsistent by sub-proof
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | | #1353.
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | (535) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 151.47/25.71 | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 151.47/25.71 | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | BETA: splitting (535) gives:
% 151.47/25.71 | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (536) all_58_6 = e3 & op(e1, e3) = e3
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | ALPHA: (536) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (537) all_58_6 = e3
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (45), (155), (160), (162), (163), (165), (168),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (220), (224), (227), (228), (230), (231), (232),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (234), (235), (236), (239), (241), (245), (246),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (247), (248), (249), (250), (251), (252), (253),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (397), (398), (399), (402), (404), (406), (419),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (420), (421), (423), (424), (435), (436), (438),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (537), (function-axioms) are inconsistent by
% 151.47/25.71 | | | | | | | | | | | | | | | | | | sub-proof #1320.
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (538) all_58_12 = e3 & op(e0, e3) = e3
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | ALPHA: (538) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (539) all_58_12 = e3
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (155), (156), (162), (165), (168), (223), (225),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (227), (228), (230), (233), (235), (237), (246),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (247), (248), (250), (251), (252), (253), (404),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (406), (408), (419), (420), (422), (424), (436),
% 151.47/25.71 | | | | | | | | | | | | | | | | | | (438), (539), (function-axioms) are inconsistent
% 151.47/25.71 | | | | | | | | | | | | | | | | | | by sub-proof #1450.
% 151.47/25.71 | | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | (540) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 151.47/25.71 | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | | REF_CLOSE: (299), (400), (404), (432), (540) are inconsistent
% 151.47/25.71 | | | | | | | | | | | | | | | | by sub-proof #1307.
% 151.47/25.71 | | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | End of split
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | Case 2:
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | (541) all_32_2 = e1
% 151.47/25.71 | | | | | | | | | | | | | | | (542) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0
% 151.47/25.71 | | | | | | | | | | | | | | | & op(e1, e1) = all_32_1 & $i(all_32_0) &
% 151.47/25.71 | | | | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 151.47/25.71 | | | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | COMBINE_EQS: (355), (541) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | (543) all_10_2 = e1
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | SIMP: (543) implies:
% 151.47/25.71 | | | | | | | | | | | | | | | (544) all_10_2 = e1
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | COMBINE_EQS: (297), (544) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | (545) all_56_12 = e1
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | REDUCE: (364), (544) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | (546) ~ (all_52_2 = e1)
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | REDUCE: (368), (544) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | (547) ~ (all_52_4 = e1)
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | REDUCE: (370), (544) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | (548) ~ (all_52_8 = e1)
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | REDUCE: (372), (544) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | (549) ~ (all_52_12 = e1)
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | REDUCE: (404), (544) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | (550) ~ (e2 = e1)
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | REDUCE: (45), (544) imply:
% 151.47/25.71 | | | | | | | | | | | | | | | (551) op(e3, e3) = e1
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | BETA: splitting (542) gives:
% 151.47/25.71 | | | | | | | | | | | | | | |
% 151.47/25.71 | | | | | | | | | | | | | | | Case 1:
% 151.47/25.71 | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | (552) ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 151.47/25.72 | | | | | | | | | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) &
% 151.47/25.72 | | | | | | | | | | | | | | | | $i(all_32_1)
% 151.47/25.72 | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | ALPHA: (552) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | (553) op(e1, e1) = all_32_1
% 151.47/25.72 | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | (554) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 151.47/25.72 | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | BETA: splitting (554) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (555) all_58_0 = e1 & op(e3, e3) = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | ALPHA: (555) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (556) all_58_0 = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (212), (220), (224), (230), (231), (232), (234),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (235), (236), (237), (245), (246), (247), (250),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (251), (252), (253), (261), (273), (277), (287),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (289), (304), (306), (385), (386), (388), (390),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (393), (397), (398), (402), (404), (418), (419),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (420), (421), (422), (423), (545), (546), (547),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (548), (549), (553), (556), (function-axioms) are
% 151.47/25.72 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1285.
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (557) all_58_1 = e1 & op(e3, e2) = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (547), (557), (function-axioms) are
% 151.47/25.72 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1284.
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | End of split
% 151.47/25.72 | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.72 | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | (558) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 151.47/25.72 | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | BETA: splitting (558) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (559) all_58_4 = e1 & op(e3, e1) = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | ALPHA: (559) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (560) all_58_4 = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | | (561) op(e3, e1) = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | (562) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 151.47/25.72 | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (220), (423), (545), (562),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | #1283.
% 151.47/25.72 | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | (563) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 151.47/25.72 | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (563) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | (564) all_58_8 = e2 & op(e1, e1) = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (398), (564), (function-axioms) are
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | (565) all_58_14 = e2 & op(e0, e1) = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | ALPHA: (565) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | (566) all_58_14 = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | (567) op(e0, e1) = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | (568) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (168), (404), (420), (568),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | #1503.
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | (569) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (569) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | (570) all_58_4 = e2 & op(e3, e1) = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | (571) op(e3, e1) = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (220), (545), (571), (function-axioms) are
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1448.
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | (572) all_58_9 = e2 & op(e3, e0) = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (572) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | (573) all_58_9 = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | (574) op(e3, e0) = e2
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | (575) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (575) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (576) all_58_4 = e3 & op(e3, e1) = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (576) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (577) all_58_4 = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (560), (577) are inconsistent by sub-proof
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | #1282.
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (578) all_58_5 = e3 & op(e2, e1) = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (578) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (579) all_58_5 = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | (580) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (580) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_58_0 = e3 & op(e3, e3) = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (581) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (582) all_58_0 = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (583) op(e3, e3) = e3
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (584) gives:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_58_0 = e1 & op(e3, e3) = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (585) implies:
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_58_0 = e1
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (220), (224), (230), (231), (232), (234),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (245), (246), (247), (250),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251), (252), (253), (261), (273), (277), (287),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (304), (306), (385), (386), (388), (390),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (397), (398), (402), (404), (418), (419),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420), (421), (422), (423), (545), (546), (547),
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548), (549), (553), (586), (function-axioms) are
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1285.
% 151.47/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_58_2 = e1 & op(e2, e3) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_58_2 = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) op(e2, e3) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) ~ (all_56_12 = e1)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (590) imply:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) $false
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (591) is inconsistent.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_56_1 = e3 & op(e3, e1) = e3
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (592) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) op(e3, e1) = e3
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (561), (579), (594), (function-axioms)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1280.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_58_8 = e0 & op(e1, e1) = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_58_8 = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) op(e1, e1) = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (599) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_58_12 = e1 & op(e0, e3) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (161),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (220), (227), (231), (233), (238), (246),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (251), (252), (397), (404), (420),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430), (545), (546), (551), (573), (579), (588),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589), (597), (598), (600), (function-axioms) are
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1272.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_58_13 = e1 & op(e0, e2) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (601) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) all_58_13 = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (603) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_58_0 = e0 & op(e3, e3) = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (604) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) op(e3, e3) = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (583), (605), (function-axioms) are
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1521.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) all_58_1 = e0 & op(e3, e2) = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (606) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) op(e3, e2) = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (430), (588), (608) are inconsistent by
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1393.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (609) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_58_5 = e0 & op(e2, e1) = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (610) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_58_5 = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (579), (611) are inconsistent by sub-proof
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1392.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_58_10 = e0 & op(e2, e0) = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (612) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_58_10 = e0
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (402), (607), (614), (function-axioms)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1302.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (615) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_58_7 = e3 & op(e1, e2) = e3
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_58_7 = e3
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (618) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_58_6 = e1 & op(e1, e3) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (619) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) op(e1, e3) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (546), (620), (function-axioms) are
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1412.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_58_7 = e1 & op(e1, e2) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (621) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_58_7 = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (617), (622) imply:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) e3 = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (623) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) e3 = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (582), (624) imply:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) all_58_0 = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (224), (230), (231), (232), (234), (235),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (237), (245), (246), (247), (250), (251),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (261), (273), (277), (287), (289),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304), (306), (385), (386), (388), (390), (393),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (398), (402), (404), (418), (419), (420),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (422), (423), (546), (547), (548), (549),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (593), (625), (function-axioms) are
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1286.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_58_8 = e1 & op(e1, e1) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (155), (234), (561), (567), (579),
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627), (function-axioms) are inconsistent by
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1270.
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_58_11 = e1 & op(e1, e0) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (628) implies:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_58_11 = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) op(e1, e0) = e1
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 151.47/25.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (39), (45), (160), (168),
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (232), (233), (251), (398), (404), (420),
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (545), (573), (593), (598), (613), (617),
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629), (630), (631), (function-axioms) are
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1267.
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (632) gives:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_58_11 = e3 & op(e1, e0) = e3
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (633) implies:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) op(e1, e0) = e3
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (630), (634), (function-axioms) are
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1275.
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_58_15 = e3 & op(e0, e0) = e3
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (635) implies:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) all_58_15 = e3
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) all_58_15 = e0 & op(e0, e0) = e0
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (39), (45), (160), (168),
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (232), (233), (251), (398), (404), (420),
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (545), (573), (598), (617), (629), (630),
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636), (637), (function-axioms) are inconsistent
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1266.
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.47/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (638) implies:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (45), (161), (168), (220),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (251), (404), (420), (545), (546), (597),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613), (617), (629), (640), (function-axioms) are
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1265.
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (641) gives:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (561) gives:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_52_8 = e1
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (593) gives:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_52_8 = e3
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (642), (643) imply:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) e3 = e1
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (582), (644) imply:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_58_0 = e1
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (224), (230), (231), (232), (234), (235),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (237), (245), (246), (247), (250), (251),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (261), (273), (277), (287), (289),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304), (306), (385), (386), (388), (390), (393),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (398), (402), (404), (418), (419), (420),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (422), (423), (546), (547), (548), (549),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (593), (645), (function-axioms) are
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1286.
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_58_15 = e1 & op(e0, e0) = e1
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (226), (566), (602),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639), (646) are inconsistent by sub-proof #1263.
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) all_58_13 = e3 & op(e0, e2) = e3
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (647) implies:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_58_13 = e3
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (602), (648) imply:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) e3 = e1
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (582), (649) imply:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_58_0 = e1
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (224), (230), (231), (232), (234), (235),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (237), (245), (246), (247), (250), (251),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (261), (273), (277), (287), (289),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304), (306), (385), (386), (388), (390), (393),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (398), (402), (404), (418), (419), (420),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (422), (423), (546), (547), (548), (549),
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (593), (650), (function-axioms) are
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1286.
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (561), (574), (651), (function-axioms)
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1262.
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (155), (397), (567), (652),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1417.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_58_14 = e0 & op(e0, e1) = e0
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (653) implies:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) op(e0, e1) = e0
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (155), (567), (654), (function-axioms) are
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1372.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (655) gives:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) all_58_6 = e1 & op(e1, e3) = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (656) implies:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) op(e1, e3) = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (546), (657), (function-axioms) are
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1412.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) all_58_12 = e1 & op(e0, e3) = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (658) implies:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_58_12 = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (155), (161),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (168), (220), (234), (235), (246),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (251), (252), (404), (419), (420),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545), (546), (551), (561), (567), (573), (579),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (658), (659), (function-axioms) are
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1257.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_58_1 = e3 & op(e3, e2) = e3
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (660) implies:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (661) op(e3, e2) = e3
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (662) gives:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_58_0 = e1 & op(e3, e3) = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (663) implies:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_58_0 = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (220), (224), (230), (231), (232), (234),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (245), (246), (247), (250),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251), (252), (253), (261), (273), (277), (287),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (304), (306), (385), (386), (388), (390),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (397), (398), (402), (404), (418), (419),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420), (421), (422), (423), (545), (546), (547),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548), (549), (553), (664), (function-axioms) are
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1285.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_58_2 = e1 & op(e2, e3) = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155), (156), (160), (161), (168), (220), (224),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (234), (242), (247), (248),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (250), (251), (252), (397), (398), (404),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420), (421), (430), (545), (546), (551), (561),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567), (573), (574), (579), (661), (665),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1249.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (161), (165),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (220), (246), (247), (248), (249), (250),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (251), (252), (404), (419), (420), (545), (546),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (551), (561), (573), (574), (661), (666),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1246.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | (667) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (560), (573), (667) are inconsistent by
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1244.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | (668) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (408), (566), (668), (function-axioms)
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1243.
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | (669) all_58_9 = e1 & op(e3, e0) = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | ALPHA: (669) implies:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | (670) all_58_9 = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (45), (168), (220), (251), (404), (420),
% 151.86/25.75 | | | | | | | | | | | | | | | | | | (545), (670), (function-axioms) are inconsistent
% 151.86/25.75 | | | | | | | | | | | | | | | | | | by sub-proof #1323.
% 151.86/25.75 | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | End of split
% 151.86/25.75 | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | Case 2:
% 151.86/25.75 | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | (671) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 151.86/25.75 | | | | | | | | | | | | | | | | $i(all_32_1)
% 151.86/25.75 | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | ALPHA: (671) implies:
% 151.86/25.75 | | | | | | | | | | | | | | | | (672) ~ (all_32_1 = e2)
% 151.86/25.75 | | | | | | | | | | | | | | | | (673) op(e1, e1) = all_32_1
% 151.86/25.75 | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 151.86/25.75 | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.75 | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | (674) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 151.86/25.75 | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | BETA: splitting (674) gives:
% 151.86/25.75 | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.75 | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | (675) all_58_0 = e1 & op(e3, e3) = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | |
% 151.86/25.75 | | | | | | | | | | | | | | | | | | ALPHA: (675) implies:
% 151.86/25.75 | | | | | | | | | | | | | | | | | | (676) all_58_0 = e1
% 151.86/25.75 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (212), (220), (224), (230), (231), (232), (234),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (235), (236), (237), (245), (246), (247), (250),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (251), (252), (253), (261), (273), (277), (287),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (289), (304), (306), (385), (386), (388), (390),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (393), (397), (402), (404), (418), (419), (420),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (421), (422), (423), (545), (546), (547), (548),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (549), (672), (673), (676), (function-axioms) are
% 151.86/25.76 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1241.
% 151.86/25.76 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (677) all_58_1 = e1 & op(e3, e2) = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (547), (677), (function-axioms) are
% 151.86/25.76 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1284.
% 151.86/25.76 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | End of split
% 151.86/25.76 | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | (678) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 151.86/25.76 | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | BETA: splitting (678) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (679) all_58_4 = e1 & op(e3, e1) = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | ALPHA: (679) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (680) all_58_4 = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | | (681) op(e3, e1) = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | (682) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (220), (423), (545), (682),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | #1283.
% 151.86/25.76 | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | (683) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (683) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | (684) all_58_8 = e2 & op(e1, e1) = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (398), (684), (function-axioms) are
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | (685) all_58_14 = e2 & op(e0, e1) = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | ALPHA: (685) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | (686) all_58_14 = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | (687) op(e0, e1) = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | (688) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (168), (404), (420), (688),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | #1503.
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | (689) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (689) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | (690) all_58_4 = e2 & op(e3, e1) = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (690) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | (691) op(e3, e1) = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (220), (545), (691), (function-axioms) are
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1448.
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | (692) all_58_9 = e2 & op(e3, e0) = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (692) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | (693) all_58_9 = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | (694) op(e3, e0) = e2
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | (695) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (695) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | (696) all_58_4 = e3 & op(e3, e1) = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (696) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | (697) all_58_4 = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (680), (697) are inconsistent by sub-proof
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | #1282.
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | (698) all_58_5 = e3 & op(e2, e1) = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (698) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | (699) all_58_5 = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | (700) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (700) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_58_0 = e3 & op(e3, e3) = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (701) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (702) all_58_0 = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (703) op(e3, e3) = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (704) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) all_58_0 = e1 & op(e3, e3) = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (705) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) all_58_0 = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (220), (224), (230), (231), (232), (234),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (245), (246), (247), (250),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251), (252), (253), (261), (273), (277), (287),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (304), (306), (385), (386), (388), (390),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (397), (402), (404), (418), (419), (420),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (422), (423), (545), (546), (547), (548),
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549), (672), (673), (706), (function-axioms) are
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1241.
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) all_58_2 = e1 & op(e2, e3) = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (707) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) all_58_2 = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) op(e2, e3) = e1
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) ~ (all_56_12 = e1)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (710) imply:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) $false
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (711) is inconsistent.
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) all_56_1 = e3 & op(e3, e1) = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (712) implies:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) op(e3, e1) = e3
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (681), (699), (714), (function-axioms)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1280.
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (715) gives:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) all_58_8 = e0 & op(e1, e1) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (716) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_58_8 = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) op(e1, e1) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (719) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_58_12 = e1 & op(e0, e3) = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (161),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (220), (227), (231), (233), (238), (246),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (251), (252), (397), (404), (420),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430), (545), (546), (551), (693), (699), (708),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709), (717), (718), (720), (function-axioms) are
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1272.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) all_58_13 = e1 & op(e0, e2) = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (721) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) all_58_13 = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (723) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_58_0 = e0 & op(e3, e3) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (724) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) op(e3, e3) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (703), (725), (function-axioms) are
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1521.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) all_58_1 = e0 & op(e3, e2) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (726) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) op(e3, e2) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (430), (708), (728) are inconsistent by
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1393.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (729) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_58_5 = e0 & op(e2, e1) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (730) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) all_58_5 = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (699), (731) are inconsistent by sub-proof
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1392.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_58_10 = e0 & op(e2, e0) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (732) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_58_10 = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (402), (727), (734), (function-axioms)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1302.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (735) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) all_58_7 = e3 & op(e1, e2) = e3
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (736) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) all_58_7 = e3
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (738) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) all_58_6 = e1 & op(e1, e3) = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (739) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) op(e1, e3) = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (546), (740), (function-axioms) are
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1412.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) all_58_7 = e1 & op(e1, e2) = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (741) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_58_7 = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (737), (742) imply:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) e3 = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (743) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) e3 = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (702), (744) imply:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) all_58_0 = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (224), (230), (231), (232), (234), (235),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (237), (245), (246), (247), (250), (251),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (261), (273), (277), (287), (289),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304), (306), (385), (386), (388), (390), (393),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (402), (404), (418), (419), (420), (421),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422), (423), (546), (547), (548), (549), (672),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673), (713), (745), (function-axioms) are
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1242.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (746) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_58_8 = e1 & op(e1, e1) = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (155), (234), (681), (687), (699),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747), (function-axioms) are inconsistent by
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1270.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) all_58_11 = e1 & op(e1, e0) = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (748) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) all_58_11 = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) op(e1, e0) = e1
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (39), (45), (160), (168),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (232), (233), (251), (398), (404), (420),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (545), (693), (713), (718), (733), (737),
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749), (750), (751), (function-axioms) are
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1267.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_58_11 = e3 & op(e1, e0) = e3
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (753) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) op(e1, e0) = e3
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (750), (754), (function-axioms) are
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1275.
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_58_15 = e3 & op(e0, e0) = e3
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (755) implies:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) all_58_15 = e3
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) all_58_15 = e0 & op(e0, e0) = e0
% 151.86/25.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (39), (45), (160), (168),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (232), (233), (251), (398), (404), (420),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (545), (693), (718), (737), (749), (750),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756), (757), (function-axioms) are inconsistent
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1266.
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (758) implies:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (45), (161), (168), (220),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (251), (404), (420), (545), (546), (717),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733), (737), (749), (760), (function-axioms) are
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1265.
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (761) gives:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (681) gives:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) all_52_8 = e1
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (713) gives:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_52_8 = e3
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (762), (763) imply:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) e3 = e1
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (702), (764) imply:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_58_0 = e1
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (224), (230), (231), (232), (234), (235),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (237), (245), (246), (247), (250), (251),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (261), (273), (277), (287), (289),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304), (306), (385), (386), (388), (390), (393),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (402), (404), (418), (419), (420), (421),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422), (423), (546), (547), (548), (549), (672),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673), (713), (765), (function-axioms) are
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1242.
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_58_15 = e1 & op(e0, e0) = e1
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (226), (686), (722),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759), (766) are inconsistent by sub-proof #1263.
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) all_58_13 = e3 & op(e0, e2) = e3
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (767) implies:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) all_58_13 = e3
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (722), (768) imply:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) e3 = e1
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (702), (769) imply:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_58_0 = e1
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (224), (230), (231), (232), (234), (235),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (237), (245), (246), (247), (250), (251),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (261), (273), (277), (287), (289),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304), (306), (385), (386), (388), (390), (393),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (402), (404), (418), (419), (420), (421),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422), (423), (546), (547), (548), (549), (672),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673), (713), (770), (function-axioms) are
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1242.
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (681), (694), (771), (function-axioms)
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1262.
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (155), (397), (687), (772),
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1417.
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 151.86/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) all_58_14 = e0 & op(e0, e1) = e0
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (773) implies:
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) op(e0, e1) = e0
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (155), (687), (774), (function-axioms) are
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1372.
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (775) gives:
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) all_58_6 = e1 & op(e1, e3) = e1
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (776) implies:
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) op(e1, e3) = e1
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (546), (777), (function-axioms) are
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1412.
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) all_58_12 = e1 & op(e0, e3) = e1
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (778) implies:
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_58_12 = e1
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (155), (161),
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (168), (220), (234), (235), (246),
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (251), (252), (404), (419), (420),
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545), (546), (551), (681), (687), (693), (699),
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702), (778), (779), (function-axioms) are
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1257.
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.78 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_58_1 = e3 & op(e3, e2) = e3
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (780) implies:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (781) op(e3, e2) = e3
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (782) gives:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_58_0 = e1 & op(e3, e3) = e1
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (783) implies:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_58_0 = e1
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (42), (45),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (116), (118), (119), (121), (126),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (132), (133), (134), (155), (156), (158),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (167),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (187), (192), (196), (199), (201), (208),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (220), (224), (230), (231), (232), (234),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (245), (246), (247), (250),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251), (252), (253), (261), (273), (277), (287),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (304), (306), (385), (386), (388), (390),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (397), (402), (404), (418), (419), (420),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (422), (423), (545), (546), (547), (548),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549), (672), (673), (784), (function-axioms) are
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1241.
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_58_2 = e1 & op(e2, e3) = e1
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155), (156), (160), (161), (168), (220), (224),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (234), (242), (247), (248),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (250), (251), (252), (397), (398), (404),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420), (421), (430), (545), (546), (551), (681),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687), (693), (694), (699), (781), (785),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1249.
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (161), (165),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (220), (246), (247), (248), (249), (250),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (251), (252), (404), (419), (420), (545), (546),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (551), (681), (693), (694), (781), (786),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1246.
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | (787) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (680), (693), (787) are inconsistent by
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1244.
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | (788) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (408), (686), (788), (function-axioms)
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1243.
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | (789) all_58_9 = e1 & op(e3, e0) = e1
% 152.06/25.79 | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | ALPHA: (789) implies:
% 152.06/25.79 | | | | | | | | | | | | | | | | | | (790) all_58_9 = e1
% 152.06/25.79 | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (45), (168), (220), (251), (404), (420),
% 152.06/25.79 | | | | | | | | | | | | | | | | | | (545), (790), (function-axioms) are inconsistent
% 152.06/25.79 | | | | | | | | | | | | | | | | | | by sub-proof #1323.
% 152.06/25.79 | | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | (791) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 152.06/25.79 | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.06/25.79 | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | | REF_CLOSE: (162), (163), (423), (424), (791),
% 152.06/25.79 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.06/25.79 | | | | | | | | | | | | | #1240.
% 152.06/25.79 | | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | (792) all_54_5 = e1 | all_54_5 = e0
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | REF_CLOSE: (282), (399), (410), (792) are inconsistent by
% 152.06/25.79 | | | | | | | | | | | | sub-proof #1239.
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | End of split
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | (793) all_30_2 = e0
% 152.06/25.79 | | | | | | | | | | (794) ( ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0 &
% 152.06/25.79 | | | | | | | | | | op(e0, e0) = all_30_1 & $i(all_30_0) &
% 152.06/25.79 | | | | | | | | | | $i(all_30_1)) | ( ~ (all_30_1 = e1) & op(e0, e0)
% 152.06/25.79 | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | COMBINE_EQS: (354), (793) imply:
% 152.06/25.79 | | | | | | | | | | (795) all_8_2 = e0
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | SIMP: (795) implies:
% 152.06/25.79 | | | | | | | | | | (796) all_8_2 = e0
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | COMBINE_EQS: (327), (796) imply:
% 152.06/25.79 | | | | | | | | | | (797) all_42_2 = e0
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | COMBINE_EQS: (360), (796) imply:
% 152.06/25.79 | | | | | | | | | | (798) all_56_13 = e0
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | REDUCE: (373), (796) imply:
% 152.06/25.79 | | | | | | | | | | (799) ~ (all_52_1 = e0)
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | REDUCE: (376), (796) imply:
% 152.06/25.79 | | | | | | | | | | (800) ~ (all_52_4 = e0)
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | REDUCE: (378), (796) imply:
% 152.06/25.79 | | | | | | | | | | (801) ~ (all_52_6 = e0)
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | REDUCE: (382), (796) imply:
% 152.06/25.79 | | | | | | | | | | (802) ~ (all_52_9 = e0)
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | REDUCE: (384), (796) imply:
% 152.06/25.79 | | | | | | | | | | (803) ~ (all_52_13 = e0)
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | BETA: splitting (794) gives:
% 152.06/25.79 | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | Case 1:
% 152.06/25.79 | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | (804) ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0 &
% 152.06/25.79 | | | | | | | | | | | op(e0, e0) = all_30_1 & $i(all_30_0) &
% 152.06/25.79 | | | | | | | | | | | $i(all_30_1)
% 152.06/25.79 | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | ALPHA: (804) implies:
% 152.06/25.79 | | | | | | | | | | | (805) op(e0, e0) = all_30_1
% 152.06/25.79 | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | BETA: splitting (216) gives:
% 152.06/25.79 | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | Case 1:
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | (806) ~ (all_56_13 = e0)
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | REDUCE: (798), (806) imply:
% 152.06/25.79 | | | | | | | | | | | | (807) $false
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | CLOSE: (807) is inconsistent.
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | Case 2:
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | (808) all_56_5 = e2 & op(e2, e0) = e2
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | ALPHA: (808) implies:
% 152.06/25.79 | | | | | | | | | | | | (809) op(e2, e0) = e2
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 152.06/25.79 | | | | | | | | | | | | all_30_1, e0, e0, simplifying with (36), (805)
% 152.06/25.79 | | | | | | | | | | | | gives:
% 152.06/25.79 | | | | | | | | | | | | (810) all_30_1 = all_4_2
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 152.06/25.79 | | | | | | | | | | | | e2, e0, e2, simplifying with (162), (809) gives:
% 152.06/25.79 | | | | | | | | | | | | (811) all_52_13 = e2
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | REDUCE: (143), (811) imply:
% 152.06/25.79 | | | | | | | | | | | | (812) ~ (all_52_1 = e2)
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | REDUCE: (115), (811) imply:
% 152.06/25.79 | | | | | | | | | | | | (813) ~ (all_52_9 = e2)
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | REDUCE: (111), (811) imply:
% 152.06/25.79 | | | | | | | | | | | | (814) ~ (all_52_12 = e2)
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | REDUCE: (108), (811) imply:
% 152.06/25.79 | | | | | | | | | | | | (815) ~ (all_52_14 = e2)
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | SIMP: (815) implies:
% 152.06/25.79 | | | | | | | | | | | | (816) ~ (all_52_14 = e2)
% 152.06/25.79 | | | | | | | | | | | |
% 152.06/25.79 | | | | | | | | | | | | REDUCE: (395), (811) imply:
% 152.06/25.80 | | | | | | | | | | | | (817) ~ (all_4_2 = e2)
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | Case 1:
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | (818) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 152.06/25.80 | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | BETA: splitting (818) gives:
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | Case 1:
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | (819) all_58_9 = e2 & op(e3, e0) = e2
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | REF_CLOSE: (166), (814), (819), (function-axioms) are
% 152.06/25.80 | | | | | | | | | | | | | | inconsistent by sub-proof #1238.
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | Case 2:
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | (820) all_58_10 = e2 & op(e2, e0) = e2
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | ALPHA: (820) implies:
% 152.06/25.80 | | | | | | | | | | | | | | (821) all_58_10 = e2
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (42), (45), (79), (82), (93), (110),
% 152.06/25.80 | | | | | | | | | | | | | | (116), (121), (123), (126), (132), (133), (134),
% 152.06/25.80 | | | | | | | | | | | | | | (137), (138), (139), (142), (144), (146), (147),
% 152.06/25.80 | | | | | | | | | | | | | | (155), (156), (157), (158), (160), (161), (163),
% 152.06/25.80 | | | | | | | | | | | | | | (165), (166), (167), (168), (187), (188), (189),
% 152.06/25.80 | | | | | | | | | | | | | | (190), (191), (192), (194), (196), (198), (199),
% 152.06/25.80 | | | | | | | | | | | | | | (200), (201), (202), (208), (209), (212), (223),
% 152.06/25.80 | | | | | | | | | | | | | | (224), (225), (226), (227), (229), (230), (231),
% 152.06/25.80 | | | | | | | | | | | | | | (232), (238), (239), (241), (243), (244), (245),
% 152.06/25.80 | | | | | | | | | | | | | | (246), (247), (248), (249), (250), (251), (252),
% 152.06/25.80 | | | | | | | | | | | | | | (261), (262), (263), (264), (265), (273), (275),
% 152.06/25.80 | | | | | | | | | | | | | | (277), (286), (287), (288), (289), (297), (299),
% 152.06/25.80 | | | | | | | | | | | | | | (304), (306), (331), (355), (362), (364), (366),
% 152.06/25.80 | | | | | | | | | | | | | | (368), (372), (374), (375), (385), (386), (387),
% 152.06/25.80 | | | | | | | | | | | | | | (388), (390), (392), (393), (394), (396), (397),
% 152.06/25.80 | | | | | | | | | | | | | | (398), (399), (400), (402), (404), (406), (408),
% 152.06/25.80 | | | | | | | | | | | | | | (797), (798), (799), (800), (801), (802), (812),
% 152.06/25.80 | | | | | | | | | | | | | | (813), (814), (816), (821), (function-axioms) are
% 152.06/25.80 | | | | | | | | | | | | | | inconsistent by sub-proof #1186.
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | End of split
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | Case 2:
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | (822) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 152.06/25.80 | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | REF_CLOSE: (36), (158), (406), (816), (822),
% 152.06/25.80 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.06/25.80 | | | | | | | | | | | | | #1185.
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | End of split
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | End of split
% 152.06/25.80 | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | Case 2:
% 152.06/25.80 | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | (823) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 &
% 152.06/25.80 | | | | | | | | | | | $i(all_30_1)
% 152.06/25.80 | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | ALPHA: (823) implies:
% 152.06/25.80 | | | | | | | | | | | (824) ~ (all_30_1 = e1)
% 152.06/25.80 | | | | | | | | | | | (825) op(e0, e0) = all_30_1
% 152.06/25.80 | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | BETA: splitting (216) gives:
% 152.06/25.80 | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | Case 1:
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | (826) ~ (all_56_13 = e0)
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | REDUCE: (798), (826) imply:
% 152.06/25.80 | | | | | | | | | | | | (827) $false
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | CLOSE: (827) is inconsistent.
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | Case 2:
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | (828) all_56_5 = e2 & op(e2, e0) = e2
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | ALPHA: (828) implies:
% 152.06/25.80 | | | | | | | | | | | | (829) op(e2, e0) = e2
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 152.06/25.80 | | | | | | | | | | | | all_30_1, e0, e0, simplifying with (36), (825)
% 152.06/25.80 | | | | | | | | | | | | gives:
% 152.06/25.80 | | | | | | | | | | | | (830) all_30_1 = all_4_2
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 152.06/25.80 | | | | | | | | | | | | e2, e0, e2, simplifying with (162), (829) gives:
% 152.06/25.80 | | | | | | | | | | | | (831) all_52_13 = e2
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | REDUCE: (143), (831) imply:
% 152.06/25.80 | | | | | | | | | | | | (832) ~ (all_52_1 = e2)
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | REDUCE: (115), (831) imply:
% 152.06/25.80 | | | | | | | | | | | | (833) ~ (all_52_9 = e2)
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | REDUCE: (111), (831) imply:
% 152.06/25.80 | | | | | | | | | | | | (834) ~ (all_52_12 = e2)
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | REDUCE: (108), (831) imply:
% 152.06/25.80 | | | | | | | | | | | | (835) ~ (all_52_14 = e2)
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | SIMP: (835) implies:
% 152.06/25.80 | | | | | | | | | | | | (836) ~ (all_52_14 = e2)
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | REDUCE: (395), (831) imply:
% 152.06/25.80 | | | | | | | | | | | | (837) ~ (all_4_2 = e2)
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | Case 1:
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | (838) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 152.06/25.80 | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | BETA: splitting (838) gives:
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | Case 1:
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | (839) all_58_9 = e2 & op(e3, e0) = e2
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | REF_CLOSE: (166), (834), (839), (function-axioms) are
% 152.06/25.80 | | | | | | | | | | | | | | inconsistent by sub-proof #1238.
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | Case 2:
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | (840) all_58_10 = e2 & op(e2, e0) = e2
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | ALPHA: (840) implies:
% 152.06/25.80 | | | | | | | | | | | | | | (841) all_58_10 = e2
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (42), (45), (79), (82), (93), (110),
% 152.06/25.80 | | | | | | | | | | | | | | (116), (121), (123), (126), (132), (133), (134),
% 152.06/25.80 | | | | | | | | | | | | | | (137), (138), (139), (142), (144), (146), (147),
% 152.06/25.80 | | | | | | | | | | | | | | (155), (156), (157), (158), (160), (161), (163),
% 152.06/25.80 | | | | | | | | | | | | | | (165), (166), (167), (168), (187), (188), (189),
% 152.06/25.80 | | | | | | | | | | | | | | (190), (191), (192), (194), (196), (198), (199),
% 152.06/25.80 | | | | | | | | | | | | | | (200), (201), (202), (208), (209), (212), (223),
% 152.06/25.80 | | | | | | | | | | | | | | (224), (225), (226), (227), (229), (230), (231),
% 152.06/25.80 | | | | | | | | | | | | | | (232), (238), (239), (241), (243), (244), (245),
% 152.06/25.80 | | | | | | | | | | | | | | (246), (247), (248), (249), (250), (251), (252),
% 152.06/25.80 | | | | | | | | | | | | | | (261), (262), (263), (264), (265), (273), (275),
% 152.06/25.80 | | | | | | | | | | | | | | (277), (286), (287), (288), (289), (297), (299),
% 152.06/25.80 | | | | | | | | | | | | | | (304), (306), (331), (355), (362), (364), (366),
% 152.06/25.80 | | | | | | | | | | | | | | (368), (372), (374), (375), (385), (386), (387),
% 152.06/25.80 | | | | | | | | | | | | | | (388), (390), (392), (393), (394), (396), (397),
% 152.06/25.80 | | | | | | | | | | | | | | (398), (399), (400), (402), (404), (406), (408),
% 152.06/25.80 | | | | | | | | | | | | | | (797), (798), (799), (800), (801), (802), (832),
% 152.06/25.80 | | | | | | | | | | | | | | (833), (834), (836), (841), (function-axioms) are
% 152.06/25.80 | | | | | | | | | | | | | | inconsistent by sub-proof #1186.
% 152.06/25.80 | | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | End of split
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | Case 2:
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | (842) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 152.06/25.80 | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | | REF_CLOSE: (36), (158), (406), (836), (842),
% 152.06/25.80 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.06/25.80 | | | | | | | | | | | | | #1185.
% 152.06/25.80 | | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | | End of split
% 152.06/25.80 | | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | | End of split
% 152.06/25.80 | | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | | End of split
% 152.06/25.80 | | | | | | | | | |
% 152.06/25.80 | | | | | | | | | End of split
% 152.06/25.80 | | | | | | | | |
% 152.06/25.80 | | | | | | | | Case 2:
% 152.06/25.80 | | | | | | | | |
% 152.06/25.80 | | | | | | | | | (843) all_28_2 = e3
% 152.06/25.81 | | | | | | | | | (844) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 &
% 152.06/25.81 | | | | | | | | | op(e3, e3) = all_28_1 & $i(all_28_0) &
% 152.06/25.81 | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3, e3) =
% 152.06/25.81 | | | | | | | | | all_28_1 & $i(all_28_1))
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | COMBINE_EQS: (339), (843) imply:
% 152.06/25.81 | | | | | | | | | (845) all_6_2 = e3
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | COMBINE_EQS: (273), (845) imply:
% 152.06/25.81 | | | | | | | | | (846) all_56_14 = e3
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | REDUCE: (385), (845) imply:
% 152.06/25.81 | | | | | | | | | (847) ~ (all_52_6 = e3)
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | REDUCE: (387), (845) imply:
% 152.06/25.81 | | | | | | | | | (848) ~ (all_52_8 = e3)
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | REDUCE: (388), (845) imply:
% 152.06/25.81 | | | | | | | | | (849) ~ (all_52_9 = e3)
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | BETA: splitting (844) gives:
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | (850) ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 &
% 152.06/25.81 | | | | | | | | | | op(e3, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | ALPHA: (850) implies:
% 152.06/25.81 | | | | | | | | | | (851) op(e3, e3) = all_28_1
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | REF_CLOSE: (6), (36), (39), (42), (45), (108), (124), (126),
% 152.06/25.81 | | | | | | | | | | (134), (137), (138), (139), (141), (142), (155),
% 152.06/25.81 | | | | | | | | | | (156), (158), (160), (161), (162), (163), (165),
% 152.06/25.81 | | | | | | | | | | (167), (168), (187), (190), (191), (193), (197),
% 152.06/25.81 | | | | | | | | | | (202), (215), (216), (220), (224), (225), (227),
% 152.06/25.81 | | | | | | | | | | (232), (241), (243), (245), (246), (247), (248),
% 152.06/25.81 | | | | | | | | | | (251), (252), (264), (265), (274), (282), (297),
% 152.06/25.81 | | | | | | | | | | (299), (306), (360), (362), (364), (368), (375),
% 152.06/25.81 | | | | | | | | | | (378), (384), (395), (396), (397), (398), (399),
% 152.06/25.81 | | | | | | | | | | (400), (402), (404), (406), (846), (847), (848),
% 152.06/25.81 | | | | | | | | | | (849), (851), (function-axioms) are inconsistent
% 152.06/25.81 | | | | | | | | | | by sub-proof #1162.
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | Case 2:
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | (852) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 152.06/25.81 | | | | | | | | | | $i(all_28_1)
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | ALPHA: (852) implies:
% 152.06/25.81 | | | | | | | | | | (853) op(e3, e3) = all_28_1
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | REF_CLOSE: (6), (36), (39), (42), (45), (108), (124), (126),
% 152.06/25.81 | | | | | | | | | | (134), (137), (138), (139), (141), (142), (155),
% 152.06/25.81 | | | | | | | | | | (156), (158), (160), (161), (162), (163), (165),
% 152.06/25.81 | | | | | | | | | | (167), (168), (187), (190), (191), (193), (197),
% 152.06/25.81 | | | | | | | | | | (202), (215), (216), (220), (224), (225), (227),
% 152.06/25.81 | | | | | | | | | | (232), (241), (243), (245), (246), (247), (248),
% 152.06/25.81 | | | | | | | | | | (251), (252), (264), (265), (274), (282), (297),
% 152.06/25.81 | | | | | | | | | | (299), (306), (360), (362), (364), (368), (375),
% 152.06/25.81 | | | | | | | | | | (378), (384), (395), (396), (397), (398), (399),
% 152.06/25.81 | | | | | | | | | | (400), (402), (404), (406), (846), (847), (848),
% 152.06/25.81 | | | | | | | | | | (849), (853), (function-axioms) are inconsistent
% 152.06/25.81 | | | | | | | | | | by sub-proof #1162.
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | End of split
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | End of split
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | Case 2:
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | (854) all_20_2 = e2
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | COMBINE_EQS: (348), (854) imply:
% 152.06/25.81 | | | | | | | | (855) all_4_2 = e2
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | SIMP: (855) implies:
% 152.06/25.81 | | | | | | | | (856) all_4_2 = e2
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | COMBINE_EQS: (261), (856) imply:
% 152.06/25.81 | | | | | | | | (857) all_56_15 = e2
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | REDUCE: (393), (856) imply:
% 152.06/25.81 | | | | | | | | (858) ~ (all_52_11 = e2)
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | REDUCE: (395), (856) imply:
% 152.06/25.81 | | | | | | | | (859) ~ (all_52_13 = e2)
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | REDUCE: (396), (856) imply:
% 152.06/25.81 | | | | | | | | (860) ~ (all_52_14 = e2)
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | REDUCE: (36), (856) imply:
% 152.06/25.81 | | | | | | | | (861) op(e0, e0) = e2
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | BETA: splitting (211) gives:
% 152.06/25.81 | | | | | | | |
% 152.06/25.81 | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | (862) ~ (all_56_15 = e2)
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | REDUCE: (857), (862) imply:
% 152.06/25.81 | | | | | | | | | (863) $false
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | CLOSE: (863) is inconsistent.
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | Case 2:
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | (864) all_56_10 = e0 & op(e0, e2) = e0
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | ALPHA: (864) implies:
% 152.06/25.81 | | | | | | | | | (865) op(e0, e2) = e0
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | BETA: splitting (216) gives:
% 152.06/25.81 | | | | | | | | |
% 152.06/25.81 | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | (866) ~ (all_56_13 = e0)
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | REDUCE: (360), (866) imply:
% 152.06/25.81 | | | | | | | | | | (867) ~ (all_8_2 = e0)
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | BETA: splitting (197) gives:
% 152.06/25.81 | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | (868) all_54_5 = e3
% 152.06/25.81 | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | REF_CLOSE: (282), (402), (868) are inconsistent by sub-proof
% 152.06/25.81 | | | | | | | | | | | #1161.
% 152.06/25.81 | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | Case 2:
% 152.06/25.81 | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | (869) ~ (all_54_5 = e3)
% 152.06/25.81 | | | | | | | | | | | (870) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 152.06/25.81 | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | BETA: splitting (870) gives:
% 152.06/25.81 | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | (871) all_54_5 = e2
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | COMBINE_EQS: (282), (871) imply:
% 152.06/25.81 | | | | | | | | | | | | (872) all_8_2 = e2
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | SIMP: (872) implies:
% 152.06/25.81 | | | | | | | | | | | | (873) all_8_2 = e2
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | COMBINE_EQS: (360), (873) imply:
% 152.06/25.81 | | | | | | | | | | | | (874) all_56_13 = e2
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | REDUCE: (378), (873) imply:
% 152.06/25.81 | | | | | | | | | | | | (875) ~ (all_52_6 = e2)
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | REDUCE: (380), (873) imply:
% 152.06/25.81 | | | | | | | | | | | | (876) ~ (all_52_7 = e2)
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | REDUCE: (382), (873) imply:
% 152.06/25.81 | | | | | | | | | | | | (877) ~ (all_52_9 = e2)
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | REDUCE: (402), (873) imply:
% 152.06/25.81 | | | | | | | | | | | | (878) ~ (e3 = e2)
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | BETA: splitting (236) gives:
% 152.06/25.81 | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | (879) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 152.06/25.81 | | | | | | | | | | | | | & op(e2, e1) = e2)
% 152.06/25.81 | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | BETA: splitting (879) gives:
% 152.06/25.81 | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | (880) all_58_4 = e2 & op(e3, e1) = e2
% 152.06/25.81 | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | ALPHA: (880) implies:
% 152.06/25.81 | | | | | | | | | | | | | | (881) all_58_4 = e2
% 152.06/25.81 | | | | | | | | | | | | | | (882) op(e3, e1) = e2
% 152.06/25.81 | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 152.06/25.81 | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | (883) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 152.06/25.81 | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 152.06/25.81 | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | BETA: splitting (883) gives:
% 152.06/25.81 | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | (884) all_58_6 = e2 & op(e1, e3) = e2
% 152.06/25.81 | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | ALPHA: (884) implies:
% 152.06/25.81 | | | | | | | | | | | | | | | | (885) all_58_6 = e2
% 152.06/25.81 | | | | | | | | | | | | | | | | (886) op(e1, e3) = e2
% 152.06/25.81 | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 152.06/25.81 | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | (887) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 152.06/25.81 | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 152.06/25.81 | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | BETA: splitting (887) gives:
% 152.06/25.81 | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (888) all_58_2 = e2 & op(e2, e3) = e2
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | ALPHA: (888) implies:
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (889) op(e2, e3) = e2
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (246), (248),
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (252), (885), (889), (function-axioms) are
% 152.06/25.81 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1152.
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (890) all_58_3 = e2 & op(e2, e2) = e2
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | ALPHA: (890) implies:
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (891) all_58_3 = e2
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 152.06/25.81 | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (156), (865) gives:
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (892) all_52_7 = e0
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 152.06/25.81 | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (161), (886) gives:
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (893) all_52_2 = e2
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 152.06/25.81 | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (882) gives:
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (894) all_52_8 = e2
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | REDUCE: (147), (893) imply:
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (895) ~ (all_52_1 = e2)
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | REDUCE: (142), (893) imply:
% 152.06/25.81 | | | | | | | | | | | | | | | | | | (896) ~ (all_52_3 = e2)
% 152.06/25.81 | | | | | | | | | | | | | | | | | |
% 152.06/25.81 | | | | | | | | | | | | | | | | | | SIMP: (896) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (897) ~ (all_52_3 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (141), (893) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (898) ~ (all_52_6 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (139), (893) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (899) ~ (all_52_14 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (138), (892) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (900) ~ (all_52_3 = e0)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (133), (892) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (901) ~ (all_52_4 = e0)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (132), (894) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (902) ~ (all_52_4 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (126), (892) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (903) ~ (all_52_6 = e0)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (123), (892) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (904) ~ (all_52_11 = e0)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | SIMP: (904) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (905) ~ (all_52_11 = e0)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (876), (892) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (906) ~ (e2 = e0)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (121), (894) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (907) ~ (all_52_9 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (119), (894) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (908) ~ (all_52_11 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (118), (894) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (909) ~ (all_52_12 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | SIMP: (909) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (910) ~ (all_52_12 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (370), (894) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (911) ~ (all_10_2 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | REDUCE: (387), (894) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | (912) ~ (all_6_2 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | (913) ~ (all_56_14 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | REDUCE: (273), (913) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | (914) ~ (all_6_2 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | (915) ~ (all_56_12 = e1)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | REDUCE: (297), (915) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | (916) ~ (all_10_2 = e1)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | (917) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (917) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | (918) all_58_0 = e0 & op(e3, e3) = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (918) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | (919) all_58_0 = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | (920) op(e3, e3) = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (921) all_54_0 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (921) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (922) all_10_2 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (922) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (923) all_56_12 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (922) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (924) ~ (all_52_1 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (922) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (925) ~ (all_52_3 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (922) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (926) ~ (all_52_4 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (922) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (927) ~ (all_52_12 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (922) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (928) op(e3, e3) = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (108),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (115), (116), (124), (131), (134),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (137), (146), (155), (156), (157), (158), (160),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (162), (163), (165), (168), (188), (190), (191),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (192), (193), (195), (196), (198), (199), (201),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (208), (213), (224), (226), (227), (229), (230),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (234), (237), (238), (239), (242),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (243), (245), (248), (249), (252), (262), (264),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (265), (273), (274), (276), (277), (286), (287),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (289), (304), (385), (388), (390), (392), (398),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (399), (402), (857), (858), (859), (860), (861),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (865), (874), (875), (877), (881), (882), (885),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (891), (895), (897), (900), (901), (902), (903),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (905), (910), (914), (919), (920), (923), (924),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (925), (926), (927), (928), (function-axioms) are
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1104.
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (929) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (400), (404), (916), (929) are inconsistent
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1307.
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | (930) all_58_2 = e0 & op(e2, e3) = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (930) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | (931) all_58_2 = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (932) all_54_0 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (932) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (933) all_10_2 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (933) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (934) all_56_12 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (933) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (935) ~ (all_52_1 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (933) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (936) ~ (all_52_3 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (933) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (937) ~ (all_52_4 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (933) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (938) ~ (all_52_12 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (933) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | (939) op(e3, e3) = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | (940) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (940) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_58_12 = e3 & op(e0, e3) = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (116), (137), (156),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | (163), (188), (190), (224), (237), (262), (264),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | (858), (861), (865), (881), (897), (900), (905),
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | (914), (936), (941), (function-axioms) are
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1143.
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | (942) all_58_13 = e3 & op(e0, e2) = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (942) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | (943) all_58_13 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_54_1 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (937), (944) are inconsistent by sub-proof
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | #1305.
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (945) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_54_1 = e2
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (902), (946) are inconsistent by sub-proof
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1304.
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) ~ (all_54_1 = e2)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) all_54_1 = e1 | all_54_1 = e0
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (948) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_54_1 = e1
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (949) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_52_4 = e1
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (950) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_52_4 = e1
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (951) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) ~ (all_52_6 = e1)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (952) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) ~ (all_52_6 = e1)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (951) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) ~ (all_52_12 = e1)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (954) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) ~ (all_52_12 = e1)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_54_9 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (956) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_52_6 = e3
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (957) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) ~ (all_52_14 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (958) implies:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) ~ (all_52_14 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (957) imply:
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) ~ (all_6_2 = e3)
% 152.06/25.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (961) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) all_58_6 = e3 & op(e1, e3) = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (962) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) all_58_6 = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (885), (963) are inconsistent by sub-proof
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1376.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) all_58_7 = e3 & op(e1, e2) = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (964) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) all_58_7 = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (966) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) all_58_1 = e1 & op(e3, e2) = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (967) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_58_1 = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (242), (891), (943), (965), (968)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1138.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) all_58_3 = e1 & op(e2, e2) = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (399), (969), (function-axioms) are
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (970) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_58_7 = e1 & op(e1, e2) = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (965), (971) are inconsistent by sub-proof
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1299.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) all_58_13 = e1 & op(e0, e2) = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (972) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) op(e0, e2) = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (865), (973), (function-axioms) are
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1396.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (974) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) all_58_8 = e3 & op(e1, e1) = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (914), (975), (function-axioms) are
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1469.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) all_58_11 = e3 & op(e1, e0) = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (976) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) op(e1, e0) = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (158), (191), (199), (265), (287), (860),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910), (938), (955), (959), (977),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1103.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (274), (289), (875), (901), (902), (903),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945), (978) are inconsistent by sub-proof #1106.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_54_1 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (901), (979) are inconsistent by sub-proof
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1115.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | (980) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (980) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_58_14 = e3 & op(e0, e1) = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (981) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_58_14 = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | (983) op(e0, e1) = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (984) all_54_1 = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (937), (984) are inconsistent by sub-proof
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | #1305.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (985) ~ (all_54_1 = e3)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (986) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (986) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) all_54_1 = e2
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (902), (987) are inconsistent by sub-proof
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1304.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) ~ (all_54_1 = e2)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) all_54_1 = e1 | all_54_1 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) all_54_12 = e3
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (936), (990) are inconsistent by sub-proof
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1234.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) ~ (all_54_12 = e3)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (993) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_58_0 = e0 & op(e3, e3) = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (994) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) all_58_0 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) op(e3, e3) = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (108),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (115), (116), (124), (131), (134),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (146), (155), (156), (157), (158), (160),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (163), (165), (168), (188), (190), (191),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (193), (195), (196), (198), (199), (201),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (213), (224), (226), (227), (229), (230),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (234), (237), (238), (239), (242),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (245), (248), (249), (252), (262), (264),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (273), (274), (276), (277), (286), (287),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (304), (385), (388), (390), (392), (398),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (402), (857), (858), (859), (860), (861),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865), (874), (875), (877), (881), (882), (885),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891), (895), (897), (900), (901), (902), (903),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905), (910), (914), (934), (935), (936), (937),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938), (939), (995), (996), (function-axioms) are
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1104.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) all_58_1 = e0 & op(e3, e2) = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (997) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) all_58_1 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (989) gives:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) all_54_1 = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (999) imply:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_52_4 = e1
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1000) imply:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) ~ (all_52_6 = e1)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1001) implies:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) ~ (all_52_6 = e1)
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (42), (156), (160), (243), (399), (865),
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998), (1002), (function-axioms) are inconsistent
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1132.
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) all_54_1 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1003) imply:
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) all_52_4 = e0
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (901), (1004) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) $false
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1005) is inconsistent.
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1006) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) all_58_4 = e0 & op(e3, e1) = e0
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (881), (1007) are inconsistent by sub-proof
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1365.
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) all_58_9 = e0 & op(e3, e0) = e0
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1008) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1009) all_58_9 = e0
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1010) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1010) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1011) all_58_12 = e1 & op(e0, e3) = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1011) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1012) all_58_12 = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013) op(e0, e3) = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (989) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1014) all_54_1 = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1014) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1015) all_52_4 = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1015) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1016) ~ (all_52_6 = e1)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1016) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017) ~ (all_52_6 = e1)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (1015) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1018) ~ (all_52_12 = e1)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1018) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1019) ~ (all_52_12 = e1)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (902), (1015) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020) ~ (e2 = e1)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1021) all_54_9 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1021) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022) all_52_6 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (1022) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023) ~ (all_52_14 = e3)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1023) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1024) ~ (all_52_14 = e3)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (1022) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025) ~ (all_6_2 = e3)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1026) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1026) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1027) all_58_9 = e3 & op(e3, e0) = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1027) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1028) all_58_9 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1009), (1028) are inconsistent by sub-proof
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1315.
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029) all_58_10 = e3 & op(e2, e0) = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1029) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1030) all_58_10 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031) all_54_3 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1031) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1032) all_52_12 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (938), (1032) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033) $false
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1033) is inconsistent.
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1034) ~ (all_54_3 = e3)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1035) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_54_3 = e2
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1036) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1037) all_52_12 = e2
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (910), (1037) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) $false
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1038) is inconsistent.
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) ~ (all_54_3 = e2)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) all_54_3 = e1 | all_54_3 = e0
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1041) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) all_58_0 = e1 & op(e3, e3) = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1042) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) all_58_0 = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1044) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1044) gives:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_58_0 = e3 & op(e3, e3) = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1045) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1046) all_58_0 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1043), (1046) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) e3 = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1047) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) e3 = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (982), (1048) imply:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) all_58_14 = e1
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (116), (137), (163), (188), (237),
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (264), (858), (881), (897), (900), (905),
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914), (992), (1049), (function-axioms) are
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1145.
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_58_2 = e3 & op(e2, e3) = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1050) implies:
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_58_2 = e3
% 152.06/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (931), (1051) are inconsistent by sub-proof
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1485.
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (116), (137), (156),
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (188), (224), (237), (262), (264), (858),
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861), (865), (881), (885), (897), (900), (905),
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914), (992), (1052), (function-axioms) are
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) all_58_1 = e1 & op(e3, e2) = e1
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1053) implies:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_58_1 = e1
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) op(e3, e2) = e1
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1040) gives:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) all_54_3 = e1
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1056) imply:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) all_52_12 = e1
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1019), (1057) imply:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) $false
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1058) is inconsistent.
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) all_54_3 = e0
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1059) imply:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) all_52_12 = e0
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (1060) imply:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) ~ (all_52_13 = e0)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1061) implies:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) ~ (all_52_13 = e0)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1060) imply:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) ~ (all_52_14 = e0)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1063) implies:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) ~ (all_52_14 = e0)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (938), (1060) imply:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) ~ (e3 = e0)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1019), (1060) imply:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) ~ (e1 = e0)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (1060) imply:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) op(e3, e0) = e0
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_54_11 = e3
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1024), (1068) are inconsistent by
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1415.
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) ~ (all_54_11 = e3)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1071) gives:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) all_58_0 = e3 & op(e3, e3) = e3
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1072) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) all_58_0 = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1074) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1075) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1076) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) op(e3, e2) = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1055), (1077), (function-axioms) are
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1256.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1078) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1079) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) op(e2, e3) = e2
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (246), (248),
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (885), (1080), (function-axioms) are
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1152.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1081) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) op(e3, e1) = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (882), (1082), (function-axioms) are
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1502.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1083) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1084) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) ~ (all_56_12 = e3)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (934), (1085) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) $false
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1086) is inconsistent.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1087) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1088) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) op(e0, e3) = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) op(e3, e0) = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1070) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_54_11 = e2
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (860), (1091) are inconsistent by sub-proof
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1414.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) ~ (all_54_11 = e2)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) all_54_11 = e1 | all_54_11 = e0
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1093) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) all_54_11 = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (1094) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_52_14 = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1095) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) all_52_14 = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (1096) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) ~ (all_6_2 = e1)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1097) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) ~ (all_6_2 = e1)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (1096) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) op(e1, e0) = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_54_7 = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (1100) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_52_13 = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1101) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_52_13 = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (1102) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) ~ (all_52_9 = e3)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_54_10 = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (914), (1104) are inconsistent by sub-proof
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1531.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) ~ (all_54_10 = e3)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1106) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_54_10 = e2
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (398), (1107) are inconsistent by sub-proof
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1530.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) ~ (all_54_10 = e2)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_54_10 = e1 | all_54_10 = e0
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1109) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_54_10 = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (1098), (1110) are inconsistent by
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1529.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_54_10 = e0
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (1111) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_6_2 = e0
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1112) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_6_2 = e0
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (1113) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) ~ (all_52_9 = e0)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) all_54_6 = e3
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (1103), (1115) are inconsistent by
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1193.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) ~ (all_54_6 = e3)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1117) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) all_54_6 = e2
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (877), (1118) are inconsistent by sub-proof
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1192.
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) ~ (all_54_6 = e2)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_54_6 = e1 | all_54_6 = e0
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1120) gives:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) all_54_6 = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (1121) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_52_9 = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1122) implies:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_52_9 = e1
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1103), (1123) imply:
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) ~ (e3 = e1)
% 152.31/25.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e3,
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (1013), (1089) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) e3 = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e0,
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (1067), (1090) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) e3 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1125), (1126) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) e1 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1073), (1126) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) all_58_0 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (116),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (156), (163), (188), (224), (237), (238),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (252), (262), (264), (399), (858), (861),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865), (881), (885), (891), (897), (900), (905),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914), (992), (1012), (1030), (1128),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1118.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) all_54_6 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (1114), (1129) are inconsistent by
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1113.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (158), (191), (265), (276), (859), (860),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062), (1064), (1099), (1130), (function-axioms)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1110.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_54_11 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1064), (1131) are inconsistent by
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1394.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1132) implies:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) ~ (all_56_12 = e3)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (934), (1133) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) $false
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1134) is inconsistent.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1135) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (162), (859), (875), (1017), (1136),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1128.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1137) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1138) implies:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) ~ (all_56_13 = e2)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (874), (1139) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) $false
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1140) is inconsistent.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1141) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1142) implies:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) op(e0, e1) = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1070) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) all_54_11 = e2
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (860), (1144) are inconsistent by sub-proof
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1414.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) all_54_11 = e1 | all_54_11 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1145) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) all_54_11 = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (1146) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) all_52_14 = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1147) implies:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) all_52_14 = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (1148) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) ~ (all_6_2 = e1)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1149) implies:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) ~ (all_6_2 = e1)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1024), (1148) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) ~ (e3 = e1)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) all_54_10 = e3
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (914), (1152) are inconsistent by sub-proof
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1531.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) ~ (all_54_10 = e3)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1154) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) all_54_10 = e2
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (398), (1155) are inconsistent by sub-proof
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1530.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) all_54_10 = e1 | all_54_10 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1156) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) all_54_10 = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (1150), (1157) are inconsistent by
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1529.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) all_54_10 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (1158) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) all_6_2 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1159) implies:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) all_6_2 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (1160) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) all_46_2 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) ~ (all_46_2 = e0)
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1161), (1162) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) $false
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1163) is inconsistent.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e1,
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (983), (1143) gives:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) e3 = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (982), (1164) imply:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) all_58_14 = e1
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (116), (137), (163), (188), (237),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (264), (858), (881), (897), (900), (905),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914), (992), (1165), (function-axioms) are
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1145.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) all_54_11 = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1064), (1166) are inconsistent by
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1394.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (42), (156), (160), (192), (213), (243),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273), (304), (398), (399), (865), (914), (1017),
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054), (1167), (function-axioms) are inconsistent
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1102.
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) all_58_2 = e3 & op(e2, e3) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1168) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) all_58_2 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (931), (1169) are inconsistent by sub-proof
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1485.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (116), (137), (156),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (188), (224), (237), (262), (264), (858),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861), (865), (881), (885), (897), (900), (905),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914), (992), (1170), (function-axioms) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (881), (1009), (1171) are inconsistent
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1100.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1172) gives:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) all_58_11 = e3 & op(e1, e0) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1173) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) op(e1, e0) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (158), (191), (199), (265), (287), (860),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910), (938), (1019), (1024), (1174),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1103.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) all_58_15 = e3 & op(e0, e0) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1175) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) op(e0, e0) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (861), (1176), (function-axioms) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1382.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (274), (289), (875), (901), (902), (903),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986), (1177) are inconsistent by sub-proof #1106.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) all_54_1 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1178) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) all_52_4 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (901), (1179) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) $false
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1180) is inconsistent.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) all_58_13 = e1 & op(e0, e2) = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1181) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) op(e0, e2) = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (865), (1182), (function-axioms) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1396.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (116), (137), (163), (188),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (262), (264), (858), (861), (881), (897),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900), (905), (914), (992), (1183),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1144.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | (1184) all_58_15 = e3 & op(e0, e0) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1184) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | (1185) op(e0, e0) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (861), (1185), (function-axioms) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1382.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | (1186) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (400), (404), (916), (1186) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1307.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | (1187) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1187) gives:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | (1188) all_58_6 = e0 & op(e1, e3) = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1188) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | (1189) all_58_6 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (885), (1189) are inconsistent by sub-proof
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | #1514.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | (1190) all_58_12 = e0 & op(e0, e3) = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1190) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | (1191) all_58_12 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | (1192) all_54_0 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (1192) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | (1193) all_10_2 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1193) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | (1194) ~ (all_52_3 = e3)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | (1195) all_54_12 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (1194), (1195) are inconsistent by
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1234.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | (1196) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | (1197) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1197) gives:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) all_58_12 = e1 & op(e0, e3) = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1198) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) all_58_12 = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1191), (1199) are inconsistent by sub-proof
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | #1513.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_58_13 = e1 & op(e0, e2) = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1200) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) op(e0, e2) = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (865), (1201), (function-axioms) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1396.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | (1202) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (116), (137), (163), (188),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | (237), (262), (264), (858), (861), (881), (897),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | (900), (905), (914), (1196), (1202),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | | #1144.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | (1203) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (400), (404), (916), (1203) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1307.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | (1204) all_56_1 = e3 & op(e3, e1) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (1204) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | (1205) op(e3, e1) = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (882), (1205), (function-axioms) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1502.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | (1206) all_56_14 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (1206) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | (1207) all_6_2 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | REDUCE: (385), (1207) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | (1208) ~ (all_52_6 = e3)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | REDUCE: (388), (1207) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | (1209) ~ (all_52_9 = e3)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | REDUCE: (390), (1207) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | (1210) ~ (all_52_11 = e3)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | (1211) ~ (all_56_12 = e1)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (297), (1211) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | (1212) ~ (all_10_2 = e1)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | (1213) all_54_0 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (1213) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | (1214) all_10_2 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | SIMP: (1214) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | (1215) all_10_2 = e3
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (1215) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | (1216) ~ (all_52_4 = e3)
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (193), (201), (274), (289), (875), (901),
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | (902), (903), (1208), (1216) are inconsistent by
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | sub-proof #1099.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | (1217) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (400), (404), (1212), (1217) are
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1307.
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | (1218) all_56_12 = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (1218) imply:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | (1219) all_10_2 = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | SIMP: (1219) implies:
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | (1220) all_10_2 = e1
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1220) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | (1221) ~ (all_52_1 = e1)
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1220) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | (1222) ~ (all_52_3 = e1)
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | (1223) all_54_14 = e3
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (1210), (1223) are inconsistent by
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | sub-proof #1413.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | (1224) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | (1225) all_54_12 = e3
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (1225) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | (1226) all_52_3 = e3
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1226) implies:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | (1227) all_52_3 = e3
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1227) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | (1228) ~ (all_52_1 = e3)
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | (1229) all_54_4 = e3
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (1229) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | (1230) all_52_1 = e3
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1228), (1230) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | (1231) $false
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1231) is inconsistent.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | (1232) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1232) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | (1233) all_54_4 = e2
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (1233) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | (1234) all_52_1 = e2
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (895), (1234) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | (1235) $false
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1235) is inconsistent.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | (1236) all_54_4 = e1 | all_54_4 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1236) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1237) all_54_4 = e1
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (1237) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1238) all_52_1 = e1
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1221), (1238) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1239) $false
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1239) is inconsistent.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1240) all_54_4 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (1240) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1241) all_52_1 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (1241) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1242) ~ (all_52_9 = e0)
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1242) implies:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | (1243) ~ (all_52_9 = e0)
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (1244) all_54_6 = e3
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (1244) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (1245) all_52_9 = e3
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1209), (1245) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (1246) $false
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1246) is inconsistent.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (1247) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1224) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1248) all_54_14 = e2
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (858), (1248) are inconsistent by sub-proof
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1232.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) all_54_14 = e1 | all_54_14 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1247) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1250) all_54_6 = e2
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (877), (1250) are inconsistent by sub-proof
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1192.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1251) all_54_6 = e1 | all_54_6 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1251) gives:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252) all_54_6 = e1
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (1252) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1253) all_52_9 = e1
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1253) implies:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1254) all_52_9 = e1
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (1254) imply:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1255) ~ (all_52_11 = e1)
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1255) implies:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1256) ~ (all_52_11 = e1)
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (905), (1249), (1256) are inconsistent by
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1399.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257) all_54_6 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (1243), (1257) are inconsistent by
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1113.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | (1258) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (897), (900), (1222), (1258) are
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1098.
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | (1259) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 152.31/25.88 | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.31/25.88 | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (859), (877), (1259),
% 152.31/25.88 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.88 | | | | | | | | | | | | | | | | | #1240.
% 152.31/25.88 | | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | (1260) all_58_7 = e2 & op(e1, e2) = e2
% 152.31/25.88 | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | ALPHA: (1260) implies:
% 152.31/25.88 | | | | | | | | | | | | | | | | (1261) op(e1, e2) = e2
% 152.31/25.88 | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | | REF_CLOSE: (160), (875), (1261), (function-axioms) are
% 152.31/25.88 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1536.
% 152.31/25.88 | | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | (1262) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 152.31/25.88 | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 152.31/25.88 | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | | REF_CLOSE: (39), (158), (398), (860), (1262),
% 152.31/25.88 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.88 | | | | | | | | | | | | | | | #1214.
% 152.31/25.88 | | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | (1263) all_58_5 = e2 & op(e2, e1) = e2
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | ALPHA: (1263) implies:
% 152.31/25.88 | | | | | | | | | | | | | | (1264) op(e2, e1) = e2
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | REF_CLOSE: (163), (877), (1264), (function-axioms) are
% 152.31/25.88 | | | | | | | | | | | | | | inconsistent by sub-proof #1441.
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | (1265) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 152.31/25.88 | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 152.31/25.88 | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | BETA: splitting (1265) gives:
% 152.31/25.88 | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | (1266) all_58_8 = e2 & op(e1, e1) = e2
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | REF_CLOSE: (39), (398), (1266), (function-axioms) are
% 152.31/25.88 | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | (1267) all_58_14 = e2 & op(e0, e1) = e2
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | | REF_CLOSE: (155), (858), (1267), (function-axioms) are
% 152.31/25.88 | | | | | | | | | | | | | | inconsistent by sub-proof #1175.
% 152.31/25.88 | | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | (1268) all_54_5 = e1 | all_54_5 = e0
% 152.31/25.88 | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | | REF_CLOSE: (282), (399), (867), (1268) are inconsistent by
% 152.31/25.88 | | | | | | | | | | | | sub-proof #1239.
% 152.31/25.88 | | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | (1269) all_56_5 = e2 & op(e2, e0) = e2
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | ALPHA: (1269) implies:
% 152.31/25.88 | | | | | | | | | | (1270) op(e2, e0) = e2
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | REF_CLOSE: (162), (859), (1270), (function-axioms) are
% 152.31/25.88 | | | | | | | | | | inconsistent by sub-proof #1535.
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | End of split
% 152.31/25.88 | | | | | | | | |
% 152.31/25.88 | | | | | | | | End of split
% 152.31/25.88 | | | | | | | |
% 152.31/25.88 | | | | | | | End of split
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | Case 2:
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | (1271) all_16_2 = e2
% 152.31/25.88 | | | | | | | (1272) ( ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0 &
% 152.31/25.88 | | | | | | | op(e2, e2) = all_16_1 & $i(all_16_0) & $i(all_16_1)) |
% 152.31/25.88 | | | | | | | ( ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 152.31/25.88 | | | | | | | $i(all_16_1))
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | COMBINE_EQS: (349), (1271) imply:
% 152.31/25.88 | | | | | | | (1273) all_10_2 = e2
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | SIMP: (1273) implies:
% 152.31/25.88 | | | | | | | (1274) all_10_2 = e2
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | COMBINE_EQS: (356), (1274) imply:
% 152.31/25.88 | | | | | | | (1275) all_38_2 = e2
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | COMBINE_EQS: (297), (1274) imply:
% 152.31/25.88 | | | | | | | (1276) all_56_12 = e2
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | REDUCE: (362), (1274) imply:
% 152.31/25.88 | | | | | | | (1277) ~ (all_52_1 = e2)
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | REDUCE: (364), (1274) imply:
% 152.31/25.88 | | | | | | | (1278) ~ (all_52_2 = e2)
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | REDUCE: (366), (1274) imply:
% 152.31/25.88 | | | | | | | (1279) ~ (all_52_3 = e2)
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | REDUCE: (368), (1274) imply:
% 152.31/25.88 | | | | | | | (1280) ~ (all_52_4 = e2)
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | REDUCE: (370), (1274) imply:
% 152.31/25.88 | | | | | | | (1281) ~ (all_52_8 = e2)
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | REDUCE: (372), (1274) imply:
% 152.31/25.88 | | | | | | | (1282) ~ (all_52_12 = e2)
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | BETA: splitting (88) gives:
% 152.31/25.88 | | | | | | |
% 152.31/25.88 | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | |
% 152.31/25.88 | | | | | | | | (1283) ~ (all_38_2 = e2)
% 152.31/25.88 | | | | | | | |
% 152.31/25.88 | | | | | | | | REDUCE: (1275), (1283) imply:
% 152.31/25.88 | | | | | | | | (1284) $false
% 152.31/25.88 | | | | | | | |
% 152.31/25.88 | | | | | | | | CLOSE: (1284) is inconsistent.
% 152.31/25.88 | | | | | | | |
% 152.31/25.88 | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | |
% 152.31/25.88 | | | | | | | | (1285) ( ~ (all_38_0 = e0) & op(all_38_1, e3) = all_38_0 &
% 152.31/25.88 | | | | | | | | op(e2, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1))
% 152.31/25.88 | | | | | | | | | ( ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 152.31/25.88 | | | | | | | | $i(all_38_1))
% 152.31/25.88 | | | | | | | |
% 152.31/25.88 | | | | | | | | BETA: splitting (1285) gives:
% 152.31/25.88 | | | | | | | |
% 152.31/25.88 | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | |
% 152.31/25.88 | | | | | | | | | (1286) ~ (all_38_0 = e0) & op(all_38_1, e3) = all_38_0 &
% 152.31/25.88 | | | | | | | | | op(e2, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 152.31/25.88 | | | | | | | | |
% 152.31/25.88 | | | | | | | | | ALPHA: (1286) implies:
% 152.31/25.88 | | | | | | | | | (1287) op(e2, e2) = all_38_1
% 152.31/25.88 | | | | | | | | |
% 152.31/25.88 | | | | | | | | | BETA: splitting (221) gives:
% 152.31/25.88 | | | | | | | | |
% 152.31/25.88 | | | | | | | | | Case 1:
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | (1288) ~ (all_56_12 = e2)
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | REDUCE: (1276), (1288) imply:
% 152.31/25.88 | | | | | | | | | | (1289) $false
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | CLOSE: (1289) is inconsistent.
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | Case 2:
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | (1290) all_56_0 = e3 & op(e3, e2) = e3
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.88 | | | | | | | | | | ALPHA: (1290) implies:
% 152.31/25.88 | | | | | | | | | | (1291) op(e3, e2) = e3
% 152.31/25.88 | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | BETA: splitting (251) gives:
% 152.31/25.89 | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | Case 1:
% 152.31/25.89 | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | (1292) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 152.31/25.89 | | | | | | | | | | | & op(e3, e2) = e2)
% 152.31/25.89 | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | BETA: splitting (1292) gives:
% 152.31/25.89 | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | Case 1:
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | (1293) all_58_0 = e2 & op(e3, e3) = e2
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | ALPHA: (1293) implies:
% 152.31/25.89 | | | | | | | | | | | | (1294) all_58_0 = e2
% 152.31/25.89 | | | | | | | | | | | | (1295) op(e3, e3) = e2
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2,
% 152.31/25.89 | | | | | | | | | | | | all_38_1, e2, e2, simplifying with (42), (1287)
% 152.31/25.89 | | | | | | | | | | | | gives:
% 152.31/25.89 | | | | | | | | | | | | (1296) all_38_1 = all_8_2
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 152.31/25.89 | | | | | | | | | | | | e2, e3, simplifying with (168), (1291) gives:
% 152.31/25.89 | | | | | | | | | | | | (1297) all_52_4 = e3
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | REDUCE: (134), (1297) imply:
% 152.31/25.89 | | | | | | | | | | | | (1298) ~ (all_52_6 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | SIMP: (1298) implies:
% 152.31/25.89 | | | | | | | | | | | | (1299) ~ (all_52_6 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | REDUCE: (133), (1297) imply:
% 152.31/25.89 | | | | | | | | | | | | (1300) ~ (all_52_7 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | SIMP: (1300) implies:
% 152.31/25.89 | | | | | | | | | | | | (1301) ~ (all_52_7 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | REDUCE: (132), (1297) imply:
% 152.31/25.89 | | | | | | | | | | | | (1302) ~ (all_52_8 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | SIMP: (1302) implies:
% 152.31/25.89 | | | | | | | | | | | | (1303) ~ (all_52_8 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | REDUCE: (131), (1297) imply:
% 152.31/25.89 | | | | | | | | | | | | (1304) ~ (all_52_12 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | SIMP: (1304) implies:
% 152.31/25.89 | | | | | | | | | | | | (1305) ~ (all_52_12 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | REDUCE: (376), (1297) imply:
% 152.31/25.89 | | | | | | | | | | | | (1306) ~ (all_8_2 = e3)
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (61),
% 152.31/25.89 | | | | | | | | | | | | (73), (76), (85), (108), (110), (111), (115),
% 152.31/25.89 | | | | | | | | | | | | (116), (118), (119), (121), (123), (124), (126),
% 152.31/25.89 | | | | | | | | | | | | (137), (138), (139), (141), (142), (143), (144),
% 152.31/25.89 | | | | | | | | | | | | (146), (147), (155), (156), (157), (158), (160),
% 152.31/25.89 | | | | | | | | | | | | (161), (162), (163), (165), (166), (167), (168),
% 152.31/25.89 | | | | | | | | | | | | (187), (188), (189), (190), (191), (192), (193),
% 152.31/25.89 | | | | | | | | | | | | (194), (195), (196), (197), (198), (199), (200),
% 152.31/25.89 | | | | | | | | | | | | (208), (209), (211), (212), (213), (215), (216),
% 152.31/25.89 | | | | | | | | | | | | (223), (224), (225), (226), (227), (228), (229),
% 152.31/25.89 | | | | | | | | | | | | (230), (231), (232), (233), (234), (235), (236),
% 152.31/25.89 | | | | | | | | | | | | (237), (238), (239), (240), (241), (242), (243),
% 152.31/25.89 | | | | | | | | | | | | (244), (246), (247), (248), (249), (252), (261),
% 152.31/25.89 | | | | | | | | | | | | (262), (263), (264), (265), (273), (274), (275),
% 152.31/25.89 | | | | | | | | | | | | (276), (277), (282), (286), (287), (288), (304),
% 152.31/25.89 | | | | | | | | | | | | (306), (335), (339), (348), (354), (360), (373),
% 152.31/25.89 | | | | | | | | | | | | (374), (375), (378), (380), (382), (384), (385),
% 152.31/25.89 | | | | | | | | | | | | (386), (387), (388), (390), (392), (393), (394),
% 152.31/25.89 | | | | | | | | | | | | (395), (396), (397), (398), (399), (402), (1272),
% 152.31/25.89 | | | | | | | | | | | | (1276), (1277), (1278), (1279), (1281), (1282),
% 152.31/25.89 | | | | | | | | | | | | (1287), (1294), (1295), (1296), (1297), (1299),
% 152.31/25.89 | | | | | | | | | | | | (1301), (1303), (1305), (function-axioms) are
% 152.31/25.89 | | | | | | | | | | | | inconsistent by sub-proof #869.
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | Case 2:
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | (1307) all_58_1 = e2 & op(e3, e2) = e2
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | ALPHA: (1307) implies:
% 152.31/25.89 | | | | | | | | | | | | (1308) op(e3, e2) = e2
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | | REF_CLOSE: (9), (168), (1291), (1308), (function-axioms) are
% 152.31/25.89 | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 152.31/25.89 | | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | End of split
% 152.31/25.89 | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | Case 2:
% 152.31/25.89 | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | (1309) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 152.31/25.89 | | | | | | | | | | | & op(e3, e0) = e2)
% 152.31/25.89 | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | | REF_CLOSE: (166), (167), (1281), (1282), (1309),
% 152.31/25.89 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.89 | | | | | | | | | | | #868.
% 152.31/25.89 | | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | | End of split
% 152.31/25.89 | | | | | | | | | |
% 152.31/25.89 | | | | | | | | | End of split
% 152.31/25.89 | | | | | | | | |
% 152.31/25.89 | | | | | | | | Case 2:
% 152.31/25.89 | | | | | | | | |
% 152.31/25.89 | | | | | | | | | (1310) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 152.31/25.89 | | | | | | | | | $i(all_38_1)
% 152.31/25.89 | | | | | | | | |
% 152.31/25.89 | | | | | | | | | ALPHA: (1310) implies:
% 152.31/25.89 | | | | | | | | | (1311) ~ (all_38_1 = e1)
% 152.31/25.89 | | | | | | | | | (1312) op(e2, e2) = all_38_1
% 152.31/25.89 | | | | | | | | |
% 152.31/25.89 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 152.31/25.89 | | | | | | | | | (61), (73), (76), (85), (108), (110), (111), (115),
% 152.31/25.89 | | | | | | | | | (116), (118), (119), (121), (123), (124), (126),
% 152.31/25.89 | | | | | | | | | (131), (132), (133), (134), (137), (138), (139),
% 152.31/25.89 | | | | | | | | | (141), (142), (143), (144), (146), (147), (155),
% 152.31/25.89 | | | | | | | | | (156), (157), (158), (160), (161), (162), (163),
% 152.31/25.89 | | | | | | | | | (165), (166), (167), (168), (187), (188), (189),
% 152.31/25.89 | | | | | | | | | (190), (191), (192), (193), (194), (195), (196),
% 152.31/25.89 | | | | | | | | | (197), (198), (199), (200), (208), (209), (211),
% 152.31/25.89 | | | | | | | | | (212), (213), (215), (216), (221), (223), (224),
% 152.31/25.89 | | | | | | | | | (225), (226), (227), (228), (229), (230), (231),
% 152.31/25.89 | | | | | | | | | (232), (233), (234), (235), (236), (237), (238),
% 152.31/25.89 | | | | | | | | | (239), (240), (241), (242), (243), (244), (246),
% 152.31/25.89 | | | | | | | | | (247), (248), (249), (251), (252), (261), (262),
% 152.31/25.89 | | | | | | | | | (263), (264), (265), (273), (274), (275), (276),
% 152.31/25.89 | | | | | | | | | (277), (282), (286), (287), (288), (304), (306),
% 152.31/25.89 | | | | | | | | | (335), (339), (348), (354), (360), (373), (374),
% 152.31/25.89 | | | | | | | | | (375), (376), (378), (380), (382), (384), (385),
% 152.31/25.89 | | | | | | | | | (386), (387), (388), (390), (392), (393), (394),
% 152.31/25.89 | | | | | | | | | (395), (396), (397), (398), (1272), (1276), (1277),
% 152.31/25.89 | | | | | | | | | (1278), (1279), (1280), (1281), (1282), (1311),
% 152.31/25.89 | | | | | | | | | (1312), (function-axioms) are inconsistent by
% 152.31/25.89 | | | | | | | | | sub-proof #867.
% 152.31/25.89 | | | | | | | | |
% 152.31/25.89 | | | | | | | | End of split
% 152.31/25.89 | | | | | | | |
% 152.31/25.89 | | | | | | | End of split
% 152.31/25.89 | | | | | | |
% 152.31/25.89 | | | | | | End of split
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | Case 2:
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | (1313) all_14_2 = e3
% 152.31/25.89 | | | | | | (1314) ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e3,
% 152.31/25.89 | | | | | | e3) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 152.31/25.89 | | | | | | (all_14_1 = e0) & op(e3, e3) = all_14_1 & $i(all_14_1))
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | COMBINE_EQS: (351), (1313) imply:
% 152.31/25.89 | | | | | | (1315) all_8_2 = e3
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | COMBINE_EQS: (333), (1315) imply:
% 152.31/25.89 | | | | | | (1316) all_22_2 = e3
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | COMBINE_EQS: (360), (1315) imply:
% 152.31/25.89 | | | | | | (1317) all_56_13 = e3
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | REDUCE: (373), (1315) imply:
% 152.31/25.89 | | | | | | (1318) ~ (all_52_1 = e3)
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | REDUCE: (376), (1315) imply:
% 152.31/25.89 | | | | | | (1319) ~ (all_52_4 = e3)
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | REDUCE: (378), (1315) imply:
% 152.31/25.89 | | | | | | (1320) ~ (all_52_6 = e3)
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | REDUCE: (380), (1315) imply:
% 152.31/25.89 | | | | | | (1321) ~ (all_52_7 = e3)
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | REDUCE: (382), (1315) imply:
% 152.31/25.89 | | | | | | (1322) ~ (all_52_9 = e3)
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | REDUCE: (384), (1315) imply:
% 152.31/25.89 | | | | | | (1323) ~ (all_52_13 = e3)
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | BETA: splitting (1314) gives:
% 152.31/25.89 | | | | | |
% 152.31/25.89 | | | | | | Case 1:
% 152.31/25.89 | | | | | | |
% 152.31/25.89 | | | | | | | (1324) ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 152.31/25.89 | | | | | | | op(e3, e3) = all_14_1 & $i(all_14_0) & $i(all_14_1)
% 152.31/25.89 | | | | | | |
% 152.31/25.89 | | | | | | | ALPHA: (1324) implies:
% 152.31/25.89 | | | | | | | (1325) op(e3, e3) = all_14_1
% 152.31/25.89 | | | | | | | (1326) op(all_14_1, e2) = all_14_0
% 152.31/25.89 | | | | | | |
% 152.31/25.89 | | | | | | | BETA: splitting (218) gives:
% 152.31/25.89 | | | | | | |
% 152.31/25.89 | | | | | | | Case 1:
% 152.31/25.89 | | | | | | | |
% 152.31/25.89 | | | | | | | | (1327) ~ (all_56_13 = e3)
% 152.31/25.89 | | | | | | | |
% 152.31/25.89 | | | | | | | | REDUCE: (1317), (1327) imply:
% 152.31/25.90 | | | | | | | | (1328) $false
% 152.31/25.90 | | | | | | | |
% 152.31/25.90 | | | | | | | | CLOSE: (1328) is inconsistent.
% 152.31/25.90 | | | | | | | |
% 152.31/25.90 | | | | | | | Case 2:
% 152.31/25.90 | | | | | | | |
% 152.31/25.90 | | | | | | | | (1329) all_56_3 = e2 & op(e2, e3) = e2
% 152.31/25.90 | | | | | | | |
% 152.31/25.90 | | | | | | | | ALPHA: (1329) implies:
% 152.31/25.90 | | | | | | | | (1330) op(e2, e3) = e2
% 152.31/25.90 | | | | | | | |
% 152.31/25.90 | | | | | | | | BETA: splitting (245) gives:
% 152.31/25.90 | | | | | | | |
% 152.31/25.90 | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | |
% 152.31/25.90 | | | | | | | | | (1331) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 152.31/25.90 | | | | | | | | | op(e2, e2) = e3)
% 152.31/25.90 | | | | | | | | |
% 152.31/25.90 | | | | | | | | | BETA: splitting (1331) gives:
% 152.31/25.90 | | | | | | | | |
% 152.31/25.90 | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | (1332) all_58_1 = e3 & op(e3, e2) = e3
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | ALPHA: (1332) implies:
% 152.31/25.90 | | | | | | | | | | (1333) op(e3, e2) = e3
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | REF_CLOSE: (168), (1319), (1333), (function-axioms) are
% 152.31/25.90 | | | | | | | | | | inconsistent by sub-proof #1540.
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | Case 2:
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | (1334) all_58_3 = e3 & op(e2, e2) = e3
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | ALPHA: (1334) implies:
% 152.31/25.90 | | | | | | | | | | (1335) all_58_3 = e3
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 152.31/25.90 | | | | | | | | | | e3, e2, simplifying with (165), (1330) gives:
% 152.31/25.90 | | | | | | | | | | (1336) all_52_1 = e2
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 152.31/25.90 | | | | | | | | | | all_14_1, e3, e3, simplifying with (45), (1325)
% 152.31/25.90 | | | | | | | | | | gives:
% 152.31/25.90 | | | | | | | | | | (1337) all_14_1 = all_10_2
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | REDUCE: (147), (1336) imply:
% 152.31/25.90 | | | | | | | | | | (1338) ~ (all_52_2 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | SIMP: (1338) implies:
% 152.31/25.90 | | | | | | | | | | (1339) ~ (all_52_2 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | REDUCE: (146), (1336) imply:
% 152.31/25.90 | | | | | | | | | | (1340) ~ (all_52_3 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | SIMP: (1340) implies:
% 152.31/25.90 | | | | | | | | | | (1341) ~ (all_52_3 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | REDUCE: (144), (1336) imply:
% 152.31/25.90 | | | | | | | | | | (1342) ~ (all_52_9 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | SIMP: (1342) implies:
% 152.31/25.90 | | | | | | | | | | (1343) ~ (all_52_9 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | REDUCE: (143), (1336) imply:
% 152.31/25.90 | | | | | | | | | | (1344) ~ (all_52_13 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | SIMP: (1344) implies:
% 152.31/25.90 | | | | | | | | | | (1345) ~ (all_52_13 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | REDUCE: (362), (1336) imply:
% 152.31/25.90 | | | | | | | | | | (1346) ~ (all_10_2 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | SIMP: (1346) implies:
% 152.31/25.90 | | | | | | | | | | (1347) ~ (all_10_2 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | REDUCE: (1318), (1336) imply:
% 152.31/25.90 | | | | | | | | | | (1348) ~ (e3 = e2)
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | REDUCE: (1326), (1337) imply:
% 152.31/25.90 | | | | | | | | | | (1349) op(all_10_2, e2) = all_14_0
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | BETA: splitting (61) gives:
% 152.31/25.90 | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | (1350) ~ (all_20_2 = e2)
% 152.31/25.90 | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | REDUCE: (348), (1350) imply:
% 152.31/25.90 | | | | | | | | | | | (1351) ~ (all_4_2 = e2)
% 152.31/25.90 | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | BETA: splitting (64) gives:
% 152.31/25.90 | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | (1352) ~ (all_22_2 = e3)
% 152.31/25.90 | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | REDUCE: (1316), (1352) imply:
% 152.31/25.90 | | | | | | | | | | | | (1353) $false
% 152.31/25.90 | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | CLOSE: (1353) is inconsistent.
% 152.31/25.90 | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | Case 2:
% 152.31/25.90 | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | (1354) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0
% 152.31/25.90 | | | | | | | | | | | | & op(e3, e3) = all_22_1 & $i(all_22_0) &
% 152.31/25.90 | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3, e3)
% 152.31/25.90 | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 152.31/25.90 | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | BETA: splitting (73) gives:
% 152.31/25.90 | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | (1355) ~ (all_28_2 = e3)
% 152.31/25.90 | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | REDUCE: (339), (1355) imply:
% 152.31/25.90 | | | | | | | | | | | | | (1356) ~ (all_6_2 = e3)
% 152.31/25.90 | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | BETA: splitting (79) gives:
% 152.31/25.90 | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | (1357) ~ (all_32_2 = e1)
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | REDUCE: (355), (1357) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1358) ~ (all_10_2 = e1)
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (39), (45), (156), (160),
% 152.31/25.90 | | | | | | | | | | | | | | (162), (163), (165), (168), (202), (223), (224),
% 152.31/25.90 | | | | | | | | | | | | | | (225), (226), (227), (228), (229), (231), (232),
% 152.31/25.90 | | | | | | | | | | | | | | (233), (234), (235), (236), (237), (238), (239),
% 152.31/25.90 | | | | | | | | | | | | | | (242), (243), (244), (246), (247), (248), (249),
% 152.31/25.90 | | | | | | | | | | | | | | (251), (252), (253), (299), (368), (398), (400),
% 152.31/25.90 | | | | | | | | | | | | | | (1320), (1321), (1322), (1323), (1330), (1335),
% 152.31/25.90 | | | | | | | | | | | | | | (1347), (1351), (1354), (1356), (1358),
% 152.31/25.90 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.90 | | | | | | | | | | | | | | #768.
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | Case 2:
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | (1359) all_32_2 = e1
% 152.31/25.90 | | | | | | | | | | | | | | (1360) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0
% 152.31/25.90 | | | | | | | | | | | | | | & op(e1, e1) = all_32_1 & $i(all_32_0) &
% 152.31/25.90 | | | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 152.31/25.90 | | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | COMBINE_EQS: (355), (1359) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1361) all_10_2 = e1
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | SIMP: (1361) implies:
% 152.31/25.90 | | | | | | | | | | | | | | (1362) all_10_2 = e1
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | COMBINE_EQS: (297), (1362) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1363) all_56_12 = e1
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | REDUCE: (364), (1362) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1364) ~ (all_52_2 = e1)
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | REDUCE: (370), (1362) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1365) ~ (all_52_8 = e1)
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | REDUCE: (372), (1362) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1366) ~ (all_52_12 = e1)
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | REDUCE: (1347), (1362) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1367) ~ (e2 = e1)
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | REDUCE: (1349), (1362) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1368) op(e1, e2) = all_14_0
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | REDUCE: (45), (1362) imply:
% 152.31/25.90 | | | | | | | | | | | | | | (1369) op(e3, e3) = e1
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | BETA: splitting (1354) gives:
% 152.31/25.90 | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | (1370) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 152.31/25.90 | | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 152.31/25.90 | | | | | | | | | | | | | | | $i(all_22_1)
% 152.31/25.90 | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | ALPHA: (1370) implies:
% 152.31/25.90 | | | | | | | | | | | | | | | (1371) ~ (all_22_0 = e0)
% 152.31/25.90 | | | | | | | | | | | | | | | (1372) op(e3, e3) = all_22_1
% 152.31/25.90 | | | | | | | | | | | | | | | (1373) op(all_22_1, e2) = all_22_0
% 152.31/25.90 | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 152.31/25.90 | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | (1374) ~ (all_56_12 = e1)
% 152.31/25.90 | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | REDUCE: (1363), (1374) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | (1375) $false
% 152.31/25.90 | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | CLOSE: (1375) is inconsistent.
% 152.31/25.90 | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | Case 2:
% 152.31/25.90 | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | (1376) all_56_1 = e3 & op(e3, e1) = e3
% 152.31/25.90 | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | ALPHA: (1376) implies:
% 152.31/25.90 | | | | | | | | | | | | | | | | (1377) all_56_1 = e3
% 152.31/25.90 | | | | | | | | | | | | | | | | (1378) op(e3, e1) = e3
% 152.31/25.90 | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 152.31/25.90 | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | (1379) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 152.31/25.90 | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 152.31/25.90 | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | BETA: splitting (1379) gives:
% 152.31/25.90 | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | (1380) all_58_0 = e1 & op(e3, e3) = e1
% 152.31/25.90 | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | ALPHA: (1380) implies:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | (1381) all_58_0 = e1
% 152.31/25.90 | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | BETA: splitting (1360) gives:
% 152.31/25.90 | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1382) ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) &
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | $i(all_32_1)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | ALPHA: (1382) implies:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1383) op(e1, e1) = all_32_1
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | all_32_1, e1, e1, simplifying with (39), (1383)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | gives:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1384) all_32_1 = all_6_2
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | all_14_0, e2, e1, simplifying with (160), (1368)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | gives:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1385) all_52_6 = all_14_0
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (1378) gives:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1386) all_52_8 = e3
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_22_1,
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (1369), (1372) gives:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1387) all_22_1 = e1
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1385) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1388) all_54_9 = all_14_0
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (141), (1385) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1389) ~ (all_52_2 = all_14_0)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1385) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1390) ~ (all_52_4 = all_14_0)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (126), (1385) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1391) ~ (all_52_7 = all_14_0)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | SIMP: (1391) implies:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1392) ~ (all_52_7 = all_14_0)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (124), (1385) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1393) ~ (all_52_14 = all_14_0)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | SIMP: (1393) implies:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1394) ~ (all_52_14 = all_14_0)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (385), (1385) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1395) ~ (all_14_0 = all_6_2)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1385) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1396) ~ (all_14_0 = e3)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1386) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1397) ~ (all_52_9 = e3)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1386) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1398) ~ (all_52_11 = e3)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | SIMP: (1398) implies:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1399) ~ (all_52_11 = e3)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1386) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1400) ~ (all_52_12 = e3)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | SIMP: (1400) implies:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1401) ~ (all_52_12 = e3)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (387), (1386) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1402) ~ (all_6_2 = e3)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | REDUCE: (1373), (1387) imply:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | (1403) op(e1, e2) = all_22_0
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | | (1404) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 152.31/25.90 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (156),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (160), (162), (163), (165), (168), (223), (224),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (225), (226), (227), (228), (229), (230), (231),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (232), (233), (234), (235), (236), (237), (238),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (239), (242), (243), (244), (246), (247), (248),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (249), (251), (252), (253), (398), (1319), (1320),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (1321), (1322), (1323), (1330), (1335), (1351),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (1356), (1369), (1372), (1378), (1381), (1404),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | #750.
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (1405) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1405) gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1406) all_58_8 = e2 & op(e1, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (398), (1406), (function-axioms) are
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1407) all_58_14 = e2 & op(e0, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1407) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1408) all_58_14 = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1409) op(e0, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (108),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (111), (116), (123), (131), (133), (137), (138),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (142), (155), (156), (158), (160), (162), (163),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (165), (166), (168), (187), (190), (191), (192),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (193), (194), (195), (199), (201), (208), (209),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (212), (213), (223), (224), (225), (226), (227),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (242), (243),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (244), (246), (247), (248), (249), (251), (252),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (253), (261), (264), (265), (273), (275), (276),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (287), (289), (304), (306), (374), (375), (386),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (390), (392), (393), (394), (395), (398), (1317),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1319), (1320), (1321), (1322), (1323), (1330),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1335), (1345), (1351), (1356), (1363), (1364),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1366), (1368), (1369), (1371), (1372), (1377),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1381), (1388), (1389), (1390), (1392), (1394),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1395), (1396), (1399), (1401), (1403), (1408),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1409), (function-axioms) are inconsistent by
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | sub-proof #669.
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1410) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | $i(all_32_1)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | ALPHA: (1410) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1411) ~ (all_32_1 = e2)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1412) op(e1, e1) = all_32_1
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | all_32_1, e1, e1, simplifying with (39), (1412)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1413) all_32_1 = all_6_2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | all_14_0, e2, e1, simplifying with (160), (1368)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1414) all_52_6 = all_14_0
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (1378) gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1415) all_52_8 = e3
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_22_1,
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (1369), (1372) gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1416) all_22_1 = e1
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1414) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1417) all_54_9 = all_14_0
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (141), (1414) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1418) ~ (all_52_2 = all_14_0)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1414) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1419) ~ (all_52_4 = all_14_0)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (126), (1414) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1420) ~ (all_52_7 = all_14_0)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | SIMP: (1420) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1421) ~ (all_52_7 = all_14_0)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (124), (1414) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1422) ~ (all_52_14 = all_14_0)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | SIMP: (1422) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1423) ~ (all_52_14 = all_14_0)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (385), (1414) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1424) ~ (all_14_0 = all_6_2)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1414) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1425) ~ (all_14_0 = e3)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1415) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1426) ~ (all_52_9 = e3)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1415) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1427) ~ (all_52_11 = e3)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | SIMP: (1427) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1428) ~ (all_52_11 = e3)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1415) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1429) ~ (all_52_12 = e3)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | SIMP: (1429) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1430) ~ (all_52_12 = e3)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (387), (1415) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1431) ~ (all_6_2 = e3)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | REDUCE: (1373), (1416) imply:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | (1432) op(e1, e2) = all_22_0
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (1433) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1433) gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1434) all_58_4 = e2 & op(e3, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1434) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1435) all_58_4 = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1436) op(e3, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (156),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (160), (162), (163), (165), (168), (223), (224),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (225), (226), (227), (228), (229), (230), (231),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (232), (233), (234), (235), (236), (237), (238),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (239), (242), (243), (244), (246), (247), (248),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (249), (251), (252), (253), (398), (1319), (1320),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1321), (1322), (1323), (1330), (1335), (1351),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1356), (1369), (1372), (1378), (1381), (1435),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1436), (function-axioms) are inconsistent by
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | sub-proof #751.
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1437) all_58_5 = e2 & op(e2, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1437) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1438) all_58_5 = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (238), (239), (1330),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1335), (1438), (function-axioms) are inconsistent
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | by sub-proof #898.
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | (1439) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1439) gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1440) all_58_8 = e2 & op(e1, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (398), (1440), (function-axioms) are
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1441) all_58_14 = e2 & op(e0, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1441) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1442) all_58_14 = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1443) op(e0, e1) = e2
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (108),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (111), (116), (123), (131), (133), (137), (138),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (142), (155), (156), (158), (160), (162), (163),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (165), (166), (168), (187), (190), (191), (192),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (193), (194), (195), (199), (201), (208), (209),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (212), (213), (223), (224), (225), (226), (227),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (242), (243),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (244), (246), (247), (248), (249), (251), (252),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (253), (261), (264), (265), (273), (275), (276),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (287), (289), (304), (306), (374), (375), (386),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (390), (392), (393), (394), (395), (398), (1317),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1319), (1320), (1321), (1322), (1323), (1330),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1335), (1345), (1351), (1356), (1363), (1364),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1366), (1368), (1369), (1371), (1372), (1377),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1381), (1417), (1418), (1419), (1421), (1423),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1424), (1425), (1428), (1430), (1432), (1442),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | (1443), (function-axioms) are inconsistent by
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | | sub-proof #669.
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.91 | | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (1444) all_58_2 = e1 & op(e2, e3) = e1
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | ALPHA: (1444) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (1445) op(e2, e3) = e1
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1330), (1445), (function-axioms) are
% 152.31/25.91 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1430.
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | End of split
% 152.31/25.91 | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | (1446) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 152.31/25.91 | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 152.31/25.91 | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | BETA: splitting (1446) gives:
% 152.31/25.91 | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (1447) all_58_6 = e1 & op(e1, e3) = e1
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | ALPHA: (1447) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (1448) all_58_6 = e1
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (156),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (160), (162), (163), (165), (168), (223), (224),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (225), (226), (227), (228), (229), (230), (231),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (232), (233), (234), (235), (236), (237), (238),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (239), (242), (243), (244), (246), (247), (248),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (249), (251), (252), (253), (398), (1319), (1320),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (1321), (1322), (1323), (1330), (1335), (1351),
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (1356), (1369), (1372), (1448), (function-axioms)
% 152.31/25.91 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #685.
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (1449) all_58_12 = e1 & op(e0, e3) = e1
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.91 | | | | | | | | | | | | | | | | | | ALPHA: (1449) implies:
% 152.31/25.91 | | | | | | | | | | | | | | | | | | (1450) all_58_12 = e1
% 152.31/25.91 | | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (156),
% 152.31/25.92 | | | | | | | | | | | | | | | | | | (160), (162), (163), (165), (168), (223), (224),
% 152.31/25.92 | | | | | | | | | | | | | | | | | | (225), (226), (227), (228), (229), (231), (232),
% 152.31/25.92 | | | | | | | | | | | | | | | | | | (233), (234), (235), (236), (237), (238), (239),
% 152.31/25.92 | | | | | | | | | | | | | | | | | | (242), (243), (244), (246), (247), (248), (249),
% 152.31/25.92 | | | | | | | | | | | | | | | | | | (251), (252), (253), (398), (1319), (1320),
% 152.31/25.92 | | | | | | | | | | | | | | | | | | (1321), (1322), (1323), (1330), (1335), (1351),
% 152.31/25.92 | | | | | | | | | | | | | | | | | | (1356), (1369), (1372), (1450), (function-axioms)
% 152.31/25.92 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #747.
% 152.31/25.92 | | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | Case 2:
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | (1451) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 152.31/25.92 | | | | | | | | | | | | | | | $i(all_22_1)
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | ALPHA: (1451) implies:
% 152.31/25.92 | | | | | | | | | | | | | | | (1452) ~ (all_22_1 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | | (1453) op(e3, e3) = all_22_1
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REF_CLOSE: (1369), (1452), (1453), (function-axioms) are
% 152.31/25.92 | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | Case 2:
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | (1454) all_28_2 = e3
% 152.31/25.92 | | | | | | | | | | | | | (1455) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0
% 152.31/25.92 | | | | | | | | | | | | | & op(e3, e3) = all_28_1 & $i(all_28_0) &
% 152.31/25.92 | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3, e3)
% 152.31/25.92 | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | COMBINE_EQS: (339), (1454) imply:
% 152.31/25.92 | | | | | | | | | | | | | (1456) all_6_2 = e3
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | COMBINE_EQS: (273), (1456) imply:
% 152.31/25.92 | | | | | | | | | | | | | (1457) all_56_14 = e3
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | REDUCE: (374), (1456) imply:
% 152.31/25.92 | | | | | | | | | | | | | (1458) ~ (all_52_2 = e3)
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | REDUCE: (387), (1456) imply:
% 152.31/25.92 | | | | | | | | | | | | | (1459) ~ (all_52_8 = e3)
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | REDUCE: (390), (1456) imply:
% 152.31/25.92 | | | | | | | | | | | | | (1460) ~ (all_52_11 = e3)
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | REDUCE: (392), (1456) imply:
% 152.31/25.92 | | | | | | | | | | | | | (1461) ~ (all_52_14 = e3)
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | REDUCE: (39), (1456) imply:
% 152.31/25.92 | | | | | | | | | | | | | (1462) op(e1, e1) = e3
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | BETA: splitting (215) gives:
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | Case 1:
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | (1463) ~ (all_56_14 = e3)
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | REDUCE: (1457), (1463) imply:
% 152.31/25.92 | | | | | | | | | | | | | | (1464) $false
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | CLOSE: (1464) is inconsistent.
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | Case 2:
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | (1465) all_56_6 = e1 & op(e1, e3) = e1
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | ALPHA: (1465) implies:
% 152.31/25.92 | | | | | | | | | | | | | | (1466) all_56_6 = e1
% 152.31/25.92 | | | | | | | | | | | | | | (1467) op(e1, e3) = e1
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | Case 1:
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | (1468) ~ (all_56_12 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REDUCE: (297), (1468) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1469) ~ (all_10_2 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 152.31/25.92 | | | | | | | | | | | | | | | (141), (155), (156), (158), (160), (161), (162),
% 152.31/25.92 | | | | | | | | | | | | | | | (163), (165), (168), (202), (208), (209), (212),
% 152.31/25.92 | | | | | | | | | | | | | | | (223), (224), (225), (226), (227), (228), (229),
% 152.31/25.92 | | | | | | | | | | | | | | | (230), (231), (232), (233), (234), (235), (236),
% 152.31/25.92 | | | | | | | | | | | | | | | (237), (238), (239), (242), (243), (244), (246),
% 152.31/25.92 | | | | | | | | | | | | | | | (247), (248), (249), (251), (252), (253), (261),
% 152.31/25.92 | | | | | | | | | | | | | | | (297), (299), (368), (386), (395), (397), (398),
% 152.31/25.92 | | | | | | | | | | | | | | | (400), (1317), (1319), (1320), (1321), (1322),
% 152.31/25.92 | | | | | | | | | | | | | | | (1323), (1330), (1335), (1339), (1343), (1347),
% 152.31/25.92 | | | | | | | | | | | | | | | (1351), (1354), (1455), (1457), (1462), (1466),
% 152.31/25.92 | | | | | | | | | | | | | | | (1467), (1469), (function-axioms) are inconsistent
% 152.31/25.92 | | | | | | | | | | | | | | | by sub-proof #566.
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | Case 2:
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | (1470) all_56_12 = e1
% 152.31/25.92 | | | | | | | | | | | | | | | (1471) all_56_1 = e3 & op(e3, e1) = e3
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | ALPHA: (1471) implies:
% 152.31/25.92 | | | | | | | | | | | | | | | (1472) op(e3, e1) = e3
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | COMBINE_EQS: (297), (1470) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1473) all_10_2 = e1
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | SIMP: (1473) implies:
% 152.31/25.92 | | | | | | | | | | | | | | | (1474) all_10_2 = e1
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | COMBINE_EQS: (355), (1474) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1475) all_32_2 = e1
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REDUCE: (364), (1474) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1476) ~ (all_52_2 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REDUCE: (366), (1474) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1477) ~ (all_52_3 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REDUCE: (368), (1474) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1478) ~ (all_52_4 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REDUCE: (370), (1474) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1479) ~ (all_52_8 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REDUCE: (1347), (1474) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1480) ~ (e2 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REDUCE: (1349), (1474) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1481) op(e1, e2) = all_14_0
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | REDUCE: (45), (1474) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | (1482) op(e3, e3) = e1
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | Case 1:
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | (1483) ~ (all_32_2 = e1)
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | REDUCE: (1475), (1483) imply:
% 152.31/25.92 | | | | | | | | | | | | | | | | (1484) $false
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | CLOSE: (1484) is inconsistent.
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | Case 2:
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | (1485) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0
% 152.31/25.92 | | | | | | | | | | | | | | | | & op(e1, e1) = all_32_1 & $i(all_32_0) &
% 152.31/25.92 | | | | | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 152.31/25.92 | | | | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | BETA: splitting (1485) gives:
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1486) ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 152.31/25.92 | | | | | | | | | | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) &
% 152.31/25.92 | | | | | | | | | | | | | | | | | $i(all_32_1)
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | | ALPHA: (1486) implies:
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1487) op(e1, e1) = all_32_1
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (108),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (115), (116), (119), (121), (123), (124), (126),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (132), (133), (134), (137), (138), (139), (141),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (142), (156), (158), (160), (161), (162), (163),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (165), (167), (168), (187), (188), (189), (190),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (191), (193), (194), (195), (196), (200), (201),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (209), (212), (223), (224), (225), (226), (227),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (242), (243),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (244), (246), (247), (248), (249), (251), (252),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (253), (261), (262), (263), (264), (265), (274),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (275), (276), (277), (288), (289), (306), (375),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (386), (393), (395), (396), (397), (398), (1317),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1319), (1320), (1321), (1322), (1323), (1330),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1335), (1339), (1341), (1343), (1345), (1351),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1354), (1455), (1457), (1458), (1459), (1460),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1461), (1462), (1467), (1470), (1472), (1476),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1477), (1478), (1479), (1481), (1482), (1487),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.92 | | | | | | | | | | | | | | | | | #420.
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1488) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 152.31/25.92 | | | | | | | | | | | | | | | | | $i(all_32_1)
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | | ALPHA: (1488) implies:
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1489) op(e1, e1) = all_32_1
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (108),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (115), (116), (119), (121), (123), (124), (126),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (132), (133), (134), (137), (138), (139), (141),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (142), (156), (158), (160), (161), (162), (163),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (165), (167), (168), (187), (188), (189), (190),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (191), (193), (194), (195), (196), (200), (201),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (209), (212), (223), (224), (225), (226), (227),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (242), (243),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (244), (246), (247), (248), (249), (251), (252),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (253), (261), (262), (263), (264), (265), (274),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (275), (276), (277), (288), (289), (306), (375),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (386), (393), (395), (396), (397), (398), (1317),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1319), (1320), (1321), (1322), (1323), (1330),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1335), (1339), (1341), (1343), (1345), (1351),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1354), (1455), (1457), (1458), (1459), (1460),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1461), (1462), (1467), (1470), (1472), (1476),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (1477), (1478), (1479), (1481), (1482), (1489),
% 152.31/25.92 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.92 | | | | | | | | | | | | | | | | | #420.
% 152.31/25.92 | | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | End of split
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | Case 2:
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | (1490) all_20_2 = e2
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | COMBINE_EQS: (348), (1490) imply:
% 152.31/25.92 | | | | | | | | | | | (1491) all_4_2 = e2
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | SIMP: (1491) implies:
% 152.31/25.92 | | | | | | | | | | | (1492) all_4_2 = e2
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | COMBINE_EQS: (261), (1492) imply:
% 152.31/25.92 | | | | | | | | | | | (1493) all_56_15 = e2
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | REDUCE: (386), (1492) imply:
% 152.31/25.92 | | | | | | | | | | | (1494) ~ (all_52_7 = e2)
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | REDUCE: (36), (1492) imply:
% 152.31/25.92 | | | | | | | | | | | (1495) op(e0, e0) = e2
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | BETA: splitting (211) gives:
% 152.31/25.92 | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | Case 1:
% 152.31/25.92 | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | (1496) ~ (all_56_15 = e2)
% 152.31/25.92 | | | | | | | | | | | |
% 152.31/25.92 | | | | | | | | | | | | REDUCE: (1493), (1496) imply:
% 152.31/25.92 | | | | | | | | | | | | (1497) $false
% 152.31/25.93 | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | CLOSE: (1497) is inconsistent.
% 152.31/25.93 | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | (1498) all_56_10 = e0 & op(e0, e2) = e0
% 152.31/25.93 | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | ALPHA: (1498) implies:
% 152.31/25.93 | | | | | | | | | | | | (1499) op(e0, e2) = e0
% 152.31/25.93 | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | BETA: splitting (232) gives:
% 152.31/25.93 | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | (1500) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 152.31/25.93 | | | | | | | | | | | | | & op(e1, e2) = e2)
% 152.31/25.93 | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | BETA: splitting (1500) gives:
% 152.31/25.93 | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | (1501) all_58_6 = e2 & op(e1, e3) = e2
% 152.31/25.93 | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | ALPHA: (1501) implies:
% 152.31/25.93 | | | | | | | | | | | | | | (1502) all_58_6 = e2
% 152.31/25.93 | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (246), (248),
% 152.31/25.93 | | | | | | | | | | | | | | (252), (1330), (1502), (function-axioms) are
% 152.31/25.93 | | | | | | | | | | | | | | inconsistent by sub-proof #1152.
% 152.31/25.93 | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | (1503) all_58_7 = e2 & op(e1, e2) = e2
% 152.31/25.93 | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | ALPHA: (1503) implies:
% 152.31/25.93 | | | | | | | | | | | | | | (1504) all_58_7 = e2
% 152.31/25.93 | | | | | | | | | | | | | | (1505) op(e1, e2) = e2
% 152.31/25.93 | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 152.31/25.93 | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | (1506) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 152.31/25.93 | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | BETA: splitting (1506) gives:
% 152.31/25.93 | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | (1507) all_58_4 = e2 & op(e3, e1) = e2
% 152.31/25.93 | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | ALPHA: (1507) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | (1508) all_58_4 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | (1509) op(e3, e1) = e2
% 152.31/25.93 | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | (1510) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 152.31/25.93 | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (165), (246),
% 152.31/25.93 | | | | | | | | | | | | | | | | | (248), (252), (1330), (1499), (1510),
% 152.31/25.93 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.93 | | | | | | | | | | | | | | | | | #1039.
% 152.31/25.93 | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | (1511) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 152.31/25.93 | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | BETA: splitting (1511) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1512) all_58_14 = e2 & op(e0, e1) = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | ALPHA: (1512) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1513) all_58_14 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (160), (162),
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (165), (168), (223), (224), (226), (227), (228),
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (229), (230), (231), (233), (235), (238), (239),
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (242), (244), (246), (247), (248), (249), (251),
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (252), (253), (1319), (1320), (1321), (1323),
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1330), (1335), (1495), (1499), (1504), (1513),
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.31/25.93 | | | | | | | | | | | | | | | | | | #604.
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1514) all_58_15 = e2 & op(e0, e0) = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | ALPHA: (1514) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1515) all_58_15 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 152.31/25.93 | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (156), (1499) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1516) all_52_7 = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 152.31/25.93 | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (160), (1505) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1517) all_52_6 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 152.31/25.93 | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (1509) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1518) all_52_8 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (138), (1516) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1519) ~ (all_52_3 = e0)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (133), (1516) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1520) ~ (all_52_4 = e0)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (132), (1518) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1521) ~ (all_52_4 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (124), (1517) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1522) ~ (all_52_14 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | SIMP: (1522) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1523) ~ (all_52_14 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (123), (1516) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1524) ~ (all_52_11 = e0)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | SIMP: (1524) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1525) ~ (all_52_11 = e0)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (1494), (1516) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1526) ~ (e2 = e0)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (119), (1518) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1527) ~ (all_52_11 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | SIMP: (1527) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1528) ~ (all_52_11 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (118), (1518) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1529) ~ (all_52_12 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | SIMP: (1529) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1530) ~ (all_52_12 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | REDUCE: (387), (1518) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | (1531) ~ (all_6_2 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | (1532) ~ (all_56_12 = e1)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | REDUCE: (297), (1532) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | (1533) ~ (all_10_2 = e1)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | (1534) ~ (all_22_2 = e3)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | REDUCE: (1316), (1534) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | (1535) $false
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | CLOSE: (1535) is inconsistent.
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | (1536) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = all_22_1 & $i(all_22_0) &
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3, e3)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1537) all_54_0 = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (1537) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1538) all_10_2 = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | SIMP: (1538) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1539) all_10_2 = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (1539) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1540) all_56_12 = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (1539) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1541) ~ (all_52_2 = e3)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1539) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1542) ~ (all_52_3 = e3)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (1539) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1543) ~ (all_52_12 = e3)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1349), (1539) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1544) op(e3, e2) = all_14_0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (1539) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | (1545) op(e3, e3) = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | (1546) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1546) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | (1547) all_58_1 = e0 & op(e3, e2) = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1547) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | (1548) all_58_1 = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | (1549) op(e3, e2) = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | (1550) all_54_12 = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (1542), (1550) are inconsistent by
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1234.
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | (1551) ~ (all_54_12 = e3)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_54_1 = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1553) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | (1554) all_52_4 = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1319), (1554) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | (1555) $false
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1555) is inconsistent.
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | (1556) ~ (all_54_1 = e3)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | (1557) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1557) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) all_54_1 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1558) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) all_52_4 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1521), (1559) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) $false
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1560) is inconsistent.
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) ~ (all_54_1 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) all_54_1 = e1 | all_54_1 = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1562) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) all_54_1 = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1563) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) all_52_4 = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1319), (1564) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) ~ (e3 = e1)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1521), (1564) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) ~ (e2 = e1)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (1564) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) op(e3, e2) = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (1335), (1548), (1568) are inconsistent
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #419.
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1569) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) all_58_7 = e1 & op(e1, e2) = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1504), (1570) are inconsistent by sub-proof
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1045.
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) all_58_13 = e1 & op(e0, e2) = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1571) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) all_58_13 = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1552) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1573) all_54_12 = e2
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (1341), (1573) are inconsistent by
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1189.
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1574) ~ (all_54_12 = e2)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1575) all_54_12 = e1 | all_54_12 = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1575) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576) all_54_12 = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (1576) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1577) all_52_3 = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1577) implies:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1578) all_52_3 = e1
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (1578) imply:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1579) ~ (all_52_2 = e1)
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1580) all_54_8 = e3
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (1541), (1580) are inconsistent by
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1425.
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1581) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1581) gives:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1582) all_54_8 = e2
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (1339), (1582) are inconsistent by
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1231.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1583) all_54_8 = e1 | all_54_8 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1583) gives:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1584) all_54_8 = e1
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (1579), (1584) are inconsistent by
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1379.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_54_8 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1585) imply:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1586) all_52_2 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1586) implies:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1587) all_52_2 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1579), (1587) imply:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1588) ~ (e1 = e0)
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (1544), (1567) gives:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1589) all_14_0 = e1
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (1544), (1549) gives:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1590) all_14_0 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1589), (1590) imply:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1591) e1 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1572), (1591) imply:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1592) all_58_13 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (243), (1335), (1504), (1548),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1592) are inconsistent by sub-proof #857.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1593) all_54_12 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (1519), (1593) are inconsistent by
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1223.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1594) all_54_1 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1594) imply:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1595) all_52_4 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1520), (1595) imply:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1596) $false
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1596) is inconsistent.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1597) all_58_3 = e0 & op(e2, e2) = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1335), (1597) are inconsistent by sub-proof
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | #910.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | (1598) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1598) gives:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1599) all_58_7 = e0 & op(e1, e2) = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1504), (1599) are inconsistent by sub-proof
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | #1468.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1600) all_58_13 = e0 & op(e0, e2) = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1600) implies:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1601) all_58_13 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (108), (110),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (111), (115), (116), (131), (137), (139), (142),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (158), (160), (162), (163), (165),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (188), (190), (191), (192), (194),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (195), (196), (199), (201), (208), (215), (223),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (229), (230), (231),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (233), (234), (235), (237), (238), (239), (242),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (243), (244), (246), (247), (248), (249), (251),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (262), (264), (265), (273), (275),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (276), (277), (287), (289), (304), (374), (388),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (390), (398), (1317), (1319), (1320), (1321),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1322), (1323), (1330), (1335), (1339), (1341),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1343), (1345), (1493), (1495), (1499), (1504),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1508), (1515), (1519), (1520), (1521), (1523),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1525), (1528), (1530), (1536), (1540), (1541),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | (1542), (1543), (1545), (1601), (function-axioms)
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #373.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | (1602) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (400), (1347), (1533), (1602) are
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1307.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | (1603) all_56_12 = e1
% 152.31/25.94 | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (201), (289), (297), (368), (1319), (1520),
% 152.31/25.94 | | | | | | | | | | | | | | | | | | | (1521), (1603) are inconsistent by sub-proof #372.
% 152.31/25.94 | | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | (1604) all_58_5 = e2 & op(e2, e1) = e2
% 152.31/25.94 | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | ALPHA: (1604) implies:
% 152.31/25.94 | | | | | | | | | | | | | | | | (1605) all_58_5 = e2
% 152.31/25.94 | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (238), (239), (1330),
% 152.31/25.94 | | | | | | | | | | | | | | | | (1335), (1605), (function-axioms) are inconsistent
% 152.31/25.94 | | | | | | | | | | | | | | | | by sub-proof #898.
% 152.31/25.94 | | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | End of split
% 152.31/25.94 | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | Case 2:
% 152.31/25.94 | | | | | | | | | | | | | | |
% 152.31/25.94 | | | | | | | | | | | | | | | (1606) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 152.31/25.94 | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 152.31/25.94 | | | | | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (156), (160),
% 152.55/25.94 | | | | | | | | | | | | | | | (162), (165), (168), (223), (224), (226), (227),
% 152.55/25.94 | | | | | | | | | | | | | | | (228), (229), (230), (231), (233), (235), (238),
% 152.55/25.94 | | | | | | | | | | | | | | | (239), (242), (244), (246), (247), (248), (249),
% 152.55/25.94 | | | | | | | | | | | | | | | (251), (252), (253), (398), (1319), (1320),
% 152.55/25.94 | | | | | | | | | | | | | | | (1321), (1323), (1330), (1335), (1495), (1499),
% 152.55/25.94 | | | | | | | | | | | | | | | (1504), (1606), (function-axioms) are inconsistent
% 152.55/25.94 | | | | | | | | | | | | | | | by sub-proof #371.
% 152.55/25.94 | | | | | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | | | | | End of split
% 152.55/25.94 | | | | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | | | | End of split
% 152.55/25.94 | | | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | | | Case 2:
% 152.55/25.94 | | | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | | | | (1607) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 152.55/25.94 | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 152.55/25.94 | | | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (156), (160),
% 152.55/25.94 | | | | | | | | | | | | | (162), (165), (223), (224), (225), (226), (227),
% 152.55/25.94 | | | | | | | | | | | | | (229), (231), (233), (235), (238), (242), (244),
% 152.55/25.94 | | | | | | | | | | | | | (246), (248), (251), (252), (398), (1320), (1321),
% 152.55/25.94 | | | | | | | | | | | | | (1323), (1330), (1335), (1495), (1499), (1607),
% 152.55/25.94 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.94 | | | | | | | | | | | | | #638.
% 152.55/25.94 | | | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | | | End of split
% 152.55/25.94 | | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | | End of split
% 152.55/25.94 | | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | End of split
% 152.55/25.94 | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | End of split
% 152.55/25.94 | | | | | | | | |
% 152.55/25.94 | | | | | | | | Case 2:
% 152.55/25.94 | | | | | | | | |
% 152.55/25.94 | | | | | | | | | (1608) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3
% 152.55/25.94 | | | | | | | | | & op(e0, e2) = e3)
% 152.55/25.94 | | | | | | | | |
% 152.55/25.94 | | | | | | | | | BETA: splitting (1608) gives:
% 152.55/25.94 | | | | | | | | |
% 152.55/25.94 | | | | | | | | | Case 1:
% 152.55/25.94 | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | (1609) all_58_7 = e3 & op(e1, e2) = e3
% 152.55/25.94 | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | REF_CLOSE: (160), (1320), (1609), (function-axioms) are
% 152.55/25.94 | | | | | | | | | | inconsistent by sub-proof #1184.
% 152.55/25.94 | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | Case 2:
% 152.55/25.94 | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | (1610) all_58_13 = e3 & op(e0, e2) = e3
% 152.55/25.94 | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | | REF_CLOSE: (156), (1321), (1610), (function-axioms) are
% 152.55/25.94 | | | | | | | | | | inconsistent by sub-proof #1449.
% 152.55/25.94 | | | | | | | | | |
% 152.55/25.94 | | | | | | | | | End of split
% 152.55/25.94 | | | | | | | | |
% 152.55/25.94 | | | | | | | | End of split
% 152.55/25.94 | | | | | | | |
% 152.55/25.94 | | | | | | | End of split
% 152.55/25.94 | | | | | | |
% 152.55/25.94 | | | | | | Case 2:
% 152.55/25.94 | | | | | | |
% 152.55/25.94 | | | | | | | (1611) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 &
% 152.55/25.94 | | | | | | | $i(all_14_1)
% 152.55/25.94 | | | | | | |
% 152.55/25.94 | | | | | | | ALPHA: (1611) implies:
% 152.55/25.94 | | | | | | | (1612) ~ (all_14_1 = e0)
% 152.55/25.94 | | | | | | | (1613) op(e3, e3) = all_14_1
% 152.55/25.94 | | | | | | |
% 152.55/25.94 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (39), (45), (61), (64),
% 152.55/25.94 | | | | | | | (73), (79), (108), (110), (111), (115), (116), (118),
% 152.55/25.94 | | | | | | | (119), (121), (123), (124), (126), (131), (132), (133),
% 152.55/25.94 | | | | | | | (134), (137), (138), (139), (141), (142), (143), (144),
% 152.55/25.94 | | | | | | | (146), (147), (155), (156), (157), (158), (160), (161),
% 152.55/25.94 | | | | | | | (162), (163), (165), (166), (167), (168), (187), (188),
% 152.55/25.94 | | | | | | | (189), (190), (191), (192), (193), (194), (195), (196),
% 152.55/25.94 | | | | | | | (199), (200), (201), (202), (208), (209), (211), (212),
% 152.55/25.94 | | | | | | | (213), (215), (218), (220), (223), (224), (225), (226),
% 152.55/25.94 | | | | | | | (227), (228), (229), (230), (231), (232), (233), (234),
% 152.55/25.94 | | | | | | | (235), (236), (237), (238), (239), (242), (243), (244),
% 152.55/25.94 | | | | | | | (245), (246), (247), (248), (249), (251), (252), (253),
% 152.55/25.94 | | | | | | | (261), (262), (263), (264), (265), (273), (274), (275),
% 152.55/25.94 | | | | | | | (276), (277), (287), (288), (289), (297), (299), (304),
% 152.55/25.94 | | | | | | | (306), (339), (348), (355), (362), (364), (366), (368),
% 152.55/25.94 | | | | | | | (370), (372), (374), (375), (385), (386), (387), (388),
% 152.55/25.94 | | | | | | | (390), (392), (393), (394), (395), (396), (397), (398),
% 152.55/25.94 | | | | | | | (1316), (1317), (1318), (1319), (1320), (1321), (1322),
% 152.55/25.94 | | | | | | | (1323), (1612), (1613), (function-axioms) are
% 152.55/25.94 | | | | | | | inconsistent by sub-proof #354.
% 152.55/25.94 | | | | | | |
% 152.55/25.94 | | | | | | End of split
% 152.55/25.94 | | | | | |
% 152.55/25.94 | | | | | End of split
% 152.55/25.94 | | | | |
% 152.55/25.94 | | | | Case 2:
% 152.55/25.94 | | | | |
% 152.55/25.94 | | | | | (1614) all_10_2 = e0
% 152.55/25.94 | | | | | (1615) ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e0,
% 152.55/25.94 | | | | | e0) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 152.55/25.94 | | | | | (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1))
% 152.55/25.94 | | | | |
% 152.55/25.94 | | | | | COMBINE_EQS: (308), (1614) imply:
% 152.55/25.94 | | | | | (1616) all_24_2 = e0
% 152.55/25.94 | | | | |
% 152.55/25.94 | | | | | COMBINE_EQS: (297), (1614) imply:
% 152.55/25.94 | | | | | (1617) all_56_12 = e0
% 152.55/25.94 | | | | |
% 152.55/25.94 | | | | | REDUCE: (362), (1614) imply:
% 152.55/25.94 | | | | | (1618) ~ (all_52_1 = e0)
% 152.55/25.94 | | | | |
% 152.55/25.94 | | | | | REDUCE: (368), (1614) imply:
% 152.55/25.94 | | | | | (1619) ~ (all_52_4 = e0)
% 152.55/25.94 | | | | |
% 152.55/25.94 | | | | | REDUCE: (370), (1614) imply:
% 152.55/25.95 | | | | | (1620) ~ (all_52_8 = e0)
% 152.55/25.95 | | | | |
% 152.55/25.95 | | | | | REDUCE: (372), (1614) imply:
% 152.55/25.95 | | | | | (1621) ~ (all_52_12 = e0)
% 152.55/25.95 | | | | |
% 152.55/25.95 | | | | | BETA: splitting (1615) gives:
% 152.55/25.95 | | | | |
% 152.55/25.95 | | | | | Case 1:
% 152.55/25.95 | | | | | |
% 152.55/25.95 | | | | | | (1622) ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e0,
% 152.55/25.95 | | | | | | e0) = all_10_1 & $i(all_10_0) & $i(all_10_1)
% 152.55/25.95 | | | | | |
% 152.55/25.95 | | | | | | ALPHA: (1622) implies:
% 152.55/25.95 | | | | | | (1623) ~ (all_10_0 = e2)
% 152.55/25.95 | | | | | | (1624) op(e0, e0) = all_10_1
% 152.55/25.95 | | | | | | (1625) op(all_10_1, e3) = all_10_0
% 152.55/25.95 | | | | | |
% 152.55/25.95 | | | | | | BETA: splitting (219) gives:
% 152.55/25.95 | | | | | |
% 152.55/25.95 | | | | | | Case 1:
% 152.55/25.95 | | | | | | |
% 152.55/25.95 | | | | | | | (1626) ~ (all_56_12 = e0)
% 152.55/25.95 | | | | | | |
% 152.55/25.95 | | | | | | | REDUCE: (1617), (1626) imply:
% 152.55/25.95 | | | | | | | (1627) $false
% 152.55/25.95 | | | | | | |
% 152.55/25.95 | | | | | | | CLOSE: (1627) is inconsistent.
% 152.55/25.95 | | | | | | |
% 152.55/25.95 | | | | | | Case 2:
% 152.55/25.95 | | | | | | |
% 152.55/25.95 | | | | | | | (1628) all_56_2 = e3 & op(e3, e0) = e3
% 152.55/25.95 | | | | | | |
% 152.55/25.95 | | | | | | | ALPHA: (1628) implies:
% 152.55/25.95 | | | | | | | (1629) all_56_2 = e3
% 152.55/25.95 | | | | | | | (1630) op(e3, e0) = e3
% 152.55/25.95 | | | | | | |
% 152.55/25.95 | | | | | | | BETA: splitting (247) gives:
% 152.55/25.95 | | | | | | |
% 152.55/25.95 | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | |
% 152.55/25.95 | | | | | | | | (1631) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 152.55/25.95 | | | | | | | | op(e3, e2) = e0)
% 152.55/25.95 | | | | | | | |
% 152.55/25.95 | | | | | | | | BETA: splitting (1631) gives:
% 152.55/25.95 | | | | | | | |
% 152.55/25.95 | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | (1632) all_58_0 = e0 & op(e3, e3) = e0
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | ALPHA: (1632) implies:
% 152.55/25.95 | | | | | | | | | (1633) all_58_0 = e0
% 152.55/25.95 | | | | | | | | | (1634) op(e3, e3) = e0
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 152.55/25.95 | | | | | | | | | all_10_1, e0, e0, simplifying with (36), (1624)
% 152.55/25.95 | | | | | | | | | gives:
% 152.55/25.95 | | | | | | | | | (1635) all_10_1 = all_4_2
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 152.55/25.95 | | | | | | | | | e3, e0, e3, simplifying with (166), (1630) gives:
% 152.55/25.95 | | | | | | | | | (1636) all_52_12 = e3
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | REDUCE: (131), (1636) imply:
% 152.55/25.95 | | | | | | | | | (1637) ~ (all_52_4 = e3)
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | REDUCE: (118), (1636) imply:
% 152.55/25.95 | | | | | | | | | (1638) ~ (all_52_8 = e3)
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | REDUCE: (111), (1636) imply:
% 152.55/25.95 | | | | | | | | | (1639) ~ (all_52_13 = e3)
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | SIMP: (1639) implies:
% 152.55/25.95 | | | | | | | | | (1640) ~ (all_52_13 = e3)
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | REDUCE: (110), (1636) imply:
% 152.55/25.95 | | | | | | | | | (1641) ~ (all_52_14 = e3)
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | SIMP: (1641) implies:
% 152.55/25.95 | | | | | | | | | (1642) ~ (all_52_14 = e3)
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | REDUCE: (394), (1636) imply:
% 152.55/25.95 | | | | | | | | | (1643) ~ (all_4_2 = e3)
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | SIMP: (1643) implies:
% 152.55/25.95 | | | | | | | | | (1644) ~ (all_4_2 = e3)
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | REDUCE: (1625), (1635) imply:
% 152.55/25.95 | | | | | | | | | (1645) op(all_4_2, e3) = all_10_0
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | BETA: splitting (253) gives:
% 152.55/25.95 | | | | | | | | |
% 152.55/25.95 | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | (1646) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 152.55/25.95 | | | | | | | | | | & op(e3, e2) = e3)
% 152.55/25.95 | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | REF_CLOSE: (7), (168), (1634), (1637), (1646),
% 152.55/25.95 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.95 | | | | | | | | | | #353.
% 152.55/25.95 | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | (1647) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 152.55/25.95 | | | | | | | | | | & op(e3, e0) = e3)
% 152.55/25.95 | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | BETA: splitting (1647) gives:
% 152.55/25.95 | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | (1648) all_58_4 = e3 & op(e3, e1) = e3
% 152.55/25.95 | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | ALPHA: (1648) implies:
% 152.55/25.95 | | | | | | | | | | | (1649) op(e3, e1) = e3
% 152.55/25.95 | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | REF_CLOSE: (167), (1638), (1649), (function-axioms) are
% 152.55/25.95 | | | | | | | | | | | inconsistent by sub-proof #1538.
% 152.55/25.95 | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | (1650) all_58_9 = e3 & op(e3, e0) = e3
% 152.55/25.95 | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | ALPHA: (1650) implies:
% 152.55/25.95 | | | | | | | | | | | (1651) all_58_9 = e3
% 152.55/25.95 | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | BETA: splitting (52) gives:
% 152.55/25.95 | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | (1652) ~ (all_14_2 = e3)
% 152.55/25.95 | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | REDUCE: (351), (1652) imply:
% 152.55/25.95 | | | | | | | | | | | | (1653) ~ (all_8_2 = e3)
% 152.55/25.95 | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | BETA: splitting (61) gives:
% 152.55/25.95 | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | (1654) ~ (all_20_2 = e2)
% 152.55/25.95 | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | REDUCE: (348), (1654) imply:
% 152.55/25.95 | | | | | | | | | | | | | (1655) ~ (all_4_2 = e2)
% 152.55/25.95 | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | BETA: splitting (67) gives:
% 152.55/25.95 | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | (1656) ~ (all_24_2 = e0)
% 152.55/25.95 | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | REDUCE: (1616), (1656) imply:
% 152.55/25.95 | | | | | | | | | | | | | | (1657) $false
% 152.55/25.95 | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | CLOSE: (1657) is inconsistent.
% 152.55/25.95 | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | (1658) ( ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0
% 152.55/25.95 | | | | | | | | | | | | | | & op(e0, e0) = all_24_1 & $i(all_24_0) &
% 152.55/25.95 | | | | | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e2) & op(e0, e0)
% 152.55/25.95 | | | | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 152.55/25.95 | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | BETA: splitting (1658) gives:
% 152.55/25.95 | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | (1659) ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 &
% 152.55/25.95 | | | | | | | | | | | | | | | op(e0, e0) = all_24_1 & $i(all_24_0) &
% 152.55/25.95 | | | | | | | | | | | | | | | $i(all_24_1)
% 152.55/25.95 | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | ALPHA: (1659) implies:
% 152.55/25.95 | | | | | | | | | | | | | | | (1660) ~ (all_24_0 = e1)
% 152.55/25.95 | | | | | | | | | | | | | | | (1661) op(e0, e0) = all_24_1
% 152.55/25.95 | | | | | | | | | | | | | | | (1662) op(all_24_1, e3) = all_24_0
% 152.55/25.95 | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 152.55/25.95 | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | (1663) all_54_15 = e3
% 152.55/25.95 | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | REF_CLOSE: (306), (1644), (1663) are inconsistent by
% 152.55/25.95 | | | | | | | | | | | | | | | | sub-proof #1543.
% 152.55/25.95 | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | (1664) ~ (all_54_15 = e3)
% 152.55/25.95 | | | | | | | | | | | | | | | | (1665) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 152.55/25.95 | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | BETA: splitting (1665) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | (1666) all_54_15 = e2
% 152.55/25.95 | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (1655), (1666) are inconsistent by
% 152.55/25.95 | | | | | | | | | | | | | | | | | sub-proof #1542.
% 152.55/25.95 | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | (1667) ~ (all_54_15 = e2)
% 152.55/25.95 | | | | | | | | | | | | | | | | | (1668) all_54_15 = e1 | all_54_15 = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | BETA: splitting (1668) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1669) all_54_15 = e1
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (397), (1669) are inconsistent by sub-proof
% 152.55/25.95 | | | | | | | | | | | | | | | | | | #1541.
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1670) all_54_15 = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (1670) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1671) all_4_2 = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | SIMP: (1671) implies:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1672) all_4_2 = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (1672) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1673) all_56_15 = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | REDUCE: (375), (1672) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1674) ~ (all_52_3 = e0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | REDUCE: (386), (1672) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1675) ~ (all_52_7 = e0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | REDUCE: (1644), (1672) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1676) ~ (e3 = e0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | REDUCE: (1655), (1672) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1677) ~ (e2 = e0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | REDUCE: (397), (1672) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1678) ~ (e1 = e0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | REDUCE: (1645), (1672) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | (1679) op(e0, e3) = all_10_0
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1680) all_58_15 = e0 & op(e0, e0) = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | ALPHA: (1680) implies:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1681) all_58_15 = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1682) op(e0, e0) = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_24_1,
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (1661), (1682) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1683) all_24_1 = e0
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | all_10_0, e3, e0, simplifying with (157), (1679)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1684) all_52_3 = all_10_0
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (1684) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1685) all_54_12 = all_10_0
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1684) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1686) ~ (all_52_1 = all_10_0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | REDUCE: (138), (1684) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1687) ~ (all_52_7 = all_10_0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | SIMP: (1687) implies:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1688) ~ (all_52_7 = all_10_0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | REDUCE: (1674), (1684) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1689) ~ (all_10_0 = e0)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | REDUCE: (1662), (1683) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1690) op(e0, e3) = all_24_0
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_0,
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | all_24_0, e3, e0, simplifying with (1679), (1690)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1691) all_24_0 = all_10_0
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | REDUCE: (1660), (1691) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | (1692) ~ (all_10_0 = e1)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | (1693) all_54_12 = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1685), (1693) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | (1694) all_10_0 = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | SIMP: (1694) implies:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | (1695) all_10_0 = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | REDUCE: (1686), (1695) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | (1696) ~ (all_52_1 = e3)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | REDUCE: (1688), (1695) imply:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | (1697) ~ (all_52_7 = e3)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | (1698) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (168), (1637), (1653), (1698),
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | #1436.
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | (1699) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1699) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | (1700) all_58_7 = e3 & op(e1, e2) = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1700) implies:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | (1701) all_58_7 = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | (1702) op(e1, e2) = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | (1703) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1703) gives:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | (1704) all_58_0 = e3 & op(e3, e3) = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1704) implies:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | (1705) op(e3, e3) = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1634), (1705), (function-axioms) are
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1521.
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | (1706) all_58_2 = e3 & op(e2, e3) = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1706) implies:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | (1707) op(e2, e3) = e3
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1696), (1707), (function-axioms) are
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1183.
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.95 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | (1708) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1708) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | (1709) all_58_6 = e3 & op(e1, e3) = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1709) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | (1710) all_58_6 = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | (1711) op(e1, e3) = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | (1712) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1712) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1713) all_58_0 = e2 & op(e3, e3) = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1633), (1713) are inconsistent by sub-proof
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1714) all_58_2 = e2 & op(e2, e3) = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1714) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1715) op(e2, e3) = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1716) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1716) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1717) all_58_6 = e0 & op(e1, e3) = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1717) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1718) all_58_6 = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1710), (1718) are inconsistent by sub-proof
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1321.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1719) all_58_7 = e0 & op(e1, e2) = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1701), (1719) are inconsistent by sub-proof
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1140.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1720) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1720) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1721) all_58_8 = e0 & op(e1, e1) = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1721) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1722) all_58_8 = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1723) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (165), (1653), (1715), (1723),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1048.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1724) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1724) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1725) all_58_5 = e3 & op(e2, e1) = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1725) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1726) all_58_5 = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1727) op(e2, e1) = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1728) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (42), (399), (1715), (1728),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1074.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1729) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1729) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1730) all_58_5 = e1 & op(e2, e1) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1730) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1731) op(e2, e1) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1727), (1731), (function-axioms) are
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1732) all_58_10 = e1 & op(e2, e0) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1732) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1733) all_58_10 = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1734) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (165), (238),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (241), (399), (1651), (1715), (1726),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1733), (1734), (function-axioms) are inconsistent
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #351.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1735) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1735) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1736) all_58_11 = e2 & op(e1, e0) = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1736) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1737) all_58_11 = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1738) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1738) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1739) all_58_0 = e1 & op(e3, e3) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1739) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1740) all_58_0 = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1633), (1740) imply:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1741) e1 = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1741) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1742) e1 = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1733), (1742) imply:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1743) all_58_10 = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (227), (397), (1651), (1737),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1743), (function-axioms) are inconsistent by
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #350.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1744) all_58_2 = e1 & op(e2, e3) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1744) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1745) op(e2, e3) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1715), (1745), (function-axioms) are
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1430.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1746) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1746) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1747) all_58_6 = e1 & op(e1, e3) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1747) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1748) op(e1, e3) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (1711), (1748), (function-axioms) are
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1164.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1749) all_58_12 = e1 & op(e0, e3) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1749) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1750) all_58_12 = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1751) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1751) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1752) all_58_1 = e0 & op(e3, e2) = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1619), (1752), (function-axioms) are
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1221.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1753) all_58_3 = e0 & op(e2, e2) = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1753) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1754) all_58_3 = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1755) op(e2, e2) = e0
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1756) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1756) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1757) all_58_12 = e3 & op(e0, e3) = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1757) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1758) all_58_12 = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (108), (115), (121), (124), (139), (143), (144),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155), (156), (158), (160), (161), (162), (163),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (198), (208), (213), (216), (224),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (231), (232), (233), (234), (235), (236),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (240), (241), (246), (248), (249),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (251), (252), (273), (286), (360), (373),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380), (384), (392), (397), (398), (399), (1623),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629), (1633), (1638), (1651), (1653), (1655),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1673), (1679), (1701), (1702), (1726), (1754),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1755), (1758), (function-axioms) are inconsistent
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #332.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1759) all_58_13 = e3 & op(e0, e2) = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (1697), (1759), (function-axioms) are
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1449.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1760) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1760) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1761) all_58_14 = e3 & op(e0, e1) = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1761) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1762) all_58_14 = e3
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1763) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1763) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1764) all_58_4 = e1 & op(e3, e1) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1764) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1765) op(e3, e1) = e1
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1766) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1766) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1767) all_58_4 = e2 & op(e3, e1) = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1767) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1768) op(e3, e1) = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1765), (1768), (function-axioms) are
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #338.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1769) all_58_5 = e2 & op(e2, e1) = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1769) implies:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1770) all_58_5 = e2
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (238), (239),
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (1715), (1733), (1770), (function-axioms)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #896.
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1771) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1771) gives:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1772) all_58_8 = e2 & op(e1, e1) = e2
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1772) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1773) all_58_8 = e2
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (230), (231), (1710),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1737), (1773) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1070.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1774) all_58_14 = e2 & op(e0, e1) = e2
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1774) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1775) all_58_14 = e2
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (156), (226), (1681), (1697),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1750), (1775), (function-axioms) are inconsistent
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1081.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1776) all_58_5 = e1 & op(e2, e1) = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1776) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1777) op(e2, e1) = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1727), (1777), (function-axioms) are
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1778) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1778) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1779) all_58_8 = e1 & op(e1, e1) = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1779) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780) all_58_8 = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (1701), (1710), (1737),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780) are inconsistent by sub-proof #1329.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1781) all_58_14 = e1 & op(e0, e1) = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1781) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1782) all_58_14 = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1762), (1782) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1147.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1783) all_58_15 = e3 & op(e0, e0) = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1783) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1784) all_58_15 = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (223), (227), (1651),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1737), (1784) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1316.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1785) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1785) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1786) all_58_7 = e0 & op(e1, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1786) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1787) all_58_7 = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1701), (1787) imply:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1788) e3 = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1710), (1788) imply:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1789) all_58_6 = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (39), (165), (231),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (252), (398), (1633), (1701), (1715),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1722), (1750), (1789), (function-axioms) are
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #346.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1790) all_58_13 = e0 & op(e0, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1790) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1791) op(e0, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (1675), (1791), (function-axioms) are
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1532.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1792) all_58_15 = e2 & op(e0, e0) = e2
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (1655), (1792), (function-axioms) are
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1452.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1793) all_58_10 = e3 & op(e2, e0) = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (227), (228), (397), (1651),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655), (1793), (function-axioms) are inconsistent
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #331.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1794) all_58_11 = e0 & op(e1, e0) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1794) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1795) all_58_11 = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1796) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (165), (1653), (1715), (1796),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1048.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1797) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1797) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1798) all_58_5 = e3 & op(e2, e1) = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1798) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1799) all_58_5 = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1800) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1800) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1801) all_58_9 = e1 & op(e3, e0) = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1801) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1802) all_58_9 = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1651), (1802) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1461.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1803) all_58_10 = e1 & op(e2, e0) = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1803) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1804) all_58_10 = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1805) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (165), (238),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (241), (399), (1651), (1715), (1799),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1804), (1805), (function-axioms) are inconsistent
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #351.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1806) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (1655), (1795), (1806),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #330.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1807) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1807) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1808) all_58_11 = e1 & op(e1, e0) = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1795), (1808) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #459.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1809) all_58_15 = e1 & op(e0, e0) = e1
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (397), (1809), (function-axioms) are
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1418.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1810) all_58_10 = e3 & op(e2, e0) = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (227), (228), (397), (1651),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655), (1810), (function-axioms) are inconsistent
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #331.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1811) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1811) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1812) all_58_6 = e2 & op(e1, e3) = e2
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1710), (1812) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | #1352.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1813) all_58_12 = e2 & op(e0, e3) = e2
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1623), (1679), (1813), (function-axioms) are
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | (1814) all_58_12 = e3 & op(e0, e3) = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1814) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | (1815) all_58_12 = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1816) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1816) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1817) all_58_1 = e0 & op(e3, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1619), (1817), (function-axioms) are
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1221.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1818) all_58_3 = e0 & op(e2, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1818) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1819) all_58_3 = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1820) op(e2, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1821) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (165), (1653), (1696), (1821),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1182.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1822) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1822) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1823) all_58_5 = e3 & op(e2, e1) = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1823) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1824) all_58_5 = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (108), (115), (121), (124), (139), (143), (144),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155), (156), (158), (160), (161), (162), (163),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (198), (208), (213), (216), (224),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (231), (232), (233), (234), (235), (236),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (240), (241), (246), (248), (249),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (251), (252), (273), (286), (360), (373),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380), (384), (392), (397), (398), (399), (1623),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629), (1633), (1638), (1651), (1653), (1655),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1673), (1679), (1701), (1702), (1815), (1819),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1820), (1824), (function-axioms) are inconsistent
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #332.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825) all_58_10 = e3 & op(e2, e0) = e3
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (227), (228), (397), (1651),
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655), (1825), (function-axioms) are inconsistent
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #331.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1826) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1826) gives:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1827) all_58_7 = e0 & op(e1, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1701), (1827) are inconsistent by sub-proof
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | #1140.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1828) all_58_13 = e0 & op(e0, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1828) implies:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1829) op(e0, e2) = e0
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (1675), (1829), (function-axioms) are
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1532.
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.97 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1830) all_58_13 = e3 & op(e0, e2) = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (1697), (1830), (function-axioms) are
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1449.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | (1831) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1831) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | (1832) all_54_12 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1685), (1832) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | (1833) all_10_0 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | SIMP: (1833) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | (1834) all_10_0 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1623), (1834) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | (1835) $false
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1835) is inconsistent.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | (1836) all_54_12 = e1 | all_54_12 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1836) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1837) all_54_12 = e1
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1685), (1837) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1838) all_10_0 = e1
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1838) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1839) all_10_0 = e1
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1692), (1839) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1840) $false
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1840) is inconsistent.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1841) all_54_12 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1685), (1841) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1842) all_10_0 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1842) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1843) all_10_0 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1689), (1843) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1844) $false
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1844) is inconsistent.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | (1845) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | ALPHA: (1845) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | (1846) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | e0) = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (227), (228),
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | (397), (1651), (1655), (1846), (function-axioms)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #326.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | (1847) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 152.55/25.98 | | | | | | | | | | | | | | | $i(all_24_1)
% 152.55/25.98 | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | ALPHA: (1847) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | (1848) ~ (all_24_1 = e2)
% 152.55/25.98 | | | | | | | | | | | | | | | (1849) op(e0, e0) = all_24_1
% 152.55/25.98 | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 152.55/25.98 | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | (1850) all_54_15 = e3
% 152.55/25.98 | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | REF_CLOSE: (306), (1644), (1850) are inconsistent by
% 152.55/25.98 | | | | | | | | | | | | | | | | sub-proof #1543.
% 152.55/25.98 | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | (1851) ~ (all_54_15 = e3)
% 152.55/25.98 | | | | | | | | | | | | | | | | (1852) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | BETA: splitting (1852) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | (1853) all_54_15 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (1655), (1853) are inconsistent by
% 152.55/25.98 | | | | | | | | | | | | | | | | | sub-proof #1542.
% 152.55/25.98 | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | (1854) ~ (all_54_15 = e2)
% 152.55/25.98 | | | | | | | | | | | | | | | | | (1855) all_54_15 = e1 | all_54_15 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | BETA: splitting (1855) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1856) all_54_15 = e1
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (397), (1856) are inconsistent by sub-proof
% 152.55/25.98 | | | | | | | | | | | | | | | | | | #1541.
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1857) all_54_15 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (1857) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1858) all_4_2 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | SIMP: (1858) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1859) all_4_2 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (1859) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1860) all_56_15 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | REDUCE: (386), (1859) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1861) ~ (all_52_7 = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | REDUCE: (1644), (1859) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1862) ~ (e3 = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | REDUCE: (397), (1859) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1863) ~ (e1 = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | REDUCE: (1645), (1859) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1864) op(e0, e3) = all_10_0
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | REDUCE: (36), (1859) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1865) op(e0, e0) = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_24_1,
% 152.55/25.98 | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (1849), (1865) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1866) all_24_1 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 152.55/25.98 | | | | | | | | | | | | | | | | | | all_10_0, e3, e0, simplifying with (157), (1864)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1867) all_52_3 = all_10_0
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | REDUCE: (1848), (1866) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | (1868) ~ (e2 = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | (1869) ~ (all_28_2 = e3)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | REDUCE: (339), (1869) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | (1870) ~ (all_6_2 = e3)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | (1871) ~ (all_30_2 = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (1871) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | (1872) ~ (all_8_2 = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | (1873) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1873) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1874) all_58_1 = e0 & op(e3, e2) = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1619), (1874), (function-axioms) are
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1221.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1875) all_58_3 = e0 & op(e2, e2) = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (165), (197), (240), (282), (373),
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (382), (384), (399), (1653), (1872), (1875),
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | #323.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | (1876) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1876) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1877) all_58_7 = e0 & op(e1, e2) = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1877) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | (1878) all_58_7 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | (1879) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1879) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | (1880) all_58_6 = e3 & op(e1, e3) = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1880) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | (1881) all_58_6 = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | (1882) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (168), (1637), (1653), (1882),
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | #1436.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | (1883) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1883) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (1884) all_58_7 = e3 & op(e1, e2) = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1884) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (1885) all_58_7 = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1878), (1885) are inconsistent by sub-proof
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | #1477.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (1886) all_58_13 = e3 & op(e0, e2) = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1886) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (1887) all_58_13 = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1888) all_54_5 = e3
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (1653), (1888) are inconsistent by
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1161.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1889) ~ (all_54_5 = e3)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1890) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1891) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1891) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1892) all_58_1 = e2 & op(e3, e2) = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1892) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1893) all_58_1 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (243), (399), (1878), (1887),
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1893), (function-axioms) are inconsistent by
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #322.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1894) all_58_3 = e2 & op(e2, e2) = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1894) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1895) all_58_3 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1896) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1896) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1897) all_58_0 = e2 & op(e3, e3) = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1897) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1898) all_58_0 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1633), (1898) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1899) e2 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1899) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900) e2 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1895), (1900) imply:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1901) all_58_3 = e0
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1891) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1902) all_58_1 = e2 & op(e3, e2) = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1902) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1903) all_58_1 = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (243), (399), (1878), (1887),
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1903), (function-axioms) are inconsistent by
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #322.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1895), (1901) are inconsistent by sub-proof
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1377.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1904) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1904) gives:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1905) all_58_7 = e2 & op(e1, e2) = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1905) implies:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1906) op(e1, e2) = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (197), (282), (378), (399), (1653), (1872),
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1906), (function-axioms) are inconsistent by
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1172.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1907) all_58_13 = e2 & op(e0, e2) = e2
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1887), (1907) are inconsistent by sub-proof
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1177.
% 152.55/25.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908) all_58_2 = e2 & op(e2, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1908) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1909) op(e2, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (282), (373), (399), (1872), (1890),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1909), (function-axioms) are inconsistent by
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #321.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1910) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1910) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1911) all_58_6 = e2 & op(e1, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1911) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1912) all_58_6 = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1881), (1912) are inconsistent by sub-proof
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1376.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1913) all_58_12 = e2 & op(e0, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1623), (1864), (1913), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1914) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1914) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1915) all_58_7 = e2 & op(e1, e2) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1915) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916) op(e1, e2) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (282), (378), (399), (1872), (1890),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916), (function-axioms) are inconsistent by
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1173.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1917) all_58_13 = e2 & op(e0, e2) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1917) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1918) all_58_13 = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1887), (1918) are inconsistent by sub-proof
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #320.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | (1919) all_58_7 = e3 & op(e1, e2) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1919) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | (1920) all_58_7 = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1878), (1920) are inconsistent by sub-proof
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | #1477.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | (1921) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1921) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | (1922) all_58_8 = e3 & op(e1, e1) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1870), (1922), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1469.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | (1923) all_58_11 = e3 & op(e1, e0) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (227), (228), (397), (1651),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | (1848), (1849), (1923), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #316.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | (1924) all_58_13 = e0 & op(e0, e2) = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1924) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | (1925) op(e0, e2) = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (1861), (1925), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1532.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | (1926) all_30_2 = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (1926) imply:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | (1927) all_8_2 = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (1927) imply:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | (1928) all_56_13 = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1927) imply:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | (1929) ~ (all_52_6 = e0)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (1927) imply:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | (1930) ~ (all_52_9 = e0)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | (1931) ~ (all_56_13 = e0)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1928), (1931) imply:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | (1932) $false
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1932) is inconsistent.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | (1933) all_56_5 = e2 & op(e2, e0) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1933) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | (1934) op(e2, e0) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | (1935) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1935) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | (1936) all_58_6 = e0 & op(e1, e3) = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1936) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | (1937) all_58_6 = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | (1938) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1938) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | (1939) all_58_6 = e3 & op(e1, e3) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1939) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | (1940) all_58_6 = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1937), (1940) are inconsistent by sub-proof
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | #1321.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | (1941) all_58_7 = e3 & op(e1, e2) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1941) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | (1942) all_58_7 = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (1943) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (163), (249), (251),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (1633), (1651), (1930), (1943), (function-axioms)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #315.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (1944) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1944) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1945) all_58_8 = e0 & op(e1, e1) = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1945) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1946) all_58_8 = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (231),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (248), (250), (252), (398), (1623), (1633),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1864), (1937), (1942), (1946), (function-axioms)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #343.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1947) all_58_14 = e0 & op(e0, e1) = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1947) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1948) all_58_14 = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1949) op(e0, e1) = e0
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1950) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1950) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1951) all_58_0 = e2 & op(e3, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1633), (1951) are inconsistent by sub-proof
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1952) all_58_2 = e2 & op(e2, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1952) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1953) op(e2, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1954) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1954) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1955) all_58_12 = e2 & op(e0, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1955) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1956) all_58_12 = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (165), (248), (252),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1937), (1953), (1956), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1063.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1957) all_58_13 = e2 & op(e0, e2) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1957) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1958) all_58_13 = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1959) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1959) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1960) all_58_12 = e3 & op(e0, e3) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1960) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1961) all_58_12 = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (248), (1633), (1937), (1953),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1961), (function-axioms) are inconsistent by
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #733.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1962) all_58_13 = e3 & op(e0, e2) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1962) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1963) all_58_13 = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1958), (1963) imply:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1964) e3 = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1964) imply:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1965) $false
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1965) is inconsistent.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1966) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1966) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1967) all_58_14 = e3 & op(e0, e1) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1948), (1967) are inconsistent by sub-proof
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #314.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1968) all_58_15 = e3 & op(e0, e0) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1968) implies:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1969) op(e0, e0) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1624), (1865), (1969), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #313.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1970) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (155), (1848), (1849), (1949), (1970),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #312.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1971) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1971) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1972) all_58_6 = e2 & op(e1, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1937), (1972) are inconsistent by sub-proof
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #345.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1973) all_58_12 = e2 & op(e0, e3) = e2
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1623), (1864), (1973), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | (1974) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1974) gives:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | (1975) all_58_8 = e3 & op(e1, e1) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1870), (1975), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1469.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | (1976) all_58_11 = e3 & op(e1, e0) = e3
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (227), (228), (397), (1651),
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | (1848), (1849), (1976), (function-axioms) are
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #316.
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/25.99 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1977) all_58_7 = e0 & op(e1, e2) = e0
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (1929), (1977), (function-axioms) are
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1301.
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | (1978) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1978) gives:
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1979) all_58_8 = e0 & op(e1, e1) = e0
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1979) implies:
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1980) op(e1, e1) = e0
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e0,
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (39), (1980) gives:
% 152.55/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1981) all_6_2 = e0
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (162), (1934) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1982) all_52_13 = e2
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (1981) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1983) all_56_14 = e0
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (1982) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1984) ~ (all_52_9 = e2)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (1982) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1985) ~ (all_52_14 = e2)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1985) implies:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1986) ~ (all_52_14 = e2)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1640), (1982) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1987) ~ (e3 = e2)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (1981) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | (1988) ~ (all_52_14 = e0)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | (1989) ~ (all_56_14 = e0)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1983), (1989) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | (1990) $false
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1990) is inconsistent.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | (1991) all_56_8 = e1 & op(e1, e0) = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1991) implies:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | (1992) all_56_8 = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | (1993) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1993) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (1994) all_58_9 = e2 & op(e3, e0) = e2
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1651), (1994) are inconsistent by sub-proof
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | #1353.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (1995) all_58_10 = e2 & op(e2, e0) = e2
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1995) implies:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (1996) all_58_10 = e2
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1997) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1651), (1996), (1997) are inconsistent
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #329.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1998) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1998) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999) all_58_11 = e1 & op(e1, e0) = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1999) implies:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2000) all_58_11 = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2001) all_54_11 = e3
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1642), (2001) are inconsistent by
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1415.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2002) ~ (all_54_11 = e3)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2003) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2003) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2004) all_54_11 = e2
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1986), (2004) are inconsistent by
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1414.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2005) ~ (all_54_11 = e2)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2006) all_54_11 = e1 | all_54_11 = e0
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2006) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2007) all_54_11 = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (2007) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2008) all_52_14 = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2008) implies:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2009) all_52_14 = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2009) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2010) ~ (all_52_2 = e1)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (2009) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2011) ~ (all_52_6 = e1)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1642), (2009) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2012) ~ (e3 = e1)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1986), (2009) imply:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2013) ~ (e2 = e1)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2014) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2014) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2015) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (165), (167),
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (238), (239), (241), (399), (1637), (1638),
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1996), (2015), (function-axioms) are inconsistent
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #311.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2016) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2016) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2017) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2017) implies:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2018) op(e1, e3) = e1
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2010), (2018), (function-axioms) are
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1412.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2019) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1629), (1860), (2019) are inconsistent by
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #309.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2020) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2020) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2021) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (163), (1860), (1984), (2011), (2021),
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #308.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2022) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2022) gives:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2023) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2023) implies:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2024) op(e0, e2) = e0
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (1861), (2024), (function-axioms) are
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1532.
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2025) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2025) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2026) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2026) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2027) ~ (all_56_15 = e0)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1860), (2027) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2028) $false
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2028) is inconsistent.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2029) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2029) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2030) all_56_8 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1992), (2030) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2031) e1 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2031) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2032) e1 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2000), (2032) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2033) all_58_11 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (227), (228),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (1651), (1848), (1849), (2033),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #305.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2034) all_54_11 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1988), (2034) are inconsistent by
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1394.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2035) all_58_15 = e1 & op(e0, e0) = e1
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (397), (2035), (function-axioms) are
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1418.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | (2036) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2036) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (2037) all_58_11 = e2 & op(e1, e0) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2037) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (2038) op(e1, e0) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1986), (2038), (function-axioms) are
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1389.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (2039) all_58_15 = e2 & op(e0, e0) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2039) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (2040) op(e0, e0) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1848), (1849), (2040), (function-axioms) are
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #317.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | (2041) all_58_11 = e0 & op(e1, e0) = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2041) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | (2042) all_58_11 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (227), (228),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | (397), (1651), (1848), (1849), (2042),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | #305.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | (2043) all_28_2 = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (2043) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | (2044) all_6_2 = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | SIMP: (2044) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | (2045) all_6_2 = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (2045) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | (2046) all_56_14 = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | REDUCE: (385), (2045) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | (2047) ~ (all_52_6 = e3)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | REDUCE: (388), (2045) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | (2048) ~ (all_52_9 = e3)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | REDUCE: (39), (2045) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | (2049) op(e1, e1) = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | (2050) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (168), (1637), (1653), (2050),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | #1436.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | (2051) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2051) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | (2052) all_58_7 = e3 & op(e1, e2) = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2047), (2052), (function-axioms) are
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1184.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | (2053) all_58_13 = e3 & op(e0, e2) = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2053) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | (2054) all_58_13 = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | (2055) ~ (all_56_14 = e3)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2046), (2055) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | (2056) $false
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2056) is inconsistent.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | (2057) all_56_6 = e1 & op(e1, e3) = e1
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2057) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | (2058) op(e1, e3) = e1
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | (2059) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2059) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | (2060) all_58_2 = e3 & op(e2, e3) = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2060) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | (2061) op(e2, e3) = e3
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | (2062) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2062) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (2063) all_58_12 = e2 & op(e0, e3) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1623), (1864), (2063), (function-axioms) are
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (2064) all_58_13 = e2 & op(e0, e2) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2054), (2064) are inconsistent by sub-proof
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | #1177.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | (2065) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2065) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (2066) all_58_14 = e2 & op(e0, e1) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2066) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (2067) op(e0, e1) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2068) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2068) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2069) all_58_6 = e0 & op(e1, e3) = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2069) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2070) all_58_6 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (165), (250), (1623), (1633), (1864),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061), (2070), (function-axioms) are inconsistent
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #303.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2071) all_58_7 = e0 & op(e1, e2) = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2071) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2072) all_58_7 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2073) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (165), (1633), (2061), (2073),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #304.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2074) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2074) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2075) all_58_6 = e2 & op(e1, e3) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2075) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2076) all_58_6 = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2077) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2077) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2078) all_58_4 = e0 & op(e3, e1) = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2078) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2079) all_58_4 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2080) op(e3, e1) = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2081) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2081) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082) all_58_0 = e2 & op(e3, e3) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2082) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2083) all_58_0 = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1633), (2083) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2084) e2 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (165), (250), (1623), (1633), (1864),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061), (2076), (2084), (function-axioms) are
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #302.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2085) all_58_1 = e2 & op(e3, e2) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (249), (1633), (1651), (2080),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2085), (function-axioms) are inconsistent by
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #349.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2086) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2086) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2087) all_58_4 = e2 & op(e3, e1) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2087) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2088) all_58_4 = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2079), (2088) imply:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2089) e2 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (165), (250), (1623), (1633), (1864),
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061), (2076), (2089), (function-axioms) are
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #302.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2090) all_58_9 = e2 & op(e3, e0) = e2
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1651), (2090) are inconsistent by sub-proof
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1353.
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2091) all_58_5 = e0 & op(e2, e1) = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2091) implies:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2092) all_58_5 = e0
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2093) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 152.97/26.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2093) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2094) all_58_12 = e1 & op(e0, e3) = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2094) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2095) all_58_12 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2096) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (399), (2061), (2096),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1122.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2097) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2097) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2098) all_58_5 = e1 & op(e2, e1) = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2092), (2098) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1121.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2099) all_58_10 = e1 & op(e2, e0) = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2099) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2100) all_58_10 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2101) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (1651), (2100), (2101) are inconsistent
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #301.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2102) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2102) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2103) all_58_11 = e2 & op(e1, e0) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2103) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2104) all_58_11 = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2105) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (161), (2047), (2058), (2105),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #300.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2106) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2106) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2107) all_58_8 = e3 & op(e1, e1) = e3
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2107) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2108) all_58_8 = e3
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2109) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2109) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2110) all_58_1 = e1 & op(e3, e2) = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2110) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2111) all_58_1 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2112) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2112) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2113) all_58_0 = e2 & op(e3, e3) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2113) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2114) all_58_0 = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1633), (2114) imply:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2115) e2 = e0
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (165), (250), (1623), (1633), (1864),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061), (2076), (2115), (function-axioms) are
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #302.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116) all_58_1 = e2 & op(e3, e2) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2111), (2116) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1213.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2117) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2117) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118) all_58_4 = e2 & op(e3, e1) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2118) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2119) op(e3, e1) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (155), (160), (223),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (233), (235), (1651), (2047),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2067), (2092), (2100), (2104), (2108), (2119),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #298.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2120) all_58_9 = e2 & op(e3, e0) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (230), (231),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (1651), (2047), (2104), (2108), (2120),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #500.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2121) all_58_3 = e1 & op(e2, e2) = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (399), (2121), (function-axioms) are
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2122) gives:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2123) all_58_7 = e1 & op(e1, e2) = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2123) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2124) all_58_7 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2072), (2124) imply:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2125) e1 = e0
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2125) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2126) e1 = e0
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2095), (2126) imply:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2127) all_58_12 = e0
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (42), (155), (168), (224),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245), (397), (1637), (1653), (2067), (2124),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2127), (function-axioms) are inconsistent by
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1416.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2128) all_58_13 = e1 & op(e0, e2) = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2128) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2129) all_58_13 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2054), (2129) imply:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) e3 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (229),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (233), (1651), (2047), (2100),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2104), (2108), (2130), (function-axioms) are
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #297.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2131) all_58_11 = e3 & op(e1, e0) = e3
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (227), (228), (397), (1651),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1848), (1849), (2131), (function-axioms) are
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #316.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2132) all_58_15 = e2 & op(e0, e0) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2132) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2133) op(e0, e0) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1848), (1849), (2133), (function-axioms) are
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #317.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2134) all_58_13 = e1 & op(e0, e2) = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2134) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2135) all_58_13 = e1
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2054), (2135) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1264.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2136) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (155), (397), (2067), (2136),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1417.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2137) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (155), (2049), (2067), (2137),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #954.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2138) all_58_12 = e2 & op(e0, e3) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1623), (1864), (2138), (function-axioms) are
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2139) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (227), (228),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (1651), (1848), (1849), (2049), (2139),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | #296.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (2140) all_58_15 = e2 & op(e0, e0) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2140) implies:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (2141) op(e0, e0) = e2
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1848), (1849), (2141), (function-axioms) are
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #317.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | (2142) all_58_3 = e3 & op(e2, e2) = e3
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (1653), (2142), (function-axioms) are
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1437.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | (2143) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (163), (227), (228), (397),
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | (1651), (1655), (2048), (2143), (function-axioms)
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #295.
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | End of split
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | (2144) all_20_2 = e2
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | COMBINE_EQS: (348), (2144) imply:
% 152.97/26.02 | | | | | | | | | | | | | (2145) all_4_2 = e2
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | COMBINE_EQS: (261), (2145) imply:
% 152.97/26.02 | | | | | | | | | | | | | (2146) all_56_15 = e2
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | REDUCE: (393), (2145) imply:
% 152.97/26.02 | | | | | | | | | | | | | (2147) ~ (all_52_11 = e2)
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | REDUCE: (395), (2145) imply:
% 152.97/26.02 | | | | | | | | | | | | | (2148) ~ (all_52_13 = e2)
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | REDUCE: (396), (2145) imply:
% 152.97/26.02 | | | | | | | | | | | | | (2149) ~ (all_52_14 = e2)
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | REDUCE: (1645), (2145) imply:
% 152.97/26.02 | | | | | | | | | | | | | (2150) op(e2, e3) = all_10_0
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | REDUCE: (36), (2145) imply:
% 152.97/26.02 | | | | | | | | | | | | | (2151) op(e0, e0) = e2
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | BETA: splitting (67) gives:
% 152.97/26.02 | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | (2152) ~ (all_24_2 = e0)
% 152.97/26.02 | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | REDUCE: (1616), (2152) imply:
% 152.97/26.02 | | | | | | | | | | | | | | (2153) $false
% 152.97/26.02 | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | CLOSE: (2153) is inconsistent.
% 152.97/26.02 | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | Case 2:
% 152.97/26.02 | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | (2154) ( ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0
% 152.97/26.02 | | | | | | | | | | | | | | & op(e0, e0) = all_24_1 & $i(all_24_0) &
% 152.97/26.02 | | | | | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e2) & op(e0, e0)
% 152.97/26.02 | | | | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 152.97/26.02 | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 152.97/26.02 | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | Case 1:
% 152.97/26.02 | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | (2155) ~ (all_56_15 = e2)
% 152.97/26.02 | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | REDUCE: (2146), (2155) imply:
% 152.97/26.02 | | | | | | | | | | | | | | | (2156) $false
% 152.97/26.02 | | | | | | | | | | | | | | |
% 152.97/26.02 | | | | | | | | | | | | | | | CLOSE: (2156) is inconsistent.
% 152.97/26.02 | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | (2157) all_56_10 = e0 & op(e0, e2) = e0
% 152.97/26.03 | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | ALPHA: (2157) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | (2158) op(e0, e2) = e0
% 152.97/26.03 | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | BETA: splitting (2154) gives:
% 152.97/26.03 | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | (2159) ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 &
% 152.97/26.03 | | | | | | | | | | | | | | | | op(e0, e0) = all_24_1 & $i(all_24_0) &
% 152.97/26.03 | | | | | | | | | | | | | | | | $i(all_24_1)
% 152.97/26.03 | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | ALPHA: (2159) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | (2160) ~ (all_24_0 = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | (2161) op(e0, e0) = all_24_1
% 152.97/26.03 | | | | | | | | | | | | | | | | (2162) op(all_24_1, e3) = all_24_0
% 152.97/26.03 | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | (2163) ~ (all_56_13 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | REDUCE: (360), (2163) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | (2164) ~ (all_8_2 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | (2165) all_54_5 = e3
% 152.97/26.03 | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (1653), (2165) are inconsistent by
% 152.97/26.03 | | | | | | | | | | | | | | | | | | sub-proof #1161.
% 152.97/26.03 | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | (2166) ~ (all_54_5 = e3)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | (2167) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 152.97/26.03 | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | BETA: splitting (2167) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2168) all_54_5 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (2168) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2169) all_8_2 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | SIMP: (2169) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2170) all_8_2 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (2170) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2171) all_56_13 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | REDUCE: (373), (2170) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2172) ~ (all_52_1 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | REDUCE: (376), (2170) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2173) ~ (all_52_4 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | REDUCE: (378), (2170) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2174) ~ (all_52_6 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | REDUCE: (380), (2170) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2175) ~ (all_52_7 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | REDUCE: (382), (2170) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2176) ~ (all_52_9 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | REDUCE: (1653), (2170) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | (2177) ~ (e3 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | (2178) all_54_1 = e3
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (1637), (2178) are inconsistent by
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | sub-proof #1305.
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | (2179) ~ (all_54_1 = e3)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | (2180) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | (2181) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2181) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | (2182) all_58_2 = e2 & op(e2, e3) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2182) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | (2183) op(e2, e3) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2172), (2183), (function-axioms) are
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1544.
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | (2184) all_58_3 = e2 & op(e2, e2) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2184) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | (2185) all_58_3 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | (2186) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (162), (1651), (2148), (2186),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | #294.
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | (2187) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2187) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (2188) all_58_11 = e2 & op(e1, e0) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2188) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (2189) op(e1, e0) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2149), (2189), (function-axioms) are
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1389.
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (2190) all_58_15 = e2 & op(e0, e0) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2190) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | (2191) all_58_15 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | (2192) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2192) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (2193) all_58_4 = e2 & op(e3, e1) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2193) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (2194) all_58_4 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (2195) op(e3, e1) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2196) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2196) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2197) all_58_6 = e2 & op(e1, e3) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2197) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2198) all_58_6 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2199) op(e1, e3) = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2180) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2200) all_54_1 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (2173), (2200) are inconsistent by
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1304.
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2201) ~ (all_54_1 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2202) all_54_1 = e1 | all_54_1 = e0
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2202) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2203) all_54_1 = e1
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (2203) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2204) all_52_4 = e1
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2204) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2205) all_52_4 = e1
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (2205) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2206) ~ (all_52_6 = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2206) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2207) ~ (all_52_6 = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (2205) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2208) ~ (all_52_7 = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2208) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2209) ~ (all_52_7 = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1637), (2205) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2210) ~ (e3 = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2173), (2205) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2211) ~ (e2 = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2212) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2212) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2213) all_58_0 = e1 & op(e3, e3) = e1
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1633), (2213) are inconsistent by sub-proof
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1495.
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2214) all_58_1 = e1 & op(e3, e2) = e1
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2214) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2215) all_58_1 = e1
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_24_1,
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (2151), (2161) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2216) all_24_1 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (156), (2158) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217) all_52_7 = e0
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (161), (2199) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2218) all_52_2 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_0, e3, e2, simplifying with (165), (2150)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2219) all_52_1 = all_10_0
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (2219) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2220) all_54_4 = all_10_0
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2219) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221) ~ (all_52_3 = all_10_0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2221) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2222) ~ (all_52_3 = all_10_0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (2219) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2223) ~ (all_52_9 = all_10_0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2223) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224) ~ (all_52_9 = all_10_0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1618), (2219) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225) ~ (all_10_0 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2218) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2226) ~ (all_52_3 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2226) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2227) ~ (all_52_3 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (2218) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2228) ~ (all_52_6 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2218) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2229) ~ (all_6_2 = e2)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (2217) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2230) ~ (all_52_3 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (2217) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2231) ~ (all_52_6 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (2217) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2232) ~ (all_52_11 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2232) implies:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2233) ~ (all_52_11 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2175), (2217) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2234) ~ (e2 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2209), (2217) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2235) ~ (e1 = e0)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2162), (2216) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2236) op(e2, e3) = all_24_0
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2237) ~ (all_56_14 = e3)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (2237) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2238) ~ (all_6_2 = e3)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_0,
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_24_0, e3, e2, simplifying with (2150), (2236)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2239) all_24_0 = all_10_0
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2160), (2239) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2240) ~ (all_10_0 = e1)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2241) all_54_4 = e3
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2220), (2241) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2242) all_10_0 = e3
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2222), (2242) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2243) ~ (all_52_3 = e3)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2224), (2242) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244) ~ (all_52_9 = e3)
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2150), (2242) imply:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245) op(e2, e3) = e3
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (116),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (155), (156), (157), (160), (162), (163),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (188), (190), (192), (208), (213), (224),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (239), (241), (243), (248), (249),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (262), (264), (273), (304), (390), (398),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (1629), (1633), (1651), (1653), (2147),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148), (2151), (2158), (2171), (2173), (2174),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2185), (2194), (2195), (2198), (2207), (2215),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2227), (2230), (2233), (2238), (2243), (2244),
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245), (function-axioms) are inconsistent by
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #291.
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2246) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2246) gives:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2247) all_54_4 = e2
% 152.97/26.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2220), (2247) imply:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2248) all_10_0 = e2
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1623), (2248) imply:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2249) $false
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2249) is inconsistent.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2250) all_54_4 = e1 | all_54_4 = e0
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2250) gives:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2251) all_54_4 = e1
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2220), (2251) imply:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2252) all_10_0 = e1
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2240), (2252) imply:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2253) $false
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2253) is inconsistent.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2254) all_54_4 = e0
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2220), (2254) imply:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2255) all_10_0 = e0
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2225), (2255) imply:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2256) $false
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2256) is inconsistent.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2257) all_56_14 = e3
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (193), (201), (273), (274), (289), (385),
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619), (1637), (2173), (2174), (2231), (2257) are
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #290.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2258) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1651), (2195), (2258),
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #289.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2259) all_54_1 = e0
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (1619), (2259) are inconsistent by
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1115.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2260) all_58_7 = e2 & op(e1, e2) = e2
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2260) implies:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2261) op(e1, e2) = e2
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2174), (2261), (function-axioms) are
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1536.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2262) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (39), (223), (227),
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (1651), (2191), (2262), (function-axioms)
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #656.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (2263) all_58_5 = e2 & op(e2, e1) = e2
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2263) implies:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (2264) op(e2, e1) = e2
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2176), (2264), (function-axioms) are
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1441.
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.97/26.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | (2265) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2265) gives:
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (2266) all_58_8 = e2 & op(e1, e1) = e2
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (398), (2266), (function-axioms) are
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (2267) all_58_14 = e2 & op(e0, e1) = e2
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (2147), (2267), (function-axioms) are
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1175.
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | (2268) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (2148), (2176), (2268),
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | | #1240.
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.04 | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | (2269) all_54_5 = e1 | all_54_5 = e0
% 153.14/26.04 | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (399), (2164), (2269) are inconsistent by
% 153.14/26.04 | | | | | | | | | | | | | | | | | | | sub-proof #1239.
% 153.14/26.04 | | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.04 | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | (2270) all_56_5 = e2 & op(e2, e0) = e2
% 153.14/26.04 | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | ALPHA: (2270) implies:
% 153.14/26.04 | | | | | | | | | | | | | | | | | (2271) op(e2, e0) = e2
% 153.14/26.04 | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2148), (2271), (function-axioms) are
% 153.14/26.04 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1535.
% 153.14/26.04 | | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | Case 2:
% 153.14/26.04 | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | (2272) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 153.14/26.04 | | | | | | | | | | | | | | | | $i(all_24_1)
% 153.14/26.04 | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | ALPHA: (2272) implies:
% 153.14/26.04 | | | | | | | | | | | | | | | | (2273) ~ (all_24_1 = e2)
% 153.14/26.04 | | | | | | | | | | | | | | | | (2274) op(e0, e0) = all_24_1
% 153.14/26.04 | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | | REF_CLOSE: (2151), (2273), (2274), (function-axioms) are
% 153.14/26.04 | | | | | | | | | | | | | | | | inconsistent by sub-proof #317.
% 153.14/26.04 | | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | Case 2:
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | (2275) all_14_2 = e3
% 153.14/26.04 | | | | | | | | | | | | (2276) ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0
% 153.14/26.04 | | | | | | | | | | | | & op(e3, e3) = all_14_1 & $i(all_14_0) &
% 153.14/26.04 | | | | | | | | | | | | $i(all_14_1)) | ( ~ (all_14_1 = e0) & op(e3, e3)
% 153.14/26.04 | | | | | | | | | | | | = all_14_1 & $i(all_14_1))
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | COMBINE_EQS: (351), (2275) imply:
% 153.14/26.04 | | | | | | | | | | | | (2277) all_8_2 = e3
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | SIMP: (2277) implies:
% 153.14/26.04 | | | | | | | | | | | | (2278) all_8_2 = e3
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | COMBINE_EQS: (333), (2278) imply:
% 153.14/26.04 | | | | | | | | | | | | (2279) all_22_2 = e3
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | COMBINE_EQS: (360), (2278) imply:
% 153.14/26.04 | | | | | | | | | | | | (2280) all_56_13 = e3
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | REDUCE: (373), (2278) imply:
% 153.14/26.04 | | | | | | | | | | | | (2281) ~ (all_52_1 = e3)
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | REDUCE: (378), (2278) imply:
% 153.14/26.04 | | | | | | | | | | | | (2282) ~ (all_52_6 = e3)
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | REDUCE: (380), (2278) imply:
% 153.14/26.04 | | | | | | | | | | | | (2283) ~ (all_52_7 = e3)
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | REDUCE: (382), (2278) imply:
% 153.14/26.04 | | | | | | | | | | | | (2284) ~ (all_52_9 = e3)
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (39), (42), (45),
% 153.14/26.04 | | | | | | | | | | | | (61), (64), (73), (79), (108), (110), (111),
% 153.14/26.04 | | | | | | | | | | | | (115), (116), (118), (119), (121), (123), (124),
% 153.14/26.04 | | | | | | | | | | | | (126), (131), (132), (133), (134), (137), (138),
% 153.14/26.04 | | | | | | | | | | | | (139), (141), (142), (143), (144), (146), (147),
% 153.14/26.04 | | | | | | | | | | | | (155), (156), (157), (158), (160), (161), (162),
% 153.14/26.04 | | | | | | | | | | | | (163), (165), (166), (167), (168), (187), (188),
% 153.14/26.04 | | | | | | | | | | | | (189), (190), (191), (192), (193), (194), (195),
% 153.14/26.04 | | | | | | | | | | | | (196), (199), (200), (201), (202), (208), (209),
% 153.14/26.04 | | | | | | | | | | | | (211), (212), (213), (215), (218), (220), (223),
% 153.14/26.04 | | | | | | | | | | | | (224), (225), (226), (227), (228), (229), (230),
% 153.14/26.04 | | | | | | | | | | | | (231), (232), (233), (234), (235), (236), (237),
% 153.14/26.04 | | | | | | | | | | | | (238), (239), (240), (241), (242), (243), (244),
% 153.14/26.04 | | | | | | | | | | | | (245), (246), (247), (248), (249), (251), (252),
% 153.14/26.04 | | | | | | | | | | | | (253), (261), (262), (263), (264), (265), (273),
% 153.14/26.04 | | | | | | | | | | | | (274), (275), (276), (277), (287), (288), (289),
% 153.14/26.04 | | | | | | | | | | | | (297), (299), (304), (306), (339), (348), (355),
% 153.14/26.04 | | | | | | | | | | | | (362), (364), (366), (368), (370), (372), (374),
% 153.14/26.04 | | | | | | | | | | | | (375), (385), (386), (387), (388), (390), (392),
% 153.14/26.04 | | | | | | | | | | | | (393), (394), (395), (396), (397), (398), (399),
% 153.14/26.04 | | | | | | | | | | | | (1617), (1618), (1619), (1620), (1624), (1629),
% 153.14/26.04 | | | | | | | | | | | | (1633), (1634), (1637), (1638), (1640), (1644),
% 153.14/26.04 | | | | | | | | | | | | (1651), (2276), (2279), (2280), (2281), (2282),
% 153.14/26.04 | | | | | | | | | | | | (2283), (2284), (function-axioms) are inconsistent
% 153.14/26.04 | | | | | | | | | | | | by sub-proof #260.
% 153.14/26.04 | | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | | |
% 153.14/26.04 | | | | | | | | | End of split
% 153.14/26.04 | | | | | | | | |
% 153.14/26.04 | | | | | | | | Case 2:
% 153.14/26.04 | | | | | | | | |
% 153.14/26.04 | | | | | | | | | (2285) all_58_1 = e0 & op(e3, e2) = e0
% 153.14/26.04 | | | | | | | | |
% 153.14/26.04 | | | | | | | | | REF_CLOSE: (168), (1619), (2285), (function-axioms) are
% 153.14/26.04 | | | | | | | | | inconsistent by sub-proof #1221.
% 153.14/26.04 | | | | | | | | |
% 153.14/26.04 | | | | | | | | End of split
% 153.14/26.04 | | | | | | | |
% 153.14/26.04 | | | | | | | Case 2:
% 153.14/26.04 | | | | | | | |
% 153.14/26.04 | | | | | | | | (2286) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 153.14/26.04 | | | | | | | | op(e3, e0) = e0)
% 153.14/26.04 | | | | | | | |
% 153.14/26.04 | | | | | | | | REF_CLOSE: (7), (166), (167), (1620), (1630), (2286),
% 153.14/26.04 | | | | | | | | (function-axioms) are inconsistent by sub-proof #257.
% 153.14/26.04 | | | | | | | |
% 153.14/26.04 | | | | | | | End of split
% 153.14/26.04 | | | | | | |
% 153.14/26.04 | | | | | | End of split
% 153.14/26.04 | | | | | |
% 153.14/26.04 | | | | | Case 2:
% 153.14/26.04 | | | | | |
% 153.14/26.04 | | | | | | (2287) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1)
% 153.14/26.04 | | | | | |
% 153.14/26.04 | | | | | | ALPHA: (2287) implies:
% 153.14/26.04 | | | | | | (2288) ~ (all_10_1 = e1)
% 153.14/26.04 | | | | | | (2289) op(e0, e0) = all_10_1
% 153.14/26.04 | | | | | |
% 153.14/26.04 | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42), (45),
% 153.14/26.04 | | | | | | (52), (61), (64), (67), (73), (76), (79), (85), (108),
% 153.14/26.04 | | | | | | (110), (111), (115), (116), (118), (119), (121), (123),
% 153.14/26.04 | | | | | | (124), (126), (131), (132), (133), (134), (137), (138),
% 153.14/26.04 | | | | | | (139), (141), (142), (143), (144), (146), (147), (155),
% 153.14/26.04 | | | | | | (156), (157), (158), (160), (161), (162), (163), (165),
% 153.14/26.04 | | | | | | (166), (167), (168), (187), (188), (189), (190), (191),
% 153.14/26.04 | | | | | | (192), (193), (194), (195), (196), (197), (198), (199),
% 153.14/26.04 | | | | | | (200), (201), (202), (208), (209), (211), (212), (213),
% 153.14/26.04 | | | | | | (215), (216), (218), (219), (220), (223), (224), (225),
% 153.14/26.04 | | | | | | (226), (227), (228), (229), (230), (231), (232), (233),
% 153.14/26.04 | | | | | | (234), (235), (236), (237), (238), (239), (240), (241),
% 153.14/26.04 | | | | | | (242), (243), (244), (245), (246), (247), (248), (249),
% 153.14/26.04 | | | | | | (251), (252), (253), (261), (262), (263), (264), (265),
% 153.14/26.04 | | | | | | (273), (274), (275), (276), (277), (282), (286), (287),
% 153.14/26.04 | | | | | | (288), (289), (297), (299), (304), (306), (333), (335),
% 153.14/26.04 | | | | | | (339), (348), (351), (354), (355), (360), (362), (364),
% 153.14/26.04 | | | | | | (366), (368), (370), (372), (373), (374), (375), (376),
% 153.14/26.04 | | | | | | (378), (380), (382), (384), (385), (386), (387), (388),
% 153.14/26.04 | | | | | | (390), (392), (393), (394), (395), (396), (398), (399),
% 153.14/26.04 | | | | | | (1616), (1617), (1618), (1619), (1620), (1621), (2288),
% 153.14/26.04 | | | | | | (2289), (function-axioms) are inconsistent by sub-proof
% 153.14/26.04 | | | | | | #216.
% 153.14/26.04 | | | | | |
% 153.14/26.04 | | | | | End of split
% 153.14/26.04 | | | | |
% 153.14/26.04 | | | | End of split
% 153.14/26.04 | | | |
% 153.14/26.04 | | | Case 2:
% 153.14/26.04 | | | |
% 153.14/26.04 | | | | (2290) all_8_2 = e1
% 153.14/26.04 | | | | (2291) ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e1, e1) =
% 153.14/26.04 | | | | all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e3) &
% 153.14/26.04 | | | | op(e1, e1) = all_8_1 & $i(all_8_1))
% 153.14/26.04 | | | |
% 153.14/26.04 | | | | COMBINE_EQS: (318), (2290) imply:
% 153.14/26.05 | | | | (2292) all_48_2 = e1
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | COMBINE_EQS: (360), (2290) imply:
% 153.14/26.05 | | | | (2293) all_56_13 = e1
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | REDUCE: (373), (2290) imply:
% 153.14/26.05 | | | | (2294) ~ (all_52_1 = e1)
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | REDUCE: (376), (2290) imply:
% 153.14/26.05 | | | | (2295) ~ (all_52_4 = e1)
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | REDUCE: (378), (2290) imply:
% 153.14/26.05 | | | | (2296) ~ (all_52_6 = e1)
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | REDUCE: (380), (2290) imply:
% 153.14/26.05 | | | | (2297) ~ (all_52_7 = e1)
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | REDUCE: (382), (2290) imply:
% 153.14/26.05 | | | | (2298) ~ (all_52_9 = e1)
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | REDUCE: (384), (2290) imply:
% 153.14/26.05 | | | | (2299) ~ (all_52_13 = e1)
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | BETA: splitting (217) gives:
% 153.14/26.05 | | | |
% 153.14/26.05 | | | | Case 1:
% 153.14/26.05 | | | | |
% 153.14/26.05 | | | | | (2300) ~ (all_56_13 = e1)
% 153.14/26.05 | | | | |
% 153.14/26.05 | | | | | REDUCE: (2293), (2300) imply:
% 153.14/26.05 | | | | | (2301) $false
% 153.14/26.05 | | | | |
% 153.14/26.05 | | | | | CLOSE: (2301) is inconsistent.
% 153.14/26.05 | | | | |
% 153.14/26.05 | | | | Case 2:
% 153.14/26.05 | | | | |
% 153.14/26.05 | | | | | (2302) all_56_4 = e2 & op(e2, e1) = e2
% 153.14/26.05 | | | | |
% 153.14/26.05 | | | | | ALPHA: (2302) implies:
% 153.14/26.05 | | | | | (2303) op(e2, e1) = e2
% 153.14/26.05 | | | | |
% 153.14/26.05 | | | | | BETA: splitting (243) gives:
% 153.14/26.05 | | | | |
% 153.14/26.05 | | | | | Case 1:
% 153.14/26.05 | | | | | |
% 153.14/26.05 | | | | | | (2304) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 153.14/26.05 | | | | | | op(e2, e2) = e1)
% 153.14/26.05 | | | | | |
% 153.14/26.05 | | | | | | BETA: splitting (2304) gives:
% 153.14/26.05 | | | | | |
% 153.14/26.05 | | | | | | Case 1:
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | (2305) all_58_1 = e1 & op(e3, e2) = e1
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | REF_CLOSE: (168), (2295), (2305), (function-axioms) are
% 153.14/26.05 | | | | | | | inconsistent by sub-proof #1284.
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | Case 2:
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | (2306) all_58_3 = e1 & op(e2, e2) = e1
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | ALPHA: (2306) implies:
% 153.14/26.05 | | | | | | | (2307) all_58_3 = e1
% 153.14/26.05 | | | | | | | (2308) op(e2, e2) = e1
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 153.14/26.05 | | | | | | | e1, e2, simplifying with (163), (2303) gives:
% 153.14/26.05 | | | | | | | (2309) all_52_9 = e2
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | REDUCE: (144), (2309) imply:
% 153.14/26.05 | | | | | | | (2310) ~ (all_52_1 = e2)
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | REDUCE: (121), (2309) imply:
% 153.14/26.05 | | | | | | | (2311) ~ (all_52_8 = e2)
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | REDUCE: (116), (2309) imply:
% 153.14/26.05 | | | | | | | (2312) ~ (all_52_11 = e2)
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | SIMP: (2312) implies:
% 153.14/26.05 | | | | | | | (2313) ~ (all_52_11 = e2)
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | REDUCE: (115), (2309) imply:
% 153.14/26.05 | | | | | | | (2314) ~ (all_52_13 = e2)
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | SIMP: (2314) implies:
% 153.14/26.05 | | | | | | | (2315) ~ (all_52_13 = e2)
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | REDUCE: (388), (2309) imply:
% 153.14/26.05 | | | | | | | (2316) ~ (all_6_2 = e2)
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | BETA: splitting (240) gives:
% 153.14/26.05 | | | | | | |
% 153.14/26.05 | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | |
% 153.14/26.05 | | | | | | | | (2317) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 153.14/26.05 | | | | | | | | op(e2, e2) = e2)
% 153.14/26.05 | | | | | | | |
% 153.14/26.05 | | | | | | | | BETA: splitting (2317) gives:
% 153.14/26.05 | | | | | | | |
% 153.14/26.05 | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | (2318) all_58_2 = e2 & op(e2, e3) = e2
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | ALPHA: (2318) implies:
% 153.14/26.05 | | | | | | | | | (2319) op(e2, e3) = e2
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | REF_CLOSE: (165), (2310), (2319), (function-axioms) are
% 153.14/26.05 | | | | | | | | | inconsistent by sub-proof #1544.
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | Case 2:
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | (2320) all_58_3 = e2 & op(e2, e2) = e2
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | REF_CLOSE: (6), (2307), (2320) are inconsistent by sub-proof
% 153.14/26.05 | | | | | | | | | #215.
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | End of split
% 153.14/26.05 | | | | | | | |
% 153.14/26.05 | | | | | | | Case 2:
% 153.14/26.05 | | | | | | | |
% 153.14/26.05 | | | | | | | | (2321) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 153.14/26.05 | | | | | | | | op(e2, e0) = e2)
% 153.14/26.05 | | | | | | | |
% 153.14/26.05 | | | | | | | | BETA: splitting (2321) gives:
% 153.14/26.05 | | | | | | | |
% 153.14/26.05 | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | (2322) all_58_5 = e2 & op(e2, e1) = e2
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | ALPHA: (2322) implies:
% 153.14/26.05 | | | | | | | | | (2323) all_58_5 = e2
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | BETA: splitting (46) gives:
% 153.14/26.05 | | | | | | | | |
% 153.14/26.05 | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | (2324) ~ (all_10_2 = e0)
% 153.14/26.05 | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | BETA: splitting (55) gives:
% 153.14/26.05 | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | (2325) ~ (all_16_2 = e2)
% 153.14/26.05 | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | REDUCE: (349), (2325) imply:
% 153.14/26.05 | | | | | | | | | | | (2326) ~ (all_10_2 = e2)
% 153.14/26.05 | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | BETA: splitting (61) gives:
% 153.14/26.05 | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | (2327) ~ (all_20_2 = e2)
% 153.14/26.05 | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | REDUCE: (348), (2327) imply:
% 153.14/26.05 | | | | | | | | | | | | (2328) ~ (all_4_2 = e2)
% 153.14/26.05 | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | BETA: splitting (73) gives:
% 153.14/26.05 | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | (2329) ~ (all_28_2 = e3)
% 153.14/26.05 | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | REDUCE: (339), (2329) imply:
% 153.14/26.05 | | | | | | | | | | | | | (2330) ~ (all_6_2 = e3)
% 153.14/26.05 | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | BETA: splitting (2291) gives:
% 153.14/26.05 | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | (2331) ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 &
% 153.14/26.05 | | | | | | | | | | | | | | op(e1, e1) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 153.14/26.05 | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | ALPHA: (2331) implies:
% 153.14/26.05 | | | | | | | | | | | | | | (2332) op(e1, e1) = all_8_1
% 153.14/26.05 | | | | | | | | | | | | | | (2333) op(all_8_1, e2) = all_8_0
% 153.14/26.05 | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 153.14/26.05 | | | | | | | | | | | | | | all_8_1, e1, e1, simplifying with (39), (2332)
% 153.14/26.05 | | | | | | | | | | | | | | gives:
% 153.14/26.05 | | | | | | | | | | | | | | (2334) all_8_1 = all_6_2
% 153.14/26.05 | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | REDUCE: (2333), (2334) imply:
% 153.14/26.05 | | | | | | | | | | | | | | (2335) op(all_6_2, e2) = all_8_0
% 153.14/26.05 | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 153.14/26.05 | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | (2336) ~ (all_32_2 = e1)
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | REDUCE: (355), (2336) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2337) ~ (all_10_2 = e1)
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (39), (45), (111), (119),
% 153.14/26.05 | | | | | | | | | | | | | | | (123), (126), (155), (156), (160), (162), (165),
% 153.14/26.05 | | | | | | | | | | | | | | | (166), (167), (168), (187), (188), (189), (192),
% 153.14/26.05 | | | | | | | | | | | | | | | (195), (200), (202), (208), (211), (213), (224),
% 153.14/26.05 | | | | | | | | | | | | | | | (225), (227), (228), (232), (237), (241), (242),
% 153.14/26.05 | | | | | | | | | | | | | | | (245), (246), (248), (251), (252), (261), (262),
% 153.14/26.05 | | | | | | | | | | | | | | | (263), (273), (276), (288), (297), (299), (304),
% 153.14/26.05 | | | | | | | | | | | | | | | (306), (362), (368), (370), (386), (387), (390),
% 153.14/26.05 | | | | | | | | | | | | | | | (395), (397), (398), (2296), (2297), (2299),
% 153.14/26.05 | | | | | | | | | | | | | | | (2307), (2311), (2313), (2315), (2323), (2324),
% 153.14/26.05 | | | | | | | | | | | | | | | (2326), (2328), (2330), (2337), (function-axioms)
% 153.14/26.05 | | | | | | | | | | | | | | | are inconsistent by sub-proof #199.
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | Case 2:
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | (2338) all_32_2 = e1
% 153.14/26.05 | | | | | | | | | | | | | | | (2339) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0
% 153.14/26.05 | | | | | | | | | | | | | | | & op(e1, e1) = all_32_1 & $i(all_32_0) &
% 153.14/26.05 | | | | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 153.14/26.05 | | | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | COMBINE_EQS: (355), (2338) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2340) all_10_2 = e1
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | SIMP: (2340) implies:
% 153.14/26.05 | | | | | | | | | | | | | | | (2341) all_10_2 = e1
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (2341) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2342) all_50_2 = e1
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | COMBINE_EQS: (297), (2341) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2343) all_56_12 = e1
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | REDUCE: (364), (2341) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2344) ~ (all_52_2 = e1)
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | REDUCE: (370), (2341) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2345) ~ (all_52_8 = e1)
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | REDUCE: (372), (2341) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2346) ~ (all_52_12 = e1)
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | REDUCE: (2326), (2341) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2347) ~ (e2 = e1)
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | REDUCE: (45), (2341) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | (2348) op(e3, e3) = e1
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 153.14/26.05 | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | (2349) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 153.14/26.05 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 153.14/26.05 | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | BETA: splitting (2349) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | (2350) all_58_9 = e1 & op(e3, e0) = e1
% 153.14/26.05 | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | ALPHA: (2350) implies:
% 153.14/26.05 | | | | | | | | | | | | | | | | | (2351) all_58_9 = e1
% 153.14/26.05 | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | (2352) ~ (all_56_12 = e1)
% 153.14/26.05 | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | REDUCE: (2343), (2352) imply:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | (2353) $false
% 153.14/26.05 | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | CLOSE: (2353) is inconsistent.
% 153.14/26.05 | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.05 | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | (2354) all_56_1 = e3 & op(e3, e1) = e3
% 153.14/26.05 | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | ALPHA: (2354) implies:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | (2355) op(e3, e1) = e3
% 153.14/26.05 | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | (2356) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.14/26.05 | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (162), (2315), (2351), (2356),
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | #198.
% 153.14/26.05 | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | (2357) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.14/26.05 | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | BETA: splitting (2357) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | (2358) all_58_11 = e2 & op(e1, e0) = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | ALPHA: (2358) implies:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | (2359) all_58_11 = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | (2360) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2360) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | (2361) all_58_12 = e1 & op(e0, e3) = e1
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2361) implies:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | (2362) all_58_12 = e1
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | (2363) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2363) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | (2364) all_58_0 = e2 & op(e3, e3) = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2326), (2364), (function-axioms) are
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1523.
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | (2365) all_58_1 = e2 & op(e3, e2) = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2365) implies:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | (2366) op(e3, e2) = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | (2367) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (165), (2310), (2326), (2367),
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | #1522.
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | (2368) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2368) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (2369) all_58_6 = e2 & op(e1, e3) = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2369) implies:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (2370) all_58_6 = e2
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2371) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (2307), (2366), (2371),
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | #197.
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2372) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2372) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2373) all_58_7 = e3 & op(e1, e2) = e3
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2373) implies:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2374) all_58_7 = e3
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2375) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2375) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2376) all_58_6 = e0 & op(e1, e3) = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2370), (2376) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1483.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2377) all_58_7 = e0 & op(e1, e2) = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2377) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2378) all_58_7 = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2374), (2378) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1477.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2379) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2379) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2380) all_58_8 = e0 & op(e1, e1) = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2380) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2381) all_58_8 = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (108), (111), (123), (124), (126), (137),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (139), (143), (146), (155), (156), (157),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (160), (161), (162), (165), (166), (167),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (189), (190), (195), (198), (208), (209),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (220), (223), (224), (225), (228), (229),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (234), (237), (238), (241), (245),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (247), (248), (249), (250), (252), (253),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261), (263), (264), (273), (276), (286), (386),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392), (394), (395), (396), (397), (398), (2293),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2294), (2295), (2296), (2297), (2307), (2310),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313), (2315), (2323), (2326), (2328), (2330),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2335), (2339), (2342), (2343), (2344), (2345),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2346), (2348), (2381), (function-axioms) are
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #176.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2382) all_58_11 = e0 & op(e1, e0) = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2359), (2382) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1470.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2383) all_58_13 = e3 & op(e0, e2) = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2383) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2384) all_58_13 = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (155), (225),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (248), (252), (2313), (2328), (2370),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2384), (function-axioms) are inconsistent by
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1174.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2385) all_58_12 = e2 & op(e0, e3) = e2
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2362), (2385) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #1511.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | (2386) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (160),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | (161), (165), (167), (168), (231), (234), (237),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | (246), (247), (248), (249), (250), (252), (253),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | (2295), (2296), (2310), (2323), (2326), (2330),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | (2344), (2348), (2355), (2361), (2362), (2386),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | #175.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | (2387) all_58_13 = e1 & op(e0, e2) = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2297), (2387), (function-axioms) are
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | (2388) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2388) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | (2389) all_58_14 = e1 & op(e0, e1) = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2389) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | (2390) all_58_14 = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | (2391) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2391) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | (2392) all_58_4 = e3 & op(e3, e1) = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2392) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | (2393) all_58_4 = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | (2394) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2394) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2395) all_58_4 = e0 & op(e3, e1) = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2393), (2395) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #1344.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2396) all_58_5 = e0 & op(e2, e1) = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2323), (2396) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #919.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | (2397) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2397) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2398) all_58_8 = e0 & op(e1, e1) = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2398) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2399) all_58_8 = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (108), (111), (123), (124), (126), (137),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (139), (143), (146), (155), (156), (157),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (160), (161), (162), (165), (166), (167),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (189), (190), (195), (198), (208), (209),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (220), (223), (224), (225), (228), (229),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (234), (237), (238), (241), (245),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (247), (248), (249), (250), (252), (253),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (261), (263), (264), (273), (276), (286), (386),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (392), (394), (395), (396), (397), (398), (2293),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2294), (2295), (2296), (2297), (2307), (2310),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2313), (2315), (2323), (2326), (2328), (2330),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2335), (2339), (2342), (2343), (2344), (2345),
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2346), (2348), (2399), (function-axioms) are
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #176.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2400) all_58_14 = e0 & op(e0, e1) = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2400) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (2401) all_58_14 = e0
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2390), (2401) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #614.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | (2402) all_58_5 = e3 & op(e2, e1) = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2402) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | (2403) all_58_5 = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2323), (2403) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | #897.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | (2404) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2404) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | (2405) all_58_8 = e3 & op(e1, e1) = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (2330), (2405), (function-axioms) are
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1469.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | (2406) all_58_14 = e3 & op(e0, e1) = e3
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2390), (2406) are inconsistent by sub-proof
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | | #872.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | (2407) all_58_15 = e1 & op(e0, e0) = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (397), (2407), (function-axioms) are
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1418.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | (2408) all_58_15 = e2 & op(e0, e0) = e2
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (2328), (2408), (function-axioms) are
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1452.
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2409) all_58_10 = e1 & op(e2, e0) = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2299), (2409), (function-axioms) are
% 153.14/26.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212.
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | (2410) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 153.14/26.06 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.14/26.06 | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | BETA: splitting (2410) gives:
% 153.14/26.06 | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2411) all_58_11 = e1 & op(e1, e0) = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | ALPHA: (2411) implies:
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2412) all_58_11 = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2413) op(e1, e0) = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (104), (108), (111), (123), (124), (126), (137),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (138), (139), (143), (146), (155), (156), (157),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (158), (160), (161), (162), (165), (166), (167),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (168), (189), (190), (195), (198), (208), (209),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (213), (220), (223), (224), (225), (228), (229),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (231), (232), (234), (237), (238), (241), (245),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (246), (247), (248), (249), (250), (252), (253),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (261), (263), (264), (273), (276), (286), (386),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (392), (394), (395), (396), (397), (398), (2293),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2294), (2295), (2296), (2297), (2307), (2310),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2313), (2315), (2323), (2326), (2328), (2330),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2335), (2339), (2342), (2343), (2344), (2345),
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2346), (2348), (2412), (2413), (function-axioms)
% 153.14/26.06 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #177.
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | (2414) all_58_15 = e1 & op(e0, e0) = e1
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (397), (2414), (function-axioms) are
% 153.14/26.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1418.
% 153.14/26.06 | | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | End of split
% 153.14/26.06 | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | (2415) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 153.14/26.06 | | | | | | | | | | | | | | $i(all_8_1)
% 153.14/26.06 | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | ALPHA: (2415) implies:
% 153.14/26.06 | | | | | | | | | | | | | | (2416) ~ (all_8_1 = e3)
% 153.14/26.06 | | | | | | | | | | | | | | (2417) op(e1, e1) = all_8_1
% 153.14/26.06 | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 153.14/26.06 | | | | | | | | | | | | | | all_8_1, e1, e1, simplifying with (39), (2417)
% 153.14/26.06 | | | | | | | | | | | | | | gives:
% 153.14/26.06 | | | | | | | | | | | | | | (2418) all_8_1 = all_6_2
% 153.14/26.06 | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 153.14/26.06 | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | Case 1:
% 153.14/26.06 | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | (2419) ~ (all_32_2 = e1)
% 153.14/26.06 | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | REDUCE: (355), (2419) imply:
% 153.14/26.06 | | | | | | | | | | | | | | | (2420) ~ (all_10_2 = e1)
% 153.14/26.06 | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (39), (45), (111), (119),
% 153.14/26.06 | | | | | | | | | | | | | | | (123), (126), (155), (156), (160), (162), (165),
% 153.14/26.06 | | | | | | | | | | | | | | | (166), (167), (168), (187), (188), (189), (192),
% 153.14/26.06 | | | | | | | | | | | | | | | (195), (200), (202), (208), (211), (213), (224),
% 153.14/26.06 | | | | | | | | | | | | | | | (225), (227), (228), (232), (237), (241), (242),
% 153.14/26.06 | | | | | | | | | | | | | | | (245), (246), (248), (251), (252), (261), (262),
% 153.14/26.06 | | | | | | | | | | | | | | | (263), (273), (276), (288), (297), (299), (304),
% 153.14/26.06 | | | | | | | | | | | | | | | (306), (362), (368), (370), (386), (387), (390),
% 153.14/26.06 | | | | | | | | | | | | | | | (395), (397), (398), (2296), (2297), (2299),
% 153.14/26.06 | | | | | | | | | | | | | | | (2307), (2311), (2313), (2315), (2323), (2324),
% 153.14/26.06 | | | | | | | | | | | | | | | (2326), (2328), (2330), (2420), (function-axioms)
% 153.14/26.06 | | | | | | | | | | | | | | | are inconsistent by sub-proof #199.
% 153.14/26.06 | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | Case 2:
% 153.14/26.06 | | | | | | | | | | | | | | |
% 153.14/26.06 | | | | | | | | | | | | | | | (2421) all_32_2 = e1
% 153.14/26.07 | | | | | | | | | | | | | | | (2422) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0
% 153.14/26.07 | | | | | | | | | | | | | | | & op(e1, e1) = all_32_1 & $i(all_32_0) &
% 153.14/26.07 | | | | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 153.14/26.07 | | | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | COMBINE_EQS: (355), (2421) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2423) all_10_2 = e1
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | SIMP: (2423) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | (2424) all_10_2 = e1
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (2424) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2425) all_50_2 = e1
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | COMBINE_EQS: (297), (2424) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2426) all_56_12 = e1
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | REDUCE: (364), (2424) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2427) ~ (all_52_2 = e1)
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | REDUCE: (370), (2424) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2428) ~ (all_52_8 = e1)
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | REDUCE: (372), (2424) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2429) ~ (all_52_12 = e1)
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | REDUCE: (2326), (2424) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2430) ~ (e2 = e1)
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | REDUCE: (45), (2424) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2431) op(e3, e3) = e1
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | BETA: splitting (2422) gives:
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | (2432) ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 153.14/26.07 | | | | | | | | | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) &
% 153.14/26.07 | | | | | | | | | | | | | | | | $i(all_32_1)
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | ALPHA: (2432) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2433) op(e1, e1) = all_32_1
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 153.14/26.07 | | | | | | | | | | | | | | | | (104), (108), (111), (123), (124), (126), (137),
% 153.14/26.07 | | | | | | | | | | | | | | | | (138), (139), (143), (146), (155), (156), (157),
% 153.14/26.07 | | | | | | | | | | | | | | | | (158), (160), (161), (162), (165), (166), (167),
% 153.14/26.07 | | | | | | | | | | | | | | | | (168), (189), (190), (195), (198), (208), (209),
% 153.14/26.07 | | | | | | | | | | | | | | | | (213), (220), (223), (224), (225), (227), (228),
% 153.14/26.07 | | | | | | | | | | | | | | | | (229), (231), (232), (233), (234), (237), (241),
% 153.14/26.07 | | | | | | | | | | | | | | | | (242), (245), (246), (247), (248), (249), (250),
% 153.14/26.07 | | | | | | | | | | | | | | | | (251), (252), (253), (261), (263), (264), (273),
% 153.14/26.07 | | | | | | | | | | | | | | | | (276), (286), (386), (392), (394), (395), (396),
% 153.14/26.07 | | | | | | | | | | | | | | | | (397), (398), (2293), (2294), (2295), (2296),
% 153.14/26.07 | | | | | | | | | | | | | | | | (2297), (2299), (2307), (2310), (2311), (2313),
% 153.14/26.07 | | | | | | | | | | | | | | | | (2315), (2323), (2326), (2328), (2330), (2425),
% 153.14/26.07 | | | | | | | | | | | | | | | | (2426), (2427), (2428), (2429), (2431), (2433),
% 153.14/26.07 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.07 | | | | | | | | | | | | | | | | #169.
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | (2434) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 153.14/26.07 | | | | | | | | | | | | | | | | $i(all_32_1)
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | ALPHA: (2434) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2435) op(e1, e1) = all_32_1
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 153.14/26.07 | | | | | | | | | | | | | | | | (104), (108), (111), (123), (124), (126), (137),
% 153.14/26.07 | | | | | | | | | | | | | | | | (138), (139), (143), (146), (155), (156), (157),
% 153.14/26.07 | | | | | | | | | | | | | | | | (158), (160), (161), (162), (165), (166), (167),
% 153.14/26.07 | | | | | | | | | | | | | | | | (168), (189), (190), (195), (198), (208), (209),
% 153.14/26.07 | | | | | | | | | | | | | | | | (213), (220), (223), (224), (225), (227), (228),
% 153.14/26.07 | | | | | | | | | | | | | | | | (229), (231), (232), (233), (234), (237), (241),
% 153.14/26.07 | | | | | | | | | | | | | | | | (242), (245), (246), (247), (248), (249), (250),
% 153.14/26.07 | | | | | | | | | | | | | | | | (251), (252), (253), (261), (263), (264), (273),
% 153.14/26.07 | | | | | | | | | | | | | | | | (276), (286), (386), (392), (394), (395), (396),
% 153.14/26.07 | | | | | | | | | | | | | | | | (397), (398), (2293), (2294), (2295), (2296),
% 153.14/26.07 | | | | | | | | | | | | | | | | (2297), (2299), (2307), (2310), (2311), (2313),
% 153.14/26.07 | | | | | | | | | | | | | | | | (2315), (2323), (2326), (2328), (2330), (2425),
% 153.14/26.07 | | | | | | | | | | | | | | | | (2426), (2427), (2428), (2429), (2431), (2435),
% 153.14/26.07 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.07 | | | | | | | | | | | | | | | | #169.
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | End of split
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | End of split
% 153.14/26.07 | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | End of split
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | (2436) all_28_2 = e3
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | COMBINE_EQS: (339), (2436) imply:
% 153.14/26.07 | | | | | | | | | | | | | (2437) all_6_2 = e3
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | COMBINE_EQS: (273), (2437) imply:
% 153.14/26.07 | | | | | | | | | | | | | (2438) all_56_14 = e3
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | REDUCE: (385), (2437) imply:
% 153.14/26.07 | | | | | | | | | | | | | (2439) ~ (all_52_6 = e3)
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | REDUCE: (387), (2437) imply:
% 153.14/26.07 | | | | | | | | | | | | | (2440) ~ (all_52_8 = e3)
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | REDUCE: (390), (2437) imply:
% 153.14/26.07 | | | | | | | | | | | | | (2441) ~ (all_52_11 = e3)
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | REDUCE: (39), (2437) imply:
% 153.14/26.07 | | | | | | | | | | | | | (2442) op(e1, e1) = e3
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | BETA: splitting (220) gives:
% 153.14/26.07 | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | (2443) ~ (all_56_12 = e1)
% 153.14/26.07 | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | REDUCE: (297), (2443) imply:
% 153.14/26.07 | | | | | | | | | | | | | | (2444) ~ (all_10_2 = e1)
% 153.14/26.07 | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 153.14/26.07 | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | (2445) ~ (all_56_14 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | REDUCE: (2438), (2445) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | (2446) $false
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | CLOSE: (2446) is inconsistent.
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | (2447) all_56_6 = e1 & op(e1, e3) = e1
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | ALPHA: (2447) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | (2448) op(e1, e3) = e1
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 153.14/26.07 | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | (2449) all_54_0 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (2449) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2450) all_10_2 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | SIMP: (2450) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2451) all_10_2 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (2451) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2452) all_56_12 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | REDUCE: (362), (2451) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2453) ~ (all_52_1 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | REDUCE: (364), (2451) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2454) ~ (all_52_2 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | REDUCE: (366), (2451) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2455) ~ (all_52_3 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | REDUCE: (368), (2451) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2456) ~ (all_52_4 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | REDUCE: (372), (2451) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | (2457) ~ (all_52_12 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | (2458) all_54_4 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (2453), (2458) are inconsistent by
% 153.14/26.07 | | | | | | | | | | | | | | | | | sub-proof #1434.
% 153.14/26.07 | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | (2459) ~ (all_54_4 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | | | (2460) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | (2461) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (2307), (2456), (2461),
% 153.14/26.07 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.07 | | | | | | | | | | | | | | | | | | #214.
% 153.14/26.07 | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | (2462) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 153.14/26.07 | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | BETA: splitting (2462) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | (2463) all_58_7 = e3 & op(e1, e2) = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2439), (2463), (function-axioms) are
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1184.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | (2464) all_58_13 = e3 & op(e0, e2) = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | ALPHA: (2464) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | (2465) all_58_13 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | (2466) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2466) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | (2467) all_58_12 = e2 & op(e0, e3) = e2
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2467) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | (2468) all_58_12 = e2
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | (2469) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2469) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | (2470) all_58_12 = e1 & op(e0, e3) = e1
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2468), (2470) are inconsistent by sub-proof
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | #1492.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | (2471) all_58_13 = e1 & op(e0, e2) = e1
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2471) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | (2472) all_58_13 = e1
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2465), (2472) are inconsistent by sub-proof
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | #1264.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | (2473) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2473) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | (2474) all_58_14 = e1 & op(e0, e1) = e1
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2474) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | (2475) all_58_14 = e1
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | (2476) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (2307), (2453), (2476),
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | #213.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | (2477) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2477) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2478) all_58_5 = e3 & op(e2, e1) = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2478) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2479) all_58_5 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2323), (2479) are inconsistent by sub-proof
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | #897.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2480) all_58_10 = e3 & op(e2, e0) = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2480) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2481) op(e2, e0) = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (2482) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2482) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2483) all_58_4 = e0 & op(e3, e1) = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2483) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2484) op(e3, e1) = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2460) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2485) all_54_4 = e2
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (2310), (2485) are inconsistent by
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1431.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2486) all_54_4 = e1 | all_54_4 = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2486) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2487) all_54_4 = e1
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (2294), (2487) are inconsistent by
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1142.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2488) all_54_4 = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (2488) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2489) all_52_1 = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2489) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2490) all_52_1 = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (2490) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2491) ~ (all_52_2 = e0)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2491) implies:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2492) ~ (all_52_2 = e0)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (2490) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2493) op(e2, e3) = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2494) ~ (all_56_15 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (261), (2494) imply:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2495) ~ (all_4_2 = e3)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2496) all_54_15 = e3
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (2495), (2496) are inconsistent by
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1543.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2497) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2497) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2498) all_54_15 = e2
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (2328), (2498) are inconsistent by
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1542.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2499) ~ (all_54_15 = e2)
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500) all_54_15 = e1 | all_54_15 = e0
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2500) gives:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2501) all_54_15 = e1
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (397), (2501) are inconsistent by sub-proof
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1541.
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2502) all_54_15 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (2502) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2503) all_4_2 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2503) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2504) all_4_2 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (2504) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2505) all_56_15 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (2504) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2506) ~ (all_52_3 = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (2504) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2507) ~ (all_52_7 = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (2504) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2508) ~ (all_52_11 = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2328), (2504) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2509) ~ (e2 = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (2504) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2510) ~ (e1 = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2511) all_54_14 = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (2511) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2512) all_52_11 = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2441), (2512) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2513) $false
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2513) is inconsistent.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2514) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2515) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2515) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2516) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2516) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2517) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2517) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2518) op(e2, e3) = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2453), (2518), (function-axioms) are
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1183.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2519) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2519) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2520) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2520) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2521) op(e2, e3) = e2
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2493), (2521), (function-axioms) are
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1156.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2522) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2522) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2523) op(e1, e3) = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (2448), (2523), (function-axioms) are
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1164.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2524) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2524) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2525) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2525) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526) op(e3, e1) = e1
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2484), (2526), (function-axioms) are
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1281.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2452), (2457), (2527), (function-axioms)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #168.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2528) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2528) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2529) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2529) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2530) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2530) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2531) op(e1, e2) = e2
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2514) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2532) all_54_14 = e2
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (2313), (2532) are inconsistent by
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1232.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2533) all_54_14 = e1 | all_54_14 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2533) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2534) all_54_14 = e1
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (2534) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2535) all_52_11 = e1
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2535) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2536) all_52_11 = e1
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (2536) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2537) ~ (all_52_8 = e1)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2538) all_54_2 = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (2440), (2538) are inconsistent by
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1210.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2539) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2539) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540) all_54_2 = e2
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (2311), (2540) are inconsistent by
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1209.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2541) all_54_2 = e1 | all_54_2 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2541) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542) all_54_2 = e1
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (2542) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2543) all_52_8 = e1
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2543) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2544) all_52_8 = e1
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2537), (2544) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2545) $false
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2545) is inconsistent.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2546) all_54_2 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (2546) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2547) all_52_8 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2547) implies:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2548) all_52_8 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (2548) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2549) ~ (all_52_4 = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550) all_54_1 = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (2550) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2551) all_52_4 = e3
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2456), (2551) imply:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2552) $false
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2552) is inconsistent.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2553) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (160), (289), (2295), (2531), (2549),
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2553), (function-axioms) are inconsistent by
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #167.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2554) all_54_14 = e0
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (2508), (2554) are inconsistent by
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1400.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2555) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (162), (2296), (2315), (2555),
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1129.
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2556) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2556) gives:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2557) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2557) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2558) op(e0, e2) = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2507), (2558), (function-axioms) are
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1532.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2559) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2559) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2560) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2560) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2561) ~ (all_56_15 = e0)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2505), (2561) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2562) $false
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2562) is inconsistent.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2563) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2563) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2564) op(e0, e1) = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2514) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2565) all_54_14 = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (2313), (2565) are inconsistent by
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1232.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2566) all_54_14 = e1 | all_54_14 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2566) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567) all_54_14 = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (2567) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2568) all_52_11 = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2568) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2569) all_52_11 = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (2569) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2570) ~ (all_52_3 = e1)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (2569) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2571) op(e0, e1) = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2572) all_54_12 = e3
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (2455), (2572) are inconsistent by
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1234.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2573) ~ (all_54_12 = e3)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2574) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2574) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2575) all_54_12 = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (2575) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576) all_52_3 = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2576) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2577) all_52_3 = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2577) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578) ~ (all_52_2 = e2)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2455), (2577) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579) ~ (e3 = e2)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2580) all_54_8 = e3
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (2454), (2580) are inconsistent by
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1425.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2581) ~ (all_54_8 = e3)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2582) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2582) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2583) all_54_8 = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (2578), (2583) are inconsistent by
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1231.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2584) ~ (all_54_8 = e2)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2585) all_54_8 = e1 | all_54_8 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2585) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2586) all_54_8 = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (2586) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2587) all_52_2 = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2587) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2588) all_52_2 = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2454), (2588) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2589) ~ (e3 = e1)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2578), (2588) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2590) ~ (e2 = e1)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e1, e1,
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (2564), (2571) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2591) e1 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2475), (2591) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2592) all_58_14 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (155), (224),
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (397), (2328), (2465), (2564), (2592),
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #224.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2593) all_54_8 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (2492), (2593) are inconsistent by
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1378.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2594) all_54_12 = e1 | all_54_12 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (2506), (2570), (2594) are inconsistent by
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1222.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2595) all_54_14 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (2508), (2595) are inconsistent by
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1400.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2596) all_56_15 = e3
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (2596) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2597) all_4_2 = e3
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2597) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2598) all_4_2 = e3
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (2598) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2599) ~ (all_52_13 = e3)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2481), (2599), (function-axioms) are
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1364.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2600) all_58_5 = e0 & op(e2, e1) = e0
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2323), (2600) are inconsistent by sub-proof
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | #919.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (2601) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (155), (224),
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (397), (2328), (2442), (2465), (2601),
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | | #223.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | (2602) all_58_15 = e1 & op(e0, e0) = e1
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (397), (2602), (function-axioms) are
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1418.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | (2603) all_58_13 = e2 & op(e0, e2) = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2465), (2603) are inconsistent by sub-proof
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | #1177.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | (2604) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2604) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | (2605) all_58_14 = e2 & op(e0, e1) = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (2313), (2605), (function-axioms) are
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1175.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | (2606) all_58_15 = e2 & op(e0, e0) = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (2328), (2606), (function-axioms) are
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1452.
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | (2607) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | REF_CLOSE: (299), (2324), (2326), (2444), (2607) are
% 153.14/26.09 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1307.
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | (2608) all_56_1 = e3 & op(e3, e1) = e3
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | ALPHA: (2608) implies:
% 153.14/26.09 | | | | | | | | | | | | | | (2609) op(e3, e1) = e3
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | REF_CLOSE: (167), (2440), (2609), (function-axioms) are
% 153.14/26.09 | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | End of split
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | (2610) all_20_2 = e2
% 153.14/26.09 | | | | | | | | | | | | (2611) ( ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0
% 153.14/26.09 | | | | | | | | | | | | & op(e2, e2) = all_20_1 & $i(all_20_0) &
% 153.14/26.09 | | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e1) & op(e2, e2)
% 153.14/26.09 | | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | COMBINE_EQS: (348), (2610) imply:
% 153.14/26.09 | | | | | | | | | | | | (2612) all_4_2 = e2
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | SIMP: (2612) implies:
% 153.14/26.09 | | | | | | | | | | | | (2613) all_4_2 = e2
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | COMBINE_EQS: (341), (2613) imply:
% 153.14/26.09 | | | | | | | | | | | | (2614) all_26_2 = e2
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | COMBINE_EQS: (261), (2613) imply:
% 153.14/26.09 | | | | | | | | | | | | (2615) all_56_15 = e2
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | REDUCE: (386), (2613) imply:
% 153.14/26.09 | | | | | | | | | | | | (2616) ~ (all_52_7 = e2)
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | REDUCE: (394), (2613) imply:
% 153.14/26.09 | | | | | | | | | | | | (2617) ~ (all_52_12 = e2)
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | REDUCE: (396), (2613) imply:
% 153.14/26.09 | | | | | | | | | | | | (2618) ~ (all_52_14 = e2)
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | BETA: splitting (70) gives:
% 153.14/26.09 | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | (2619) ~ (all_26_2 = e2)
% 153.14/26.09 | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | REDUCE: (2614), (2619) imply:
% 153.14/26.09 | | | | | | | | | | | | | (2620) $false
% 153.14/26.09 | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | CLOSE: (2620) is inconsistent.
% 153.14/26.09 | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | (2621) ( ~ (all_26_0 = e1) & op(all_26_1, e0) = all_26_0
% 153.14/26.09 | | | | | | | | | | | | | & op(e2, e2) = all_26_1 & $i(all_26_0) &
% 153.14/26.09 | | | | | | | | | | | | | $i(all_26_1)) | ( ~ (all_26_1 = e3) & op(e2, e2)
% 153.14/26.09 | | | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 153.14/26.09 | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | BETA: splitting (2621) gives:
% 153.14/26.09 | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | (2622) ~ (all_26_0 = e1) & op(all_26_1, e0) = all_26_0 &
% 153.14/26.09 | | | | | | | | | | | | | | op(e2, e2) = all_26_1 & $i(all_26_0) &
% 153.14/26.09 | | | | | | | | | | | | | | $i(all_26_1)
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | ALPHA: (2622) implies:
% 153.14/26.09 | | | | | | | | | | | | | | (2623) ~ (all_26_0 = e1)
% 153.14/26.09 | | | | | | | | | | | | | | (2624) op(e2, e2) = all_26_1
% 153.14/26.09 | | | | | | | | | | | | | | (2625) op(all_26_1, e0) = all_26_0
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 153.14/26.09 | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | (2626) ~ (all_56_15 = e2)
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | REDUCE: (2615), (2626) imply:
% 153.14/26.09 | | | | | | | | | | | | | | | (2627) $false
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | CLOSE: (2627) is inconsistent.
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | (2628) all_56_10 = e0 & op(e0, e2) = e0
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | ALPHA: (2628) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | (2629) op(e0, e2) = e0
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 153.14/26.09 | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | (2630) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 153.14/26.09 | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | REF_CLOSE: (162), (166), (2315), (2617), (2630),
% 153.14/26.09 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.09 | | | | | | | | | | | | | | | | #166.
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | (2631) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 153.14/26.09 | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | BETA: splitting (2631) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | (2632) all_58_11 = e2 & op(e1, e0) = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | ALPHA: (2632) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | (2633) op(e1, e0) = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2618), (2633), (function-axioms) are
% 153.14/26.09 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1389.
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | (2634) all_58_15 = e2 & op(e0, e0) = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | ALPHA: (2634) implies:
% 153.14/26.09 | | | | | | | | | | | | | | | | | (2635) all_58_15 = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | | (2636) op(e0, e0) = e2
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 153.14/26.09 | | | | | | | | | | | | | | | | |
% 153.14/26.09 | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.09 | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | (2637) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | BETA: splitting (2637) gives:
% 153.14/26.10 | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | (2638) all_58_0 = e2 & op(e3, e3) = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2326), (2638), (function-axioms) are
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1523.
% 153.14/26.10 | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | (2639) all_58_1 = e2 & op(e3, e2) = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | ALPHA: (2639) implies:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | (2640) all_58_1 = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | (2641) op(e3, e2) = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | (2642) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (165), (2310), (2326), (2642),
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | #1522.
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | (2643) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2643) gives:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2644) all_58_6 = e2 & op(e1, e3) = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2644) implies:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2645) all_58_6 = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2646) op(e1, e3) = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (156), (2629) gives:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2647) all_52_7 = e0
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (161), (2646) gives:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2648) all_52_2 = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_26_1,
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (2308), (2624) gives:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2649) all_26_1 = e1
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (168), (2641) gives:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2650) all_52_4 = e2
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2648) imply:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2651) ~ (all_52_3 = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | SIMP: (2651) implies:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2652) ~ (all_52_3 = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2648) imply:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2653) ~ (all_52_14 = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (2650) imply:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2654) ~ (all_52_6 = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | SIMP: (2654) implies:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2655) ~ (all_52_6 = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (2650) imply:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2656) ~ (all_52_8 = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (2650) imply:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2657) ~ (all_10_2 = e2)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (2647) imply:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2658) ~ (all_52_6 = e0)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (2647) imply:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2659) ~ (all_52_11 = e0)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | SIMP: (2659) implies:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2660) ~ (all_52_11 = e0)
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2616), (2647) imply:
% 153.14/26.10 | | | | | | | | | | | | | | | | | | | | | (2661) ~ (e2 = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2297), (2647) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | (2662) ~ (e1 = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2625), (2649) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | (2663) op(e1, e0) = all_26_0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | (2664) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (2307), (2641), (2664),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | #197.
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | (2665) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2665) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | (2666) all_58_7 = e3 & op(e1, e2) = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2666) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | (2667) all_58_7 = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2611) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | (2668) ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0 &
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_20_1 & $i(all_20_0) &
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2668) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | (2669) op(e2, e2) = all_20_1
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | (2670) op(all_20_1, e0) = all_20_0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | (2671) all_54_9 = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (2671) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | (2672) all_52_6 = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (2672) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | (2673) ~ (all_52_14 = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2673) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | (2674) ~ (all_52_14 = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (2672) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | (2675) ~ (all_6_2 = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2675) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | (2676) ~ (all_6_2 = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (2677) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2677) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678) all_58_0 = e0 & op(e3, e3) = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2324), (2678), (function-axioms) are
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679) all_58_2 = e0 & op(e2, e3) = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2679) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680) all_58_2 = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2681) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (2307), (2680), (2681) are inconsistent
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #163.
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2682) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2682) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2683) all_58_5 = e3 & op(e2, e1) = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2683) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2684) all_58_5 = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2323), (2684) are inconsistent by sub-proof
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #897.
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2685) all_58_10 = e3 & op(e2, e0) = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2685) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686) all_58_10 = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2687) op(e2, e0) = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2688) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2688) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2679) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2689) op(e2, e3) = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_26_0, e0, e1, simplifying with (158), (2663)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2690) all_52_14 = all_26_0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (162), (2687) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2691) all_52_13 = e3
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_20_1,
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (2308), (2669) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2692) all_20_1 = e1
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (2689) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) all_52_1 = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (2690) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) all_54_11 = all_26_0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2693) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) ~ (all_52_3 = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2695) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) ~ (all_52_3 = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (2691), (2693) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) ~ (e3 = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (2693) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) ~ (all_10_2 = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (2691) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2699) ~ (all_52_12 = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (2690) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2700) ~ (all_26_0 = all_6_2)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2674), (2690) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701) ~ (all_26_0 = e3)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2618), (2690) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2702) ~ (all_26_0 = e2)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2670), (2692) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703) op(e1, e0) = all_20_0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2704) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (2296), (2645), (2704),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1137.
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2705) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2706) all_58_8 = e1 & op(e1, e1) = e1
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2706) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2707) all_58_8 = e1
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2708) ~ (all_56_14 = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (2708) imply:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2709) ~ (all_6_2 = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2710) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2710) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2711) all_58_4 = e0 & op(e3, e1) = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2711) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2712) all_58_4 = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (137), (155), (160),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (165), (166), (167), (168), (188), (190),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (192), (200), (202), (208), (238), (246),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (252), (253), (262), (264), (273), (288),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297), (299), (304), (366), (370), (372), (387),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (398), (2296), (2307), (2311), (2313),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2315), (2323), (2324), (2326), (2641), (2645),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2652), (2655), (2660), (2663), (2676), (2680),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686), (2687), (2694), (2696), (2699), (2700),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701), (2702), (2703), (2709), (2712),
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #156.
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2713) all_58_5 = e0 & op(e2, e1) = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2323), (2713) are inconsistent by sub-proof
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #180.
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2714) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2714) gives:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2715) all_58_8 = e0 & op(e1, e1) = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2715) implies:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2716) all_58_8 = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2707), (2716) are inconsistent by sub-proof
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1445.
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2717) all_58_14 = e0 & op(e0, e1) = e0
% 153.44/26.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (155), (156), (160),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (242), (246), (248), (252),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2616), (2629), (2636), (2640), (2645),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658), (2717), (function-axioms) are inconsistent
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2718) all_56_14 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (2718) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2719) all_6_2 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2719) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2720) all_6_2 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (2720) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2721) ~ (all_52_8 = e0)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2722) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2722) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2723) all_58_4 = e0 & op(e3, e1) = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2721), (2723), (function-axioms) are
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #259.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2724) all_58_5 = e0 & op(e2, e1) = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2323), (2724) are inconsistent by sub-proof
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #180.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2725) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2725) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2726) all_58_8 = e0 & op(e1, e1) = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2707), (2726) are inconsistent by sub-proof
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1271.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2727) all_58_14 = e0 & op(e0, e1) = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (155), (156), (160),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (242), (246), (248), (252),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2616), (2629), (2636), (2640), (2645),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658), (2727), (function-axioms) are inconsistent
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2728) all_58_11 = e1 & op(e1, e0) = e1
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2728) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2729) op(e1, e0) = e1
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2730) ~ (all_56_14 = e0)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (2730) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2731) ~ (all_6_2 = e0)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2732) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2732) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2733) all_58_4 = e0 & op(e3, e1) = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2733) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2734) all_58_4 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (137), (155), (160),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (165), (166), (167), (168), (188), (190),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (192), (200), (202), (208), (238), (246),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (252), (253), (262), (264), (273), (288),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297), (299), (304), (366), (370), (372), (387),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (398), (2296), (2307), (2311), (2313),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2315), (2323), (2324), (2326), (2641), (2645),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2652), (2655), (2660), (2663), (2676), (2680),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686), (2687), (2694), (2696), (2699), (2700),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701), (2702), (2703), (2731), (2734),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #156.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2735) all_58_5 = e0 & op(e2, e1) = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2323), (2735) are inconsistent by sub-proof
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #180.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2736) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2736) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2737) all_58_8 = e0 & op(e1, e1) = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2737) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2738) op(e1, e1) = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2739) all_54_10 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (2676), (2739) are inconsistent by
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1531.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2740) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2741) all_54_11 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2694), (2701), (2741) are inconsistent by
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #162.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2742) ~ (all_54_11 = e3)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2743) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2740) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2744) all_54_10 = e2
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (398), (2744) are inconsistent by sub-proof
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1530.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2745) ~ (all_54_10 = e2)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2746) all_54_10 = e1 | all_54_10 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2746) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2747) all_54_10 = e1
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (2747) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2748) all_6_2 = e1
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (390), (2748) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2749) ~ (all_52_11 = e1)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (2748) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2750) ~ (e2 = e1)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2751) all_54_14 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (2751) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2752) all_52_11 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2752) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2753) all_52_11 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (2753) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2754) ~ (all_52_8 = e3)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2755) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2755) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2756) all_58_0 = e3 & op(e3, e3) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2756) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2757) all_58_0 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (137), (155), (160),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (165), (166), (167), (168), (188), (190),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200), (202), (208), (238), (246), (248), (252),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (264), (273), (288), (297), (299), (304),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (370), (372), (387), (390), (2296), (2307),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311), (2313), (2315), (2323), (2324), (2326),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2641), (2645), (2652), (2655), (2660), (2663),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680), (2686), (2687), (2694), (2696), (2700),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701), (2702), (2703), (2731), (2743), (2746),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2757), (function-axioms) are inconsistent by
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #157.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2758) all_58_2 = e3 & op(e2, e3) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2758) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2759) all_58_2 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2680), (2759) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2760) e3 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2760) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2761) e3 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2667), (2761) imply:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2762) all_58_7 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (233), (2645), (2729), (2738),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2762), (function-axioms) are inconsistent by
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1269.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2763) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2763) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2764) all_58_6 = e3 & op(e1, e3) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2764) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2765) all_58_6 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2645), (2765) are inconsistent by sub-proof
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1376.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2766) all_58_12 = e3 & op(e0, e3) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2766) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2767) all_58_12 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2768) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2768) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2769) all_58_0 = e3 & op(e3, e3) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2769) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) all_58_0 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (165), (246),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (252), (2310), (2326), (2645),
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680), (2767), (2770), (function-axioms) are
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1506.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) all_58_1 = e3 & op(e3, e2) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2771) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) op(e3, e2) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2641), (2772), (function-axioms) are
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2773) gives:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) all_58_4 = e3 & op(e3, e1) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2774) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) op(e3, e1) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2754), (2775), (function-axioms) are
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) all_58_9 = e3 & op(e3, e0) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2776) implies:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) op(e3, e0) = e3
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2699), (2777), (function-axioms) are
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (2313), (2660), (2749), (2778) are
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1149.
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) all_54_10 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (2779) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) all_6_2 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2731), (2780) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) $false
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2781) is inconsistent.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) all_58_14 = e0 & op(e0, e1) = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (155), (156), (160),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (242), (246), (248), (252),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2616), (2629), (2636), (2640), (2645),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658), (2782), (function-axioms) are inconsistent
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) all_56_14 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (2783) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) all_6_2 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2784) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) all_6_2 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2700), (2785) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) ~ (all_26_0 = e0)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) all_54_11 = e3
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2694), (2701), (2787) are inconsistent by
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #162.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2788) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) all_54_11 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2694), (2702), (2789) are inconsistent by
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #159.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) all_54_11 = e1 | all_54_11 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2790) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) all_54_11 = e1
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2623), (2694), (2791) are inconsistent by
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #158.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) all_54_11 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2694), (2792) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) all_26_0 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2793) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) all_26_0 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2786), (2794) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) $false
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2795) is inconsistent.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) all_58_3 = e0 & op(e2, e2) = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2307), (2796) are inconsistent by sub-proof
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #161.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2797) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2798) all_58_5 = e0 & op(e2, e1) = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2323), (2798) are inconsistent by sub-proof
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #180.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2799) all_58_10 = e0 & op(e2, e0) = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2799) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2800) all_58_10 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2686), (2800) are inconsistent by sub-proof
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1061.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2801) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (160), (224),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (242), (2307), (2629), (2636), (2640),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2645), (2658), (2801), (function-axioms) are
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2802) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2802) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2803) all_54_9 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (274), (2655), (2803) are inconsistent by
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1180.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2804) all_54_9 = e1 | all_54_9 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (274), (2296), (2658), (2804) are inconsistent by
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1169.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | (2805) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 &
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2308), (2805), (function-axioms) are inconsistent
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #152.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | (2806) all_58_13 = e3 & op(e0, e2) = e3
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (160), (242), (2307), (2640),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | (2658), (2806), (function-axioms) are inconsistent
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #155.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2807) all_58_12 = e2 & op(e0, e3) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2807) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2808) all_58_12 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (223), (224),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (226), (2629), (2635), (2636), (2808),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | #151.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | (2809) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (167), (2311), (2617), (2809),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.12 | | | | | | | | | | | | | | | | | | #868.
% 153.44/26.12 | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | End of split
% 153.44/26.12 | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | (2810) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 &
% 153.44/26.12 | | | | | | | | | | | | | | $i(all_26_1)
% 153.44/26.12 | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | ALPHA: (2810) implies:
% 153.44/26.12 | | | | | | | | | | | | | | (2811) ~ (all_26_1 = e3)
% 153.44/26.12 | | | | | | | | | | | | | | (2812) op(e2, e2) = all_26_1
% 153.44/26.12 | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 153.44/26.12 | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | (2813) ~ (all_56_15 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | REDUCE: (2615), (2813) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | (2814) $false
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | CLOSE: (2814) is inconsistent.
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | (2815) all_56_10 = e0 & op(e0, e2) = e0
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | ALPHA: (2815) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | (2816) op(e0, e2) = e0
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 153.44/26.12 | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | (2817) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 153.44/26.12 | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | REF_CLOSE: (162), (166), (2315), (2617), (2817),
% 153.44/26.12 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.12 | | | | | | | | | | | | | | | | #166.
% 153.44/26.12 | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | (2818) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 153.44/26.12 | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | BETA: splitting (2818) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | (2819) all_58_11 = e2 & op(e1, e0) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | ALPHA: (2819) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | (2820) op(e1, e0) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2618), (2820), (function-axioms) are
% 153.44/26.12 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1389.
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | (2821) all_58_15 = e2 & op(e0, e0) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | ALPHA: (2821) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | (2822) all_58_15 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | (2823) op(e0, e0) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | (2824) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | BETA: splitting (2824) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | (2825) all_58_0 = e2 & op(e3, e3) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2326), (2825), (function-axioms) are
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1523.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | (2826) all_58_1 = e2 & op(e3, e2) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | ALPHA: (2826) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | (2827) all_58_1 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | (2828) op(e3, e2) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | (2829) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (165), (2310), (2326), (2829),
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | #1522.
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | (2830) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2830) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2831) all_58_6 = e2 & op(e1, e3) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2831) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2832) all_58_6 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2833) op(e1, e3) = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (156), (2816) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2834) all_52_7 = e0
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (161), (2833) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2835) all_52_2 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_26_1,
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (2308), (2812) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2836) all_26_1 = e1
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (168), (2828) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2837) all_52_4 = e2
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2835) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2838) ~ (all_52_3 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | SIMP: (2838) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2839) ~ (all_52_3 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2835) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2840) ~ (all_52_14 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (2837) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2841) ~ (all_52_6 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | SIMP: (2841) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2842) ~ (all_52_6 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (2837) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2843) ~ (all_52_8 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (2837) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2844) ~ (all_52_12 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (2837) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2845) ~ (all_10_2 = e2)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (2834) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2846) ~ (all_52_6 = e0)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (2834) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2847) ~ (all_52_11 = e0)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | SIMP: (2847) implies:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2848) ~ (all_52_11 = e0)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2616), (2834) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2849) ~ (e2 = e0)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2297), (2834) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2850) ~ (e1 = e0)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2811), (2836) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | (2851) ~ (e3 = e1)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | (2852) ~ (all_56_14 = e3)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (2852) imply:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | (2853) ~ (all_6_2 = e3)
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2611) gives:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.12 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | (2854) ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0 &
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_20_1 & $i(all_20_0) &
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2854) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | (2855) op(e2, e2) = all_20_1
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | (2856) op(all_20_1, e0) = all_20_0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | (2857) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2857) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | (2858) all_58_0 = e0 & op(e3, e3) = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2324), (2858), (function-axioms) are
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | (2859) all_58_2 = e0 & op(e2, e3) = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2859) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | (2860) all_58_2 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | (2861) op(e2, e3) = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (2862) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (2307), (2860), (2862) are inconsistent
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #163.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (2863) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2863) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2864) all_58_5 = e3 & op(e2, e1) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2864) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2865) all_58_5 = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2323), (2865) are inconsistent by sub-proof
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | #897.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2866) all_58_10 = e3 & op(e2, e0) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2866) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2867) op(e2, e0) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (162), (2867) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2868) all_52_13 = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_20_1,
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (2308), (2855) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2869) all_20_1 = e1
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (2861) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2870) all_52_1 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2870) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2871) ~ (all_52_3 = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2871) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2872) ~ (all_52_3 = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (2868), (2870) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2873) ~ (e3 = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (2870) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2874) ~ (all_10_2 = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (2868) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2875) ~ (all_52_12 = e3)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2856), (2869) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2876) op(e1, e0) = all_20_0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2877) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2877) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2878) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2878) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2879) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2879) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2880) op(e3, e2) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2828), (2880), (function-axioms) are
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2881) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2881) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2882) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2882) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2883) op(e2, e3) = e2
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2861), (2883), (function-axioms) are
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1156.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2884) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2884) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2885) ~ (all_56_14 = e1)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2886) op(e1, e3) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2887) op(e3, e1) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (2885) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2888) ~ (all_6_2 = e1)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2889) all_54_10 = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (2853), (2889) are inconsistent by
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1531.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2890) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2890) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2891) all_54_10 = e2
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (398), (2891) are inconsistent by sub-proof
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1530.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2892) ~ (all_54_10 = e2)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2893) all_54_10 = e1 | all_54_10 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2893) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2894) all_54_10 = e1
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (2888), (2894) are inconsistent by
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1529.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2895) all_54_10 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (2895) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2896) all_6_2 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2896) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2897) all_6_2 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (2897) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2898) all_56_14 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (2897) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2899) ~ (all_52_8 = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2900) all_56_12 = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (2900) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2901) all_10_2 = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (2901) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2902) ~ (all_52_8 = e3)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (166), (167), (200), (251), (288),
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311), (2326), (2617), (2827), (2833), (2886),
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2887), (2899), (2902), (function-axioms) are
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1208.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2903) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2903) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2904) all_56_13 = e2
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2293), (2904) are inconsistent by sub-proof
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #150.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2905) all_56_14 = e1 | all_56_15 = e0
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (2615), (2898), (2905) are inconsistent
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #149.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2906) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2906) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2907) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2907) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2908) ~ (all_56_12 = e3)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (297), (2908) imply:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2909) ~ (all_10_2 = e3)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (119), (167), (188), (202), (209),
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (262), (273), (297), (299), (390), (2293),
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313), (2324), (2326), (2615), (2848), (2909),
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #148.
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2910) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2910) gives:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2911) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2911) implies:
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2912) op(e3, e0) = e3
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2875), (2912), (function-axioms) are
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2913) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2913) implies:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2914) ~ (all_56_12 = e3)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (297), (2914) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2915) ~ (all_10_2 = e3)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (119), (167), (188), (202), (209),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (262), (273), (297), (299), (390), (2293),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313), (2324), (2326), (2615), (2848), (2915),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #148.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2916) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2916) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2917) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (162), (2296), (2315), (2842), (2917),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1128.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2918) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2918) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2919) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2919) implies:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2920) op(e2, e0) = e0
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e0, e0,
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (2867), (2920) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2921) e3 = e0
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (2921) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2922) $false
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2922) is inconsistent.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2923) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2923) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2924) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2924) implies:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2925) ~ (all_56_15 = e0)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2926) op(e0, e1) = e1
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2927) op(e1, e0) = e1
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, e0, simplifying with (155), (2926) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2928) all_52_11 = e1
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e1, simplifying with (158), (2927) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929) all_52_14 = e1
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_20_0, e0, e1, simplifying with (158), (2876)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2930) all_52_14 = all_20_0
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2929), (2930) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2931) all_20_0 = e1
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (2928) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2932) ~ (all_52_3 = e1)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2618), (2929) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2933) ~ (e2 = e1)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2934) all_54_12 = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (2934) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2935) all_52_3 = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2935) implies:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2936) all_52_3 = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2936) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2937) ~ (all_10_2 = e3)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2937) implies:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2938) ~ (all_10_2 = e3)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (119), (167), (188), (202), (209),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (262), (273), (297), (299), (390), (2293),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313), (2324), (2326), (2615), (2848), (2938),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #148.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2939) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (2839), (2872), (2932), (2939) are
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1098.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2940) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (192), (213), (273), (304), (398), (2853),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2940) are inconsistent by sub-proof #205.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | (2941) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (160), (224),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | (226), (242), (2307), (2816), (2823), (2827),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | (2832), (2846), (2941), (function-axioms) are
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | (2942) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 &
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2308), (2942), (function-axioms) are inconsistent
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #152.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | (2943) all_56_14 = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (2943) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | (2944) all_6_2 = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2944) implies:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | (2945) all_6_2 = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (2945) imply:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | (2946) ~ (all_52_6 = e3)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | (2947) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (2307), (2828), (2947),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | #197.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | (2948) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2948) gives:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | (2949) all_58_7 = e3 & op(e1, e2) = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2946), (2949), (function-axioms) are
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1184.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | (2950) all_58_13 = e3 & op(e0, e2) = e3
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (160), (242), (2307), (2827),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | (2846), (2950), (function-axioms) are inconsistent
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #155.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | (2951) all_58_12 = e2 & op(e0, e3) = e2
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2951) implies:
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | (2952) all_58_12 = e2
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (223), (224),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | (226), (2816), (2822), (2823), (2952),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | | #151.
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | (2953) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 153.44/26.14 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 153.44/26.14 | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (167), (2311), (2617), (2953),
% 153.44/26.14 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.14 | | | | | | | | | | | | | | | | | | #868.
% 153.44/26.14 | | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | End of split
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | Case 2:
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | (2954) all_16_2 = e2
% 153.44/26.14 | | | | | | | | | | | (2955) ( ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0
% 153.44/26.14 | | | | | | | | | | | & op(e2, e2) = all_16_1 & $i(all_16_0) &
% 153.44/26.14 | | | | | | | | | | | $i(all_16_1)) | ( ~ (all_16_1 = e0) & op(e2, e2)
% 153.44/26.14 | | | | | | | | | | | = all_16_1 & $i(all_16_1))
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | COMBINE_EQS: (349), (2954) imply:
% 153.44/26.14 | | | | | | | | | | | (2956) all_10_2 = e2
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | SIMP: (2956) implies:
% 153.44/26.14 | | | | | | | | | | | (2957) all_10_2 = e2
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | COMBINE_EQS: (356), (2957) imply:
% 153.44/26.14 | | | | | | | | | | | (2958) all_38_2 = e2
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | COMBINE_EQS: (297), (2957) imply:
% 153.44/26.14 | | | | | | | | | | | (2959) all_56_12 = e2
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | REDUCE: (364), (2957) imply:
% 153.44/26.14 | | | | | | | | | | | (2960) ~ (all_52_2 = e2)
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | REDUCE: (366), (2957) imply:
% 153.44/26.14 | | | | | | | | | | | (2961) ~ (all_52_3 = e2)
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | REDUCE: (368), (2957) imply:
% 153.44/26.14 | | | | | | | | | | | (2962) ~ (all_52_4 = e2)
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | REDUCE: (372), (2957) imply:
% 153.44/26.14 | | | | | | | | | | | (2963) ~ (all_52_12 = e2)
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | BETA: splitting (88) gives:
% 153.44/26.14 | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | Case 1:
% 153.44/26.14 | | | | | | | | | | | |
% 153.44/26.14 | | | | | | | | | | | | (2964) ~ (all_38_2 = e2)
% 153.44/26.14 | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | REDUCE: (2958), (2964) imply:
% 153.44/26.15 | | | | | | | | | | | | (2965) $false
% 153.44/26.15 | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | CLOSE: (2965) is inconsistent.
% 153.44/26.15 | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | (2966) ( ~ (all_38_0 = e0) & op(all_38_1, e3) = all_38_0
% 153.44/26.15 | | | | | | | | | | | | & op(e2, e2) = all_38_1 & $i(all_38_0) &
% 153.44/26.15 | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e1) & op(e2, e2)
% 153.44/26.15 | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 153.44/26.15 | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | BETA: splitting (221) gives:
% 153.44/26.15 | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | (2967) ~ (all_56_12 = e2)
% 153.44/26.15 | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | REDUCE: (2959), (2967) imply:
% 153.44/26.15 | | | | | | | | | | | | | (2968) $false
% 153.44/26.15 | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | CLOSE: (2968) is inconsistent.
% 153.44/26.15 | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | (2969) all_56_0 = e3 & op(e3, e2) = e3
% 153.44/26.15 | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | ALPHA: (2969) implies:
% 153.44/26.15 | | | | | | | | | | | | | (2970) op(e3, e2) = e3
% 153.44/26.15 | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | BETA: splitting (2955) gives:
% 153.44/26.15 | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | (2971) ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0 &
% 153.44/26.15 | | | | | | | | | | | | | | op(e2, e2) = all_16_1 & $i(all_16_0) &
% 153.44/26.15 | | | | | | | | | | | | | | $i(all_16_1)
% 153.44/26.15 | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | ALPHA: (2971) implies:
% 153.44/26.15 | | | | | | | | | | | | | | (2972) ~ (all_16_0 = e1)
% 153.44/26.15 | | | | | | | | | | | | | | (2973) op(e2, e2) = all_16_1
% 153.44/26.15 | | | | | | | | | | | | | | (2974) op(all_16_1, e3) = all_16_0
% 153.44/26.15 | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 153.44/26.15 | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | (2975) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 153.44/26.15 | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 153.44/26.15 | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | BETA: splitting (2975) gives:
% 153.44/26.15 | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | (2976) all_58_0 = e2 & op(e3, e3) = e2
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | ALPHA: (2976) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | (2977) all_58_0 = e2
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_16_1,
% 153.44/26.15 | | | | | | | | | | | | | | | | e2, e2, simplifying with (2308), (2973) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | (2978) all_16_1 = e1
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 153.44/26.15 | | | | | | | | | | | | | | | | e2, e3, simplifying with (168), (2970) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | (2979) all_52_4 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | REDUCE: (131), (2979) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | (2980) ~ (all_52_12 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | SIMP: (2980) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | (2981) ~ (all_52_12 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | REDUCE: (2974), (2978) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | (2982) op(e1, e3) = all_16_0
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | BETA: splitting (2966) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2983) ~ (all_38_0 = e0) & op(all_38_1, e3) = all_38_0 &
% 153.44/26.15 | | | | | | | | | | | | | | | | | op(e2, e2) = all_38_1 & $i(all_38_0) &
% 153.44/26.15 | | | | | | | | | | | | | | | | | $i(all_38_1)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | ALPHA: (2983) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2984) ~ (all_38_0 = e0)
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2985) op(e2, e2) = all_38_1
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2986) op(all_38_1, e3) = all_38_0
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 153.44/26.15 | | | | | | | | | | | | | | | | | all_16_0, e3, e1, simplifying with (161), (2982)
% 153.44/26.15 | | | | | | | | | | | | | | | | | gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2987) all_52_2 = all_16_0
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_38_1,
% 153.44/26.15 | | | | | | | | | | | | | | | | | e2, e2, simplifying with (2308), (2985) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2988) all_38_1 = e1
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (2987) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2989) all_54_8 = all_16_0
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | REDUCE: (147), (2987) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2990) ~ (all_52_1 = all_16_0)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | REDUCE: (142), (2987) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2991) ~ (all_52_3 = all_16_0)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | SIMP: (2991) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2992) ~ (all_52_3 = all_16_0)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | REDUCE: (141), (2987) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2993) ~ (all_52_6 = all_16_0)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | SIMP: (2993) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2994) ~ (all_52_6 = all_16_0)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | REDUCE: (139), (2987) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2995) ~ (all_52_14 = all_16_0)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | SIMP: (2995) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2996) ~ (all_52_14 = all_16_0)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | REDUCE: (374), (2987) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2997) ~ (all_16_0 = all_6_2)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | REDUCE: (2960), (2987) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2998) ~ (all_16_0 = e2)
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | REDUCE: (2986), (2988) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | (2999) op(e1, e3) = all_38_0
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | (3000) ~ (all_56_14 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | REDUCE: (273), (3000) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | (3001) ~ (all_6_2 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | (3002) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (247), (249),
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | (2323), (2970), (2977), (3002), (function-axioms)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #147.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | (3003) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (3003) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | (3004) all_58_8 = e3 & op(e1, e1) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3001), (3004), (function-axioms) are
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1469.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | (3005) all_58_14 = e3 & op(e0, e1) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | ALPHA: (3005) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | (3006) all_58_14 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | (3007) op(e0, e1) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | (3008) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3008) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3009) all_58_12 = e1 & op(e0, e3) = e1
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3009) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3010) all_58_12 = e1
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3011) op(e0, e3) = e1
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | e3, e1, e0, simplifying with (155), (3007) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3012) all_52_11 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (157), (3011) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3013) all_52_3 = e1
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_0,
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | all_38_0, e3, e1, simplifying with (2982), (2999)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3014) all_38_0 = all_16_0
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (3013) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3015) ~ (all_52_7 = e1)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2992), (3013) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3016) ~ (all_16_0 = e1)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (3013) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3017) ~ (all_4_2 = e1)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2961), (3013) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3018) ~ (e2 = e1)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3012) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3019) ~ (all_52_7 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (3012) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3020) ~ (all_52_8 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (3012) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3021) ~ (all_4_2 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | SIMP: (3021) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3022) ~ (all_4_2 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2984), (3014) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | (3023) ~ (all_16_0 = e0)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | (3024) all_54_8 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2989), (3024) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | (3025) all_16_0 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2990), (3025) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | (3026) ~ (all_52_1 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2994), (3025) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | (3027) ~ (all_52_6 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2996), (3025) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | (3028) ~ (all_52_14 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2997), (3025) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | (3029) ~ (all_6_2 = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | (3030) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (2307), (3026), (3030),
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | #213.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | (3031) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3031) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | (3032) all_58_5 = e3 & op(e2, e1) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3032) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | (3033) all_58_5 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2323), (3033) are inconsistent by sub-proof
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | #897.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | (3034) all_58_10 = e3 & op(e2, e0) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3034) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | (3035) all_58_10 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | (3036) op(e2, e0) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (3037) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3037) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3038) all_58_0 = e3 & op(e3, e3) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2977), (3038) are inconsistent by sub-proof
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1336.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3039) all_58_2 = e3 & op(e2, e3) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3039) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3040) op(e2, e3) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3026), (3040), (function-axioms) are
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1183.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (3041) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3041) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3042) all_58_6 = e3 & op(e1, e3) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3042) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3043) all_58_6 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3044) op(e1, e3) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3045) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3045) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3046) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (167), (168), (2970), (3020), (3026),
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3046), (function-axioms) are inconsistent by
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #145.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3047) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3047) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3048) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3048) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3049) op(e1, e3) = e1
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (3044), (3049), (function-axioms) are
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1164.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3050) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3050) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3051) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3051) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3052) op(e3, e0) = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2981), (3052), (function-axioms) are
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3053) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3053) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3054) op(e0, e3) = e0
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e0, e3,
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (3011), (3054) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3055) e1 = e0
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (3055) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3056) $false
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3056) is inconsistent.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3057) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3057) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3058) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3058) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3059) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3059) implies:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3060) ~ (all_56_14 = e1)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3061) op(e1, e2) = e2
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (3060) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3062) ~ (all_6_2 = e1)
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3063) all_54_10 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (3063) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3064) all_6_2 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3064) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3065) all_56_14 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (215), (3044), (3065),
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #144.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3066) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3067) all_56_12 = e3
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2959), (3067) are inconsistent by sub-proof
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #886.
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3068) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3066) gives:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3069) all_54_10 = e2
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (3069) imply:
% 153.44/26.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3070) all_6_2 = e2
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (3070) imply:
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3071) $false
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3071) is inconsistent.
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3072) all_54_10 = e1 | all_54_10 = e0
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3068) gives:
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3073) all_56_13 = e2
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2293), (3073) are inconsistent by sub-proof
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #150.
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3074) all_56_14 = e1 | all_56_15 = e0
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3074) gives:
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.44/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3075) all_56_14 = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3075) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3076) all_6_2 = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3062), (3076) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3077) $false
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3077) is inconsistent.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3078) all_56_15 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (3078) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3079) all_4_2 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (3079) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3080) ~ (all_52_7 = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (119), (123), (126), (160), (188), (189), (200),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (263), (288), (304), (387), (390), (2297),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311), (2313), (3020), (3061), (3062), (3072),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3080), (function-axioms) are inconsistent by
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #206.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3081) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (162), (2296), (2315), (3081),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1129.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3082) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3082) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3083) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3083) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3084) op(e2, e0) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3036), (3084), (function-axioms) are
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #143.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3085) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3085) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3086) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3086) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3087) ~ (all_56_15 = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3088) op(e1, e0) = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (261), (3087) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3089) ~ (all_4_2 = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3090) all_58_15 = e0 & op(e0, e0) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3090) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3091) all_58_15 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3092) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3092) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3093) all_58_12 = e2 & op(e0, e3) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3093) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3094) all_58_12 = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (246), (248), (252),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2977), (3043), (3094) are inconsistent by
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1331.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3095) all_58_13 = e2 & op(e0, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3095) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3096) op(e0, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3097) all_54_15 = e3
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (3022), (3097) are inconsistent by
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1543.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3098) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3098) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3099) all_54_15 = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (211), (261), (306), (3096), (3099),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #287.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3100) all_54_15 = e1 | all_54_15 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (397), (3089), (3100) are inconsistent by
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1295.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3101) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3101) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3102) all_58_14 = e2 & op(e0, e1) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3102) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3103) all_58_14 = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (156), (226), (3010), (3019),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3091), (3103), (function-axioms) are inconsistent
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1081.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3104) all_58_15 = e2 & op(e0, e0) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3104) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3105) all_58_15 = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3091), (3105) are inconsistent by sub-proof
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1462.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3106) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3106) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3107) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3108) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3108) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3109) all_58_9 = e0 & op(e3, e0) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3109) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3110) op(e3, e0) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3111) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3111) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3112) all_58_1 = e2 & op(e3, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3112) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3113) op(e3, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2970), (3113), (function-axioms) are
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3114) all_58_3 = e2 & op(e2, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2307), (3114) are inconsistent by sub-proof
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #215.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3115) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3115) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3116) all_58_7 = e2 & op(e1, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3116) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3117) op(e1, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3118) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (246), (248),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (2977), (3006), (3010), (3043), (3107),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3118), (function-axioms) are inconsistent by
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #142.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3119) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3119) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3120) all_58_14 = e2 & op(e0, e1) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (2313), (3120), (function-axioms) are
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1175.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3121) all_58_15 = e2 & op(e0, e0) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3121) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3122) all_58_15 = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3123) op(e0, e0) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3124) all_56_12 = e3
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (223), (224),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (2959), (3006), (3019), (3122), (3123),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3124), (function-axioms) are inconsistent by
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #141.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3125) ~ (all_56_12 = e3)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3126) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2959), (3125) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127) ~ (e3 = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3126) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3128) all_56_13 = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2293), (3128) are inconsistent by sub-proof
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #150.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3129) ~ (all_56_13 = e2)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3130) all_56_14 = e1 | all_56_15 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3131) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3131) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3132) all_58_9 = e1 & op(e3, e0) = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3132) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3133) op(e3, e0) = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3110), (3133), (function-axioms) are
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #140.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3134) all_58_10 = e1 & op(e2, e0) = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2299), (3134), (function-axioms) are
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3135) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3135) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3136) all_58_11 = e1 & op(e1, e0) = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3136) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3137) all_58_11 = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3138) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3138) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3139) all_58_6 = e0 & op(e1, e3) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3139) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3140) all_58_6 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3043), (3140) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3141) e3 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3035), (3141) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3142) all_58_10 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (165), (241), (2307), (2323),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3026), (3142), (function-axioms) are inconsistent
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #184.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) all_58_7 = e0 & op(e1, e2) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3143) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) op(e1, e2) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3117), (3144), (function-axioms) are
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3145) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3145) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3146) all_58_8 = e0 & op(e1, e1) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3146) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3147) all_58_8 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3130) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3148) all_56_14 = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3148) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3149) all_6_2 = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (3149) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3150) ~ (all_52_8 = e1)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3001), (3149) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3151) ~ (e3 = e1)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3152) all_54_2 = e3
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (3020), (3152) are inconsistent by
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1210.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3153) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (167), (235), (288), (2303),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311), (3006), (3147), (3150), (3153),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #138.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3154) all_56_15 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (3154) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3155) all_4_2 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3089), (3155) imply:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3156) $false
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3156) is inconsistent.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3157) all_58_11 = e0 & op(e1, e0) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3137), (3157) are inconsistent by sub-proof
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #577.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3158) all_58_15 = e1 & op(e0, e0) = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3158) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3159) op(e0, e0) = e1
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3123), (3159), (function-axioms) are
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1386.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3160) all_58_13 = e2 & op(e0, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3160) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3161) op(e0, e2) = e2
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (156), (3006), (3010), (3107),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3161), (function-axioms) are inconsistent by
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #845.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3162) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3162) gives:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3163) all_58_10 = e0 & op(e2, e0) = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3163) implies:
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3164) all_58_10 = e0
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (165), (241), (2307), (2323),
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3026), (3164), (function-axioms) are inconsistent
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #184.
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3165) all_58_11 = e0 & op(e1, e0) = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3165) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3166) all_58_11 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3167) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (246), (248),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (2977), (3006), (3010), (3043), (3107),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3167), (function-axioms) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #142.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3168) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3168) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3169) all_58_14 = e2 & op(e0, e1) = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (2313), (3169), (function-axioms) are
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1175.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3170) all_58_15 = e2 & op(e0, e0) = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3170) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3171) all_58_15 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3172) all_54_15 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (3022), (3172) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1543.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173) ~ (all_54_15 = e3)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3174) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3175) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3175) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3176) all_58_6 = e1 & op(e1, e3) = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3176) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3177) op(e1, e3) = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (3044), (3177), (function-axioms) are
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1164.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3178) all_58_7 = e1 & op(e1, e2) = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3178) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3179) op(e1, e2) = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2296), (3179), (function-axioms) are
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1166.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3180) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3180) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3181) all_58_8 = e1 & op(e1, e1) = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3181) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3182) all_58_8 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3174) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3183) all_54_15 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (3183) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3184) all_4_2 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3184) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3185) all_4_2 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (3185) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3186) all_56_15 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (3185) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3187) ~ (all_52_7 = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (396), (3185) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3188) ~ (all_52_14 = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3022), (3185) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3189) ~ (e3 = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3185) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3190) op(e0, e0) = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3191) all_54_13 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (3019), (3191) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1435.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3192) ~ (all_54_13 = e3)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3193) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3194) all_56_12 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (223), (224),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (2959), (3006), (3019), (3171), (3190),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3194), (function-axioms) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #141.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3195) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3193) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3196) all_54_13 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (3187), (3196) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1370.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3197) ~ (all_54_13 = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3198) all_54_13 = e1 | all_54_13 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3195) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3199) all_56_13 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2293), (3199) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3200) e2 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3200) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3201) $false
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3201) is inconsistent.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3202) ~ (all_56_13 = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3203) all_56_14 = e1 | all_56_15 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3198) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3204) all_54_13 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (2297), (3204) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #876.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3205) all_54_13 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (3205) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3206) all_52_7 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3206) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207) all_52_7 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (3207) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3208) ~ (all_52_6 = e0)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3019), (3207) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3209) ~ (e3 = e0)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3187), (3207) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3210) ~ (e2 = e0)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2297), (3207) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3211) ~ (e1 = e0)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3203) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3212) all_56_14 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3212) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3213) all_6_2 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3213) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3214) all_6_2 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (3214) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3215) ~ (all_52_8 = e1)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (3214) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3216) ~ (all_52_14 = e1)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3217) all_54_11 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (3028), (3217) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1415.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3218) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3219) all_54_2 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (3020), (3219) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1210.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3220) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3218) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3221) all_54_11 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (3188), (3221) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1414.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3222) all_54_11 = e1 | all_54_11 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3222) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3223) all_54_11 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (3216), (3223) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1228.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3224) all_54_11 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (3224) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3225) all_52_14 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3225) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3226) all_52_14 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (3226) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3227) ~ (all_52_12 = e0)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (3226) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3228) op(e1, e0) = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3229) all_54_3 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (287), (2981), (3229) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1233.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3230) ~ (all_54_3 = e3)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3231) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3231) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3232) all_54_3 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (3232) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3233) all_52_12 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3233) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3234) all_52_12 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2963), (3234) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3235) $false
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3235) is inconsistent.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3236) ~ (all_54_3 = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3237) all_54_3 = e1 | all_54_3 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3237) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3238) all_54_3 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (3238) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3239) all_52_12 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3239) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3240) all_52_12 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2981), (3240) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3241) ~ (e3 = e1)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e1, e0,
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (3088), (3228) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3242) e1 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3182), (3242) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3243) all_58_8 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (167), (235), (288), (2303),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311), (3006), (3215), (3220), (3243),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #138.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3244) all_54_3 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (287), (3227), (3244) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1290.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3245) all_56_15 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3186), (3245) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3246) e2 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3246) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3247) e2 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3171), (3247) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3248) all_58_15 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3249) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (247), (249),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2315), (2970), (2977), (3249), (function-axioms)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3250) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3250) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3251) all_58_11 = e2 & op(e1, e0) = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3251) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3252) op(e1, e0) = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3253) all_54_9 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (3253) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3254) all_52_6 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3027), (3254) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3255) $false
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3255) is inconsistent.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3256) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3256) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3257) all_54_9 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (3257) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3258) all_52_6 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (3258) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3259) ~ (all_52_14 = e2)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3188), (3252), (function-axioms) are
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1389.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3260) all_54_9 = e1 | all_54_9 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (274), (2296), (3208), (3260) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1169.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3171), (3248) are inconsistent by sub-proof
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1462.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3261) all_54_15 = e1 | all_54_15 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (397), (3089), (3261) are inconsistent by
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1295.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3262) all_58_11 = e1 & op(e1, e0) = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3262) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3263) all_58_11 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3166), (3263) are inconsistent by sub-proof
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1297.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3264) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (192), (213), (273), (304), (398), (3001),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3264) are inconsistent by sub-proof #205.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3265) all_58_12 = e3 & op(e0, e3) = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3265) implies:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3266) all_58_12 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3010), (3266) are inconsistent by sub-proof
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1516.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | (3267) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3267) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | (3268) all_54_8 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2989), (3268) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | (3269) all_16_0 = e2
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2998), (3269) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | (3270) $false
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3270) is inconsistent.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | (3271) all_54_8 = e1 | all_54_8 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3271) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | (3272) all_54_8 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2989), (3272) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | (3273) all_16_0 = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2972), (3273) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | (3274) $false
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3274) is inconsistent.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | (3275) all_54_8 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2989), (3275) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | (3276) all_16_0 = e0
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3023), (3276) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | (3277) $false
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3277) is inconsistent.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | (3278) all_58_13 = e1 & op(e0, e2) = e1
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2297), (3278), (function-axioms) are
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | (3279) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (397), (3006), (3279),
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | | #256.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.17 | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | (3280) all_56_14 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3280) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | (3281) all_6_2 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | REDUCE: (2997), (3281) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | (3282) ~ (all_16_0 = e3)
% 153.70/26.17 | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 153.70/26.17 | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | (3283) all_54_8 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2989), (3283) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | (3284) all_16_0 = e3
% 153.70/26.17 | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | REDUCE: (3282), (3284) imply:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | (3285) $false
% 153.70/26.17 | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | | CLOSE: (3285) is inconsistent.
% 153.70/26.17 | | | | | | | | | | | | | | | | | | |
% 153.70/26.17 | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.17 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | (3286) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (3286) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | (3287) all_54_8 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2989), (3287) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | (3288) all_16_0 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (2998), (3288) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | (3289) $false
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | CLOSE: (3289) is inconsistent.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | (3290) all_54_8 = e1 | all_54_8 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3290) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | (3291) all_54_8 = e1
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2989), (3291) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | (3292) all_16_0 = e1
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2972), (3292) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | (3293) $false
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3293) is inconsistent.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | (3294) all_54_8 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2989), (3294) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | (3295) all_16_0 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2990), (3295) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | (3296) ~ (all_52_1 = e0)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3297) all_54_4 = e3
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (3297) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3298) all_52_1 = e3
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (3298) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3299) ~ (all_52_13 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | SIMP: (3299) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3300) ~ (all_52_13 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | (3301) all_54_7 = e3
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (3301) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | (3302) all_52_13 = e3
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3300), (3302) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | (3303) $false
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3303) is inconsistent.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | (3304) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | (3305) all_56_12 = e3
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2959), (3305) are inconsistent by sub-proof
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | #886.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | (3306) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (261), (276), (395), (2293), (2299),
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | (2315), (3280), (3304), (3306) are inconsistent by
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #136.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3307) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (2294), (2310), (3296), (3307) are
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1187.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3308) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 153.70/26.18 | | | | | | | | | | | | | | | | | $i(all_38_1)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | ALPHA: (3308) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3309) ~ (all_38_1 = e1)
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3310) op(e2, e2) = all_38_1
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (61), (73), (76), (85), (108), (110), (111),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (115), (116), (118), (119), (121), (123), (124),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (126), (131), (132), (133), (134), (137), (138),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (139), (141), (142), (143), (144), (146), (147),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (155), (156), (157), (158), (160), (161), (162),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (163), (165), (166), (167), (168), (187), (188),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (189), (190), (191), (192), (193), (194), (195),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (196), (197), (198), (199), (200), (208), (209),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (211), (212), (213), (215), (216), (221), (223),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (228), (229), (230),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (231), (232), (233), (234), (235), (236), (237),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (238), (239), (240), (241), (242), (243), (244),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (246), (247), (248), (249), (251), (252), (261),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (262), (263), (264), (265), (273), (274), (275),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (276), (277), (282), (286), (287), (288), (304),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (306), (335), (339), (348), (354), (360), (373),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (374), (375), (376), (378), (380), (382), (384),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (385), (386), (387), (388), (390), (392), (393),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (394), (395), (396), (397), (398), (2310), (2311),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (2955), (2959), (2960), (2961), (2962), (2963),
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3309), (3310), (function-axioms) are inconsistent
% 153.70/26.18 | | | | | | | | | | | | | | | | | by sub-proof #867.
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | (3311) all_58_1 = e2 & op(e3, e2) = e2
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | ALPHA: (3311) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3312) op(e3, e2) = e2
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2970), (3312), (function-axioms) are
% 153.70/26.18 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | (3313) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 153.70/26.18 | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | REF_CLOSE: (166), (167), (2311), (2963), (3313),
% 153.70/26.18 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.18 | | | | | | | | | | | | | | | #868.
% 153.70/26.18 | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | (3314) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 153.70/26.18 | | | | | | | | | | | | | | $i(all_16_1)
% 153.70/26.18 | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | ALPHA: (3314) implies:
% 153.70/26.18 | | | | | | | | | | | | | | (3315) ~ (all_16_1 = e0)
% 153.70/26.18 | | | | | | | | | | | | | | (3316) op(e2, e2) = all_16_1
% 153.70/26.18 | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 153.70/26.18 | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | (3317) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 153.70/26.18 | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | BETA: splitting (3317) gives:
% 153.70/26.18 | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | (3318) all_58_0 = e2 & op(e3, e3) = e2
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | ALPHA: (3318) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3319) all_58_0 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_16_1,
% 153.70/26.18 | | | | | | | | | | | | | | | | e2, e2, simplifying with (2308), (3316) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3320) all_16_1 = e1
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 153.70/26.18 | | | | | | | | | | | | | | | | e2, e3, simplifying with (168), (2970) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3321) all_52_4 = e3
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | REDUCE: (134), (3321) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3322) ~ (all_52_6 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | SIMP: (3322) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3323) ~ (all_52_6 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | REDUCE: (133), (3321) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3324) ~ (all_52_7 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | SIMP: (3324) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3325) ~ (all_52_7 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | REDUCE: (132), (3321) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3326) ~ (all_52_8 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | SIMP: (3326) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3327) ~ (all_52_8 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | REDUCE: (131), (3321) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3328) ~ (all_52_12 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | SIMP: (3328) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | (3329) ~ (all_52_12 = e3)
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | BETA: splitting (2966) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3330) ~ (all_38_0 = e0) & op(all_38_1, e3) = all_38_0 &
% 153.70/26.18 | | | | | | | | | | | | | | | | | op(e2, e2) = all_38_1 & $i(all_38_0) &
% 153.70/26.18 | | | | | | | | | | | | | | | | | $i(all_38_1)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | ALPHA: (3330) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3331) ~ (all_38_0 = e0)
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3332) op(e2, e2) = all_38_1
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3333) op(all_38_1, e3) = all_38_0
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_38_1,
% 153.70/26.18 | | | | | | | | | | | | | | | | | e2, e2, simplifying with (2308), (3332) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3334) all_38_1 = e1
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | REDUCE: (3333), (3334) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3335) op(e1, e3) = all_38_0
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 153.70/26.18 | | | | | | | | | | | | | | | | | all_38_0, e3, e1, simplifying with (161), (3335)
% 153.70/26.18 | | | | | | | | | | | | | | | | | gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3336) all_52_2 = all_38_0
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (3336) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3337) all_54_8 = all_38_0
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | REDUCE: (147), (3336) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3338) ~ (all_52_1 = all_38_0)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | REDUCE: (141), (3336) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3339) ~ (all_52_6 = all_38_0)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | SIMP: (3339) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3340) ~ (all_52_6 = all_38_0)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | REDUCE: (139), (3336) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3341) ~ (all_52_14 = all_38_0)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | SIMP: (3341) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3342) ~ (all_52_14 = all_38_0)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | REDUCE: (374), (3336) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3343) ~ (all_38_0 = all_6_2)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | REDUCE: (2960), (3336) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | (3344) ~ (all_38_0 = e2)
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | (3345) ~ (all_20_2 = e2)
% 153.70/26.18 | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | REDUCE: (348), (3345) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | (3346) ~ (all_4_2 = e2)
% 153.70/26.18 | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | (3347) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (247), (249),
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | (2315), (2970), (3319), (3347), (function-axioms)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | (3348) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (3348) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | (3349) all_58_11 = e2 & op(e1, e0) = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | ALPHA: (3349) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | (3350) all_58_11 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | (3351) op(e1, e0) = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | (3352) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3352) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3353) all_58_12 = e2 & op(e0, e3) = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3353) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3354) all_58_12 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (246), (248), (252),
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3319), (3354) are inconsistent by sub-proof #999.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3355) all_58_13 = e2 & op(e0, e2) = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3355) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | (3356) op(e0, e2) = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | (3357) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3357) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | (3358) all_58_9 = e1 & op(e3, e0) = e1
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3358) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | (3359) all_58_9 = e1
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | (3360) op(e3, e0) = e1
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | (3361) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (45), (2324), (2970), (3361),
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | #135.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | (3362) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3362) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (3363) all_58_4 = e0 & op(e3, e1) = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3363) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (3364) op(e3, e1) = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3365) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3365) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3366) all_58_1 = e0 & op(e3, e2) = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3366) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3367) op(e3, e2) = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2970), (3367), (function-axioms) are
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1303.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3368) all_58_3 = e0 & op(e2, e2) = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3368) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3369) op(e2, e2) = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3315), (3316), (3369), (function-axioms) are
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #966.
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3370) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3370) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3371) all_58_7 = e0 & op(e1, e2) = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3371) implies:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3372) all_58_7 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3373) op(e1, e2) = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (156), (3356) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3374) all_52_7 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (158), (3351) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3375) all_52_14 = e2
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (160), (3373) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3376) all_52_6 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e3, simplifying with (166), (3360) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3377) all_52_12 = e1
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (3364) gives:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3378) all_52_8 = e0
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3340), (3376) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3379) ~ (all_38_0 = e0)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3325), (3374) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3380) ~ (e3 = e2)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (3378) imply:
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3381) ~ (all_52_11 = e0)
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3381) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3382) ~ (all_52_11 = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (3377), (3378) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3383) ~ (e1 = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (3378) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3384) ~ (all_6_2 = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3384) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3385) ~ (all_6_2 = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2311), (3378) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3386) ~ (e2 = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (3377) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3387) ~ (all_52_13 = e1)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (3377) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3388) ~ (all_4_2 = e1)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2963), (3377) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3389) ~ (e2 = e1)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3342), (3375) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3390) ~ (all_38_0 = e2)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (396), (3375) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3391) ~ (all_4_2 = e2)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3392) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3392) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3393) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3393) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3394) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3394) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3395) op(e2, e3) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3396) ~ (all_48_2 = e1)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2292), (3396) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3397) $false
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3397) is inconsistent.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3398) ( ~ (all_48_0 = e3) & op(all_48_1, e2) = all_48_0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_48_1 & $i(all_48_0) &
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e0) & op(e1, e1)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3398) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (3395) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3399) all_52_1 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (3399) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3400) ~ (all_52_13 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3400) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401) ~ (all_52_13 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3338), (3399) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3402) ~ (all_38_0 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3402) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3403) ~ (all_38_0 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (160), (161), (187), (192), (194),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195), (209), (230), (231), (233), (261), (273),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276), (304), (306), (395), (397), (398), (2293),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2299), (2315), (2959), (3323), (3331), (3335),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3337), (3343), (3344), (3346), (3350), (3385),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401), (3403), (function-axioms) are inconsistent
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #133.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3404) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3404) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3405) ~ (all_48_1 = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3406) op(e1, e1) = all_48_1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_48_1, e1, e1, simplifying with (39), (3406)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3407) all_48_1 = all_6_2
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (3395) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3408) all_52_1 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (3408) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3409) ~ (all_52_13 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3409) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3410) ~ (all_52_13 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3338), (3408) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3411) ~ (all_38_0 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3411) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3412) ~ (all_38_0 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (160), (161), (187), (192), (194),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195), (209), (230), (231), (233), (261), (273),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276), (304), (306), (395), (397), (398), (2293),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2299), (2315), (2959), (3323), (3331), (3335),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3337), (3343), (3344), (3346), (3350), (3385),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3410), (3412), (function-axioms) are inconsistent
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #133.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3413) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (168), (2970), (3327), (3413),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #146.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3414) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3414) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3415) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3415) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3416) op(e3, e1) = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3364), (3416), (function-axioms) are
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1281.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3417) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3417) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3418) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3418) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3419) op(e3, e0) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3329), (3419), (function-axioms) are
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3420) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3420) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3421) op(e3, e0) = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3360), (3421), (function-axioms) are
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #140.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3422) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3422) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3423) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (162), (2296), (2315), (3373), (3423),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #132.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3424) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3424) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3425) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3425) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3426) op(e0, e2) = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (3356), (3426), (function-axioms) are
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1040.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3427) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3427) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3428) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3428) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3429) ~ (all_56_15 = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3430) op(e1, e0) = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (261), (3429) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3431) ~ (all_4_2 = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3432) all_54_15 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (3432) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3433) all_4_2 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3433) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3434) all_4_2 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (3434) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3435) all_56_15 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (3434) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3436) ~ (all_52_11 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (3434) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3437) ~ (all_52_13 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3438) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3438) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3439) all_58_4 = e3 & op(e3, e1) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (247), (249), (2970),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3319), (3439), (function-axioms) are inconsistent
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1093.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3440) all_58_5 = e3 & op(e2, e1) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3440) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3441) all_58_5 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2323), (3441) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3442) e3 = e2
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3442) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3443) e3 = e2
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3435), (3443) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3444) all_56_15 = e2
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (211), (3356), (3444),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #892.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3445) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3445) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3446) all_58_8 = e3 & op(e1, e1) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3446) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3447) all_58_8 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3448) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (247), (2303), (2970), (3319),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3359), (3448), (function-axioms) are inconsistent
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #922.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3449) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3449) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3450) all_58_8 = e1 & op(e1, e1) = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3450) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3451) all_58_8 = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3447), (3451) are inconsistent by sub-proof
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #950.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3452) all_58_14 = e1 & op(e0, e1) = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3452) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3453) all_58_14 = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3454) op(e0, e1) = e1
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3455) all_58_15 = e0 & op(e0, e0) = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3455) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3456) all_58_15 = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (229), (247),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (2970), (3319), (3430), (3437), (3456),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #131.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3457) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3457) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3458) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3459) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3458) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3460) all_58_12 = e0 & op(e0, e3) = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3460) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3461) all_58_12 = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3462) all_56_12 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2959), (3462) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3463) e3 = e2
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3463) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3464) e3 = e2
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3447), (3464) imply:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3465) all_58_8 = e2
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (230), (231),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (3323), (3350), (3465), (function-axioms)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1068.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3466) ~ (all_56_12 = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3467) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3468) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3468) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3469) all_58_9 = e3 & op(e3, e0) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3469) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3470) all_58_9 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (227), (228),
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (3346), (3459), (3470), (function-axioms)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #326.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3471) all_58_10 = e3 & op(e2, e0) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3471) implies:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3472) all_58_10 = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (3350), (3359), (3459), (3472) are
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1060.
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3473) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3473) gives:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3474) all_58_11 = e3 & op(e1, e0) = e3
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3474) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3475) all_58_11 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3476) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3476) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3477) all_58_9 = e2 & op(e3, e0) = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3477) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3478) all_58_9 = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3359), (3478) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1324.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3479) all_58_10 = e2 & op(e2, e0) = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3479) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3480) op(e2, e0) = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2315), (3480), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1535.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3348) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (230), (231),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (3323), (3349), (3447), (3475),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #711.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3481) all_58_15 = e2 & op(e0, e0) = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (3346), (3481), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1452.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3482) all_58_15 = e3 & op(e0, e0) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3482) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3483) all_58_15 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3484) all_54_14 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (3436), (3484) are inconsistent by
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1413.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3485) ~ (all_54_14 = e3)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3486) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3486) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3487) all_54_14 = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (2313), (3487) are inconsistent by
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1232.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3488) ~ (all_54_14 = e2)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3489) all_54_14 = e1 | all_54_14 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3489) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3490) all_54_14 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (3490) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3491) all_52_11 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3491) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3492) all_52_11 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (390), (3492) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3493) ~ (all_6_2 = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3493) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3494) ~ (all_6_2 = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3436), (3492) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3495) ~ (e3 = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3496) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (238), (241),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2323), (3319), (3496), (function-axioms)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #130.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3497) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3497) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3498) all_58_6 = e1 & op(e1, e3) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3498) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3499) op(e1, e3) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3500) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3500) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3501) all_58_0 = e3 & op(e3, e3) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3501) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3502) all_58_0 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3319), (3502) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3503) e3 = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3503) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3504) e3 = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3447), (3504) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3505) all_58_8 = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (230), (231),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (3323), (3350), (3505), (function-axioms)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1068.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3506) all_58_2 = e3 & op(e2, e3) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3506) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3507) all_58_2 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3508) all_54_10 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (3508) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3509) all_6_2 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3509) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3510) all_6_2 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3510) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3511) all_56_14 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3467) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3512) all_56_13 = e2
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2293), (3512) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3513) e2 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3513) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3514) e2 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3350), (3514) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3515) all_58_11 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (39), (232), (248), (398),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3319), (3372), (3461), (3507), (3515),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #927.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3516) ~ (all_56_13 = e2)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3517) all_56_14 = e1 | all_56_15 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3517) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3518) all_56_14 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3511), (3518) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3519) e3 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (3519) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3520) $false
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3520) is inconsistent.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3521) all_56_15 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3435), (3521) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3522) e3 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3483), (3522) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3523) all_58_15 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (229), (247),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (2970), (3319), (3430), (3437), (3523),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #131.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3524) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (398), (3385), (3494), (3524) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1527.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3525) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3525) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3526) all_58_6 = e3 & op(e1, e3) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3526) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3527) op(e1, e3) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (3499), (3527), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1164.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3528) all_58_12 = e3 & op(e0, e3) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3528) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3529) all_58_12 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3461), (3529) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3530) e3 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3530) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3531) e3 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3483), (3531) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3532) all_58_15 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (229), (247),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (2970), (3319), (3430), (3437), (3532),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #131.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3533) all_58_12 = e1 & op(e0, e3) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3533) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3534) all_58_12 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (156), (3356), (3453), (3458), (3534),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #613.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3535) all_54_14 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (3382), (3535) are inconsistent by
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1400.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3536) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3536) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3537) all_58_13 = e0 & op(e0, e2) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3537) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3538) op(e0, e2) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (3356), (3538), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1040.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3539) all_58_14 = e0 & op(e0, e1) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3539) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3540) op(e0, e1) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3454), (3540), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3541) all_58_14 = e3 & op(e0, e1) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3541) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3542) all_58_14 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3543) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3543) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3544) all_58_12 = e1 & op(e0, e3) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3544) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3545) all_58_12 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3546) all_58_15 = e0 & op(e0, e0) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3546) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3547) all_58_15 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (229), (247),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (2970), (3319), (3430), (3437), (3547),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #131.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3548) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3548) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3549) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (156), (3356), (3542), (3545),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3549), (function-axioms) are inconsistent by
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #845.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3550) all_58_13 = e1 & op(e0, e2) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3550) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3551) op(e0, e2) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (156), (3356), (3551), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1319.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3552) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3552) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3553) all_58_14 = e1 & op(e0, e1) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3542), (3553) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #844.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3554) all_58_15 = e1 & op(e0, e0) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (397), (3554), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1418.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3555) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (397), (3346), (3431), (3555) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1014.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3556) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3556) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3557) ~ (all_56_14 = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3558) op(e0, e1) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (3557) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3559) ~ (all_6_2 = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3560) all_54_10 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (3560) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3561) all_6_2 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3561) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3562) all_6_2 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3562) imply:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3563) all_56_14 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3564) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (247), (249),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323), (2970), (3319), (3564), (function-axioms)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #147.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3565) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3565) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3566) all_58_8 = e3 & op(e1, e1) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3566) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3567) all_58_8 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3568) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (247), (2303), (2970), (3319),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3359), (3568), (function-axioms) are inconsistent
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #922.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3569) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3569) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3570) all_58_8 = e1 & op(e1, e1) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3570) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3571) all_58_8 = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3567), (3571) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #950.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3572) all_58_14 = e1 & op(e0, e1) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3572) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3573) op(e0, e1) = e1
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3558), (3573), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3574) all_58_14 = e3 & op(e0, e1) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3574) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3575) all_58_14 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3576) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3576) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3577) all_58_6 = e3 & op(e1, e3) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3577) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3578) op(e1, e3) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (215), (3563), (3578),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #144.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3579) all_58_7 = e3 & op(e1, e2) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3323), (3579), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1184.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3580) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3580) gives:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3581) all_58_8 = e3 & op(e1, e1) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3581) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3582) all_58_8 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (235), (247), (249),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2303), (2970), (3319), (3364), (3575), (3582),
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #920.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3583) all_58_11 = e3 & op(e1, e0) = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3583) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3584) all_58_11 = e3
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3350), (3584) are inconsistent by sub-proof
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1049.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3585) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (398), (3385), (3559), (3585) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1527.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3586) all_58_13 = e0 & op(e0, e2) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3586) implies:
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3587) op(e0, e2) = e0
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (3356), (3587), (function-axioms) are
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1040.
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (3588) all_58_9 = e0 & op(e3, e0) = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3588) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (3589) all_58_9 = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3359), (3589) are inconsistent by sub-proof
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | #1101.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | (3590) all_58_10 = e1 & op(e2, e0) = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2299), (3590), (function-axioms) are
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | (3591) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (397), (3350), (3591),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | #249.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | (3592) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3592) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3593) all_58_14 = e2 & op(e0, e1) = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (2313), (3593), (function-axioms) are
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1175.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3594) all_58_15 = e2 & op(e0, e0) = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (3346), (3594), (function-axioms) are
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1452.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | (3595) all_58_15 = e2 & op(e0, e0) = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (3346), (3595), (function-axioms) are
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1452.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | (3596) all_20_2 = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (3596) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | (3597) all_4_2 = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | SIMP: (3597) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | (3598) all_4_2 = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (3598) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | (3599) all_56_15 = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | REDUCE: (396), (3598) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | (3600) ~ (all_52_14 = e2)
% 153.70/26.21 | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | (3601) ~ (all_56_15 = e2)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | REDUCE: (3599), (3601) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | (3602) $false
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | CLOSE: (3602) is inconsistent.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | (3603) all_56_10 = e0 & op(e0, e2) = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | ALPHA: (3603) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | (3604) op(e0, e2) = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | (3605) all_56_12 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2959), (3605) are inconsistent by sub-proof
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | #886.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | (3606) ~ (all_56_12 = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | (3607) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | REDUCE: (2959), (3606) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | (3608) ~ (e3 = e2)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3607) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | (3609) all_56_13 = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2293), (3609) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | (3610) e2 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3610) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | (3611) $false
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3611) is inconsistent.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | (3612) all_56_14 = e1 | all_56_15 = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3612) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3613) all_56_14 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3613) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3614) all_6_2 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | SIMP: (3614) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3615) all_6_2 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (3615) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3616) ~ (all_52_8 = e1)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (3615) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3617) ~ (all_52_14 = e1)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3343), (3615) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3618) ~ (all_38_0 = e1)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (3615) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | (3619) ~ (e2 = e1)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | (3620) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (247), (249),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | (2315), (2970), (3319), (3620), (function-axioms)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | (3621) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3621) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | (3622) all_58_11 = e2 & op(e1, e0) = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3622) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | (3623) op(e1, e0) = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3600), (3623), (function-axioms) are
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1389.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | (3624) all_58_15 = e2 & op(e0, e0) = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3624) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | (3625) all_58_15 = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | (3626) op(e0, e0) = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | (3627) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3627) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (3628) all_58_12 = e1 & op(e0, e3) = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3628) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (3629) all_58_12 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3630) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (247), (249),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323), (2970), (3319), (3630), (function-axioms)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #147.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3631) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3631) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3632) all_58_8 = e3 & op(e1, e1) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3632) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3633) all_58_8 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (167), (200),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (235), (247), (249), (273), (288), (387),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2303), (2311), (2970), (3319), (3325), (3327),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3599), (3612), (3626), (3629), (3633),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #128.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3634) all_58_14 = e3 & op(e0, e1) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3634) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3635) all_58_14 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3636) op(e0, e1) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3637) all_58_15 = e0 & op(e0, e0) = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3625), (3637) are inconsistent by sub-proof
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #885.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3638) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3638) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3639) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3640) all_54_2 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (3640) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3641) all_52_8 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3327), (3641) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3642) $false
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3642) is inconsistent.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3643) ~ (all_54_2 = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3644) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3644) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3645) all_54_2 = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (3645) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3646) all_52_8 = e2
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2311), (3646) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3647) $false
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3647) is inconsistent.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3648) ~ (all_54_2 = e2)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3649) all_54_2 = e1 | all_54_2 = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3650) all_54_8 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3337), (3650) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3651) all_38_0 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3651) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3652) all_38_0 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3338), (3652) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3653) ~ (all_52_1 = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3342), (3652) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3654) ~ (all_52_14 = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3655) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3655) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3656) all_58_2 = e3 & op(e2, e3) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3656) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3657) op(e2, e3) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3653), (3657), (function-axioms) are
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1183.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3658) all_58_3 = e3 & op(e2, e2) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3658) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3659) all_58_3 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2307), (3659) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3660) e3 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3635), (3660) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3661) all_58_14 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (161), (167),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (200), (226), (235), (237), (238), (241),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247), (248), (249), (273), (288), (387), (2303),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2311), (2323), (2970), (3319), (3325),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3327), (3331), (3335), (3337), (3344), (3599),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3612), (3618), (3626), (3661), (function-axioms)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #126.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3662) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3662) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3663) all_58_5 = e3 & op(e2, e1) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (223), (224),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (2323), (3325), (3625), (3626), (3635),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3663), (function-axioms) are inconsistent by
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #883.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3664) all_58_10 = e3 & op(e2, e0) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3664) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3665) all_58_10 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3666) op(e2, e0) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3649) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3667) all_54_2 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (3667) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3668) all_52_8 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3616), (3668) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3669) $false
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3669) is inconsistent.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3670) all_54_2 = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (3670) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3671) all_52_8 = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3327), (3671) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3672) ~ (e3 = e0)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2311), (3671) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3673) ~ (e2 = e0)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3616), (3671) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3674) ~ (e1 = e0)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (3671) imply:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3675) op(e3, e1) = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3676) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3676) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3677) all_58_9 = e1 & op(e3, e0) = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3677) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3678) all_58_9 = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3679) op(e3, e0) = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3680) all_54_11 = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (3654), (3680) are inconsistent by
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1415.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3681) ~ (all_54_11 = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3682) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3683) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3683) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3684) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (167), (168), (2970), (3327), (3653),
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3684), (function-axioms) are inconsistent by
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #145.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3685) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3685) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3686) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3686) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3687) op(e3, e1) = e1
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3675), (3687), (function-axioms) are
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1281.
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3688) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3688) gives:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3689) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3689) implies:
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3690) op(e3, e0) = e3
% 153.70/26.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3329), (3690), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3691) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3691) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3692) op(e3, e0) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3682) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3693) all_54_11 = e2
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (3600), (3693) are inconsistent by
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1414.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3694) ~ (all_54_11 = e2)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3695) all_54_11 = e1 | all_54_11 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3695) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3696) all_54_11 = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (3617), (3696) are inconsistent by
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1228.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3697) all_54_11 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (3697) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3698) all_52_14 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3698) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3699) all_52_14 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e1, e0,
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (3679), (3692) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3700) e1 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3678), (3700) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3701) all_58_9 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (249), (2970), (3319), (3599),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3612), (3613), (3675), (3701), (function-axioms)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #125.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3702) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3702) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3703) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (162), (2296), (2315), (3613), (3703),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3704) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3704) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3705) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3705) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3706) op(e2, e0) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3666), (3706), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #143.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3707) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3707) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3708) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3708) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3709) ~ (all_56_15 = e0)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3710) op(e0, e1) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3711) op(e1, e0) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3712) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (165), (223),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (226), (3319), (3325), (3625), (3626),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3635), (3653), (3712), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #123.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3713) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3713) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3714) all_58_6 = e3 & op(e1, e3) = e3
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3714) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3715) all_58_6 = e3
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3682) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3716) all_54_11 = e2
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (3600), (3716) are inconsistent by
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1414.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3717) ~ (all_54_11 = e2)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3718) all_54_11 = e1 | all_54_11 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3718) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3719) all_54_11 = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (3617), (3719) are inconsistent by
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1228.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3720) all_54_11 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (3720) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3721) all_52_14 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3721) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3722) all_52_14 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (3722) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3723) op(e1, e0) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e1,
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (3636), (3710) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3724) e3 = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e1, e0,
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (3711), (3723) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3725) e1 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3724), (3725) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3726) e3 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3715), (3726) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3727) all_58_6 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3728) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (165), (223),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (226), (3319), (3325), (3625), (3626),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3635), (3653), (3728), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #123.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3713) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3665), (3726) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3729) all_58_10 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (165), (241), (2307), (2323),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3653), (3729), (function-axioms) are inconsistent
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #184.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3730) all_58_12 = e3 & op(e0, e3) = e3
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (161), (167),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (200), (226), (235), (237), (238), (241),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247), (248), (249), (273), (288), (387), (2303),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2311), (2323), (2970), (3319), (3325),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3327), (3331), (3335), (3337), (3344), (3599),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3612), (3618), (3626), (3629), (3635), (3730),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #122.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3731) all_58_12 = e3 & op(e0, e3) = e3
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (161), (167),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (200), (226), (235), (237), (238), (241),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247), (248), (249), (273), (288), (387), (2303),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2311), (2323), (2970), (3319), (3325),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3327), (3331), (3335), (3337), (3344), (3599),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3612), (3618), (3626), (3629), (3635), (3731),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #122.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3732) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3732) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3733) ~ (all_56_14 = e1)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3613), (3733) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3734) $false
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3734) is inconsistent.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3735) all_58_10 = e1 & op(e2, e0) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2299), (3735), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3736) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3736) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3737) all_58_11 = e1 & op(e1, e0) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3737) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3738) all_58_11 = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3739) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2970), (3319), (3739),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1255.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3740) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3740) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3741) all_58_4 = e1 & op(e3, e1) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3741) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742) op(e3, e1) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3675), (3742), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1281.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743) all_58_9 = e1 & op(e3, e0) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3743) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3744) all_58_9 = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3639) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3745) all_58_9 = e0 & op(e3, e0) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3745) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3746) all_58_9 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (249), (2970), (3319), (3599),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3612), (3613), (3675), (3746), (function-axioms)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #125.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3747) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3747) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3748) all_58_10 = e0 & op(e2, e0) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3748) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3749) all_58_10 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (165), (241), (2307), (2323),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3653), (3749), (function-axioms) are inconsistent
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #184.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3750) all_58_11 = e0 & op(e1, e0) = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3750) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3751) all_58_11 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3738), (3751) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3752) e1 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3744), (3752) imply:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3753) all_58_9 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (249), (2970), (3319), (3599),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3612), (3613), (3675), (3753), (function-axioms)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #125.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3754) all_58_15 = e1 & op(e0, e0) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3754) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3755) op(e0, e0) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3626), (3755), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1386.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3756) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3331), (3337), (3344), (3618), (3756) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #127.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (3757) all_58_13 = e1 & op(e0, e2) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3757) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (3758) op(e0, e2) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (3604), (3758), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1396.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | (3759) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3759) gives:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (3760) all_58_14 = e1 & op(e0, e1) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3760) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (3761) all_58_14 = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (161), (167),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (200), (226), (235), (237), (238), (241),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (247), (248), (249), (273), (288), (387), (2303),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2311), (2323), (2970), (3319), (3325),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (3327), (3331), (3335), (3337), (3344), (3599),
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (3612), (3618), (3626), (3761), (function-axioms)
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #126.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (3762) all_58_15 = e1 & op(e0, e0) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3762) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (3763) op(e0, e0) = e1
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3626), (3763), (function-axioms) are
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1386.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | (3764) all_56_15 = e0
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3599), (3764) are inconsistent by sub-proof
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | | #871.
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | (3765) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 153.70/26.22 | | | | | | | | | | | | | | | | | $i(all_38_1)
% 153.70/26.22 | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | ALPHA: (3765) implies:
% 153.70/26.22 | | | | | | | | | | | | | | | | | (3766) ~ (all_38_1 = e1)
% 153.70/26.22 | | | | | | | | | | | | | | | | | (3767) op(e2, e2) = all_38_1
% 153.70/26.22 | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (61), (73), (76), (85), (108), (110), (111),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (115), (116), (118), (119), (121), (123), (124),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (126), (131), (132), (133), (134), (137), (138),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (139), (141), (142), (143), (144), (146), (147),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (155), (156), (157), (158), (160), (161), (162),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (163), (165), (166), (167), (168), (187), (188),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (189), (190), (191), (192), (193), (194), (195),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (196), (197), (198), (199), (200), (208), (209),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (211), (212), (213), (215), (216), (221), (223),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (228), (229), (230),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (231), (232), (233), (234), (235), (236), (237),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (238), (239), (240), (241), (242), (243), (244),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (246), (247), (248), (249), (251), (252), (261),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (262), (263), (264), (265), (273), (274), (275),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (276), (277), (282), (286), (287), (288), (304),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (306), (335), (339), (348), (354), (360), (373),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (374), (375), (376), (378), (380), (382), (384),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (385), (386), (387), (388), (390), (392), (393),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (394), (395), (396), (397), (398), (2310), (2311),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (2955), (2959), (2960), (2961), (2962), (2963),
% 153.70/26.22 | | | | | | | | | | | | | | | | | (3766), (3767), (function-axioms) are inconsistent
% 153.70/26.22 | | | | | | | | | | | | | | | | | by sub-proof #867.
% 153.70/26.22 | | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | End of split
% 153.70/26.22 | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | Case 2:
% 153.70/26.22 | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | (3768) all_58_1 = e2 & op(e3, e2) = e2
% 153.70/26.22 | | | | | | | | | | | | | | | |
% 153.70/26.22 | | | | | | | | | | | | | | | | ALPHA: (3768) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | (3769) op(e3, e2) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (2970), (3769), (function-axioms) are
% 153.70/26.23 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | (3770) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | REF_CLOSE: (166), (167), (2311), (2963), (3770),
% 153.70/26.23 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 153.70/26.23 | | | | | | | | | | | | | | | #868.
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | (3771) all_10_2 = e0
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | COMBINE_EQS: (297), (3771) imply:
% 153.70/26.23 | | | | | | | | | | (3772) all_56_12 = e0
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | REDUCE: (362), (3771) imply:
% 153.70/26.23 | | | | | | | | | | (3773) ~ (all_52_1 = e0)
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | BETA: splitting (198) gives:
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | (3774) all_54_4 = e3
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | COMBINE_EQS: (286), (3774) imply:
% 153.70/26.23 | | | | | | | | | | | (3775) all_52_1 = e3
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | SIMP: (3775) implies:
% 153.70/26.23 | | | | | | | | | | | (3776) all_52_1 = e3
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | REDUCE: (143), (3776) imply:
% 153.70/26.23 | | | | | | | | | | | (3777) ~ (all_52_13 = e3)
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | SIMP: (3777) implies:
% 153.70/26.23 | | | | | | | | | | | (3778) ~ (all_52_13 = e3)
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | BETA: splitting (219) gives:
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | (3779) ~ (all_56_12 = e0)
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | REDUCE: (3772), (3779) imply:
% 153.70/26.23 | | | | | | | | | | | | (3780) $false
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | CLOSE: (3780) is inconsistent.
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | (3781) all_56_2 = e3 & op(e3, e0) = e3
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | ALPHA: (3781) implies:
% 153.70/26.23 | | | | | | | | | | | | (3782) op(e3, e0) = e3
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | BETA: splitting (195) gives:
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | (3783) all_54_7 = e3
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | REF_CLOSE: (276), (3778), (3783) are inconsistent by
% 153.70/26.23 | | | | | | | | | | | | | sub-proof #1428.
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | (3784) ~ (all_54_7 = e3)
% 153.70/26.23 | | | | | | | | | | | | | (3785) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | BETA: splitting (3785) gives:
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | (3786) all_54_7 = e2
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | REF_CLOSE: (276), (2315), (3786) are inconsistent by
% 153.70/26.23 | | | | | | | | | | | | | | sub-proof #1427.
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | (3787) all_54_7 = e1 | all_54_7 = e0
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | BETA: splitting (3787) gives:
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | (3788) all_54_7 = e1
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | REF_CLOSE: (276), (2299), (3788) are inconsistent by
% 153.70/26.23 | | | | | | | | | | | | | | | sub-proof #1426.
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | (3789) all_54_7 = e0
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | COMBINE_EQS: (276), (3789) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3790) all_52_13 = e0
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | SIMP: (3790) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | (3791) all_52_13 = e0
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | REDUCE: (108), (3791) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3792) ~ (all_52_14 = e0)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | SIMP: (3792) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | (3793) ~ (all_52_14 = e0)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | REDUCE: (395), (3791) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3794) ~ (all_4_2 = e0)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | SIMP: (3794) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | (3795) ~ (all_4_2 = e0)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | REDUCE: (3778), (3791) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3796) ~ (e3 = e0)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | (3797) ~ (all_56_15 = e3)
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | REDUCE: (261), (3797) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | | (3798) ~ (all_4_2 = e3)
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3799) all_54_15 = e3
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (3798), (3799) are inconsistent by
% 153.70/26.23 | | | | | | | | | | | | | | | | | sub-proof #1543.
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3800) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | BETA: splitting (3800) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | (3801) all_54_15 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (3801) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | (3802) all_4_2 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | SIMP: (3802) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | (3803) all_4_2 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (3803) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | (3804) all_56_15 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | REDUCE: (396), (3803) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | (3805) ~ (all_52_14 = e2)
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | (3806) all_56_12 = e3
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3772), (3806) are inconsistent by sub-proof
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | #280.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | (3807) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (3807) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | (3808) all_56_13 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2293), (3808) are inconsistent by sub-proof
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | #150.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | (3809) all_56_14 = e1 | all_56_15 = e0
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3809) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3810) all_56_14 = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (3810) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3811) all_6_2 = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (3811) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3812) ~ (all_52_14 = e1)
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (166), (191), (265), (3782), (3793),
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3805), (3812), (function-axioms) are inconsistent
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | by sub-proof #121.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3813) all_56_15 = e0
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3804), (3813) are inconsistent by sub-proof
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | #871.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | (3814) all_54_15 = e1 | all_54_15 = e0
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (397), (3795), (3814) are inconsistent by
% 153.70/26.23 | | | | | | | | | | | | | | | | | | sub-proof #1295.
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | (3815) all_56_15 = e3
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (3815) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | | (3816) all_4_2 = e3
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | REDUCE: (394), (3816) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | | (3817) ~ (all_52_12 = e3)
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3782), (3817), (function-axioms) are
% 153.70/26.23 | | | | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | (3818) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | REF_CLOSE: (286), (2294), (2310), (3773), (3818) are
% 153.70/26.23 | | | | | | | | | | | inconsistent by sub-proof #1187.
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | |
% 153.70/26.23 | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | |
% 153.70/26.23 | | | | | | | | | (3819) all_58_10 = e2 & op(e2, e0) = e2
% 153.70/26.23 | | | | | | | | |
% 153.70/26.23 | | | | | | | | | ALPHA: (3819) implies:
% 153.70/26.23 | | | | | | | | | (3820) op(e2, e0) = e2
% 153.70/26.23 | | | | | | | | |
% 153.70/26.23 | | | | | | | | | REF_CLOSE: (162), (2315), (3820), (function-axioms) are
% 153.70/26.23 | | | | | | | | | inconsistent by sub-proof #1535.
% 153.70/26.23 | | | | | | | | |
% 153.70/26.23 | | | | | | | | End of split
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | End of split
% 153.70/26.23 | | | | | | |
% 153.70/26.23 | | | | | | End of split
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | Case 2:
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | (3821) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 153.70/26.23 | | | | | | op(e0, e2) = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | REF_CLOSE: (156), (160), (2296), (2297), (3821), (function-axioms)
% 153.70/26.23 | | | | | | are inconsistent by sub-proof #120.
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | End of split
% 153.70/26.23 | | | | |
% 153.70/26.23 | | | | End of split
% 153.70/26.23 | | | |
% 153.70/26.23 | | | End of split
% 153.70/26.23 | | |
% 153.70/26.23 | | Case 2:
% 153.70/26.23 | | |
% 153.70/26.23 | | | (3822) all_6_2 = e2
% 153.70/26.23 | | | (3823) ( ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 & op(e2, e2) =
% 153.70/26.23 | | | all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e3) &
% 153.70/26.23 | | | op(e2, e2) = all_6_1 & $i(all_6_1))
% 153.70/26.23 | | |
% 153.70/26.23 | | | COMBINE_EQS: (346), (3822) imply:
% 153.70/26.23 | | | (3824) all_18_2 = e2
% 153.70/26.23 | | |
% 153.70/26.23 | | | COMBINE_EQS: (273), (3822) imply:
% 153.70/26.23 | | | (3825) all_56_14 = e2
% 153.70/26.23 | | |
% 153.70/26.23 | | | REDUCE: (374), (3822) imply:
% 153.70/26.23 | | | (3826) ~ (all_52_2 = e2)
% 153.70/26.23 | | |
% 153.70/26.23 | | | REDUCE: (385), (3822) imply:
% 153.70/26.23 | | | (3827) ~ (all_52_6 = e2)
% 153.70/26.23 | | |
% 153.70/26.23 | | | REDUCE: (387), (3822) imply:
% 153.70/26.23 | | | (3828) ~ (all_52_8 = e2)
% 153.70/26.23 | | |
% 153.70/26.23 | | | REDUCE: (388), (3822) imply:
% 153.70/26.23 | | | (3829) ~ (all_52_9 = e2)
% 153.70/26.23 | | |
% 153.70/26.23 | | | REDUCE: (390), (3822) imply:
% 153.70/26.23 | | | (3830) ~ (all_52_11 = e2)
% 153.70/26.23 | | |
% 153.70/26.23 | | | REDUCE: (392), (3822) imply:
% 153.70/26.23 | | | (3831) ~ (all_52_14 = e2)
% 153.70/26.23 | | |
% 153.70/26.23 | | | BETA: splitting (214) gives:
% 153.70/26.23 | | |
% 153.70/26.23 | | | Case 1:
% 153.70/26.23 | | | |
% 153.70/26.23 | | | | (3832) ~ (all_56_14 = e2)
% 153.70/26.23 | | | |
% 153.70/26.23 | | | | REDUCE: (3825), (3832) imply:
% 153.70/26.23 | | | | (3833) $false
% 153.70/26.23 | | | |
% 153.70/26.23 | | | | CLOSE: (3833) is inconsistent.
% 153.70/26.23 | | | |
% 153.70/26.23 | | | Case 2:
% 153.70/26.23 | | | |
% 153.70/26.23 | | | | (3834) all_56_7 = e1 & op(e1, e2) = e1
% 153.70/26.23 | | | |
% 153.70/26.23 | | | | ALPHA: (3834) implies:
% 153.70/26.23 | | | | (3835) op(e1, e2) = e1
% 153.70/26.23 | | | |
% 153.70/26.23 | | | | BETA: splitting (236) gives:
% 153.70/26.23 | | | |
% 153.70/26.23 | | | | Case 1:
% 153.70/26.23 | | | | |
% 153.70/26.23 | | | | | (3836) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 153.70/26.23 | | | | | e1) = e2)
% 153.70/26.23 | | | | |
% 153.70/26.23 | | | | | REF_CLOSE: (163), (167), (3828), (3829), (3836), (function-axioms) are
% 153.70/26.23 | | | | | inconsistent by sub-proof #119.
% 153.70/26.23 | | | | |
% 153.70/26.23 | | | | Case 2:
% 153.70/26.23 | | | | |
% 153.70/26.23 | | | | | (3837) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 153.70/26.23 | | | | | e1) = e2)
% 153.70/26.23 | | | | |
% 153.70/26.23 | | | | | BETA: splitting (3837) gives:
% 153.70/26.23 | | | | |
% 153.70/26.23 | | | | | Case 1:
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | (3838) all_58_8 = e2 & op(e1, e1) = e2
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | ALPHA: (3838) implies:
% 153.70/26.23 | | | | | | (3839) all_58_8 = e2
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1, e2,
% 153.70/26.23 | | | | | | e1, simplifying with (160), (3835) gives:
% 153.70/26.23 | | | | | | (3840) all_52_6 = e1
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | REDUCE: (141), (3840) imply:
% 153.70/26.23 | | | | | | (3841) ~ (all_52_2 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | REDUCE: (134), (3840) imply:
% 153.70/26.23 | | | | | | (3842) ~ (all_52_4 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | REDUCE: (126), (3840) imply:
% 153.70/26.23 | | | | | | (3843) ~ (all_52_7 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | SIMP: (3843) implies:
% 153.70/26.23 | | | | | | (3844) ~ (all_52_7 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | REDUCE: (124), (3840) imply:
% 153.70/26.23 | | | | | | (3845) ~ (all_52_14 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | SIMP: (3845) implies:
% 153.70/26.23 | | | | | | (3846) ~ (all_52_14 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | REDUCE: (378), (3840) imply:
% 153.70/26.23 | | | | | | (3847) ~ (all_8_2 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | SIMP: (3847) implies:
% 153.70/26.23 | | | | | | (3848) ~ (all_8_2 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | REDUCE: (3827), (3840) imply:
% 153.70/26.23 | | | | | | (3849) ~ (e2 = e1)
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | BETA: splitting (231) gives:
% 153.70/26.23 | | | | | |
% 153.70/26.23 | | | | | | Case 1:
% 153.70/26.23 | | | | | | |
% 153.70/26.23 | | | | | | | (3850) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 153.70/26.23 | | | | | | | op(e1, e2) = e1)
% 153.70/26.23 | | | | | | |
% 153.70/26.23 | | | | | | | BETA: splitting (3850) gives:
% 153.70/26.23 | | | | | | |
% 153.70/26.23 | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | | (3851) all_58_6 = e1 & op(e1, e3) = e1
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | | ALPHA: (3851) implies:
% 153.70/26.23 | | | | | | | | (3852) op(e1, e3) = e1
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | | REF_CLOSE: (161), (3841), (3852), (function-axioms) are
% 153.70/26.23 | | | | | | | | inconsistent by sub-proof #1412.
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | | (3853) all_58_7 = e1 & op(e1, e2) = e1
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | | ALPHA: (3853) implies:
% 153.70/26.23 | | | | | | | | (3854) all_58_7 = e1
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | | BETA: splitting (46) gives:
% 153.70/26.23 | | | | | | | |
% 153.70/26.23 | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | |
% 153.70/26.23 | | | | | | | | | (3855) ~ (all_10_2 = e0)
% 153.70/26.23 | | | | | | | | |
% 153.70/26.23 | | | | | | | | | BETA: splitting (52) gives:
% 153.70/26.23 | | | | | | | | |
% 153.70/26.23 | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | (3856) ~ (all_14_2 = e3)
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | REDUCE: (351), (3856) imply:
% 153.70/26.23 | | | | | | | | | | (3857) ~ (all_8_2 = e3)
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | BETA: splitting (58) gives:
% 153.70/26.23 | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | (3858) ~ (all_18_2 = e2)
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | REDUCE: (3824), (3858) imply:
% 153.70/26.23 | | | | | | | | | | | (3859) $false
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | CLOSE: (3859) is inconsistent.
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | (3860) ( ~ (all_18_0 = e3) & op(all_18_1, e1) = all_18_0
% 153.70/26.23 | | | | | | | | | | | & op(e2, e2) = all_18_1 & $i(all_18_0) &
% 153.70/26.23 | | | | | | | | | | | $i(all_18_1)) | ( ~ (all_18_1 = e0) & op(e2, e2)
% 153.70/26.23 | | | | | | | | | | | = all_18_1 & $i(all_18_1))
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | BETA: splitting (55) gives:
% 153.70/26.23 | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | (3861) ~ (all_16_2 = e2)
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | REDUCE: (349), (3861) imply:
% 153.70/26.23 | | | | | | | | | | | | (3862) ~ (all_10_2 = e2)
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | BETA: splitting (76) gives:
% 153.70/26.23 | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | (3863) ~ (all_30_2 = e0)
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | REDUCE: (354), (3863) imply:
% 153.70/26.23 | | | | | | | | | | | | | (3864) ~ (all_8_2 = e0)
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | BETA: splitting (197) gives:
% 153.70/26.23 | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | (3865) all_54_5 = e3
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | COMBINE_EQS: (282), (3865) imply:
% 153.70/26.23 | | | | | | | | | | | | | | (3866) all_8_2 = e3
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | REDUCE: (3857), (3866) imply:
% 153.70/26.23 | | | | | | | | | | | | | | (3867) $false
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | CLOSE: (3867) is inconsistent.
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | (3868) ~ (all_54_5 = e3)
% 153.70/26.23 | | | | | | | | | | | | | | (3869) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | BETA: splitting (3869) gives:
% 153.70/26.23 | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | (3870) all_54_5 = e2
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | COMBINE_EQS: (282), (3870) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3871) all_8_2 = e2
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | COMBINE_EQS: (360), (3871) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3872) all_56_13 = e2
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | REDUCE: (376), (3871) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3873) ~ (all_52_4 = e2)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | REDUCE: (384), (3871) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3874) ~ (all_52_13 = e2)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | REDUCE: (3857), (3871) imply:
% 153.70/26.23 | | | | | | | | | | | | | | | (3875) ~ (e3 = e2)
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 153.70/26.23 | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | (3876) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | BETA: splitting (3876) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3877) all_58_0 = e2 & op(e3, e3) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3862), (3877), (function-axioms) are
% 153.70/26.23 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1523.
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3878) all_58_2 = e2 & op(e2, e3) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | ALPHA: (3878) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3879) op(e2, e3) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (282), (373), (3848), (3864), (3869),
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3879), (function-axioms) are inconsistent by
% 153.70/26.23 | | | | | | | | | | | | | | | | | sub-proof #321.
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | (3880) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 153.70/26.23 | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | BETA: splitting (3880) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3881) all_58_6 = e2 & op(e1, e3) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | ALPHA: (3881) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3882) all_58_6 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (233), (3839),
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3854), (3882), (function-axioms) are inconsistent
% 153.70/26.23 | | | | | | | | | | | | | | | | | by sub-proof #116.
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3883) all_58_12 = e2 & op(e0, e3) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | ALPHA: (3883) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3884) all_58_12 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | (3885) op(e0, e3) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | (3886) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 153.70/26.23 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | BETA: splitting (3886) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | (3887) all_58_12 = e1 & op(e0, e3) = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3884), (3887) are inconsistent by sub-proof
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | #1492.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | (3888) all_58_13 = e1 & op(e0, e2) = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (3844), (3888), (function-axioms) are
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | (3889) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 153.70/26.23 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | BETA: splitting (3889) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | (3890) all_58_14 = e1 & op(e0, e1) = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | ALPHA: (3890) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | (3891) op(e0, e1) = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | (3892) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (246), (248),
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | (252), (3873), (3884), (3892), (function-axioms)
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #115.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | (3893) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3893) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3894) all_58_4 = e2 & op(e3, e1) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3894) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3895) op(e3, e1) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3828), (3895), (function-axioms) are
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1212.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3896) all_58_9 = e2 & op(e3, e0) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3896) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3897) all_58_9 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | (3898) op(e3, e0) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | (3899) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3899) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | (3900) all_58_9 = e1 & op(e3, e0) = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3900) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | (3901) all_58_9 = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3897), (3901) are inconsistent by sub-proof
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | #1324.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | (3902) all_58_10 = e1 & op(e2, e0) = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3902) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | (3903) all_58_10 = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | (3904) op(e2, e0) = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | (3905) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3905) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3906) all_58_2 = e2 & op(e2, e3) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3906) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3907) op(e2, e3) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (282), (373), (3848), (3864), (3869),
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3907), (function-axioms) are inconsistent by
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #321.
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3908) all_58_3 = e2 & op(e2, e2) = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3908) implies:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3909) all_58_3 = e2
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, e0, simplifying with (155), (3891) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3910) all_52_11 = e1
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (157), (3885) gives:
% 153.70/26.23 | | | | | | | | | | | | | | | | | | | | | | | | | (3911) all_52_3 = e2
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e2, simplifying with (162), (3904) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3912) all_52_13 = e1
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (166), (3898) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3913) all_52_12 = e2
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (3911) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3914) ~ (all_52_7 = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3914) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3915) ~ (all_52_7 = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (3913) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3916) ~ (all_52_14 = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (3913) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3917) ~ (all_10_2 = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (3913) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3918) ~ (all_4_2 = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3918) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3919) ~ (all_4_2 = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (3912) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | (3920) ~ (all_4_2 = e1)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (3921) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3921) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3922) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3922) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3923) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3923) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3924) ~ (all_56_13 = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3872), (3924) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3925) $false
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3925) is inconsistent.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3926) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3926) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3927) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3927) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3928) op(e3, e2) = e2
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3873), (3928), (function-axioms) are
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1539.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3929) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3929) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3930) op(e1, e3) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3931) op(e3, e1) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3932) ~ (all_56_15 = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (261), (3932) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3933) ~ (all_4_2 = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3934) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3934) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3935) all_58_9 = e3 & op(e3, e0) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (168), (251), (3862), (3873), (3931),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3935), (function-axioms) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1287.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3936) all_58_10 = e3 & op(e2, e0) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3936) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3937) all_58_10 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3903), (3937) are inconsistent by sub-proof
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1120.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3938) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3938) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3939) all_58_11 = e3 & op(e1, e0) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3939) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3940) op(e1, e0) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3941) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3941) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3942) all_58_6 = e0 & op(e1, e3) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3942) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3943) op(e1, e3) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3930), (3943), (function-axioms) are
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3944) all_58_7 = e0 & op(e1, e2) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3944) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3945) all_58_7 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3854), (3945) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3946) e1 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3903), (3946) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3947) all_58_10 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (227), (397), (3897), (3940),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3947), (function-axioms) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #264.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3948) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3948) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3949) all_58_8 = e0 & op(e1, e1) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (165), (240), (282), (373), (382),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384), (3839), (3848), (3864), (3869), (3909),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3949), (function-axioms) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #113.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3950) all_58_11 = e0 & op(e1, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3950) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3951) op(e1, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3940), (3951), (function-axioms) are
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #118.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3952) all_58_15 = e3 & op(e0, e0) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3952) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3953) all_58_15 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3954) all_54_15 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (3933), (3954) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1543.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3955) ~ (all_54_15 = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3956) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3956) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3957) all_54_15 = e2
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (3919), (3957) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1542.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3958) ~ (all_54_15 = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3959) all_54_15 = e1 | all_54_15 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3959) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3960) all_54_15 = e1
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (397), (3960) are inconsistent by sub-proof
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1541.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3961) all_54_15 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (3961) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3962) all_4_2 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3962) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3963) all_4_2 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (396), (3963) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3964) ~ (all_52_14 = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3933), (3963) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3965) ~ (e3 = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3919), (3963) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3966) ~ (e2 = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (3963) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3967) ~ (e1 = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3968) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3968) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3969) all_58_6 = e0 & op(e1, e3) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3969) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3970) all_58_6 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3971) all_58_15 = e0 & op(e0, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3953), (3971) are inconsistent by sub-proof
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1013.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3972) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3972) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3973) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3974) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3974) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3975) all_58_6 = e3 & op(e1, e3) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3975) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3976) all_58_6 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3970), (3976) are inconsistent by sub-proof
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1321.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3977) all_58_7 = e3 & op(e1, e2) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3854), (3977) are inconsistent by sub-proof
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1421.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3978) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3978) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3979) all_58_8 = e3 & op(e1, e1) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3839), (3979) are inconsistent by sub-proof
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #112.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3980) all_58_11 = e3 & op(e1, e0) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3980) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3981) op(e1, e0) = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3973) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3982) all_58_9 = e0 & op(e3, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3982) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3983) op(e3, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3898), (3983), (function-axioms) are
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1500.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3984) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3984) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3985) all_58_10 = e0 & op(e2, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3985) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3986) all_58_10 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (227), (397), (3897), (3981),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3986), (function-axioms) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #264.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3987) all_58_11 = e0 & op(e1, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3987) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3988) op(e1, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3981), (3988), (function-axioms) are
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #118.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3989) all_58_7 = e0 & op(e1, e2) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3854), (3989) are inconsistent by sub-proof
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #992.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3990) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3990) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3991) all_58_8 = e0 & op(e1, e1) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (165), (240), (282), (373), (382),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384), (3839), (3848), (3864), (3869), (3909),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3991), (function-axioms) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #113.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3992) all_58_11 = e0 & op(e1, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3992) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3993) op(e1, e0) = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (191), (265), (3831), (3846), (3964),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3993), (function-axioms) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #111.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3994) all_56_15 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (3994) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3995) all_4_2 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3995) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3996) all_4_2 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (3996) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3997) ~ (all_52_7 = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3998) all_54_13 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (3997), (3998) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1435.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3999) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3999) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4000) all_54_13 = e2
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (3915), (4000) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1370.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4001) all_54_13 = e1 | all_54_13 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4001) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4002) all_54_13 = e1
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (3844), (4002) are inconsistent by
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #876.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003) all_54_13 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (4003) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4004) all_52_7 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4004) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4005) all_52_7 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (4005) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4006) ~ (all_52_4 = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4007) all_54_1 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (4007) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4008) all_52_4 = e3
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (4008) imply:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4009) ~ (all_52_8 = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4009) implies:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4010) ~ (all_52_8 = e3)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3931), (4010), (function-axioms) are
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (3842), (3873), (4006), (4011) are
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4012) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (161), (187), (212), (261), (306), (397),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3841), (3898), (3919), (4012), (function-axioms)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #110.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (4013) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4013) gives:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4014) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (162), (282), (378), (3848), (3864),
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3869), (3872), (3874), (4014), (function-axioms)
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #109.
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4015) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4015) gives:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4016) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4016) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4017) ~ (all_56_13 = e2)
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3872), (4017) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4018) $false
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4018) is inconsistent.
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4019) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4019) gives:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4020) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4020) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4021) op(e1, e0) = e1
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3846), (4021), (function-axioms) are
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #108.
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4022) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4022) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4023) op(e0, e1) = e0
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3891), (4023), (function-axioms) are
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129.
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | (4024) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (282), (382), (3848), (3864),
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | (3869), (3874), (4024), (function-axioms) are
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | (4025) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (230), (233),
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | (397), (3839), (3854), (4025), (function-axioms)
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #104.
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | (4026) all_58_15 = e1 & op(e0, e0) = e1
% 153.70/26.25 | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (397), (4026), (function-axioms) are
% 153.70/26.25 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1418.
% 153.70/26.25 | | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | (4027) all_54_5 = e1 | all_54_5 = e0
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | REF_CLOSE: (282), (3848), (3864), (4027) are inconsistent by
% 153.70/26.25 | | | | | | | | | | | | | | | sub-proof #1239.
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | (4028) all_30_2 = e0
% 153.70/26.25 | | | | | | | | | | | | | (4029) ( ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0
% 153.70/26.25 | | | | | | | | | | | | | & op(e0, e0) = all_30_1 & $i(all_30_0) &
% 153.70/26.25 | | | | | | | | | | | | | $i(all_30_1)) | ( ~ (all_30_1 = e1) & op(e0, e0)
% 153.70/26.25 | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | COMBINE_EQS: (354), (4028) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4030) all_8_2 = e0
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | SIMP: (4030) implies:
% 153.70/26.25 | | | | | | | | | | | | | (4031) all_8_2 = e0
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | COMBINE_EQS: (360), (4031) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4032) all_56_13 = e0
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | REDUCE: (373), (4031) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4033) ~ (all_52_1 = e0)
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | REDUCE: (380), (4031) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4034) ~ (all_52_7 = e0)
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | REDUCE: (382), (4031) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4035) ~ (all_52_9 = e0)
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | REDUCE: (384), (4031) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4036) ~ (all_52_13 = e0)
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | REDUCE: (3857), (4031) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4037) ~ (e3 = e0)
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | REDUCE: (3848), (4031) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4038) ~ (e1 = e0)
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | REDUCE: (42), (4031) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4039) op(e2, e2) = e0
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | BETA: splitting (4029) gives:
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | (4040) ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0 &
% 153.70/26.25 | | | | | | | | | | | | | | op(e0, e0) = all_30_1 & $i(all_30_0) &
% 153.70/26.25 | | | | | | | | | | | | | | $i(all_30_1)
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | ALPHA: (4040) implies:
% 153.70/26.25 | | | | | | | | | | | | | | (4041) op(e0, e0) = all_30_1
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (42), (45), (108),
% 153.70/26.25 | | | | | | | | | | | | | | (111), (155), (156), (158), (161), (162), (163),
% 153.70/26.25 | | | | | | | | | | | | | | (165), (166), (167), (168), (208), (216), (223),
% 153.70/26.25 | | | | | | | | | | | | | | (224), (225), (227), (228), (229), (230), (233),
% 153.70/26.25 | | | | | | | | | | | | | | (234), (237), (238), (239), (241), (245), (246),
% 153.70/26.25 | | | | | | | | | | | | | | (248), (250), (251), (252), (253), (261), (395),
% 153.70/26.25 | | | | | | | | | | | | | | (397), (3823), (3828), (3835), (3839), (3844),
% 153.70/26.25 | | | | | | | | | | | | | | (3848), (3854), (3855), (3857), (3860), (3862),
% 153.70/26.25 | | | | | | | | | | | | | | (4032), (4033), (4034), (4035), (4036), (4039),
% 153.70/26.25 | | | | | | | | | | | | | | (4041), (function-axioms) are inconsistent by
% 153.70/26.25 | | | | | | | | | | | | | | sub-proof #94.
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | (4042) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 &
% 153.70/26.25 | | | | | | | | | | | | | | $i(all_30_1)
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | ALPHA: (4042) implies:
% 153.70/26.25 | | | | | | | | | | | | | | (4043) op(e0, e0) = all_30_1
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (42), (45), (108),
% 153.70/26.25 | | | | | | | | | | | | | | (111), (155), (156), (158), (161), (162), (163),
% 153.70/26.25 | | | | | | | | | | | | | | (165), (166), (167), (168), (208), (216), (223),
% 153.70/26.25 | | | | | | | | | | | | | | (224), (225), (227), (228), (229), (230), (233),
% 153.70/26.25 | | | | | | | | | | | | | | (234), (237), (238), (239), (241), (245), (246),
% 153.70/26.25 | | | | | | | | | | | | | | (248), (250), (251), (252), (253), (261), (395),
% 153.70/26.25 | | | | | | | | | | | | | | (397), (3823), (3828), (3835), (3839), (3844),
% 153.70/26.25 | | | | | | | | | | | | | | (3848), (3854), (3855), (3857), (3860), (3862),
% 153.70/26.25 | | | | | | | | | | | | | | (4032), (4033), (4034), (4035), (4036), (4039),
% 153.70/26.25 | | | | | | | | | | | | | | (4043), (function-axioms) are inconsistent by
% 153.70/26.25 | | | | | | | | | | | | | | sub-proof #94.
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | (4044) all_16_2 = e2
% 153.70/26.25 | | | | | | | | | | | | (4045) ( ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0
% 153.70/26.25 | | | | | | | | | | | | & op(e2, e2) = all_16_1 & $i(all_16_0) &
% 153.70/26.25 | | | | | | | | | | | | $i(all_16_1)) | ( ~ (all_16_1 = e0) & op(e2, e2)
% 153.70/26.25 | | | | | | | | | | | | = all_16_1 & $i(all_16_1))
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | COMBINE_EQS: (349), (4044) imply:
% 153.70/26.25 | | | | | | | | | | | | (4046) all_10_2 = e2
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | SIMP: (4046) implies:
% 153.70/26.25 | | | | | | | | | | | | (4047) all_10_2 = e2
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | COMBINE_EQS: (356), (4047) imply:
% 153.70/26.25 | | | | | | | | | | | | (4048) all_38_2 = e2
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | COMBINE_EQS: (297), (4047) imply:
% 153.70/26.25 | | | | | | | | | | | | (4049) all_56_12 = e2
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | REDUCE: (362), (4047) imply:
% 153.70/26.25 | | | | | | | | | | | | (4050) ~ (all_52_1 = e2)
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | REDUCE: (368), (4047) imply:
% 153.70/26.25 | | | | | | | | | | | | (4051) ~ (all_52_4 = e2)
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | REDUCE: (372), (4047) imply:
% 153.70/26.25 | | | | | | | | | | | | (4052) ~ (all_52_12 = e2)
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | BETA: splitting (88) gives:
% 153.70/26.25 | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | (4053) ~ (all_38_2 = e2)
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | REDUCE: (4048), (4053) imply:
% 153.70/26.25 | | | | | | | | | | | | | (4054) $false
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | CLOSE: (4054) is inconsistent.
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | (4055) ( ~ (all_38_0 = e0) & op(all_38_1, e3) = all_38_0
% 153.70/26.25 | | | | | | | | | | | | | & op(e2, e2) = all_38_1 & $i(all_38_0) &
% 153.70/26.25 | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e1) & op(e2, e2)
% 153.70/26.25 | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | BETA: splitting (4055) gives:
% 153.70/26.25 | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | (4056) ~ (all_38_0 = e0) & op(all_38_1, e3) = all_38_0 &
% 153.70/26.25 | | | | | | | | | | | | | | op(e2, e2) = all_38_1 & $i(all_38_0) &
% 153.70/26.25 | | | | | | | | | | | | | | $i(all_38_1)
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | ALPHA: (4056) implies:
% 153.70/26.25 | | | | | | | | | | | | | | (4057) op(e2, e2) = all_38_1
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | (4058) ~ (all_56_12 = e2)
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | REDUCE: (4049), (4058) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | (4059) $false
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | CLOSE: (4059) is inconsistent.
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | (4060) all_56_0 = e3 & op(e3, e2) = e3
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | ALPHA: (4060) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | (4061) op(e3, e2) = e3
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | (4062) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | BETA: splitting (4062) gives:
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4063) all_58_0 = e2 & op(e3, e3) = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | ALPHA: (4063) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4064) all_58_0 = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2,
% 153.70/26.25 | | | | | | | | | | | | | | | | | all_38_1, e2, e2, simplifying with (42), (4057)
% 153.70/26.25 | | | | | | | | | | | | | | | | | gives:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4065) all_38_1 = all_8_2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 153.70/26.25 | | | | | | | | | | | | | | | | | e2, e3, simplifying with (168), (4061) gives:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4066) all_52_4 = e3
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REDUCE: (133), (4066) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4067) ~ (all_52_7 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | SIMP: (4067) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4068) ~ (all_52_7 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REDUCE: (132), (4066) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4069) ~ (all_52_8 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | SIMP: (4069) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4070) ~ (all_52_8 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REDUCE: (131), (4066) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4071) ~ (all_52_12 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | SIMP: (4071) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4072) ~ (all_52_12 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REDUCE: (376), (4066) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4073) ~ (all_8_2 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (61),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (76), (108), (110), (123), (138), (143), (146),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (155), (156), (157), (158), (160), (161), (162),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (165), (166), (167), (168), (189), (190), (191),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (197), (198), (208), (209), (223), (224), (225),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (226), (227), (228), (229), (230), (233), (237),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (239), (242), (243), (246), (247), (248), (249),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (252), (261), (263), (264), (265), (282), (286),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (348), (354), (360), (373), (375), (378), (380),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (384), (386), (394), (395), (396), (397), (3825),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (3830), (3831), (3835), (3839), (3841), (3844),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (3846), (3848), (3854), (3855), (3857), (4045),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4049), (4052), (4057), (4064), (4065), (4066),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4068), (4070), (4072), (function-axioms) are
% 153.70/26.25 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86.
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4074) all_58_2 = e2 & op(e2, e3) = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | ALPHA: (4074) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4075) op(e2, e3) = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4050), (4075), (function-axioms) are
% 153.70/26.25 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1544.
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | (4076) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 153.70/26.25 | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | BETA: splitting (4076) gives:
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4077) all_58_6 = e2 & op(e1, e3) = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | ALPHA: (4077) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4078) all_58_6 = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (233), (3839),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (3854), (4078), (function-axioms) are inconsistent
% 153.70/26.25 | | | | | | | | | | | | | | | | | by sub-proof #116.
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4079) all_58_12 = e2 & op(e0, e3) = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | ALPHA: (4079) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4080) all_58_12 = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (167), (168),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (246), (248), (251), (252), (3828), (4052),
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4061), (4080), (function-axioms) are inconsistent
% 153.70/26.25 | | | | | | | | | | | | | | | | | by sub-proof #101.
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | End of split
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | (4081) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 153.70/26.25 | | | | | | | | | | | | | | $i(all_38_1)
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | ALPHA: (4081) implies:
% 153.70/26.25 | | | | | | | | | | | | | | (4082) ~ (all_38_1 = e1)
% 153.70/26.25 | | | | | | | | | | | | | | (4083) op(e2, e2) = all_38_1
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 153.70/26.25 | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | (4084) ~ (all_56_12 = e2)
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | REDUCE: (4049), (4084) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | (4085) $false
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | CLOSE: (4085) is inconsistent.
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | Case 2:
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | (4086) all_56_0 = e3 & op(e3, e2) = e3
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | ALPHA: (4086) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | (4087) op(e3, e2) = e3
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 153.70/26.25 | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | (4088) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | BETA: splitting (4088) gives:
% 153.70/26.25 | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | Case 1:
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4089) all_58_0 = e2 & op(e3, e3) = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | ALPHA: (4089) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4090) all_58_0 = e2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2,
% 153.70/26.25 | | | | | | | | | | | | | | | | | all_38_1, e2, e2, simplifying with (42), (4083)
% 153.70/26.25 | | | | | | | | | | | | | | | | | gives:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4091) all_38_1 = all_8_2
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 153.70/26.25 | | | | | | | | | | | | | | | | | e2, e3, simplifying with (168), (4087) gives:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4092) all_52_4 = e3
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REDUCE: (133), (4092) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4093) ~ (all_52_7 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | SIMP: (4093) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4094) ~ (all_52_7 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REDUCE: (132), (4092) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4095) ~ (all_52_8 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | SIMP: (4095) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4096) ~ (all_52_8 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REDUCE: (131), (4092) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4097) ~ (all_52_12 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | SIMP: (4097) implies:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4098) ~ (all_52_12 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 153.70/26.25 | | | | | | | | | | | | | | | | | REDUCE: (376), (4092) imply:
% 153.70/26.25 | | | | | | | | | | | | | | | | | (4099) ~ (all_8_2 = e3)
% 153.70/26.25 | | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (61),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (76), (108), (110), (123), (138), (143), (146),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (155), (156), (157), (158), (160), (161), (162),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (165), (166), (167), (168), (189), (190), (191),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (197), (198), (208), (209), (223), (224), (225),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (226), (227), (228), (229), (230), (233), (237),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (239), (242), (243), (246), (247), (248), (249),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (252), (261), (263), (264), (265), (282), (286),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (348), (354), (360), (373), (375), (378), (380),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (384), (386), (394), (395), (396), (397), (3825),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (3830), (3831), (3835), (3839), (3841), (3844),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (3846), (3848), (3854), (3855), (3857), (4045),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (4049), (4052), (4083), (4090), (4091), (4092),
% 154.01/26.25 | | | | | | | | | | | | | | | | | (4094), (4096), (4098), (function-axioms) are
% 154.01/26.25 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86.
% 154.01/26.25 | | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.25 | | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | | (4100) all_58_2 = e2 & op(e2, e3) = e2
% 154.01/26.25 | | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | | ALPHA: (4100) implies:
% 154.01/26.25 | | | | | | | | | | | | | | | | | (4101) op(e2, e3) = e2
% 154.01/26.25 | | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4050), (4101), (function-axioms) are
% 154.01/26.25 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1544.
% 154.01/26.25 | | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | End of split
% 154.01/26.25 | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | Case 2:
% 154.01/26.25 | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | (4102) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 154.01/26.25 | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 154.01/26.25 | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | BETA: splitting (4102) gives:
% 154.01/26.25 | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.25 | | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | | (4103) all_58_6 = e2 & op(e1, e3) = e2
% 154.01/26.25 | | | | | | | | | | | | | | | | |
% 154.01/26.25 | | | | | | | | | | | | | | | | | ALPHA: (4103) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4104) all_58_6 = e2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (233), (3839),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (3854), (4104), (function-axioms) are inconsistent
% 154.01/26.26 | | | | | | | | | | | | | | | | | by sub-proof #116.
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4105) all_58_12 = e2 & op(e0, e3) = e2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | ALPHA: (4105) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4106) all_58_12 = e2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (167), (168),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (246), (248), (251), (252), (3828), (4052),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4087), (4106), (function-axioms) are inconsistent
% 154.01/26.26 | | | | | | | | | | | | | | | | | by sub-proof #101.
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | (4107) all_14_2 = e3
% 154.01/26.26 | | | | | | | | | | (4108) ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0
% 154.01/26.26 | | | | | | | | | | & op(e3, e3) = all_14_1 & $i(all_14_0) &
% 154.01/26.26 | | | | | | | | | | $i(all_14_1)) | ( ~ (all_14_1 = e0) & op(e3, e3)
% 154.01/26.26 | | | | | | | | | | = all_14_1 & $i(all_14_1))
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | COMBINE_EQS: (351), (4107) imply:
% 154.01/26.26 | | | | | | | | | | (4109) all_8_2 = e3
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | SIMP: (4109) implies:
% 154.01/26.26 | | | | | | | | | | (4110) all_8_2 = e3
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | COMBINE_EQS: (333), (4110) imply:
% 154.01/26.26 | | | | | | | | | | (4111) all_22_2 = e3
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | COMBINE_EQS: (360), (4110) imply:
% 154.01/26.26 | | | | | | | | | | (4112) all_56_13 = e3
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | REDUCE: (373), (4110) imply:
% 154.01/26.26 | | | | | | | | | | (4113) ~ (all_52_1 = e3)
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | REDUCE: (380), (4110) imply:
% 154.01/26.26 | | | | | | | | | | (4114) ~ (all_52_7 = e3)
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | REDUCE: (382), (4110) imply:
% 154.01/26.26 | | | | | | | | | | (4115) ~ (all_52_9 = e3)
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | REDUCE: (384), (4110) imply:
% 154.01/26.26 | | | | | | | | | | (4116) ~ (all_52_13 = e3)
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | BETA: splitting (58) gives:
% 154.01/26.26 | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | (4117) ~ (all_18_2 = e2)
% 154.01/26.26 | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | REDUCE: (3824), (4117) imply:
% 154.01/26.26 | | | | | | | | | | | (4118) $false
% 154.01/26.26 | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | CLOSE: (4118) is inconsistent.
% 154.01/26.26 | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | (4119) ( ~ (all_18_0 = e3) & op(all_18_1, e1) = all_18_0
% 154.01/26.26 | | | | | | | | | | | & op(e2, e2) = all_18_1 & $i(all_18_0) &
% 154.01/26.26 | | | | | | | | | | | $i(all_18_1)) | ( ~ (all_18_1 = e0) & op(e2, e2)
% 154.01/26.26 | | | | | | | | | | | = all_18_1 & $i(all_18_1))
% 154.01/26.26 | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | BETA: splitting (241) gives:
% 154.01/26.26 | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | (4120) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 154.01/26.26 | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.01/26.26 | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | BETA: splitting (4120) gives:
% 154.01/26.26 | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | (4121) all_58_2 = e3 & op(e2, e3) = e3
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | ALPHA: (4121) implies:
% 154.01/26.26 | | | | | | | | | | | | | (4122) op(e2, e3) = e3
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | REF_CLOSE: (165), (4113), (4122), (function-axioms) are
% 154.01/26.26 | | | | | | | | | | | | | inconsistent by sub-proof #1183.
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | (4123) all_58_3 = e3 & op(e2, e2) = e3
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | ALPHA: (4123) implies:
% 154.01/26.26 | | | | | | | | | | | | | (4124) all_58_3 = e3
% 154.01/26.26 | | | | | | | | | | | | | (4125) op(e2, e2) = e3
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | BETA: splitting (218) gives:
% 154.01/26.26 | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | (4126) ~ (all_56_13 = e3)
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | REDUCE: (4112), (4126) imply:
% 154.01/26.26 | | | | | | | | | | | | | | (4127) $false
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | CLOSE: (4127) is inconsistent.
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | (4128) all_56_3 = e2 & op(e2, e3) = e2
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | ALPHA: (4128) implies:
% 154.01/26.26 | | | | | | | | | | | | | | (4129) op(e2, e3) = e2
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | BETA: splitting (4119) gives:
% 154.01/26.26 | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | (4130) ~ (all_18_0 = e3) & op(all_18_1, e1) = all_18_0 &
% 154.01/26.26 | | | | | | | | | | | | | | | op(e2, e2) = all_18_1 & $i(all_18_0) &
% 154.01/26.26 | | | | | | | | | | | | | | | $i(all_18_1)
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | ALPHA: (4130) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | (4131) ~ (all_18_0 = e3)
% 154.01/26.26 | | | | | | | | | | | | | | | (4132) op(e2, e2) = all_18_1
% 154.01/26.26 | | | | | | | | | | | | | | | (4133) op(all_18_1, e1) = all_18_0
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | BETA: splitting (3823) gives:
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | (4134) ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 &
% 154.01/26.26 | | | | | | | | | | | | | | | | op(e2, e2) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | ALPHA: (4134) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | (4135) ~ (all_6_0 = e0)
% 154.01/26.26 | | | | | | | | | | | | | | | | (4136) op(e2, e2) = all_6_1
% 154.01/26.26 | | | | | | | | | | | | | | | | (4137) op(all_6_1, e1) = all_6_0
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | BETA: splitting (4108) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4138) ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 154.01/26.26 | | | | | | | | | | | | | | | | | op(e3, e3) = all_14_1 & $i(all_14_0) &
% 154.01/26.26 | | | | | | | | | | | | | | | | | $i(all_14_1)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | ALPHA: (4138) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4139) op(e3, e3) = all_14_1
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 154.01/26.26 | | | | | | | | | | | | | | | | | all_18_1, e2, e2, simplifying with (4132), (4136)
% 154.01/26.26 | | | | | | | | | | | | | | | | | gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4140) all_18_1 = all_6_1
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_18_1,
% 154.01/26.26 | | | | | | | | | | | | | | | | | e2, e2, simplifying with (4125), (4132) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4141) all_18_1 = e3
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 154.01/26.26 | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (4129) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4142) all_52_1 = e2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 154.01/26.26 | | | | | | | | | | | | | | | | | all_14_1, e3, e3, simplifying with (45), (4139)
% 154.01/26.26 | | | | | | | | | | | | | | | | | gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4143) all_14_1 = all_10_2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4140), (4141) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4144) all_6_1 = e3
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (147), (4142) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4145) ~ (all_52_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (144), (4142) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4146) ~ (all_52_9 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (143), (4142) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4147) ~ (all_52_13 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | SIMP: (4147) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4148) ~ (all_52_13 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (362), (4142) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4149) ~ (all_10_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | SIMP: (4149) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4150) ~ (all_10_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (4113), (4142) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4151) ~ (e3 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (64), (110),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (115), (121), (139), (161), (162), (163), (165),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (166), (167), (168), (191), (194), (195), (196),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (200), (202), (208), (220), (233), (234), (237),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (239), (246), (247), (248), (249), (251), (252),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (265), (275), (276), (277), (288), (297), (299),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (364), (370), (3826), (3828), (3829), (3831),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (3835), (3839), (3841), (3842), (3846), (3848),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (3854), (3855), (4111), (4113), (4115), (4116),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4124), (4131), (4133), (4135), (4137), (4139),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4141), (4142), (4143), (4144), (4148), (4150),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.26 | | | | | | | | | | | | | | | | | #75.
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4152) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 &
% 154.01/26.26 | | | | | | | | | | | | | | | | | $i(all_14_1)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | ALPHA: (4152) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4153) ~ (all_14_1 = e0)
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4154) op(e3, e3) = all_14_1
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 154.01/26.26 | | | | | | | | | | | | | | | | | all_18_1, e2, e2, simplifying with (4132), (4136)
% 154.01/26.26 | | | | | | | | | | | | | | | | | gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4155) all_18_1 = all_6_1
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_18_1,
% 154.01/26.26 | | | | | | | | | | | | | | | | | e2, e2, simplifying with (4125), (4132) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4156) all_18_1 = e3
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 154.01/26.26 | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (4129) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4157) all_52_1 = e2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 154.01/26.26 | | | | | | | | | | | | | | | | | all_14_1, e3, e3, simplifying with (45), (4154)
% 154.01/26.26 | | | | | | | | | | | | | | | | | gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4158) all_14_1 = all_10_2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4155), (4156) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4159) all_6_1 = e3
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (147), (4157) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4160) ~ (all_52_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (144), (4157) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4161) ~ (all_52_9 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (143), (4157) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4162) ~ (all_52_13 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | SIMP: (4162) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4163) ~ (all_52_13 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (362), (4157) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4164) ~ (all_10_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | SIMP: (4164) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4165) ~ (all_10_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (4113), (4157) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4166) ~ (e3 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (64), (110),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (115), (121), (139), (161), (162), (163), (165),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (166), (167), (168), (191), (194), (195), (196),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (200), (202), (208), (220), (233), (234), (237),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (239), (246), (247), (248), (249), (251), (252),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (265), (275), (276), (277), (288), (297), (299),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (364), (370), (3826), (3828), (3829), (3831),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (3835), (3839), (3841), (3842), (3846), (3848),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (3854), (3855), (4111), (4113), (4115), (4116),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4124), (4131), (4133), (4135), (4137), (4154),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4156), (4157), (4158), (4159), (4163), (4165),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.26 | | | | | | | | | | | | | | | | | #75.
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | (4167) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 &
% 154.01/26.26 | | | | | | | | | | | | | | | | $i(all_6_1)
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | ALPHA: (4167) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | (4168) ~ (all_6_1 = e3)
% 154.01/26.26 | | | | | | | | | | | | | | | | (4169) op(e2, e2) = all_6_1
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | REF_CLOSE: (4125), (4132), (4168), (4169), (function-axioms)
% 154.01/26.26 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #95.
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | End of split
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | (4170) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 &
% 154.01/26.26 | | | | | | | | | | | | | | | $i(all_18_1)
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | ALPHA: (4170) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | (4171) ~ (all_18_1 = e0)
% 154.01/26.26 | | | | | | | | | | | | | | | (4172) op(e2, e2) = all_18_1
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | BETA: splitting (3823) gives:
% 154.01/26.26 | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | (4173) ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 &
% 154.01/26.26 | | | | | | | | | | | | | | | | op(e2, e2) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | ALPHA: (4173) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | (4174) ~ (all_6_0 = e0)
% 154.01/26.26 | | | | | | | | | | | | | | | | (4175) op(e2, e2) = all_6_1
% 154.01/26.26 | | | | | | | | | | | | | | | | (4176) op(all_6_1, e1) = all_6_0
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | BETA: splitting (4108) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4177) ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 154.01/26.26 | | | | | | | | | | | | | | | | | op(e3, e3) = all_14_1 & $i(all_14_0) &
% 154.01/26.26 | | | | | | | | | | | | | | | | | $i(all_14_1)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | ALPHA: (4177) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4178) op(e3, e3) = all_14_1
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 154.01/26.26 | | | | | | | | | | | | | | | | | all_18_1, e2, e2, simplifying with (4172), (4175)
% 154.01/26.26 | | | | | | | | | | | | | | | | | gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4179) all_18_1 = all_6_1
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_18_1,
% 154.01/26.26 | | | | | | | | | | | | | | | | | e2, e2, simplifying with (4125), (4172) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4180) all_18_1 = e3
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 154.01/26.26 | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (4129) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4181) all_52_1 = e2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 154.01/26.26 | | | | | | | | | | | | | | | | | all_14_1, e3, e3, simplifying with (45), (4178)
% 154.01/26.26 | | | | | | | | | | | | | | | | | gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4182) all_14_1 = all_10_2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4179), (4180) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4183) all_6_1 = e3
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (147), (4181) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4184) ~ (all_52_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (144), (4181) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4185) ~ (all_52_9 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (143), (4181) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4186) ~ (all_52_13 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | SIMP: (4186) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4187) ~ (all_52_13 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (362), (4181) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4188) ~ (all_10_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | SIMP: (4188) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4189) ~ (all_10_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (4113), (4181) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4190) ~ (e3 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (42), (61),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (64), (108), (110), (115), (116), (118), (121),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (123), (139), (155), (156), (158), (161), (162),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (163), (165), (166), (167), (168), (187), (189),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (191), (194), (195), (196), (200), (208), (209),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (211), (212), (223), (224), (225), (226), (227),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (228), (230), (233), (234), (235), (237), (238),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (239), (241), (243), (246), (247), (248), (249),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (251), (252), (261), (263), (265), (275), (276),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (277), (288), (297), (306), (348), (364), (368),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (370), (372), (386), (394), (395), (396), (397),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (3825), (3826), (3828), (3829), (3830), (3831),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (3835), (3839), (3841), (3842), (3844), (3846),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (3848), (3854), (3855), (4111), (4112), (4113),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4114), (4115), (4116), (4124), (4174), (4176),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4178), (4181), (4182), (4183), (4187), (4189),
% 154.01/26.26 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.26 | | | | | | | | | | | | | | | | | #69.
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4191) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 &
% 154.01/26.26 | | | | | | | | | | | | | | | | | $i(all_14_1)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | ALPHA: (4191) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4192) ~ (all_14_1 = e0)
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4193) op(e3, e3) = all_14_1
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 154.01/26.26 | | | | | | | | | | | | | | | | | all_18_1, e2, e2, simplifying with (4172), (4175)
% 154.01/26.26 | | | | | | | | | | | | | | | | | gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4194) all_18_1 = all_6_1
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_18_1,
% 154.01/26.26 | | | | | | | | | | | | | | | | | e2, e2, simplifying with (4125), (4172) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4195) all_18_1 = e3
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 154.01/26.26 | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (4129) gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4196) all_52_1 = e2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 154.01/26.26 | | | | | | | | | | | | | | | | | all_14_1, e3, e3, simplifying with (45), (4193)
% 154.01/26.26 | | | | | | | | | | | | | | | | | gives:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4197) all_14_1 = all_10_2
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4194), (4195) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4198) all_6_1 = e3
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (147), (4196) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4199) ~ (all_52_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (144), (4196) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4200) ~ (all_52_9 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (143), (4196) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4201) ~ (all_52_13 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | SIMP: (4201) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4202) ~ (all_52_13 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (362), (4196) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4203) ~ (all_10_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | SIMP: (4203) implies:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4204) ~ (all_10_2 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.26 | | | | | | | | | | | | | | | | | REDUCE: (4113), (4196) imply:
% 154.01/26.26 | | | | | | | | | | | | | | | | | (4205) ~ (e3 = e2)
% 154.01/26.26 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (42), (61),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (64), (108), (110), (115), (116), (118), (121),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (123), (139), (155), (156), (158), (161), (162),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (163), (165), (166), (167), (168), (187), (189),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (191), (194), (195), (196), (200), (208), (209),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (211), (212), (223), (224), (225), (226), (227),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (228), (230), (233), (234), (235), (237), (238),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (239), (241), (243), (246), (247), (248), (249),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (251), (252), (261), (263), (265), (275), (276),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (277), (288), (297), (306), (348), (364), (368),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (370), (372), (386), (394), (395), (396), (397),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (3825), (3826), (3828), (3829), (3830), (3831),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (3835), (3839), (3841), (3842), (3844), (3846),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (3848), (3854), (3855), (4111), (4112), (4113),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4114), (4115), (4116), (4124), (4174), (4176),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4193), (4196), (4197), (4198), (4202), (4204),
% 154.01/26.27 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | | | | | | | | | | #69.
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | (4206) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 &
% 154.01/26.27 | | | | | | | | | | | | | | | | $i(all_6_1)
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | ALPHA: (4206) implies:
% 154.01/26.27 | | | | | | | | | | | | | | | | (4207) ~ (all_6_1 = e3)
% 154.01/26.27 | | | | | | | | | | | | | | | | (4208) op(e2, e2) = all_6_1
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | REF_CLOSE: (4125), (4172), (4207), (4208), (function-axioms)
% 154.01/26.27 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #95.
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | (4209) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 154.01/26.27 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 154.01/26.27 | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | REF_CLOSE: (162), (163), (4115), (4116), (4209),
% 154.01/26.27 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | | | | | #261.
% 154.01/26.27 | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | (4210) all_10_2 = e0
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | COMBINE_EQS: (297), (4210) imply:
% 154.01/26.27 | | | | | | | | | (4211) all_56_12 = e0
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | REDUCE: (364), (4210) imply:
% 154.01/26.27 | | | | | | | | | (4212) ~ (all_52_2 = e0)
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | REDUCE: (368), (4210) imply:
% 154.01/26.27 | | | | | | | | | (4213) ~ (all_52_4 = e0)
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | REF_CLOSE: (6), (131), (139), (166), (191), (194), (201),
% 154.01/26.27 | | | | | | | | | (209), (219), (261), (265), (275), (289), (360),
% 154.01/26.27 | | | | | | | | | (376), (396), (3825), (3826), (3831), (3841),
% 154.01/26.27 | | | | | | | | | (3842), (3846), (4211), (4212), (4213),
% 154.01/26.27 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | | #68.
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | End of split
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | End of split
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | Case 2:
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | (4214) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 154.01/26.27 | | | | | | | op(e1, e0) = e1)
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | BETA: splitting (4214) gives:
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | (4215) all_58_8 = e1 & op(e1, e1) = e1
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | REF_CLOSE: (6), (3839), (4215) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | #1340.
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | (4216) all_58_11 = e1 & op(e1, e0) = e1
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | ALPHA: (4216) implies:
% 154.01/26.27 | | | | | | | | (4217) all_58_11 = e1
% 154.01/26.27 | | | | | | | | (4218) op(e1, e0) = e1
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | BETA: splitting (243) gives:
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | (4219) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 154.01/26.27 | | | | | | | | | op(e2, e2) = e1)
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | BETA: splitting (4219) gives:
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | (4220) all_58_1 = e1 & op(e3, e2) = e1
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | REF_CLOSE: (168), (3842), (4220), (function-axioms) are
% 154.01/26.27 | | | | | | | | | | inconsistent by sub-proof #1284.
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | (4221) all_58_3 = e1 & op(e2, e2) = e1
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | REF_CLOSE: (42), (3848), (4221), (function-axioms) are
% 154.01/26.27 | | | | | | | | | | inconsistent by sub-proof #1423.
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | (4222) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1
% 154.01/26.27 | | | | | | | | | & op(e0, e2) = e1)
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | BETA: splitting (4222) gives:
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | (4223) all_58_7 = e1 & op(e1, e2) = e1
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | ALPHA: (4223) implies:
% 154.01/26.27 | | | | | | | | | | (4224) all_58_7 = e1
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (233), (3839),
% 154.01/26.27 | | | | | | | | | | (4217), (4218), (4224), (function-axioms) are
% 154.01/26.27 | | | | | | | | | | inconsistent by sub-proof #105.
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | (4225) all_58_13 = e1 & op(e0, e2) = e1
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | REF_CLOSE: (156), (3844), (4225), (function-axioms) are
% 154.01/26.27 | | | | | | | | | | inconsistent by sub-proof #192.
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | End of split
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | End of split
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | End of split
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | Case 2:
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | | (4226) all_58_14 = e2 & op(e0, e1) = e2
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | | REF_CLOSE: (155), (3830), (4226), (function-axioms) are inconsistent
% 154.01/26.27 | | | | | | by sub-proof #1175.
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | End of split
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | End of split
% 154.01/26.27 | | | |
% 154.01/26.27 | | | End of split
% 154.01/26.27 | | |
% 154.01/26.27 | | End of split
% 154.01/26.27 | |
% 154.01/26.27 | Case 2:
% 154.01/26.27 | |
% 154.01/26.27 | | (4227) all_4_2 = e1
% 154.01/26.27 | | (4228) ( ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 & op(e1, e1) =
% 154.01/26.27 | | all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e2) &
% 154.01/26.27 | | op(e1, e1) = all_4_1 & $i(all_4_1))
% 154.01/26.27 | |
% 154.01/26.27 | | COMBINE_EQS: (353), (4227) imply:
% 154.01/26.27 | | (4229) all_12_2 = e1
% 154.01/26.27 | |
% 154.01/26.27 | | COMBINE_EQS: (261), (4227) imply:
% 154.01/26.27 | | (4230) all_56_15 = e1
% 154.01/26.27 | |
% 154.01/26.27 | | REDUCE: (375), (4227) imply:
% 154.01/26.27 | | (4231) ~ (all_52_3 = e1)
% 154.01/26.27 | |
% 154.01/26.27 | | REDUCE: (386), (4227) imply:
% 154.01/26.27 | | (4232) ~ (all_52_7 = e1)
% 154.01/26.27 | |
% 154.01/26.27 | | REDUCE: (393), (4227) imply:
% 154.01/26.27 | | (4233) ~ (all_52_11 = e1)
% 154.01/26.27 | |
% 154.01/26.27 | | REDUCE: (394), (4227) imply:
% 154.01/26.27 | | (4234) ~ (all_52_12 = e1)
% 154.01/26.27 | |
% 154.01/26.27 | | REDUCE: (395), (4227) imply:
% 154.01/26.27 | | (4235) ~ (all_52_13 = e1)
% 154.01/26.27 | |
% 154.01/26.27 | | REDUCE: (396), (4227) imply:
% 154.01/26.27 | | (4236) ~ (all_52_14 = e1)
% 154.01/26.27 | |
% 154.01/26.27 | | BETA: splitting (227) gives:
% 154.01/26.27 | |
% 154.01/26.27 | | Case 1:
% 154.01/26.27 | | |
% 154.01/26.27 | | | (4237) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 154.01/26.27 | | | = e1)
% 154.01/26.27 | | |
% 154.01/26.27 | | | BETA: splitting (4237) gives:
% 154.01/26.27 | | |
% 154.01/26.27 | | | Case 1:
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | (4238) all_58_9 = e1 & op(e3, e0) = e1
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | REF_CLOSE: (166), (4234), (4238), (function-axioms) are inconsistent by
% 154.01/26.27 | | | | sub-proof #67.
% 154.01/26.27 | | | |
% 154.01/26.27 | | | Case 2:
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | (4239) all_58_10 = e1 & op(e2, e0) = e1
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | REF_CLOSE: (162), (4235), (4239), (function-axioms) are inconsistent by
% 154.01/26.27 | | | | sub-proof #212.
% 154.01/26.27 | | | |
% 154.01/26.27 | | | End of split
% 154.01/26.27 | | |
% 154.01/26.27 | | Case 2:
% 154.01/26.27 | | |
% 154.01/26.27 | | | (4240) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 154.01/26.27 | | | e0) = e1)
% 154.01/26.27 | | |
% 154.01/26.27 | | | BETA: splitting (4240) gives:
% 154.01/26.27 | | |
% 154.01/26.27 | | | Case 1:
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | (4241) all_58_11 = e1 & op(e1, e0) = e1
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | ALPHA: (4241) implies:
% 154.01/26.27 | | | | (4242) op(e1, e0) = e1
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | REF_CLOSE: (158), (4236), (4242), (function-axioms) are inconsistent by
% 154.01/26.27 | | | | sub-proof #108.
% 154.01/26.27 | | | |
% 154.01/26.27 | | | Case 2:
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | (4243) all_58_15 = e1 & op(e0, e0) = e1
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | ALPHA: (4243) implies:
% 154.01/26.27 | | | | (4244) all_58_15 = e1
% 154.01/26.27 | | | | (4245) op(e0, e0) = e1
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | BETA: splitting (210) gives:
% 154.01/26.27 | | | |
% 154.01/26.27 | | | | Case 1:
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | (4246) ~ (all_56_15 = e1)
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | REDUCE: (4230), (4246) imply:
% 154.01/26.27 | | | | | (4247) $false
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | CLOSE: (4247) is inconsistent.
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | Case 2:
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | (4248) all_56_11 = e0 & op(e0, e1) = e0
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | ALPHA: (4248) implies:
% 154.01/26.27 | | | | | (4249) op(e0, e1) = e0
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, e0, e1,
% 154.01/26.27 | | | | | e0, simplifying with (155), (4249) gives:
% 154.01/26.27 | | | | | (4250) all_52_11 = e0
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | REDUCE: (137), (4250) imply:
% 154.01/26.27 | | | | | (4251) ~ (all_52_3 = e0)
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | REDUCE: (123), (4250) imply:
% 154.01/26.27 | | | | | (4252) ~ (all_52_7 = e0)
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | REDUCE: (119), (4250) imply:
% 154.01/26.27 | | | | | (4253) ~ (all_52_8 = e0)
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | REDUCE: (116), (4250) imply:
% 154.01/26.27 | | | | | (4254) ~ (all_52_9 = e0)
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | REDUCE: (390), (4250) imply:
% 154.01/26.27 | | | | | (4255) ~ (all_6_2 = e0)
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | SIMP: (4255) implies:
% 154.01/26.27 | | | | | (4256) ~ (all_6_2 = e0)
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | REDUCE: (4233), (4250) imply:
% 154.01/26.27 | | | | | (4257) ~ (e1 = e0)
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | BETA: splitting (223) gives:
% 154.01/26.27 | | | | |
% 154.01/26.27 | | | | | Case 1:
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | | (4258) all_58_15 = e0 & op(e0, e0) = e0
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | | REF_CLOSE: (4), (4244), (4258) are inconsistent by sub-proof #1410.
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | Case 2:
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | | (4259) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 154.01/26.27 | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0))
% 154.01/26.27 | | | | | | & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.01/26.27 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | | ALPHA: (4259) implies:
% 154.01/26.27 | | | | | | (4260) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.01/26.27 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | | BETA: splitting (4260) gives:
% 154.01/26.27 | | | | | |
% 154.01/26.27 | | | | | | Case 1:
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | (4261) all_58_12 = e0 & op(e0, e3) = e0
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | ALPHA: (4261) implies:
% 154.01/26.27 | | | | | | | (4262) op(e0, e3) = e0
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | REF_CLOSE: (157), (4251), (4262), (function-axioms) are
% 154.01/26.27 | | | | | | | inconsistent by sub-proof #89.
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | Case 2:
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | (4263) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 154.01/26.27 | | | | | | | op(e0, e1) = e0)
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | BETA: splitting (4263) gives:
% 154.01/26.27 | | | | | | |
% 154.01/26.27 | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | (4264) all_58_13 = e0 & op(e0, e2) = e0
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | ALPHA: (4264) implies:
% 154.01/26.27 | | | | | | | | (4265) op(e0, e2) = e0
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | REF_CLOSE: (156), (4252), (4265), (function-axioms) are
% 154.01/26.27 | | | | | | | | inconsistent by sub-proof #1532.
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | (4266) all_58_14 = e0 & op(e0, e1) = e0
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | ALPHA: (4266) implies:
% 154.01/26.27 | | | | | | | | (4267) all_58_14 = e0
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | BETA: splitting (40) gives:
% 154.01/26.27 | | | | | | | |
% 154.01/26.27 | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | (4268) ~ (all_6_2 = e2)
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | BETA: splitting (43) gives:
% 154.01/26.27 | | | | | | | | |
% 154.01/26.27 | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | (4269) ~ (all_8_2 = e1)
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | BETA: splitting (46) gives:
% 154.01/26.27 | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | (4270) ~ (all_10_2 = e0)
% 154.01/26.27 | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | BETA: splitting (52) gives:
% 154.01/26.27 | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | (4271) ~ (all_14_2 = e3)
% 154.01/26.27 | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | REDUCE: (351), (4271) imply:
% 154.01/26.27 | | | | | | | | | | | | (4272) ~ (all_8_2 = e3)
% 154.01/26.27 | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | BETA: splitting (55) gives:
% 154.01/26.27 | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | (4273) ~ (all_16_2 = e2)
% 154.01/26.27 | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | REDUCE: (349), (4273) imply:
% 154.01/26.27 | | | | | | | | | | | | | (4274) ~ (all_10_2 = e2)
% 154.01/26.27 | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | BETA: splitting (73) gives:
% 154.01/26.27 | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | (4275) ~ (all_28_2 = e3)
% 154.01/26.27 | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | REDUCE: (339), (4275) imply:
% 154.01/26.27 | | | | | | | | | | | | | | (4276) ~ (all_6_2 = e3)
% 154.01/26.27 | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 154.01/26.27 | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | (4277) all_54_10 = e3
% 154.01/26.27 | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | REF_CLOSE: (304), (4276), (4277) are inconsistent by
% 154.01/26.27 | | | | | | | | | | | | | | | sub-proof #1531.
% 154.01/26.27 | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | (4278) ~ (all_54_10 = e3)
% 154.01/26.27 | | | | | | | | | | | | | | | (4279) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.01/26.27 | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | BETA: splitting (4279) gives:
% 154.01/26.27 | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | (4280) all_54_10 = e2
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | REF_CLOSE: (304), (4268), (4280) are inconsistent by
% 154.01/26.27 | | | | | | | | | | | | | | | | sub-proof #1530.
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | (4281) ~ (all_54_10 = e2)
% 154.01/26.27 | | | | | | | | | | | | | | | | (4282) all_54_10 = e1 | all_54_10 = e0
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | BETA: splitting (4282) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4283) all_54_10 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (4283) imply:
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4284) all_6_2 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | SIMP: (4284) implies:
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4285) all_6_2 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (4285) imply:
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4286) all_56_14 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | REDUCE: (385), (4285) imply:
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4287) ~ (all_52_6 = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | REDUCE: (387), (4285) imply:
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4288) ~ (all_52_8 = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | REDUCE: (388), (4285) imply:
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4289) ~ (all_52_9 = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | REDUCE: (4276), (4285) imply:
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4290) ~ (e3 = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | REDUCE: (4268), (4285) imply:
% 154.01/26.27 | | | | | | | | | | | | | | | | | (4291) ~ (e2 = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | (4292) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | BETA: splitting (4292) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | (4293) all_58_2 = e1 & op(e2, e3) = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | ALPHA: (4293) implies:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | (4294) all_58_2 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | (4295) op(e2, e3) = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | (4296) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4296) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | (4297) all_58_1 = e1 & op(e3, e2) = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4297) implies:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | (4298) all_58_1 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | (4299) op(e3, e2) = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | (4300) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4300) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | (4301) all_58_4 = e1 & op(e3, e1) = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4301) implies:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | (4302) all_58_4 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | (4303) op(e3, e1) = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | (4304) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4304) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4305) all_58_4 = e3 & op(e3, e1) = e3
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4302), (4305) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | #195.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4306) all_58_5 = e3 & op(e2, e1) = e3
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4306) implies:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4307) all_58_5 = e3
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (39), (155), (236), (4249), (4268),
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4303), (4307), (function-axioms) are inconsistent
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #66.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | (4308) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4309) all_58_8 = e3 & op(e1, e1) = e3
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4276), (4309), (function-axioms) are
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1469.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4310) all_58_14 = e3 & op(e0, e1) = e3
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4267), (4310) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | #314.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | (4311) all_58_5 = e1 & op(e2, e1) = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (155), (236),
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | (237), (4249), (4267), (4268), (4276), (4311),
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | #65.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | (4312) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4312) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | (4313) all_58_8 = e1 & op(e1, e1) = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4313) implies:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | (4314) all_58_8 = e1
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | (4315) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4315) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4316) all_58_0 = e0 & op(e3, e3) = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4270), (4316), (function-axioms) are
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4317) all_58_2 = e0 & op(e2, e3) = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4294), (4317) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | #1351.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | (4318) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4318) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4319) all_58_6 = e0 & op(e1, e3) = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4319) implies:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4320) all_58_6 = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | (4321) op(e1, e3) = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (4322) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4322) gives:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4323) all_58_0 = e0 & op(e3, e3) = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4270), (4323), (function-axioms) are
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4324) all_58_1 = e0 & op(e3, e2) = e0
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4298), (4324) are inconsistent by sub-proof
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1327.
% 154.01/26.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (4325) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4325) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4326) all_58_4 = e0 & op(e3, e1) = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4253), (4326), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #259.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4327) all_58_9 = e0 & op(e3, e0) = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4327) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4328) op(e3, e0) = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4329) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4329) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4330) all_58_0 = e2 & op(e3, e3) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4274), (4330), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1523.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4331) all_58_1 = e2 & op(e3, e2) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4298), (4331) are inconsistent by sub-proof
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1213.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4332) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4332) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4333) all_58_4 = e2 & op(e3, e1) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4333) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4334) all_58_4 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4335) op(e3, e1) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4336) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (4274), (4295), (4336),
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1429.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4337) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4337) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4338) all_58_6 = e2 & op(e1, e3) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4338) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4339) all_58_6 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4320), (4339) are inconsistent by sub-proof
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1514.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4340) all_58_12 = e2 & op(e0, e3) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4340) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4341) all_58_12 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4342) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4342) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4343) all_58_4 = e3 & op(e3, e1) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4343) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4344) op(e3, e1) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4335), (4344), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1502.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4345) all_58_5 = e3 & op(e2, e1) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4345) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4346) all_58_5 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4347) op(e2, e1) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4348) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4348) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4349) all_58_12 = e3 & op(e0, e3) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4349) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4350) all_58_12 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4341), (4350) are inconsistent by sub-proof
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1490.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4351) all_58_13 = e3 & op(e0, e2) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4351) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4352) op(e0, e2) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4353) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4353) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4354) all_58_0 = e3 & op(e3, e3) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4354) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4355) all_58_0 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4356) op(e3, e3) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (156), (4352) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4357) all_52_7 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (161), (4321) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4358) all_52_2 = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (163), (4347) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4359) all_52_9 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (165), (4295) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4360) all_52_1 = e1
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (166), (4328) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4361) all_52_12 = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (167), (4335) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4362) all_52_8 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (168), (4299) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4363) all_52_4 = e1
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (45), (4356) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4364) all_10_2 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (4358) imply:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4365) ~ (all_52_6 = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4365) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4366) ~ (all_52_6 = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (4363) imply:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4367) ~ (all_52_6 = e1)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (4357) imply:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4368) ~ (all_52_6 = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4369) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4369) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4370) all_58_6 = e3 & op(e1, e3) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4370) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4371) all_58_6 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (45), (246), (250),
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4274), (4294), (4295), (4356), (4371),
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1348.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4372) all_58_7 = e3 & op(e1, e2) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4368), (4372), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1184.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4373) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4373) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4374) all_58_8 = e3 & op(e1, e1) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4276), (4374), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1469.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4375) all_58_11 = e3 & op(e1, e0) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4375) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4376) op(e1, e0) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4377) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4377) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4378) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4378) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4379) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4379) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4380) op(e2, e3) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4295), (4380), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1494.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4381) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4381) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4382) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4382) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4383) op(e2, e3) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (246), (248),
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (4341), (4383), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1062.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4384) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4384) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4385) op(e1, e3) = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4321), (4385), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4386) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4386) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4387) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4387) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4388) op(e3, e1) = e1
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (39), (155), (236), (4249), (4268),
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4346), (4388), (function-axioms) are inconsistent
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #66.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4389) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (166), (4251), (4328), (4389),
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #64.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4390) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4390) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4391) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4391) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4392) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4392) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4393) ~ (all_56_14 = e1)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4286), (4393) imply:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4394) $false
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4394) is inconsistent.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4395) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4395) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4396) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4396) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4397) op(e1, e2) = e1
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4287), (4397), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1166.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4398) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4398) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4399) ~ (all_56_15 = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4400) op(e0, e2) = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4401) all_54_9 = e3
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (274), (4368), (4401) are inconsistent by
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1181.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4402) ~ (all_54_9 = e3)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4403) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4403) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4404) all_54_9 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (4404) imply:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4405) all_52_6 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4405) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4406) all_52_6 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4368), (4406) imply:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4407) ~ (e3 = e2)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e2,
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (4352), (4400) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4408) e3 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4355), (4408) imply:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4409) all_58_0 = e2
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (246), (248), (252),
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4341), (4409) are inconsistent by sub-proof #999.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4410) all_54_9 = e1 | all_54_9 = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (274), (4287), (4366), (4410) are inconsistent by
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1169.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4411) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4411) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4412) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4412) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4413) op(e0, e2) = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4252), (4413), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1532.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4414) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4414) gives:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4415) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4415) implies:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4416) op(e0, e1) = e1
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4249), (4416), (function-axioms) are
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129.
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4417) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4417) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4418) op(e1, e0) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4376), (4418), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #118.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4419) all_58_2 = e3 & op(e2, e3) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4419) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4420) op(e2, e3) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4295), (4420), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1494.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4421) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4421) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4422) all_58_6 = e3 & op(e1, e3) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4422) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4423) op(e1, e3) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4321), (4423), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4424) all_58_12 = e3 & op(e0, e3) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4424) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4425) all_58_12 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4341), (4425) are inconsistent by sub-proof
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1490.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4426) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (234), (4244), (4314), (4334),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4346), (4426) are inconsistent by sub-proof #63.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4427) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (4267), (4276), (4427),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #245.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4428) all_58_9 = e2 & op(e3, e0) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4428) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4429) op(e3, e0) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4328), (4429), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1500.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | (4430) all_58_12 = e0 & op(e0, e3) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4430) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | (4431) op(e0, e3) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4251), (4431), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #89.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4432) all_58_14 = e1 & op(e0, e1) = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4432) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4433) op(e0, e1) = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4249), (4433), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | (4434) all_58_3 = e1 & op(e2, e2) = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4269), (4434), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | (4435) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (160), (4232), (4287), (4435),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | #120.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | (4436) all_58_3 = e1 & op(e2, e2) = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4269), (4436), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | (4437) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | BETA: splitting (4437) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | (4438) all_58_5 = e1 & op(e2, e1) = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (155), (236),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | (237), (4249), (4267), (4268), (4276), (4438),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | #65.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | (4439) all_58_10 = e1 & op(e2, e0) = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4235), (4439), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | (4440) all_54_10 = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (4256), (4440) are inconsistent by
% 154.01/26.29 | | | | | | | | | | | | | | | | | sub-proof #1528.
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | (4441) all_28_2 = e3
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | COMBINE_EQS: (339), (4441) imply:
% 154.01/26.29 | | | | | | | | | | | | | | (4442) all_6_2 = e3
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | SIMP: (4442) implies:
% 154.01/26.29 | | | | | | | | | | | | | | (4443) all_6_2 = e3
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | COMBINE_EQS: (273), (4443) imply:
% 154.01/26.29 | | | | | | | | | | | | | | (4444) all_56_14 = e3
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | REDUCE: (385), (4443) imply:
% 154.01/26.29 | | | | | | | | | | | | | | (4445) ~ (all_52_6 = e3)
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | REDUCE: (387), (4443) imply:
% 154.01/26.29 | | | | | | | | | | | | | | (4446) ~ (all_52_8 = e3)
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | REDUCE: (388), (4443) imply:
% 154.01/26.29 | | | | | | | | | | | | | | (4447) ~ (all_52_9 = e3)
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 154.01/26.29 | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | (4448) ~ (all_56_14 = e3)
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | REDUCE: (4444), (4448) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | (4449) $false
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | CLOSE: (4449) is inconsistent.
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | (4450) all_56_6 = e1 & op(e1, e3) = e1
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | ALPHA: (4450) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | (4451) op(e1, e3) = e1
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 154.01/26.29 | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | (4452) ~ (all_56_12 = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | REDUCE: (297), (4452) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | (4453) ~ (all_10_2 = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | (4454) all_54_0 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (4454) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | (4455) all_10_2 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (4455) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | (4456) all_56_12 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | REDUCE: (362), (4455) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | (4457) ~ (all_52_1 = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | REDUCE: (366), (4455) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | (4458) ~ (all_52_3 = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | (4459) all_54_12 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4458), (4459) are inconsistent by
% 154.01/26.29 | | | | | | | | | | | | | | | | | | sub-proof #1234.
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | (4460) ~ (all_54_12 = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | (4461) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | (4462) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (165), (4272), (4457), (4462),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | #1182.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | (4463) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (4463) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | (4464) all_58_5 = e3 & op(e2, e1) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (4464) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | (4465) op(e2, e1) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4447), (4465), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1196.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | (4466) all_58_10 = e3 & op(e2, e0) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (4466) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | (4467) op(e2, e0) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | (4468) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4468) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | (4469) all_58_12 = e2 & op(e0, e3) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4469) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | (4470) all_58_12 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4461) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4471) all_54_12 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (4471) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4472) all_52_3 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4472) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4473) all_52_3 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (4473) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4474) ~ (all_52_1 = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (4473) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4475) ~ (all_52_2 = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (4473) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4476) ~ (all_52_7 = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4476) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4477) ~ (all_52_7 = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4458), (4473) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4478) ~ (e3 = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (4473) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | (4479) op(e0, e3) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | (4480) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4480) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | (4481) all_58_0 = e3 & op(e3, e3) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4481) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | (4482) all_58_0 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (4483) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4483) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4484) all_58_4 = e3 & op(e3, e1) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4484) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4485) op(e3, e1) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4446), (4485), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4486) all_58_5 = e3 & op(e2, e1) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4486) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4487) op(e2, e1) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4447), (4487), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1196.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (4488) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4488) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4489) all_58_8 = e3 & op(e1, e1) = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4489) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4490) all_58_8 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (161), (4451) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4491) all_52_2 = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (162), (4467) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4492) all_52_13 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (4491) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4493) ~ (all_52_1 = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (4491) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4494) ~ (all_52_6 = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4494) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4495) ~ (all_52_6 = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4475), (4491) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4496) ~ (e2 = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (384), (4492) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4497) ~ (all_8_2 = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4498) ~ (all_56_13 = e0)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (4498) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4499) ~ (all_8_2 = e0)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4500) all_54_5 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (4500) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4501) all_8_2 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4272), (4501) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4502) $false
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4502) is inconsistent.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4503) ~ (all_54_5 = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4504) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4505) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4505) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4506) all_58_4 = e2 & op(e3, e1) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4506) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4507) op(e3, e1) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4508) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4508) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4509) all_58_0 = e1 & op(e3, e3) = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4509) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4510) all_58_0 = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4482), (4510) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4511) e3 = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4456), (4511) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4512) all_56_12 = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (220), (4507), (4512), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1448.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4513) all_58_1 = e1 & op(e3, e2) = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4513) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4514) all_58_1 = e1
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4515) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4515) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4516) all_58_2 = e0 & op(e2, e3) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4516) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4517) all_58_2 = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4518) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4518) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4519) all_58_1 = e0 & op(e3, e2) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4514), (4519) are inconsistent by sub-proof
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1327.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4520) all_58_3 = e0 & op(e2, e2) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4520) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4521) all_58_3 = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (165), (240), (282), (373), (382),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384), (4269), (4499), (4504), (4521),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #324.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4522) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4522) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4523) all_58_7 = e0 & op(e1, e2) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4523) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4524) op(e1, e2) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4525) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (248), (252),
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4470), (4517), (4524), (4525), (function-axioms)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #62.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4526) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4526) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4527) all_58_8 = e2 & op(e1, e1) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4268), (4527), (function-axioms) are
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4528) all_58_11 = e2 & op(e1, e0) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4528) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4529) all_58_11 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4530) op(e1, e0) = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4504) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4531) all_54_5 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (4531) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4532) all_8_2 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4532) implies:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4533) all_8_2 = e2
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (4533) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4534) ~ (all_52_4 = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (4533) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4535) ~ (all_52_6 = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (4533) imply:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4536) ~ (all_52_9 = e2)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4537) all_54_6 = e3
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (4447), (4537) are inconsistent by
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1193.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4538) ~ (all_54_6 = e3)
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4539) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4540) all_58_15 = e0 & op(e0, e0) = e0
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4244), (4540) are inconsistent by sub-proof
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1059.
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4541) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4541) gives:
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4542) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4542) gives:
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4543) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 154.01/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4543) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4544) op(e2, e3) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4457), (4544), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1183.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4545) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (168), (4451), (4534), (4545),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #61.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4546) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (157), (160), (230), (231),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (277), (4251), (4254), (4445), (4447),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4479), (4490), (4507), (4529), (4536), (4539),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4546), (function-axioms) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #60.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4547) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4547) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4548) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4548) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4549) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4549) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4550) op(e1, e2) = e2
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4535), (4550), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1536.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4551) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (160), (4477), (4495), (4551),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #59.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4552) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (156), (4252), (4260), (4470), (4530),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4552), (function-axioms) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #57.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4553) all_54_5 = e1 | all_54_5 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (4269), (4499), (4553) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1239.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4554) all_58_13 = e0 & op(e0, e2) = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4554) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4555) op(e0, e2) = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4252), (4555), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1532.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4556) all_58_3 = e0 & op(e2, e2) = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4556) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4557) all_58_3 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (165), (240), (282), (373), (382),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384), (4269), (4499), (4504), (4557),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #324.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4558) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4558) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4559) all_58_5 = e0 & op(e2, e1) = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4559) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4560) op(e2, e1) = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4254), (4560), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1300.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4561) all_58_10 = e0 & op(e2, e0) = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4561) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4562) op(e2, e0) = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4467), (4562), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #143.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4563) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (4234), (4507), (4563),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #56.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4564) all_58_5 = e2 & op(e2, e1) = e2
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (282), (382), (4269), (4499), (4504),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4564), (function-axioms) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #915.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4565) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (155), (4249), (4268), (4565),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #333.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4566) all_56_13 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (4566) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4567) all_8_2 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4567) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4568) all_8_2 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4568) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4569) ~ (all_52_1 = e0)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4570) all_54_4 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (4570) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4571) all_52_1 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4457), (4571) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4572) $false
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4572) is inconsistent.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4573) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (4474), (4493), (4569), (4573) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1187.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4574) all_58_14 = e3 & op(e0, e1) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4267), (4574) are inconsistent by sub-proof
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | #314.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | (4575) all_58_2 = e3 & op(e2, e3) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4575) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | (4576) op(e2, e3) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4457), (4576), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1183.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | (4577) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4577) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | (4578) all_58_6 = e3 & op(e1, e3) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4578) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | (4579) op(e1, e3) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (4451), (4579), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1164.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | (4580) all_58_12 = e3 & op(e0, e3) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4580) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | (4581) all_58_12 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4470), (4581) are inconsistent by sub-proof
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | | #1490.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | (4582) all_54_12 = e1 | all_54_12 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4231), (4251), (4582) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1222.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | (4583) all_58_13 = e2 & op(e0, e2) = e2
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4583) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | (4584) op(e0, e2) = e2
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (138), (156), (264), (4231), (4251), (4461),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | (4584), (function-axioms) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | sub-proof #55.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | (4585) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (155), (4245), (4249), (4585),
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | #54.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | (4586) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (4270), (4274), (4453), (4586) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1307.
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | (4587) all_56_1 = e3 & op(e3, e1) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | ALPHA: (4587) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | (4588) op(e3, e1) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4446), (4588), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | (4589) all_16_2 = e2
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | COMBINE_EQS: (349), (4589) imply:
% 154.17/26.30 | | | | | | | | | | | | | (4590) all_10_2 = e2
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | COMBINE_EQS: (297), (4590) imply:
% 154.17/26.30 | | | | | | | | | | | | | (4591) all_56_12 = e2
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | REDUCE: (366), (4590) imply:
% 154.17/26.30 | | | | | | | | | | | | | (4592) ~ (all_52_3 = e2)
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | REDUCE: (370), (4590) imply:
% 154.17/26.30 | | | | | | | | | | | | | (4593) ~ (all_52_8 = e2)
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | REDUCE: (372), (4590) imply:
% 154.17/26.30 | | | | | | | | | | | | | (4594) ~ (all_52_12 = e2)
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (39), (132), (138), (155), (156), (158),
% 154.17/26.30 | | | | | | | | | | | | | (160), (161), (166), (167), (168), (189), (190),
% 154.17/26.30 | | | | | | | | | | | | | (200), (209), (221), (223), (224), (226), (231),
% 154.17/26.30 | | | | | | | | | | | | | (236), (237), (246), (248), (251), (252), (263),
% 154.17/26.30 | | | | | | | | | | | | | (264), (273), (288), (360), (374), (380), (385),
% 154.17/26.30 | | | | | | | | | | | | | (392), (4230), (4231), (4232), (4244), (4249),
% 154.17/26.30 | | | | | | | | | | | | | (4251), (4252), (4256), (4267), (4268), (4591),
% 154.17/26.30 | | | | | | | | | | | | | (4592), (4593), (4594), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | inconsistent by sub-proof #51.
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | End of split
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | (4595) all_14_2 = e3
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | COMBINE_EQS: (351), (4595) imply:
% 154.17/26.30 | | | | | | | | | | | | (4596) all_8_2 = e3
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | SIMP: (4596) implies:
% 154.17/26.30 | | | | | | | | | | | | (4597) all_8_2 = e3
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | COMBINE_EQS: (360), (4597) imply:
% 154.17/26.30 | | | | | | | | | | | | (4598) all_56_13 = e3
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | REDUCE: (376), (4597) imply:
% 154.17/26.30 | | | | | | | | | | | | (4599) ~ (all_52_4 = e3)
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | REDUCE: (378), (4597) imply:
% 154.17/26.30 | | | | | | | | | | | | (4600) ~ (all_52_6 = e3)
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | REDUCE: (380), (4597) imply:
% 154.17/26.30 | | | | | | | | | | | | (4601) ~ (all_52_7 = e3)
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | BETA: splitting (221) gives:
% 154.17/26.30 | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | (4602) ~ (all_56_12 = e2)
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | REDUCE: (297), (4602) imply:
% 154.17/26.30 | | | | | | | | | | | | | (4603) ~ (all_10_2 = e2)
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | BETA: splitting (218) gives:
% 154.17/26.30 | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | (4604) ~ (all_56_13 = e3)
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | REDUCE: (4598), (4604) imply:
% 154.17/26.30 | | | | | | | | | | | | | | (4605) $false
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | CLOSE: (4605) is inconsistent.
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | (4606) all_56_3 = e2 & op(e2, e3) = e2
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | ALPHA: (4606) implies:
% 154.17/26.30 | | | | | | | | | | | | | | (4607) op(e2, e3) = e2
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 154.17/26.30 | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | (4608) all_54_13 = e3
% 154.17/26.30 | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | REF_CLOSE: (263), (4601), (4608) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | sub-proof #1435.
% 154.17/26.30 | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | (4609) ~ (all_54_13 = e3)
% 154.17/26.30 | | | | | | | | | | | | | | | (4610) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.17/26.30 | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | BETA: splitting (4610) gives:
% 154.17/26.30 | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | (4611) all_54_13 = e2
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (4611) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | (4612) all_52_7 = e2
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | SIMP: (4612) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | (4613) all_52_7 = e2
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | REDUCE: (138), (4613) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | (4614) ~ (all_52_3 = e2)
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | (4615) all_54_12 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (4615) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | | (4616) all_52_3 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | SIMP: (4616) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | (4617) all_52_3 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | REDUCE: (366), (4617) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | | (4618) ~ (all_10_2 = e3)
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | SIMP: (4618) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | (4619) ~ (all_10_2 = e3)
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | (4620) all_54_0 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (4619), (4620) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | | | | sub-proof #50.
% 154.17/26.30 | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | (4621) ~ (all_54_0 = e3)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | (4622) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | BETA: splitting (4622) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | (4623) all_54_0 = e2
% 154.17/26.30 | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (4603), (4623) are inconsistent by
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | sub-proof #1310.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | (4624) ~ (all_54_0 = e2)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | (4625) all_54_0 = e1 | all_54_0 = e0
% 154.17/26.30 | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | (4626) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4626) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | (4627) all_58_1 = e3 & op(e3, e2) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4627) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | (4628) op(e3, e2) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4599), (4628), (function-axioms) are
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1540.
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | (4629) all_58_3 = e3 & op(e2, e2) = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4629) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | (4630) all_58_3 = e3
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4625) gives:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | (4631) all_54_0 = e1
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (4631) imply:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | (4632) all_10_2 = e1
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4632) implies:
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | (4633) all_10_2 = e1
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.30 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (4633) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4634) all_56_12 = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4619), (4633) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4635) ~ (e3 = e1)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4603), (4633) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4636) ~ (e2 = e1)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | (4637) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4637) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4638) all_58_4 = e2 & op(e3, e1) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4638) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4639) op(e3, e1) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (220), (4634), (4639), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1448.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4640) all_58_5 = e2 & op(e2, e1) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4640) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4641) all_58_5 = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (238), (239), (4607),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4630), (4641), (function-axioms) are inconsistent
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #898.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | (4642) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (155), (4249), (4268), (4642),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | #333.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4643) all_54_0 = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (4270), (4643) are inconsistent by
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1309.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | (4644) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4644) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | (4645) all_58_7 = e3 & op(e1, e2) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4600), (4645), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1184.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | (4646) all_58_13 = e3 & op(e0, e2) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4601), (4646), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1449.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | (4647) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4231), (4251), (4614), (4647) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1098.
% 154.17/26.31 | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | (4648) all_54_13 = e1 | all_54_13 = e0
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | REF_CLOSE: (263), (4232), (4252), (4648) are inconsistent by
% 154.17/26.31 | | | | | | | | | | | | | | | | sub-proof #875.
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | (4649) all_56_0 = e3 & op(e3, e2) = e3
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | ALPHA: (4649) implies:
% 154.17/26.31 | | | | | | | | | | | | | (4650) op(e3, e2) = e3
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | REF_CLOSE: (168), (4599), (4650), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | inconsistent by sub-proof #1540.
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | (4651) all_10_2 = e0
% 154.17/26.31 | | | | | | | | | | | (4652) ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0
% 154.17/26.31 | | | | | | | | | | | & op(e0, e0) = all_10_1 & $i(all_10_0) &
% 154.17/26.31 | | | | | | | | | | | $i(all_10_1)) | ( ~ (all_10_1 = e1) & op(e0, e0)
% 154.17/26.31 | | | | | | | | | | | = all_10_1 & $i(all_10_1))
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | COMBINE_EQS: (308), (4651) imply:
% 154.17/26.31 | | | | | | | | | | | (4653) all_24_2 = e0
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | COMBINE_EQS: (297), (4651) imply:
% 154.17/26.31 | | | | | | | | | | | (4654) all_56_12 = e0
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | REDUCE: (362), (4651) imply:
% 154.17/26.31 | | | | | | | | | | | (4655) ~ (all_52_1 = e0)
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | REDUCE: (364), (4651) imply:
% 154.17/26.31 | | | | | | | | | | | (4656) ~ (all_52_2 = e0)
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | REDUCE: (368), (4651) imply:
% 154.17/26.31 | | | | | | | | | | | (4657) ~ (all_52_4 = e0)
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | REDUCE: (372), (4651) imply:
% 154.17/26.31 | | | | | | | | | | | (4658) ~ (all_52_12 = e0)
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | REDUCE: (45), (4651) imply:
% 154.17/26.31 | | | | | | | | | | | (4659) op(e3, e3) = e0
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | BETA: splitting (67) gives:
% 154.17/26.31 | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | (4660) ~ (all_24_2 = e0)
% 154.17/26.31 | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | REDUCE: (4653), (4660) imply:
% 154.17/26.31 | | | | | | | | | | | | (4661) $false
% 154.17/26.31 | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | CLOSE: (4661) is inconsistent.
% 154.17/26.31 | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | (4662) ( ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0
% 154.17/26.31 | | | | | | | | | | | | & op(e0, e0) = all_24_1 & $i(all_24_0) &
% 154.17/26.31 | | | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e2) & op(e0, e0)
% 154.17/26.31 | | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 154.17/26.31 | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | BETA: splitting (4652) gives:
% 154.17/26.31 | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | (4663) ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 154.17/26.31 | | | | | | | | | | | | | op(e0, e0) = all_10_1 & $i(all_10_0) &
% 154.17/26.31 | | | | | | | | | | | | | $i(all_10_1)
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | ALPHA: (4663) implies:
% 154.17/26.31 | | | | | | | | | | | | | (4664) ~ (all_10_0 = e2)
% 154.17/26.31 | | | | | | | | | | | | | (4665) op(e0, e0) = all_10_1
% 154.17/26.31 | | | | | | | | | | | | | (4666) op(all_10_1, e3) = all_10_0
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | BETA: splitting (219) gives:
% 154.17/26.31 | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | (4667) ~ (all_56_12 = e0)
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | REDUCE: (4654), (4667) imply:
% 154.17/26.31 | | | | | | | | | | | | | | (4668) $false
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | CLOSE: (4668) is inconsistent.
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | (4669) all_56_2 = e3 & op(e3, e0) = e3
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | ALPHA: (4669) implies:
% 154.17/26.31 | | | | | | | | | | | | | | (4670) op(e3, e0) = e3
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 154.17/26.31 | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | (4671) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 154.17/26.31 | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 154.17/26.31 | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | BETA: splitting (4671) gives:
% 154.17/26.31 | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | (4672) all_58_0 = e0 & op(e3, e3) = e0
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | ALPHA: (4672) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | (4673) all_58_0 = e0
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_10_1,
% 154.17/26.31 | | | | | | | | | | | | | | | | e0, e0, simplifying with (4245), (4665) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | (4674) all_10_1 = e1
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 154.17/26.31 | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (166), (4670) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | (4675) all_52_12 = e3
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | REDUCE: (131), (4675) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | (4676) ~ (all_52_4 = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | REDUCE: (118), (4675) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | (4677) ~ (all_52_8 = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | REDUCE: (111), (4675) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | (4678) ~ (all_52_13 = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | SIMP: (4678) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | (4679) ~ (all_52_13 = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | REDUCE: (4666), (4674) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | (4680) op(e1, e3) = all_10_0
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | (4681) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | BETA: splitting (4681) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | (4682) all_58_9 = e3 & op(e3, e0) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | ALPHA: (4682) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | (4683) all_58_9 = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | BETA: splitting (4662) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4684) ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 &
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_24_1 & $i(all_24_0) &
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | $i(all_24_1)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | ALPHA: (4684) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4685) ~ (all_24_0 = e1)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4686) op(e0, e0) = all_24_1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4687) op(all_24_1, e3) = all_24_0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_24_1,
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (4245), (4686) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4688) all_24_1 = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | all_10_0, e3, e1, simplifying with (161), (4680)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4689) all_52_2 = all_10_0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (4689) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4690) all_54_8 = all_10_0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | REDUCE: (147), (4689) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4691) ~ (all_52_1 = all_10_0)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | REDUCE: (142), (4689) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4692) ~ (all_52_3 = all_10_0)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | SIMP: (4692) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4693) ~ (all_52_3 = all_10_0)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | REDUCE: (141), (4689) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4694) ~ (all_52_6 = all_10_0)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | SIMP: (4694) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4695) ~ (all_52_6 = all_10_0)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4689) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4696) ~ (all_10_0 = all_6_2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | REDUCE: (4656), (4689) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4697) ~ (all_10_0 = e0)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | REDUCE: (4687), (4688) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4698) op(e1, e3) = all_24_0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_0,
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | all_24_0, e3, e1, simplifying with (4680), (4698)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4699) all_24_0 = all_10_0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | REDUCE: (4685), (4699) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | (4700) ~ (all_10_0 = e1)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | (4701) ~ (all_56_14 = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (4701) imply:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | (4702) ~ (all_6_2 = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | (4703) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4703) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4704) all_58_0 = e1 & op(e3, e3) = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4704) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4705) all_58_0 = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (166), (167), (168), (247), (4253),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4657), (4670), (4705), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #49.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4706) all_58_2 = e1 & op(e2, e3) = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4706) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4707) op(e2, e3) = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | (4708) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (4673), (4707), (4708),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | #347.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | (4709) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4709) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4710) all_58_6 = e2 & op(e1, e3) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (155), (160), (162), (166),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (194), (223), (225), (226), (228), (233), (246),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (248), (252), (4244), (4245), (4249), (4267),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4664), (4670), (4683), (4690), (4695), (4696),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4697), (4700), (4710), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4711) all_58_12 = e2 & op(e0, e3) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (121), (132), (138), (146),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (155), (156), (157), (160), (162), (163), (165),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (166), (167), (168), (190), (192), (194), (198),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (200), (201), (208), (223), (225), (226), (228),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (233), (246), (248), (252), (264), (273), (286),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (288), (289), (304), (385), (387), (4231), (4244),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4245), (4249), (4251), (4252), (4253), (4256),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4267), (4268), (4655), (4657), (4664), (4670),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4676), (4677), (4683), (4690), (4691), (4693),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4695), (4696), (4697), (4700), (4702), (4711),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | #36.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | (4712) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4712) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4713) all_58_6 = e1 & op(e1, e3) = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4713) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | (4714) op(e1, e3) = e1
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | (4715) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4715) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4716) all_58_4 = e3 & op(e3, e1) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4716) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4717) op(e3, e1) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4677), (4717), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4718) all_58_5 = e3 & op(e2, e1) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4718) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | (4719) all_58_5 = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4720) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4720) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4721) all_58_6 = e3 & op(e1, e3) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4721) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4722) op(e1, e3) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (4714), (4722), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1164.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4723) all_58_7 = e3 & op(e1, e2) = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4723) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (4724) all_58_7 = e3
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4725) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4725) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4726) all_58_6 = e2 & op(e1, e3) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (155), (160), (162), (166),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (223), (225), (226), (228), (233), (246),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (252), (4244), (4245), (4249), (4267),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4664), (4670), (4683), (4690), (4695), (4696),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4697), (4700), (4726), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4727) all_58_7 = e2 & op(e1, e2) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4724), (4727) are inconsistent by sub-proof
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1203.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4728) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4728) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4729) all_58_8 = e2 & op(e1, e1) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4268), (4729), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4730) all_58_11 = e2 & op(e1, e0) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4730) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4731) op(e1, e0) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4732) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4732) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4733) all_58_4 = e2 & op(e3, e1) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4733) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4734) op(e3, e1) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4735) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4735) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4736) all_58_6 = e0 & op(e1, e3) = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4736) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4737) all_58_6 = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4738) op(e1, e3) = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (166), (167),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (247), (248), (250), (252), (4253), (4657),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4659), (4670), (4737), (4738), (function-axioms)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4739) all_58_7 = e0 & op(e1, e2) = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4724), (4739) are inconsistent by sub-proof
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1140.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4740) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4740) gives:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4741) all_58_8 = e0 & op(e1, e1) = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4741) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4742) all_58_8 = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (235), (4267), (4719), (4734),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4742), (function-axioms) are inconsistent by
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #335.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4743) all_58_11 = e0 & op(e1, e0) = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4743) implies:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4744) op(e1, e0) = e0
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4731), (4744), (function-axioms) are
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #58.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4745) all_58_5 = e2 & op(e2, e1) = e2
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4719), (4745) are inconsistent by sub-proof
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #250.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4746) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (155), (4249), (4268), (4746),
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #333.
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | (4747) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 154.17/26.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (39), (162), (166),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | (223), (228), (4244), (4245), (4670), (4683),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | (4702), (4747), (function-axioms) are inconsistent
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #46.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (4748) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (4267), (4702), (4748),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | #245.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | (4749) all_58_12 = e1 & op(e0, e3) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4749) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | (4750) all_58_12 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (4751) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4751) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | (4752) all_58_12 = e3 & op(e0, e3) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4750), (4752) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | #1278.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | (4753) all_58_13 = e3 & op(e0, e2) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4753) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | (4754) all_58_13 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | (4755) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4755) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4756) all_58_0 = e2 & op(e3, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4673), (4756) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4757) all_58_2 = e2 & op(e2, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4757) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4758) op(e2, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4759) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4759) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4760) all_58_12 = e2 & op(e0, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4760) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4761) all_58_12 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (165), (248), (252),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4673), (4758), (4761), (function-axioms) are
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4762) all_58_13 = e2 & op(e0, e2) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4754), (4762) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1177.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4763) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (155), (4245), (4249), (4763),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | #54.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | (4764) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4764) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4765) all_58_6 = e2 & op(e1, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4765) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4766) all_58_6 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (155), (225), (246),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (252), (4245), (4249), (4754), (4766),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | #45.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4767) all_58_12 = e2 & op(e0, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (121), (132), (138), (146),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (155), (156), (157), (160), (162), (163), (165),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (167), (168), (190), (192), (194), (198),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (200), (201), (208), (223), (225), (226), (228),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (246), (248), (252), (264), (273), (286),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (288), (289), (304), (385), (387), (4231), (4244),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4245), (4249), (4251), (4252), (4253), (4256),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4267), (4268), (4655), (4657), (4664), (4670),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4676), (4677), (4683), (4690), (4691), (4693),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4695), (4696), (4697), (4700), (4702), (4767),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | #36.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (4768) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (4244), (4267), (4768) are inconsistent
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #33.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | (4769) all_56_14 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (4769) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | (4770) all_6_2 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (4696), (4770) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | (4771) ~ (all_10_0 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (4664), (4690), (4697), (4700), (4771) are
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #31.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4772) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | $i(all_24_1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | ALPHA: (4772) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4773) ~ (all_24_1 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4774) op(e0, e0) = all_24_1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_24_1,
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (4245), (4774) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4775) all_24_1 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | all_10_0, e3, e1, simplifying with (161), (4680)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4776) all_52_2 = all_10_0
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (4776) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4777) all_54_8 = all_10_0
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | REDUCE: (147), (4776) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4778) ~ (all_52_1 = all_10_0)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | REDUCE: (142), (4776) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4779) ~ (all_52_3 = all_10_0)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | SIMP: (4779) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4780) ~ (all_52_3 = all_10_0)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | REDUCE: (141), (4776) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4781) ~ (all_52_6 = all_10_0)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | SIMP: (4781) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4782) ~ (all_52_6 = all_10_0)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4776) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4783) ~ (all_10_0 = all_6_2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | REDUCE: (4656), (4776) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4784) ~ (all_10_0 = e0)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | REDUCE: (4773), (4775) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | (4785) ~ (e2 = e1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | (4786) ~ (all_14_2 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (4786) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | (4787) ~ (all_8_2 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | (4788) ~ (all_28_2 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (4788) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | (4789) ~ (all_6_2 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | (4790) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4790) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (4791) all_58_4 = e3 & op(e3, e1) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4791) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (4792) op(e3, e1) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4677), (4792), (function-axioms) are
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (4793) all_58_5 = e3 & op(e2, e1) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4793) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (4794) all_58_5 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | (4795) op(e2, e1) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | (4796) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4796) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | (4797) all_58_4 = e2 & op(e3, e1) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4797) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | (4798) all_58_4 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | (4799) op(e3, e1) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4800) all_54_10 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (4789), (4800) are inconsistent by
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1531.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4801) ~ (all_54_10 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (4802) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4803) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4803) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4804) all_58_4 = e1 & op(e3, e1) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4804) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4805) op(e3, e1) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4799), (4805), (function-axioms) are
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #338.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4806) all_58_5 = e1 & op(e2, e1) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4806) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4807) op(e2, e1) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4795), (4807), (function-axioms) are
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4808) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4808) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4809) all_58_8 = e1 & op(e1, e1) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4809) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4810) all_58_8 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4802) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4811) all_54_10 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (4268), (4811) are inconsistent by
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1530.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4812) ~ (all_54_10 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4813) all_54_10 = e1 | all_54_10 = e0
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4814) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4814) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4815) all_58_2 = e1 & op(e2, e3) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4815) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4816) op(e2, e3) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4813) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4817) all_54_10 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (4817) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4818) all_6_2 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4818) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4819) all_6_2 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (4819) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4820) all_56_14 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (4819) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4821) ~ (all_52_6 = e1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (4819) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4822) ~ (all_52_8 = e1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4783), (4819) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4823) ~ (all_10_0 = e1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4824) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4824) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4825) all_58_1 = e1 & op(e3, e2) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4825) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4826) op(e3, e2) = e1
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4827) all_54_2 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (4677), (4827) are inconsistent by
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1210.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4828) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4829) all_54_8 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4777), (4829) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4830) all_10_0 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4830) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4831) all_10_0 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4778), (4831) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4832) ~ (all_52_1 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4780), (4831) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4833) ~ (all_52_3 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4782), (4831) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4834) ~ (all_52_6 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4835) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4835) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4836) all_58_12 = e3 & op(e0, e3) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4836) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4837) all_58_12 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4838) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4838) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4839) all_58_1 = e3 & op(e3, e2) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4839) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4840) op(e3, e2) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4826), (4840), (function-axioms) are
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1256.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4841) all_58_3 = e3 & op(e2, e2) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4787), (4841), (function-axioms) are
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1437.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4842) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4842) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4843) all_58_7 = e3 & op(e1, e2) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4834), (4843), (function-axioms) are
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1184.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4844) all_58_13 = e3 & op(e0, e2) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4844) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4845) all_58_13 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4846) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (4673), (4816), (4846),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #347.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4847) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4847) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4848) all_58_6 = e2 & op(e1, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4848) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4849) all_58_6 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (155), (225), (246),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (252), (4249), (4773), (4774), (4845),
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4849), (function-axioms) are inconsistent by
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4850) all_58_12 = e2 & op(e0, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4837), (4850) are inconsistent by sub-proof
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1451.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4851) all_58_13 = e3 & op(e0, e2) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4851) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4852) all_58_13 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4853) all_54_12 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4833), (4853) are inconsistent by
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1234.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4854) ~ (all_54_12 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4855) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4828) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4856) all_54_2 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (4856) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4857) all_52_8 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4857) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4858) all_52_8 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (4858) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4859) ~ (all_52_4 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (4858) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4860) ~ (all_52_9 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4860) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4861) ~ (all_52_9 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4855) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4862) all_54_12 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (4862) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4863) all_52_3 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4863) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4864) all_52_3 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (4864) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4865) ~ (all_52_1 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (4864) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4866) ~ (all_52_7 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4866) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4867) ~ (all_52_7 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4833), (4864) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4868) ~ (e3 = e2)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (4864) imply:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4869) op(e0, e3) = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4870) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4870) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4871) all_58_6 = e3 & op(e1, e3) = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4871) implies:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4872) all_58_6 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4873) all_54_4 = e3
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (4832), (4873) are inconsistent by
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1434.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4874) ~ (all_54_4 = e3)
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4875) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4875) gives:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4876) all_54_4 = e2
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (4865), (4876) are inconsistent by
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1431.
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4877) ~ (all_54_4 = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4878) all_54_4 = e1 | all_54_4 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4879) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4879) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4880) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (168), (286), (4655), (4799), (4832),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4859), (4878), (4880), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #39.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4881) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4881) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4882) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4882) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4883) op(e3, e1) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4799), (4883), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #338.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4884) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4884) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4885) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4885) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4886) op(e0, e3) = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4878) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4887) all_54_4 = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (4887) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4888) all_52_1 = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4888) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4889) all_52_1 = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4832), (4889) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4890) ~ (e3 = e1)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e3,
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (4869), (4886) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4891) e3 = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4872), (4891) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4892) all_58_6 = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (155), (225), (246),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (252), (4249), (4773), (4774), (4852),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4892), (function-axioms) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4893) all_54_4 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (4655), (4893) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1237.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4894) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4894) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4895) op(e0, e3) = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4251), (4895), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #89.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4896) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (160), (163), (4249), (4252), (4820),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4821), (4861), (4867), (4896), (function-axioms)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #37.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4897) all_58_7 = e3 & op(e1, e2) = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4834), (4897), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1184.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4898) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (39), (162), (166),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (228), (4244), (4245), (4670), (4683),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4789), (4898), (function-axioms) are inconsistent
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #46.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4899) all_54_12 = e1 | all_54_12 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4231), (4251), (4899) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1222.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4900) all_54_2 = e1 | all_54_2 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (4253), (4822), (4900) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #561.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4901) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (234), (4244), (4794), (4798),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4810), (4901) are inconsistent by sub-proof #63.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4902) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4664), (4777), (4784), (4823), (4902) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #41.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4903) all_58_3 = e1 & op(e2, e2) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4269), (4903), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4904) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (160), (4232), (4821), (4904),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #120.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4905) all_54_10 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (4256), (4905) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1528.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4906) all_58_3 = e1 & op(e2, e2) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4269), (4906), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4907) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4907) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4908) all_58_5 = e1 & op(e2, e1) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4908) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4909) op(e2, e1) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4795), (4909), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4910) all_58_10 = e1 & op(e2, e0) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4235), (4910), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4911) all_58_14 = e1 & op(e0, e1) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4911) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4912) op(e0, e1) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4249), (4912), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4913) all_58_5 = e2 & op(e2, e1) = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4794), (4913) are inconsistent by sub-proof
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | #250.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | (4914) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (155), (4249), (4268), (4914),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | #333.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | (4915) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (4267), (4789), (4915),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | #245.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | (4916) all_28_2 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (4916) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | (4917) all_6_2 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | SIMP: (4917) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | (4918) all_6_2 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (4918) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | (4919) all_56_14 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (4918) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | (4920) ~ (all_52_6 = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (4918) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | (4921) ~ (all_52_9 = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4783), (4918) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | (4922) ~ (all_10_0 = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (4918) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | (4923) op(e1, e1) = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | (4924) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4924) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | (4925) all_58_2 = e3 & op(e2, e3) = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4925) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | (4926) op(e2, e3) = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | (4927) all_56_12 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4654), (4927) are inconsistent by sub-proof
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | #280.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | (4928) ~ (all_56_12 = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | (4929) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4654), (4928) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | (4930) ~ (e3 = e0)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4929) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4931) all_56_13 = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (4931) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4932) all_8_2 = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (4932) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4933) ~ (all_52_4 = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (4932) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4934) ~ (all_52_6 = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (4932) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4935) ~ (all_52_9 = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (384), (4932) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4936) ~ (all_52_13 = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4787), (4932) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | (4937) ~ (e3 = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4938) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4938) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4939) all_58_0 = e1 & op(e3, e3) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4939) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4940) all_58_0 = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (166), (167), (168), (247), (4253),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4657), (4670), (4940), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #49.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4941) all_58_2 = e1 & op(e2, e3) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4941) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4942) op(e2, e3) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4926), (4942), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1494.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (4943) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4943) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944) all_58_6 = e1 & op(e1, e3) = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4944) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4945) all_58_6 = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4946) all_54_7 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (4679), (4946) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1428.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4947) ~ (all_54_7 = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4948) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4948) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4949) all_54_7 = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (4936), (4949) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1427.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4950) ~ (all_54_7 = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4951) all_54_7 = e1 | all_54_7 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4952) all_54_8 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4777), (4922), (4952) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #32.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4953) ~ (all_54_8 = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4954) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4951) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4955) all_54_7 = e1
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (4235), (4955) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1426.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4956) all_54_7 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (4956) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4957) all_52_13 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4957) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4958) all_52_13 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4936), (4958) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4959) ~ (e2 = e0)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (4958) imply:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4960) op(e2, e0) = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4961) all_54_6 = e3
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (4921), (4961) are inconsistent by
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1193.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4962) ~ (all_54_6 = e3)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4963) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4964) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4964) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4965) all_58_6 = e2 & op(e1, e3) = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (261), (276), (395), (4235), (4919),
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4929), (4931), (4936), (4945), (4948), (4965) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #29.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4966) all_58_7 = e2 & op(e1, e2) = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4966) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4967) op(e1, e2) = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4934), (4967), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1536.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4968) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4968) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4969) all_58_8 = e2 & op(e1, e1) = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4268), (4969), (function-axioms) are
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1440.
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4970) all_58_11 = e2 & op(e1, e0) = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4970) implies:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4971) all_58_11 = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4972) op(e1, e0) = e2
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4973) all_58_15 = e0 & op(e0, e0) = e0
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4244), (4973) are inconsistent by sub-proof
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1059.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4259) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4974) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4975) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (165), (4673), (4926), (4975),
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #304.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4976) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4976) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4977) all_58_6 = e2 & op(e1, e3) = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (261), (276), (395), (4235), (4919),
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4929), (4931), (4936), (4945), (4948), (4977) are
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #29.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978) all_58_12 = e2 & op(e0, e3) = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4978) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4979) all_58_12 = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4980) op(e0, e3) = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4981) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4981) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4982) all_58_4 = e2 & op(e3, e1) = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4982) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983) all_58_4 = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4984) op(e3, e1) = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4985) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (4269), (4926), (4985),
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1122.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4986) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4986) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4987) all_58_5 = e1 & op(e2, e1) = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4987) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4988) all_58_5 = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4989) op(e2, e1) = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4990) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4990) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4991) all_58_4 = e3 & op(e3, e1) = e3
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4991) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4992) op(e3, e1) = e3
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4984), (4992), (function-axioms) are
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1502.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4993) all_58_5 = e3 & op(e2, e1) = e3
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4993) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4994) op(e2, e1) = e3
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4989), (4994), (function-axioms) are
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4995) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4995) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4996) all_58_8 = e3 & op(e1, e1) = e3
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4996) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4997) all_58_8 = e3
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4998) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4998) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4999) all_58_6 = e0 & op(e1, e3) = e0
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4999) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5000) all_58_6 = e0
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5001) op(e1, e3) = e0
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (166), (167),
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (247), (248), (250), (252), (4253), (4657),
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4659), (4670), (5000), (5001), (function-axioms)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5002) all_58_7 = e0 & op(e1, e2) = e0
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5002) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5003) op(e1, e2) = e0
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5004) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5004) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5005) all_58_0 = e1 & op(e3, e3) = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5005) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5006) all_58_0 = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (166), (167), (168), (247), (4253),
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4657), (4670), (5006), (function-axioms) are
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #49.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5007) all_58_1 = e1 & op(e3, e2) = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5007) implies:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5008) op(e3, e2) = e1
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4954) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5009) all_54_8 = e2
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4664), (4777), (5009) are inconsistent by
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43.
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5010) ~ (all_54_8 = e2)
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5011) all_54_8 = e1 | all_54_8 = e0
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5011) gives:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.17/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5012) all_54_8 = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4777), (5012) imply:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5013) all_10_0 = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5013) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5014) all_10_0 = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4782), (5014) imply:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5015) ~ (all_52_6 = e1)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4922), (5014) imply:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5016) ~ (e3 = e1)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4680), (5014) imply:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5017) op(e1, e3) = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5018) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5018) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5019) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5019) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5020) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5020) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5021) op(e3, e2) = e3
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5008), (5021), (function-axioms) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1256.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5022) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (168), (4933), (5017), (5022),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #61.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5023) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (157), (160), (230), (231),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (277), (4251), (4254), (4920), (4921),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4935), (4963), (4971), (4980), (4984), (4997),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5023), (function-axioms) are inconsistent by
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #60.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5024) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5024) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5025) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5025) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5026) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5026) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5027) op(e1, e2) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5003), (5027), (function-axioms) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5028) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5028) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5029) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5029) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5030) op(e1, e2) = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5015), (5030), (function-axioms) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1166.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5031) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5031) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5032) op(e2, e0) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (162), (4960), (5032), (function-axioms) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1397.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5033) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (156), (4252), (4260), (4972), (4979),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5033), (function-axioms) are inconsistent by
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #57.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5034) all_54_8 = e0
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4777), (4784), (5034) are inconsistent by
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #42.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5035) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (4234), (4984), (5035),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #56.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5036) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5036) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5037) all_58_8 = e0 & op(e1, e1) = e0
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5037) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5038) op(e1, e1) = e0
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4923), (5038), (function-axioms) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1466.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5039) all_58_11 = e0 & op(e1, e0) = e0
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5039) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5040) op(e1, e0) = e0
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4972), (5040), (function-axioms) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #58.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5041) all_58_14 = e3 & op(e0, e1) = e3
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5041) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5042) all_58_14 = e3
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (234), (4923), (4983), (4988),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5042), (function-axioms) are inconsistent by
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #925.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5043) all_58_10 = e1 & op(e2, e0) = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (4683), (4971), (4974), (5043) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1457.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5044) all_58_5 = e2 & op(e2, e1) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5044) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5045) op(e2, e1) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4935), (5045), (function-axioms) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1441.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5046) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5046) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5047) all_58_8 = e2 & op(e1, e1) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5047) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5048) all_58_8 = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (230), (231),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (4920), (4971), (5048), (function-axioms)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1068.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5049) all_58_14 = e2 & op(e0, e1) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5049) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5050) op(e0, e1) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (155), (4249), (5050), (function-axioms) are
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1372.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5051) all_58_12 = e1 & op(e0, e3) = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5051) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5052) all_58_12 = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5053) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5053) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5054) all_58_12 = e3 & op(e0, e3) = e3
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5054) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5055) all_58_12 = e3
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5052), (5055) are inconsistent by sub-proof
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1516.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5056) all_58_13 = e3 & op(e0, e2) = e3
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5056) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5057) all_58_13 = e3
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5058) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (165), (4673), (4926), (5058),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #304.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5059) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5059) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5060) all_58_6 = e2 & op(e1, e3) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5060) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5061) all_58_6 = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (155), (225), (246),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (252), (4249), (4773), (4774), (5057),
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5061), (function-axioms) are inconsistent by
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #30.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5062) all_58_12 = e2 & op(e0, e3) = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5062) implies:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5063) all_58_12 = e2
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5052), (5063) are inconsistent by sub-proof
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1486.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5064) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (4244), (4267), (5064) are inconsistent
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #33.
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | (5065) all_56_14 = e1 | all_56_15 = e0
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5065) gives:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (5066) all_56_14 = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4919), (5066) imply:
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (5067) e3 = e1
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5067) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (5068) $false
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5068) is inconsistent.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (5069) all_56_15 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4230), (5069) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (5070) e1 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (5070) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (5071) $false
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5071) is inconsistent.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | (5072) all_58_3 = e3 & op(e2, e2) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4787), (5072), (function-axioms) are
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1437.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | (5073) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (4679), (4921), (5073),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | #261.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5074) all_14_2 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (5074) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5075) all_8_2 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | SIMP: (5075) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5076) all_8_2 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (5076) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5077) all_56_13 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (5076) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5078) ~ (all_52_1 = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (5076) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5079) ~ (all_52_7 = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (5076) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5080) ~ (all_52_9 = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | (5081) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5081) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | (5082) all_58_2 = e3 & op(e2, e3) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5082) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | (5083) op(e2, e3) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5078), (5083), (function-axioms) are
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1183.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | (5084) all_58_3 = e3 & op(e2, e2) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5084) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | (5085) all_58_3 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | (5086) ~ (all_56_13 = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5077), (5086) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | (5087) $false
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5087) is inconsistent.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | (5088) all_56_3 = e2 & op(e2, e3) = e2
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5088) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | (5089) op(e2, e3) = e2
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | (5090) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5090) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5091) all_58_12 = e3 & op(e0, e3) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5091) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5092) all_58_12 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (5093) all_54_13 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (5079), (5093) are inconsistent by
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1435.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (5094) ~ (all_54_13 = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (5095) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5095) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5096) all_54_13 = e2
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (5096) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5097) all_52_7 = e2
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5097) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5098) all_52_7 = e2
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (5098) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5099) ~ (all_52_3 = e2)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5079), (5098) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5100) ~ (e3 = e2)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5101) all_56_12 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4654), (5101) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5102) e3 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5102) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5103) $false
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5103) is inconsistent.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5104) ~ (all_56_12 = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5105) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4654), (5104) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5106) ~ (e3 = e0)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5105) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5107) all_56_13 = e2
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (165), (248), (252),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4673), (5077), (5089), (5092), (5107),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #473.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5108) all_56_14 = e1 | all_56_15 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5108) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5109) all_56_14 = e1
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (5109) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5110) all_6_2 = e1
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4783), (5110) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5111) ~ (all_10_0 = e1)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5112) all_54_12 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (5112) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5113) all_52_3 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5113) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5114) all_52_3 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4780), (5114) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5115) ~ (all_10_0 = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5115) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5116) ~ (all_10_0 = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (4664), (4777), (4784), (5111), (5116) are
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #31.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5117) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4231), (4251), (5099), (5117) are
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1098.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5118) all_56_15 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4230), (5118) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5119) e1 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (5119) imply:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5120) $false
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5120) is inconsistent.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5121) all_54_13 = e1 | all_54_13 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (4232), (4252), (5121) are inconsistent by
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #875.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5122) all_58_13 = e3 & op(e0, e2) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (5079), (5122), (function-axioms) are
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1449.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | (5123) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5123) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5124) all_58_14 = e3 & op(e0, e1) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5124) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5125) all_58_14 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4267), (5125) are inconsistent by sub-proof
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | #1444.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5126) all_58_15 = e3 & op(e0, e0) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5126) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5127) all_58_15 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5128) op(e0, e0) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (227), (228),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (238), (239), (4683), (5085), (5089), (5127),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | (5128), (function-axioms) are inconsistent by
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #589.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | (5129) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (4679), (5080), (5129),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | | #261.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | (5130) all_58_10 = e3 & op(e2, e0) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | ALPHA: (5130) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | (5131) op(e2, e0) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4679), (5131), (function-axioms) are
% 154.35/26.35 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1364.
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | (5132) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 154.35/26.35 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | BETA: splitting (5132) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | (5133) all_58_11 = e3 & op(e1, e0) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | ALPHA: (5133) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | (5134) all_58_11 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | (5135) op(e1, e0) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | (5136) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (4659), (4676), (5136),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | #353.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | (5137) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 154.35/26.35 | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (5137) gives:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5138) all_58_4 = e3 & op(e3, e1) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (5138) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5139) op(e3, e1) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4677), (5139), (function-axioms) are
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1538.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5140) all_58_9 = e3 & op(e3, e0) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (5140) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5141) all_58_9 = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (166), (223),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (228), (4244), (4245), (4670), (5134), (5135),
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | (5141), (function-axioms) are inconsistent by
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | | sub-proof #47.
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | (5142) all_58_15 = e3 & op(e0, e0) = e3
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4244), (5142) are inconsistent by sub-proof
% 154.35/26.35 | | | | | | | | | | | | | | | | | | #1054.
% 154.35/26.35 | | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | (5143) all_58_2 = e0 & op(e2, e3) = e0
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4655), (5143), (function-axioms) are
% 154.35/26.35 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1433.
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | (5144) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 154.35/26.35 | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 154.35/26.35 | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | BETA: splitting (5144) gives:
% 154.35/26.35 | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | (5145) all_58_6 = e0 & op(e1, e3) = e0
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | ALPHA: (5145) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | (5146) all_58_6 = e0
% 154.35/26.35 | | | | | | | | | | | | | | | | (5147) op(e1, e3) = e0
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (166), (167),
% 154.35/26.35 | | | | | | | | | | | | | | | | (168), (247), (248), (250), (252), (4253), (4657),
% 154.35/26.35 | | | | | | | | | | | | | | | | (4659), (4670), (5146), (5147), (function-axioms)
% 154.35/26.35 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34.
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | (5148) all_58_12 = e0 & op(e0, e3) = e0
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | ALPHA: (5148) implies:
% 154.35/26.35 | | | | | | | | | | | | | | | | (5149) op(e0, e3) = e0
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4251), (5149), (function-axioms) are
% 154.35/26.35 | | | | | | | | | | | | | | | | inconsistent by sub-proof #89.
% 154.35/26.35 | | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | (5150) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 &
% 154.35/26.35 | | | | | | | | | | | | | $i(all_10_1)
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | ALPHA: (5150) implies:
% 154.35/26.35 | | | | | | | | | | | | | (5151) ~ (all_10_1 = e1)
% 154.35/26.35 | | | | | | | | | | | | | (5152) op(e0, e0) = all_10_1
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 154.35/26.35 | | | | | | | | | | | | | (45), (52), (61), (64), (67), (73), (76), (79),
% 154.35/26.35 | | | | | | | | | | | | | (85), (108), (110), (111), (115), (116), (118),
% 154.35/26.35 | | | | | | | | | | | | | (119), (121), (123), (124), (126), (131), (132),
% 154.35/26.35 | | | | | | | | | | | | | (133), (134), (137), (138), (139), (141), (142),
% 154.35/26.35 | | | | | | | | | | | | | (143), (144), (146), (147), (155), (156), (157),
% 154.35/26.35 | | | | | | | | | | | | | (158), (160), (161), (162), (163), (165), (166),
% 154.35/26.35 | | | | | | | | | | | | | (167), (168), (187), (188), (189), (190), (191),
% 154.35/26.35 | | | | | | | | | | | | | (192), (193), (194), (195), (196), (197), (198),
% 154.35/26.35 | | | | | | | | | | | | | (199), (200), (201), (202), (208), (209), (211),
% 154.35/26.35 | | | | | | | | | | | | | (212), (213), (215), (216), (218), (219), (220),
% 154.35/26.35 | | | | | | | | | | | | | (223), (224), (225), (226), (227), (228), (229),
% 154.35/26.35 | | | | | | | | | | | | | (230), (231), (232), (233), (234), (235), (236),
% 154.35/26.35 | | | | | | | | | | | | | (237), (238), (239), (240), (241), (242), (243),
% 154.35/26.35 | | | | | | | | | | | | | (244), (245), (246), (247), (248), (249), (251),
% 154.35/26.35 | | | | | | | | | | | | | (252), (253), (261), (262), (263), (264), (265),
% 154.35/26.35 | | | | | | | | | | | | | (273), (274), (275), (276), (277), (282), (286),
% 154.35/26.35 | | | | | | | | | | | | | (287), (288), (289), (297), (299), (304), (306),
% 154.35/26.35 | | | | | | | | | | | | | (333), (335), (339), (348), (351), (354), (355),
% 154.35/26.35 | | | | | | | | | | | | | (360), (362), (364), (366), (368), (370), (372),
% 154.35/26.35 | | | | | | | | | | | | | (373), (374), (375), (376), (378), (380), (382),
% 154.35/26.35 | | | | | | | | | | | | | (384), (385), (386), (387), (388), (390), (392),
% 154.35/26.35 | | | | | | | | | | | | | (393), (394), (395), (396), (4253), (4268),
% 154.35/26.35 | | | | | | | | | | | | | (4269), (4653), (4654), (4655), (4657), (4658),
% 154.35/26.35 | | | | | | | | | | | | | (5151), (5152), (function-axioms) are inconsistent
% 154.35/26.35 | | | | | | | | | | | | | by sub-proof #216.
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | End of split
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | (5153) all_8_2 = e1
% 154.35/26.35 | | | | | | | | | | (5154) ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 &
% 154.35/26.35 | | | | | | | | | | op(e1, e1) = all_8_1 & $i(all_8_0) &
% 154.35/26.35 | | | | | | | | | | $i(all_8_1)) | ( ~ (all_8_1 = e3) & op(e1, e1) =
% 154.35/26.35 | | | | | | | | | | all_8_1 & $i(all_8_1))
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | COMBINE_EQS: (318), (5153) imply:
% 154.35/26.35 | | | | | | | | | | (5155) all_48_2 = e1
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | COMBINE_EQS: (360), (5153) imply:
% 154.35/26.35 | | | | | | | | | | (5156) all_56_13 = e1
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | REDUCE: (376), (5153) imply:
% 154.35/26.35 | | | | | | | | | | (5157) ~ (all_52_4 = e1)
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | REDUCE: (378), (5153) imply:
% 154.35/26.35 | | | | | | | | | | (5158) ~ (all_52_6 = e1)
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | REDUCE: (382), (5153) imply:
% 154.35/26.35 | | | | | | | | | | (5159) ~ (all_52_9 = e1)
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | BETA: splitting (217) gives:
% 154.35/26.35 | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | (5160) ~ (all_56_13 = e1)
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | REDUCE: (5156), (5160) imply:
% 154.35/26.35 | | | | | | | | | | | (5161) $false
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | CLOSE: (5161) is inconsistent.
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | (5162) all_56_4 = e2 & op(e2, e1) = e2
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | ALPHA: (5162) implies:
% 154.35/26.35 | | | | | | | | | | | (5163) op(e2, e1) = e2
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | BETA: splitting (101) gives:
% 154.35/26.35 | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | (5164) ~ (all_48_2 = e1)
% 154.35/26.35 | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | REDUCE: (5155), (5164) imply:
% 154.35/26.35 | | | | | | | | | | | | (5165) $false
% 154.35/26.35 | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | CLOSE: (5165) is inconsistent.
% 154.35/26.35 | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | Case 2:
% 154.35/26.35 | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | (5166) ( ~ (all_48_0 = e3) & op(all_48_1, e2) = all_48_0
% 154.35/26.35 | | | | | | | | | | | | & op(e1, e1) = all_48_1 & $i(all_48_0) &
% 154.35/26.35 | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e0) & op(e1, e1)
% 154.35/26.35 | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 154.35/26.35 | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | BETA: splitting (5166) gives:
% 154.35/26.35 | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | (5167) ~ (all_48_0 = e3) & op(all_48_1, e2) = all_48_0 &
% 154.35/26.35 | | | | | | | | | | | | | op(e1, e1) = all_48_1 & $i(all_48_0) &
% 154.35/26.35 | | | | | | | | | | | | | $i(all_48_1)
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | ALPHA: (5167) implies:
% 154.35/26.35 | | | | | | | | | | | | | (5168) op(e1, e1) = all_48_1
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | BETA: splitting (243) gives:
% 154.35/26.35 | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | Case 1:
% 154.35/26.35 | | | | | | | | | | | | | |
% 154.35/26.35 | | | | | | | | | | | | | | (5169) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 154.35/26.35 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | BETA: splitting (5169) gives:
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | (5170) all_58_1 = e1 & op(e3, e2) = e1
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REF_CLOSE: (168), (5157), (5170), (function-axioms) are
% 154.35/26.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #1284.
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | (5171) all_58_3 = e1 & op(e2, e2) = e1
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | ALPHA: (5171) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | (5172) all_58_3 = e1
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 154.35/26.36 | | | | | | | | | | | | | | | all_48_1, e1, e1, simplifying with (39), (5168)
% 154.35/26.36 | | | | | | | | | | | | | | | gives:
% 154.35/26.36 | | | | | | | | | | | | | | | (5173) all_48_1 = all_6_2
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 154.35/26.36 | | | | | | | | | | | | | | | e1, e2, simplifying with (163), (5163) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | (5174) all_52_9 = e2
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (144), (5174) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5175) ~ (all_52_1 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (121), (5174) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5176) ~ (all_52_8 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (115), (5174) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5177) ~ (all_52_13 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | SIMP: (5177) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | (5178) ~ (all_52_13 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (388), (5174) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5179) ~ (all_6_2 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | (5180) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | BETA: splitting (5180) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5181) all_58_4 = e2 & op(e3, e1) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | ALPHA: (5181) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5182) op(e3, e1) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5176), (5182), (function-axioms) are
% 154.35/26.36 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1212.
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5183) all_58_5 = e2 & op(e2, e1) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | ALPHA: (5183) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5184) all_58_5 = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (45), (46), (49), (55),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (73), (85), (118), (132), (138), (155), (156),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (157), (158), (160), (161), (162), (165), (166),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (167), (168), (189), (190), (192), (200), (201),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (202), (208), (209), (215), (219), (220), (221),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (223), (224), (225), (226), (228), (231), (232),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (235), (236), (237), (241), (242), (246), (247),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (248), (249), (251), (252), (263), (264), (273),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (288), (289), (297), (299), (304), (335), (339),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (349), (360), (362), (366), (368), (370), (372),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (374), (380), (385), (387), (392), (4228), (4229),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (4230), (4231), (4232), (4234), (4236), (4244),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (4245), (4249), (4251), (4252), (4253), (4256),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (4267), (4268), (5154), (5156), (5157), (5158),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5163), (5172), (5175), (5176), (5178), (5184),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.36 | | | | | | | | | | | | | | | | | #16.
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | (5185) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.35/26.36 | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (155), (4249), (4268), (5185),
% 154.35/26.36 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.36 | | | | | | | | | | | | | | | | #333.
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | (5186) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 154.35/26.36 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | REF_CLOSE: (156), (160), (4232), (5158), (5186),
% 154.35/26.36 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.36 | | | | | | | | | | | | | | #120.
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | (5187) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 154.35/26.36 | | | | | | | | | | | | | $i(all_48_1)
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | ALPHA: (5187) implies:
% 154.35/26.36 | | | | | | | | | | | | | (5188) ~ (all_48_1 = e0)
% 154.35/26.36 | | | | | | | | | | | | | (5189) op(e1, e1) = all_48_1
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | BETA: splitting (243) gives:
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | (5190) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 154.35/26.36 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | BETA: splitting (5190) gives:
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | (5191) all_58_1 = e1 & op(e3, e2) = e1
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REF_CLOSE: (168), (5157), (5191), (function-axioms) are
% 154.35/26.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #1284.
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | (5192) all_58_3 = e1 & op(e2, e2) = e1
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | ALPHA: (5192) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | (5193) all_58_3 = e1
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 154.35/26.36 | | | | | | | | | | | | | | | all_48_1, e1, e1, simplifying with (39), (5189)
% 154.35/26.36 | | | | | | | | | | | | | | | gives:
% 154.35/26.36 | | | | | | | | | | | | | | | (5194) all_48_1 = all_6_2
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 154.35/26.36 | | | | | | | | | | | | | | | e1, e2, simplifying with (163), (5163) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | (5195) all_52_9 = e2
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (144), (5195) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5196) ~ (all_52_1 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (121), (5195) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5197) ~ (all_52_8 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (115), (5195) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5198) ~ (all_52_13 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | SIMP: (5198) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | (5199) ~ (all_52_13 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (388), (5195) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5200) ~ (all_6_2 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | (5201) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | BETA: splitting (5201) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5202) all_58_4 = e2 & op(e3, e1) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | ALPHA: (5202) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5203) op(e3, e1) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5197), (5203), (function-axioms) are
% 154.35/26.36 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1212.
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5204) all_58_5 = e2 & op(e2, e1) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | ALPHA: (5204) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5205) all_58_5 = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (45), (46), (49), (55),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (73), (85), (118), (132), (138), (155), (156),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (157), (158), (160), (161), (162), (165), (166),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (167), (168), (189), (190), (192), (200), (201),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (202), (208), (209), (215), (219), (220), (221),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (223), (224), (225), (226), (228), (231), (232),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (235), (236), (237), (241), (242), (246), (247),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (248), (249), (251), (252), (263), (264), (273),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (288), (289), (297), (299), (304), (335), (339),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (349), (360), (362), (366), (368), (370), (372),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (374), (380), (385), (387), (392), (4228), (4229),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (4230), (4231), (4232), (4234), (4236), (4244),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (4245), (4249), (4251), (4252), (4253), (4256),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (4267), (4268), (5154), (5156), (5157), (5158),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5163), (5193), (5196), (5197), (5199), (5205),
% 154.35/26.36 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.36 | | | | | | | | | | | | | | | | | #16.
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | (5206) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.35/26.36 | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (155), (4249), (4268), (5206),
% 154.35/26.36 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.36 | | | | | | | | | | | | | | | | #333.
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | (5207) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 154.35/26.36 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | REF_CLOSE: (156), (160), (4232), (5158), (5207),
% 154.35/26.36 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.36 | | | | | | | | | | | | | | #120.
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | (5208) all_6_2 = e2
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | COMBINE_EQS: (273), (5208) imply:
% 154.35/26.36 | | | | | | | | | (5209) all_56_14 = e2
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | REDUCE: (374), (5208) imply:
% 154.35/26.36 | | | | | | | | | (5210) ~ (all_52_2 = e2)
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | REDUCE: (385), (5208) imply:
% 154.35/26.36 | | | | | | | | | (5211) ~ (all_52_6 = e2)
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | REDUCE: (387), (5208) imply:
% 154.35/26.36 | | | | | | | | | (5212) ~ (all_52_8 = e2)
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | REDUCE: (388), (5208) imply:
% 154.35/26.36 | | | | | | | | | (5213) ~ (all_52_9 = e2)
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | REDUCE: (392), (5208) imply:
% 154.35/26.36 | | | | | | | | | (5214) ~ (all_52_14 = e2)
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | BETA: splitting (49) gives:
% 154.35/26.36 | | | | | | | | |
% 154.35/26.36 | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | (5215) ~ (all_12_2 = e1)
% 154.35/26.36 | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | REDUCE: (4229), (5215) imply:
% 154.35/26.36 | | | | | | | | | | (5216) $false
% 154.35/26.36 | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | CLOSE: (5216) is inconsistent.
% 154.35/26.36 | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | (5217) ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0
% 154.35/26.36 | | | | | | | | | | & op(e1, e1) = all_12_1 & $i(all_12_0) &
% 154.35/26.36 | | | | | | | | | | $i(all_12_1)) | ( ~ (all_12_1 = e3) & op(e1, e1)
% 154.35/26.36 | | | | | | | | | | = all_12_1 & $i(all_12_1))
% 154.35/26.36 | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | BETA: splitting (5217) gives:
% 154.35/26.36 | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | (5218) ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 &
% 154.35/26.36 | | | | | | | | | | | op(e1, e1) = all_12_1 & $i(all_12_0) &
% 154.35/26.36 | | | | | | | | | | | $i(all_12_1)
% 154.35/26.36 | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | ALPHA: (5218) implies:
% 154.35/26.36 | | | | | | | | | | | (5219) ~ (all_12_0 = e2)
% 154.35/26.36 | | | | | | | | | | | (5220) op(e1, e1) = all_12_1
% 154.35/26.36 | | | | | | | | | | | (5221) op(all_12_1, e0) = all_12_0
% 154.35/26.36 | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | BETA: splitting (214) gives:
% 154.35/26.36 | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | (5222) ~ (all_56_14 = e2)
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | REDUCE: (5209), (5222) imply:
% 154.35/26.36 | | | | | | | | | | | | (5223) $false
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | CLOSE: (5223) is inconsistent.
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | (5224) all_56_7 = e1 & op(e1, e2) = e1
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | ALPHA: (5224) implies:
% 154.35/26.36 | | | | | | | | | | | | (5225) op(e1, e2) = e1
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.35/26.36 | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | (5226) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.35/26.36 | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | REF_CLOSE: (163), (167), (5212), (5213), (5226),
% 154.35/26.36 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.36 | | | | | | | | | | | | | #119.
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | (5227) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.35/26.36 | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | BETA: splitting (5227) gives:
% 154.35/26.36 | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | (5228) all_58_8 = e2 & op(e1, e1) = e2
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | ALPHA: (5228) implies:
% 154.35/26.36 | | | | | | | | | | | | | | (5229) all_58_8 = e2
% 154.35/26.36 | | | | | | | | | | | | | | (5230) op(e1, e1) = e2
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | BETA: splitting (4228) gives:
% 154.35/26.36 | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | (5231) ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 154.35/26.36 | | | | | | | | | | | | | | | op(e1, e1) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | ALPHA: (5231) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | (5232) ~ (all_4_0 = e3)
% 154.35/26.36 | | | | | | | | | | | | | | | (5233) op(e1, e1) = all_4_1
% 154.35/26.36 | | | | | | | | | | | | | | | (5234) op(all_4_1, e0) = all_4_0
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 154.35/26.36 | | | | | | | | | | | | | | | all_12_1, e1, e1, simplifying with (5220), (5233)
% 154.35/26.36 | | | | | | | | | | | | | | | gives:
% 154.35/26.36 | | | | | | | | | | | | | | | (5235) all_12_1 = all_4_1
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_12_1,
% 154.35/26.36 | | | | | | | | | | | | | | | e1, e1, simplifying with (5220), (5230) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | (5236) all_12_1 = e2
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 154.35/26.36 | | | | | | | | | | | | | | | e2, e1, simplifying with (160), (5225) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | (5237) all_52_6 = e1
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | COMBINE_EQS: (5235), (5236) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5238) all_4_1 = e2
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (141), (5237) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5239) ~ (all_52_2 = e1)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (134), (5237) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5240) ~ (all_52_4 = e1)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (126), (5237) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5241) ~ (all_52_7 = e1)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (124), (5237) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5242) ~ (all_52_14 = e1)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (378), (5237) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5243) ~ (all_8_2 = e1)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | SIMP: (5243) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | (5244) ~ (all_8_2 = e1)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (5211), (5237) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5245) ~ (e2 = e1)
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (5221), (5236) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5246) op(e2, e0) = all_12_0
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | REDUCE: (5234), (5238) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | (5247) op(e2, e0) = all_4_0
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 154.35/26.36 | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | (5248) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 154.35/26.36 | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | BETA: splitting (5248) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5249) all_58_1 = e1 & op(e3, e2) = e1
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5240), (5249), (function-axioms) are
% 154.35/26.36 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1284.
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5250) all_58_3 = e1 & op(e2, e2) = e1
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5244), (5250), (function-axioms) are
% 154.35/26.36 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | (5251) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 154.35/26.36 | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | BETA: splitting (5251) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5252) all_58_7 = e1 & op(e1, e2) = e1
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | ALPHA: (5252) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5253) all_58_7 = e1
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 154.35/26.36 | | | | | | | | | | | | | | | | | all_4_0, e0, e2, simplifying with (162), (5247)
% 154.35/26.36 | | | | | | | | | | | | | | | | | gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5254) all_52_13 = all_4_0
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 154.35/26.36 | | | | | | | | | | | | | | | | | all_12_0, e0, e2, simplifying with (162), (5246)
% 154.35/26.36 | | | | | | | | | | | | | | | | | gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5255) all_52_13 = all_12_0
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | COMBINE_EQS: (5254), (5255) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5256) all_12_0 = all_4_0
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | SIMP: (5256) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5257) all_12_0 = all_4_0
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (5254) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5258) all_54_7 = all_4_0
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REDUCE: (111), (5254) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5259) ~ (all_52_12 = all_4_0)
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REDUCE: (108), (5254) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5260) ~ (all_52_14 = all_4_0)
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | SIMP: (5260) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5261) ~ (all_52_14 = all_4_0)
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REDUCE: (384), (5254) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5262) ~ (all_8_2 = all_4_0)
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | SIMP: (5262) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5263) ~ (all_8_2 = all_4_0)
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REDUCE: (4235), (5254) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5264) ~ (all_4_0 = e1)
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | REDUCE: (5219), (5257) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | (5265) ~ (all_4_0 = e2)
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | (5266) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 154.35/26.36 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 154.35/26.36 | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | BETA: splitting (5266) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | (5267) all_58_1 = e0 & op(e3, e2) = e0
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | ALPHA: (5267) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | (5268) op(e3, e2) = e0
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5269) all_54_7 = e3
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5258), (5269) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5270) all_4_0 = e3
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | REDUCE: (5232), (5270) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5271) $false
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | CLOSE: (5271) is inconsistent.
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5272) ~ (all_54_7 = e3)
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5273) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (131), (133), (138), (156), (157), (158),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (168),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (189), (190), (191), (195), (197), (199), (208),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (209), (230), (240), (263), (264), (265), (282),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (287), (297), (360), (366), (373), (376), (378),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (380), (382), (384), (4230), (4231), (4232),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (4234), (4236), (4249), (4251), (5209), (5214),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5225), (5229), (5232), (5239), (5240), (5244),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5247), (5253), (5258), (5259), (5261), (5263),
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5264), (5265), (5268), (5273), (function-axioms)
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #5.
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | (5274) all_58_3 = e0 & op(e2, e2) = e0
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | ALPHA: (5274) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | (5275) all_58_3 = e0
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | (5276) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5276) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | (5277) all_58_9 = e2 & op(e3, e0) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5277) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | (5278) op(e3, e0) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | (5279) all_54_7 = e3
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5258), (5279) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | (5280) all_4_0 = e3
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5232), (5280) imply:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | (5281) $false
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5281) is inconsistent.
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | (5282) ~ (all_54_7 = e3)
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | (5283) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | (5284) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5284) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | (5285) all_58_2 = e2 & op(e2, e3) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5285) implies:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | (5286) op(e2, e3) = e2
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | | (5287) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5287) gives:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (5288) all_58_0 = e1 & op(e3, e3) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5288) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (5289) all_58_0 = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5290) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5290) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5291) all_58_0 = e0 & op(e3, e3) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5289), (5291) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1520.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5292) all_58_1 = e0 & op(e3, e2) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5292) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5293) op(e3, e2) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (131), (133), (138), (156), (157), (158),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (161), (162), (163), (165), (166), (168),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (190), (191), (195), (197), (199), (208),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (230), (240), (263), (264), (265), (282),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287), (297), (360), (366), (373), (376), (378),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380), (382), (384), (4230), (4231), (4232),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4234), (4236), (4249), (4251), (5209), (5214),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5225), (5229), (5232), (5239), (5240), (5244),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5247), (5253), (5258), (5259), (5261), (5263),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5264), (5265), (5283), (5293), (function-axioms)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #5.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5294) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5294) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5295) all_58_4 = e0 & op(e3, e1) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4253), (5295), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #259.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5296) all_58_9 = e0 & op(e3, e0) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5296) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5297) op(e3, e0) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5278), (5297), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1500.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (5298) all_58_2 = e1 & op(e2, e3) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5298) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (5299) op(e2, e3) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5286), (5299), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1430.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (5300) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5300) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (5301) all_58_6 = e1 & op(e1, e3) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5301) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (5302) op(e1, e3) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5239), (5302), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1412.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (5303) all_58_12 = e1 & op(e0, e3) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5303) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (5304) all_58_12 = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5305) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5305) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5306) all_58_12 = e2 & op(e0, e3) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5306) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5307) all_58_12 = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5304), (5307) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1486.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5308) all_58_13 = e2 & op(e0, e2) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5308) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5309) op(e0, e2) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5310) all_54_12 = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (5310) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5311) all_52_3 = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5311) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5312) all_52_3 = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (5312) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5313) ~ (all_52_7 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5313) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5314) ~ (all_52_7 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5315) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (156), (5304), (5314), (5315),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #996.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5316) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5316) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5317) all_58_14 = e3 & op(e0, e1) = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4267), (5317) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #314.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5318) all_58_15 = e3 & op(e0, e0) = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4244), (5318) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1054.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5319) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (138), (156), (264), (4231), (4251), (5309),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5319), (function-axioms) are inconsistent by
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #55.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5320) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (155), (4245), (4249), (5320),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | #54.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5321) all_58_3 = e2 & op(e2, e2) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5321) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5322) all_58_3 = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5275), (5322) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | #1377.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5323) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5323) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5324) all_58_5 = e2 & op(e2, e1) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5324) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5325) op(e2, e1) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5213), (5325), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1441.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5326) all_58_10 = e2 & op(e2, e0) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5326) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5327) op(e2, e0) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5247), (5258), (5264), (5265), (5283),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5327), (function-axioms) are inconsistent by
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5328) all_58_10 = e2 & op(e2, e0) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5328) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5329) op(e2, e0) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5330) all_54_7 = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5258), (5330) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5331) all_4_0 = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5232), (5331) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5332) $false
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5332) is inconsistent.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5333) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5247), (5258), (5264), (5265), (5329),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5333), (function-axioms) are inconsistent by
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | sub-proof #7.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | (5334) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (4245), (5214), (5334),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | #4.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | (5335) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (4252), (5253), (5335),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | #3.
% 154.35/26.37 | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5336) all_58_13 = e1 & op(e0, e2) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4232), (5336), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | (5337) ~ (all_4_1 = e2) & op(e1, e1) = all_4_1 &
% 154.35/26.37 | | | | | | | | | | | | | | | $i(all_4_1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | ALPHA: (5337) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | (5338) ~ (all_4_1 = e2)
% 154.35/26.37 | | | | | | | | | | | | | | | (5339) op(e1, e1) = all_4_1
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REF_CLOSE: (5220), (5230), (5338), (5339), (function-axioms)
% 154.35/26.37 | | | | | | | | | | | | | | | are inconsistent by sub-proof #2.
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | (5340) all_58_14 = e2 & op(e0, e1) = e2
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | ALPHA: (5340) implies:
% 154.35/26.37 | | | | | | | | | | | | | | (5341) op(e0, e1) = e2
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | REF_CLOSE: (5), (155), (4249), (5341), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | inconsistent by sub-proof #1372.
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | (5342) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 154.35/26.37 | | | | | | | | | | | $i(all_12_1)
% 154.35/26.37 | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | ALPHA: (5342) implies:
% 154.35/26.37 | | | | | | | | | | | (5343) ~ (all_12_1 = e3)
% 154.35/26.37 | | | | | | | | | | | (5344) op(e1, e1) = all_12_1
% 154.35/26.37 | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | BETA: splitting (214) gives:
% 154.35/26.37 | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | (5345) ~ (all_56_14 = e2)
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | REDUCE: (5209), (5345) imply:
% 154.35/26.37 | | | | | | | | | | | | (5346) $false
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | CLOSE: (5346) is inconsistent.
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | (5347) all_56_7 = e1 & op(e1, e2) = e1
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | ALPHA: (5347) implies:
% 154.35/26.37 | | | | | | | | | | | | (5348) op(e1, e2) = e1
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | BETA: splitting (236) gives:
% 154.35/26.37 | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | (5349) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 154.35/26.37 | | | | | | | | | | | | | & op(e2, e1) = e2)
% 154.35/26.37 | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | REF_CLOSE: (163), (167), (5212), (5213), (5349),
% 154.35/26.37 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | #119.
% 154.35/26.37 | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | (5350) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 154.35/26.37 | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 154.35/26.37 | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | BETA: splitting (5350) gives:
% 154.35/26.37 | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | (5351) all_58_8 = e2 & op(e1, e1) = e2
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | ALPHA: (5351) implies:
% 154.35/26.37 | | | | | | | | | | | | | | (5352) all_58_8 = e2
% 154.35/26.37 | | | | | | | | | | | | | | (5353) op(e1, e1) = e2
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | BETA: splitting (4228) gives:
% 154.35/26.37 | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | (5354) ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 154.35/26.37 | | | | | | | | | | | | | | | op(e1, e1) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | ALPHA: (5354) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | (5355) ~ (all_4_0 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | (5356) op(e1, e1) = all_4_1
% 154.35/26.37 | | | | | | | | | | | | | | | (5357) op(all_4_1, e0) = all_4_0
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 154.35/26.37 | | | | | | | | | | | | | | | all_12_1, e1, e1, simplifying with (5344), (5356)
% 154.35/26.37 | | | | | | | | | | | | | | | gives:
% 154.35/26.37 | | | | | | | | | | | | | | | (5358) all_12_1 = all_4_1
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_12_1,
% 154.35/26.37 | | | | | | | | | | | | | | | e1, e1, simplifying with (5344), (5353) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | (5359) all_12_1 = e2
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 154.35/26.37 | | | | | | | | | | | | | | | e2, e1, simplifying with (160), (5348) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | (5360) all_52_6 = e1
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | COMBINE_EQS: (5358), (5359) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5361) all_4_1 = e2
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REDUCE: (141), (5360) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5362) ~ (all_52_2 = e1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REDUCE: (134), (5360) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5363) ~ (all_52_4 = e1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REDUCE: (126), (5360) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5364) ~ (all_52_7 = e1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REDUCE: (124), (5360) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5365) ~ (all_52_14 = e1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REDUCE: (378), (5360) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5366) ~ (all_8_2 = e1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | SIMP: (5366) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | (5367) ~ (all_8_2 = e1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REDUCE: (5211), (5360) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5368) ~ (e2 = e1)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REDUCE: (5343), (5359) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5369) ~ (e3 = e2)
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | REDUCE: (5357), (5361) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | (5370) op(e2, e0) = all_4_0
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 154.35/26.37 | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | (5371) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.35/26.37 | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | BETA: splitting (5371) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5372) all_58_1 = e1 & op(e3, e2) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5363), (5372), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1284.
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5373) all_58_3 = e1 & op(e2, e2) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5367), (5373), (function-axioms) are
% 154.35/26.37 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | (5374) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 154.35/26.37 | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 154.35/26.37 | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | BETA: splitting (5374) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5375) all_58_7 = e1 & op(e1, e2) = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | ALPHA: (5375) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5376) all_58_7 = e1
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 154.35/26.37 | | | | | | | | | | | | | | | | | all_4_0, e0, e2, simplifying with (162), (5370)
% 154.35/26.37 | | | | | | | | | | | | | | | | | gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5377) all_52_13 = all_4_0
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (5377) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5378) all_54_7 = all_4_0
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | REDUCE: (143), (5377) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5379) ~ (all_52_1 = all_4_0)
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | REDUCE: (111), (5377) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5380) ~ (all_52_12 = all_4_0)
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | REDUCE: (108), (5377) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5381) ~ (all_52_14 = all_4_0)
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | SIMP: (5381) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5382) ~ (all_52_14 = all_4_0)
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | REDUCE: (384), (5377) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5383) ~ (all_8_2 = all_4_0)
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | SIMP: (5383) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5384) ~ (all_8_2 = all_4_0)
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | REDUCE: (4235), (5377) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | (5385) ~ (all_4_0 = e1)
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | (5386) ~ (all_10_2 = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | (5387) ~ (all_14_2 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | REDUCE: (351), (5387) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | (5388) ~ (all_8_2 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | (5389) ~ (all_16_2 = e2)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (5389) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | (5390) ~ (all_10_2 = e2)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5391) ~ (all_30_2 = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (5391) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5392) ~ (all_8_2 = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5393) all_54_5 = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (5388), (5393) are inconsistent by
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1161.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5394) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5395) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5395) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5396) all_58_1 = e0 & op(e3, e2) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5396) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5397) op(e3, e2) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (133), (156), (157), (158), (160), (161),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (162), (163), (165), (166), (168), (189), (191),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (195), (208), (230), (240), (263), (265), (282),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (360), (373), (378), (380), (382), (384), (4232),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (4236), (4249), (4251), (4252), (5214), (5352),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5355), (5362), (5367), (5370), (5376), (5378),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5382), (5384), (5385), (5392), (5394), (5397),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | #6.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5398) all_58_3 = e0 & op(e2, e2) = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5398) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (5399) all_58_3 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (165), (240), (282), (373), (382),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (384), (5367), (5392), (5394), (5399),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | | #324.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5400) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (4252), (5376), (5400),
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | #3.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5401) all_30_2 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (5401) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5402) all_8_2 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | SIMP: (5402) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5403) all_8_2 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (5403) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5404) all_56_13 = e0
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (5403) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5405) ~ (all_52_1 = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (5403) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5406) ~ (all_52_4 = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5384), (5403) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5407) ~ (all_4_0 = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | SIMP: (5407) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | (5408) ~ (all_4_0 = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5409) ~ (all_56_13 = e0)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5404), (5409) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5410) $false
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5410) is inconsistent.
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5411) all_56_5 = e2 & op(e2, e0) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5411) implies:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | (5412) op(e2, e0) = e2
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5413) all_56_12 = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (5413) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5414) all_10_2 = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (5414) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5415) ~ (all_52_1 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (5414) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5416) ~ (all_52_2 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (5414) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5417) ~ (all_52_3 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (5414) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5418) ~ (all_52_4 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (5414) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5419) ~ (all_52_8 = e3)
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (5414) imply:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | (5420) op(e3, e3) = e3
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | (5421) all_54_2 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (5419), (5421) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1210.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | (5422) ~ (all_54_2 = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | (5423) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5423) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | (5424) all_54_2 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (5212), (5424) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1209.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | (5425) ~ (all_54_2 = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | (5426) all_54_2 = e1 | all_54_2 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (5427) all_54_1 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (5427) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (5428) all_52_4 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5418), (5428) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (5429) $false
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5429) is inconsistent.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (5430) ~ (all_54_1 = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (5431) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5432) all_54_12 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (5417), (5432) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1234.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5433) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5434) all_54_7 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5355), (5378), (5434) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #11.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5435) ~ (all_54_7 = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5436) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5437) all_54_8 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (5416), (5437) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1425.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5438) ~ (all_54_8 = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5439) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5426) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5440) all_54_2 = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (5440) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5441) all_52_8 = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5441) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5442) all_52_8 = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5419), (5442) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5443) ~ (e3 = e1)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (5442) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5444) op(e3, e1) = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5445) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5445) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5446) all_58_2 = e1 & op(e2, e3) = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5446) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5447) op(e2, e3) = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5448) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (5388), (5447), (5448),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #884.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5449) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5449) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5450) all_58_5 = e3 & op(e2, e1) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5450) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5451) all_58_5 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5452) op(e2, e1) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5453) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (5390), (5447), (5453),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1429.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5454) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5454) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5455) all_58_6 = e2 & op(e1, e3) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5455) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5456) all_58_6 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (230), (233), (5352),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5376), (5456), (function-axioms) are inconsistent
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #116.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5457) all_58_12 = e2 & op(e0, e3) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5457) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5458) all_58_12 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5459) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5459) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5460) all_58_12 = e3 & op(e0, e3) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5460) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5461) all_58_12 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (138), (155), (156), (225), (264),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4231), (4245), (4249), (4251), (5433), (5461),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #17.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5462) all_58_13 = e3 & op(e0, e2) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5462) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5463) all_58_13 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5436) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5464) all_54_7 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5378), (5464) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5465) all_4_0 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5465) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5466) all_4_0 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5379), (5466) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5467) ~ (all_52_1 = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5380), (5466) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5468) ~ (all_52_12 = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5469) all_54_4 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (5415), (5469) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1434.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5470) ~ (all_54_4 = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5471) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5472) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5472) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5473) all_58_9 = e2 & op(e3, e0) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (5468), (5473), (function-axioms) are
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1238.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5474) all_58_10 = e2 & op(e2, e0) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5474) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5475) all_58_10 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5476) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5476) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5477) all_58_0 = e2 & op(e3, e3) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5477) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5478) all_58_0 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (246), (248), (252),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5458), (5478) are inconsistent by sub-proof #999.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5479) all_58_1 = e2 & op(e3, e2) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5479) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5480) all_58_1 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5471) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5481) all_54_4 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (5467), (5481) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1431.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5482) all_54_4 = e1 | all_54_4 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5483) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5483) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5484) all_58_6 = e3 & op(e1, e3) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5484) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5485) all_58_6 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (45), (165), (246), (250),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5390), (5405), (5420), (5447), (5485),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1194.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5486) all_58_7 = e3 & op(e1, e2) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5486) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5487) all_58_7 = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5376), (5487) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5488) e3 = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5463), (5488) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5489) all_58_13 = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (168), (245), (5376), (5388), (5418),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5489), (function-axioms) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1419.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5490) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5490) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5491) all_58_8 = e3 & op(e1, e1) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5491) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5492) op(e1, e1) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5343), (5344), (5492), (function-axioms) are
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #21.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5493) all_58_11 = e3 & op(e1, e0) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5493) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5494) op(e1, e0) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5495) all_58_15 = e0 & op(e0, e0) = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5495) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5496) all_58_15 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4244), (5496) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5497) e1 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5497) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5498) e1 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5376), (5498) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5499) all_58_7 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (243), (5367), (5463),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5480), (5499), (function-axioms) are inconsistent
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #322.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4259) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5500) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5439) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5501) all_54_8 = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (5210), (5501) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1231.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5502) ~ (all_54_8 = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5503) all_54_8 = e1 | all_54_8 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5503) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5504) all_54_8 = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (5362), (5504) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1379.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5505) all_54_8 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (5505) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5506) all_52_2 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5506) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5507) all_52_2 = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (5507) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5508) ~ (all_52_14 = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5508) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5509) ~ (all_52_14 = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5416), (5507) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5510) ~ (e3 = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5210), (5507) imply:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5511) ~ (e2 = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5512) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5512) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5513) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5513) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5514) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5514) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5515) op(e2, e3) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (286), (5405), (5415), (5482), (5515),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1236.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5516) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5516) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5517) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5517) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5518) op(e2, e3) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (42), (5367), (5445), (5518),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1074.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5519) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (5451), (5475), (5519) are inconsistent
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1090.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5520) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (230), (5352), (5376), (5494),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5520), (function-axioms) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #15.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5521) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5521) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5522) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5522) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5523) op(e1, e3) = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5362), (5523), (function-axioms) are
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1412.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5524) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5524) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5525) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5525) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5526) op(e3, e0) = e3
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (162), (166), (5412), (5494), (5500),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5526), (function-axioms) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #48.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5527) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5527) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5528) op(e0, e3) = e0
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4251), (5528), (function-axioms) are
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #89.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5529) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5529) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5530) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5530) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5531) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5531) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5532) op(e1, e2) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (160), (289), (5363), (5406), (5431),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5532), (function-axioms) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #167.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5533) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5533) gives:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5534) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5534) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5535) op(e2, e1) = e1
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5452), (5535), (function-axioms) are
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5536) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5536) implies:
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5537) op(e0, e2) = e2
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (138), (156), (264), (4231), (4251), (5433),
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5537), (function-axioms) are inconsistent by
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #55.
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5538) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5538) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5539) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5539) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5540) op(e0, e2) = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4252), (5540), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1532.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5541) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5541) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5542) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5542) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5543) op(e0, e1) = e1
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (156), (4252), (4260), (5458), (5543),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #97.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5544) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5544) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5545) op(e1, e0) = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (191), (265), (4236), (5214), (5509),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5545), (function-axioms) are inconsistent by
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #111.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5546) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5546) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5547) all_58_4 = e2 & op(e3, e1) = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5547) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5548) op(e3, e1) = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5444), (5548), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #338.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5549) all_58_9 = e2 & op(e3, e0) = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (5468), (5549), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1238.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5550) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (4245), (5214), (5550),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #4.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5551) ~ (all_54_7 = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5378), (5551) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5552) ~ (all_4_0 = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5370), (5378), (5385), (5412), (5436),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5552), (function-axioms) are inconsistent by
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5553) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (4244), (4267), (5553) are inconsistent
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #33.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5554) all_58_10 = e3 & op(e2, e0) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (131), (158), (166), (228), (289), (4245), (5214),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5363), (5406), (5418), (5431), (5554),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5555) all_58_3 = e1 & op(e2, e2) = e1
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5367), (5555), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1423.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5556) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5556) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5557) all_58_5 = e1 & op(e2, e1) = e1
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5557) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5558) op(e2, e1) = e1
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5559) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (165), (5388), (5415), (5559),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1182.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5560) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5560) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5561) all_58_5 = e3 & op(e2, e1) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5561) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5562) op(e2, e1) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5558), (5562), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5563) all_58_10 = e3 & op(e2, e0) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (131), (158), (166), (228), (289), (4245), (5214),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5363), (5406), (5418), (5431), (5563),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5564) all_58_10 = e1 & op(e2, e0) = e1
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4235), (5564), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5565) all_54_2 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (288), (4253), (5565) are inconsistent by
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #207.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | (5566) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5566) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5567) all_56_13 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5404), (5567) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | #1190.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5568) all_56_14 = e1 | all_56_15 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (4230), (5209), (5568) are inconsistent
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #13.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | (5569) all_16_2 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (5569) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | (5570) all_10_2 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (5570) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | (5571) all_56_12 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (5570) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | (5572) ~ (all_52_4 = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (5570) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | (5573) ~ (all_52_12 = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | (5574) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5574) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | (5575) all_58_12 = e2 & op(e0, e3) = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5575) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | (5576) all_58_12 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | (5577) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (246), (248),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | (252), (5572), (5576), (5577), (function-axioms)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #115.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | (5578) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (167), (5212), (5573), (5578),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | #868.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | (5579) all_58_13 = e2 & op(e0, e2) = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5579) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | (5580) all_58_13 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | (5581) op(e0, e2) = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | (5582) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5582) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5583) all_58_1 = e3 & op(e3, e2) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5583) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5584) op(e3, e2) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | (5585) all_56_12 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5571), (5585) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | (5586) e3 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5586) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | (5587) $false
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5587) is inconsistent.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | (5588) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5588) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (5589) all_56_13 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (5589) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (5590) all_8_2 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5590) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (5591) all_8_2 = e2
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (5591) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (5592) ~ (all_52_7 = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (5581), (5592), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1479.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (5593) all_56_14 = e1 | all_56_15 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5593) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5594) all_56_14 = e1
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5209), (5594) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | #93.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5595) all_56_15 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4230), (5595) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5596) e1 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5596) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5597) e1 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5376), (5597) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5598) all_58_7 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (156), (243), (5367), (5581),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5584), (5598), (function-axioms) are inconsistent
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1076.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5599) all_58_3 = e3 & op(e2, e2) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5388), (5599), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1437.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | (5600) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5600) gives:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5601) all_58_7 = e3 & op(e1, e2) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5601) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5602) all_58_7 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5376), (5602) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | #1330.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5603) all_58_13 = e3 & op(e0, e2) = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5603) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | (5604) all_58_13 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5580), (5604) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | | #320.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | (5605) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (155), (4245), (4249), (5605),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | | #54.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | (5606) all_14_2 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (5606) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | (5607) all_8_2 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | SIMP: (5607) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | (5608) all_8_2 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (5608) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | (5609) all_56_13 = e3
% 154.35/26.39 | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | REDUCE: (380), (5608) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | (5610) ~ (all_52_7 = e3)
% 154.35/26.39 | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (138), (189), (190), (209), (263),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | (264), (297), (366), (4230), (4231), (4232),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | (4251), (4252), (5209), (5609), (5610) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12.
% 154.35/26.39 | | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | (5611) all_10_2 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (5611) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | (5612) all_56_12 = e0
% 154.35/26.39 | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | REDUCE: (364), (5611) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | (5613) ~ (all_52_2 = e0)
% 154.35/26.39 | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | REDUCE: (368), (5611) imply:
% 154.35/26.39 | | | | | | | | | | | | | | | | | | (5614) ~ (all_52_4 = e0)
% 154.35/26.39 | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (131), (139), (166), (191), (194), (201),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | (209), (219), (261), (265), (275), (289), (360),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | (376), (396), (4236), (5209), (5210), (5214),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | (5362), (5363), (5612), (5613), (5614),
% 154.35/26.39 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 154.35/26.39 | | | | | | | | | | | | | | | | | | #68.
% 154.35/26.39 | | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | (5615) all_58_13 = e1 & op(e0, e2) = e1
% 154.35/26.39 | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4232), (5615), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 154.35/26.39 | | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | (5616) ~ (all_4_1 = e2) & op(e1, e1) = all_4_1 &
% 154.35/26.39 | | | | | | | | | | | | | | | $i(all_4_1)
% 154.35/26.39 | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | ALPHA: (5616) implies:
% 154.35/26.39 | | | | | | | | | | | | | | | (5617) ~ (all_4_1 = e2)
% 154.35/26.39 | | | | | | | | | | | | | | | (5618) op(e1, e1) = all_4_1
% 154.35/26.39 | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | | REF_CLOSE: (5344), (5353), (5617), (5618), (function-axioms)
% 154.35/26.39 | | | | | | | | | | | | | | | are inconsistent by sub-proof #2.
% 154.35/26.39 | | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | Case 2:
% 154.35/26.39 | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | (5619) all_58_14 = e2 & op(e0, e1) = e2
% 154.35/26.39 | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | ALPHA: (5619) implies:
% 154.35/26.39 | | | | | | | | | | | | | | (5620) op(e0, e1) = e2
% 154.35/26.39 | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | | REF_CLOSE: (5), (155), (4249), (5620), (function-axioms) are
% 154.35/26.39 | | | | | | | | | | | | | | inconsistent by sub-proof #1372.
% 154.35/26.39 | | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | | |
% 154.35/26.39 | | | | | | | | | End of split
% 154.35/26.39 | | | | | | | | |
% 154.35/26.39 | | | | | | | | End of split
% 154.35/26.39 | | | | | | | |
% 154.35/26.39 | | | | | | | End of split
% 154.35/26.39 | | | | | | |
% 154.35/26.39 | | | | | | End of split
% 154.35/26.39 | | | | | |
% 154.35/26.39 | | | | | End of split
% 154.35/26.39 | | | | |
% 154.35/26.39 | | | | End of split
% 154.35/26.39 | | | |
% 154.35/26.39 | | | End of split
% 154.35/26.39 | | |
% 154.35/26.39 | | End of split
% 154.35/26.39 | |
% 154.35/26.39 | End of split
% 154.35/26.39 |
% 154.35/26.39 End of proof
% 154.35/26.39
% 154.35/26.39 Sub-proof #1 shows that the following formulas are inconsistent:
% 154.35/26.39 ----------------------------------------------------------------
% 154.35/26.39 (1) all_58_10 = e3 & op(e2, e0) = e3
% 154.35/26.39 (2) op(e3, e0) = all_52_12
% 154.35/26.39 (3) ~ (all_52_14 = e2)
% 154.35/26.39 (4) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.35/26.39 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.35/26.39 (5) all_54_1 = all_52_4
% 154.35/26.39 (6) ~ (all_52_4 = all_52_12)
% 154.35/26.39 (7) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.35/26.39 (8) ~ (all_52_4 = e0)
% 154.35/26.39 (9) ~ (all_52_4 = e1)
% 154.35/26.39 (10) ~ (all_52_4 = e3)
% 154.35/26.39 (11) op(e1, e0) = all_52_14
% 154.35/26.39 (12) op(e0, e0) = e1
% 154.35/26.39 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.35/26.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.35/26.39
% 154.35/26.39 Begin of proof
% 154.35/26.39 |
% 154.35/26.39 | ALPHA: (1) implies:
% 154.35/26.39 | (14) all_58_10 = e3
% 154.35/26.39 |
% 154.35/26.39 | BETA: splitting (7) gives:
% 154.35/26.39 |
% 154.35/26.39 | Case 1:
% 154.35/26.39 | |
% 154.35/26.40 | | (15) all_54_1 = e2
% 154.35/26.40 | |
% 154.35/26.40 | | COMBINE_EQS: (5), (15) imply:
% 154.35/26.40 | | (16) all_52_4 = e2
% 154.35/26.40 | |
% 154.35/26.40 | | SIMP: (16) implies:
% 154.35/26.40 | | (17) all_52_4 = e2
% 154.35/26.40 | |
% 154.35/26.40 | | REDUCE: (6), (17) imply:
% 154.35/26.40 | | (18) ~ (all_52_12 = e2)
% 154.35/26.40 | |
% 154.35/26.40 | | SIMP: (18) implies:
% 154.35/26.40 | | (19) ~ (all_52_12 = e2)
% 154.35/26.40 | |
% 154.35/26.40 | | REDUCE: (10), (17) imply:
% 154.35/26.40 | | (20) ~ (e3 = e2)
% 154.35/26.40 | |
% 154.35/26.40 | | SIMP: (20) implies:
% 154.35/26.40 | | (21) ~ (e3 = e2)
% 154.35/26.40 | |
% 154.35/26.40 | | REDUCE: (9), (17) imply:
% 154.35/26.40 | | (22) ~ (e2 = e1)
% 154.35/26.40 | |
% 154.35/26.40 | | BETA: splitting (4) gives:
% 154.35/26.40 | |
% 154.35/26.40 | | Case 1:
% 154.35/26.40 | | |
% 154.35/26.40 | | | (23) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 154.35/26.40 | | | e2)
% 154.35/26.40 | | |
% 154.35/26.40 | | | BETA: splitting (23) gives:
% 154.35/26.40 | | |
% 154.35/26.40 | | | Case 1:
% 154.35/26.40 | | | |
% 154.35/26.40 | | | | (24) all_58_9 = e2 & op(e3, e0) = e2
% 154.35/26.40 | | | |
% 154.35/26.40 | | | | REF_CLOSE: (2), (13), (19), (24) are inconsistent by sub-proof #1238.
% 154.35/26.40 | | | |
% 154.35/26.40 | | | Case 2:
% 154.35/26.40 | | | |
% 154.35/26.40 | | | | (25) all_58_10 = e2 & op(e2, e0) = e2
% 154.35/26.40 | | | |
% 154.35/26.40 | | | | REF_CLOSE: (14), (21), (25) are inconsistent by sub-proof #1050.
% 154.35/26.40 | | | |
% 154.35/26.40 | | | End of split
% 154.35/26.40 | | |
% 154.35/26.40 | | Case 2:
% 154.35/26.40 | | |
% 154.35/26.40 | | | (26) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0)
% 154.35/26.40 | | | = e2)
% 154.35/26.40 | | |
% 154.35/26.40 | | | REF_CLOSE: (3), (11), (12), (13), (22), (26) are inconsistent by sub-proof
% 154.35/26.40 | | | #4.
% 154.35/26.40 | | |
% 154.35/26.40 | | End of split
% 154.35/26.40 | |
% 154.35/26.40 | Case 2:
% 154.35/26.40 | |
% 154.35/26.40 | | (27) all_54_1 = e1 | all_54_1 = e0
% 154.35/26.40 | |
% 154.35/26.40 | | REF_CLOSE: (5), (8), (9), (27) are inconsistent by sub-proof #1108.
% 154.35/26.40 | |
% 154.35/26.40 | End of split
% 154.35/26.40 |
% 154.35/26.40 End of proof
% 154.35/26.40
% 154.35/26.40 Sub-proof #2 shows that the following formulas are inconsistent:
% 154.35/26.40 ----------------------------------------------------------------
% 154.35/26.40 (1) ~ (all_4_1 = e2)
% 154.35/26.40 (2) op(e1, e1) = all_12_1
% 154.35/26.40 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.35/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.35/26.40 (4) op(e1, e1) = all_4_1
% 154.35/26.40 (5) op(e1, e1) = e2
% 154.35/26.40
% 154.35/26.40 Begin of proof
% 154.35/26.40 |
% 154.35/26.40 | GROUND_INST: instantiating (3) with all_4_1, all_12_1, e1, e1, simplifying
% 154.35/26.40 | with (2), (4) gives:
% 154.35/26.40 | (6) all_12_1 = all_4_1
% 154.35/26.40 |
% 154.35/26.40 | GROUND_INST: instantiating (3) with e2, all_12_1, e1, e1, simplifying with
% 154.35/26.40 | (2), (5) gives:
% 154.35/26.40 | (7) all_12_1 = e2
% 154.35/26.40 |
% 154.35/26.40 | COMBINE_EQS: (6), (7) imply:
% 154.35/26.40 | (8) all_4_1 = e2
% 154.35/26.40 |
% 154.35/26.40 | REDUCE: (1), (8) imply:
% 154.35/26.40 | (9) $false
% 154.35/26.40 |
% 154.35/26.40 | CLOSE: (9) is inconsistent.
% 154.35/26.40 |
% 154.35/26.40 End of proof
% 154.35/26.40
% 154.35/26.40 Sub-proof #3 shows that the following formulas are inconsistent:
% 154.35/26.40 ----------------------------------------------------------------
% 154.35/26.40 (1) all_58_7 = e1
% 154.35/26.40 (2) ~ (all_52_7 = e0)
% 154.35/26.40 (3) ~ (e1 = e0)
% 154.35/26.40 (4) op(e0, e2) = all_52_7
% 154.35/26.40 (5) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 154.35/26.40 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.35/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.35/26.40
% 154.35/26.40 Begin of proof
% 154.35/26.40 |
% 154.35/26.40 | BETA: splitting (5) gives:
% 154.35/26.40 |
% 154.35/26.40 | Case 1:
% 154.35/26.40 | |
% 154.35/26.40 | | (7) all_58_7 = e0 & op(e1, e2) = e0
% 154.35/26.40 | |
% 154.35/26.40 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #992.
% 154.35/26.40 | |
% 154.35/26.40 | Case 2:
% 154.35/26.40 | |
% 154.35/26.40 | | (8) all_58_13 = e0 & op(e0, e2) = e0
% 154.35/26.40 | |
% 154.35/26.40 | | ALPHA: (8) implies:
% 154.35/26.40 | | (9) op(e0, e2) = e0
% 154.35/26.40 | |
% 154.35/26.40 | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #1532.
% 154.35/26.40 | |
% 154.35/26.40 | End of split
% 154.35/26.40 |
% 154.35/26.40 End of proof
% 154.35/26.40
% 154.35/26.40 Sub-proof #4 shows that the following formulas are inconsistent:
% 154.35/26.40 ----------------------------------------------------------------
% 154.35/26.40 (1) ~ (all_52_14 = e2)
% 154.35/26.40 (2) ~ (e2 = e1)
% 154.35/26.40 (3) op(e1, e0) = all_52_14
% 154.35/26.40 (4) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.35/26.40 (5) op(e0, e0) = e1
% 154.35/26.40 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.35/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.35/26.40
% 154.35/26.40 Begin of proof
% 154.55/26.40 |
% 154.55/26.40 | BETA: splitting (4) gives:
% 154.55/26.40 |
% 154.55/26.40 | Case 1:
% 154.55/26.40 | |
% 154.55/26.40 | | (7) all_58_11 = e2 & op(e1, e0) = e2
% 154.55/26.40 | |
% 154.55/26.40 | | ALPHA: (7) implies:
% 154.55/26.40 | | (8) op(e1, e0) = e2
% 154.55/26.40 | |
% 154.55/26.40 | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1389.
% 154.55/26.40 | |
% 154.55/26.40 | Case 2:
% 154.55/26.40 | |
% 154.55/26.40 | | (9) all_58_15 = e2 & op(e0, e0) = e2
% 154.55/26.40 | |
% 154.55/26.40 | | ALPHA: (9) implies:
% 154.55/26.40 | | (10) op(e0, e0) = e2
% 154.55/26.40 | |
% 154.55/26.40 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1386.
% 154.55/26.40 | |
% 154.55/26.40 | End of split
% 154.55/26.40 |
% 154.55/26.40 End of proof
% 154.55/26.40
% 154.55/26.40 Sub-proof #5 shows that the following formulas are inconsistent:
% 154.55/26.40 ----------------------------------------------------------------
% 154.55/26.40 (1) ~ (all_52_14 = all_4_0)
% 154.55/26.40 (2) ~ (all_52_3 = e1)
% 154.55/26.40 (3) op(e0, e3) = all_52_3
% 154.55/26.40 (4) op(e3, e0) = all_52_12
% 154.55/26.40 (5) ~ (all_52_14 = e2)
% 154.55/26.40 (6) all_54_13 = all_52_7
% 154.55/26.40 (7) all_56_12 = all_10_2
% 154.55/26.40 (8) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.40 (9) ~ (all_52_1 = all_8_2)
% 154.55/26.40 (10) all_56_14 = e2
% 154.55/26.40 (11) op(e3, e2) = all_52_4
% 154.55/26.40 (12) ~ (all_52_3 = e0)
% 154.55/26.40 (13) all_56_13 = all_8_2
% 154.55/26.40 (14) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 154.55/26.40 (15) ~ (all_52_4 = all_52_12)
% 154.55/26.40 (16) op(e2, e1) = all_52_9
% 154.55/26.40 (17) op(e2, e3) = all_52_1
% 154.55/26.40 (18) ~ (all_4_0 = e2)
% 154.55/26.40 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 154.55/26.40 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 154.55/26.40 (20) op(e1, e3) = all_52_2
% 154.55/26.40 (21) op(e2, e0) = all_52_13
% 154.55/26.40 (22) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.55/26.40 (23) ~ (all_4_0 = e3)
% 154.55/26.40 (24) ~ (all_52_6 = all_8_2)
% 154.55/26.40 (25) op(e1, e2) = all_52_6
% 154.55/26.40 (26) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.40 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.40 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.40 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.40 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.40 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.40 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.40 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.40 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.40 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.40 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.40 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.40 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.40 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.40 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.40 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.40 = e0)
% 154.55/26.40 (27) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 154.55/26.40 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 154.55/26.40 (28) ~ (all_8_2 = all_4_0)
% 154.55/26.40 (29) all_58_7 = e1
% 154.55/26.40 (30) op(e1, e2) = e1
% 154.55/26.40 (31) ~ (all_52_3 = all_10_2)
% 154.55/26.40 (32) op(e3, e2) = e0
% 154.55/26.40 (33) ~ (all_52_4 = e1)
% 154.55/26.40 (34) ~ (all_52_2 = e1)
% 154.55/26.40 (35) ~ (all_52_4 = all_8_2)
% 154.55/26.40 (36) op(e2, e0) = all_4_0
% 154.55/26.40 (37) all_54_3 = all_52_12
% 154.55/26.40 (38) all_58_8 = e2
% 154.55/26.40 (39) ~ (all_52_4 = all_52_7)
% 154.55/26.40 (40) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.40 (41) op(e0, e1) = e0
% 154.55/26.40 (42) ~ (all_8_2 = e1)
% 154.55/26.40 (43) ~ (all_52_7 = all_8_2)
% 154.55/26.40 (44) ~ (all_4_0 = e1)
% 154.55/26.40 (45) all_54_7 = all_4_0
% 154.55/26.40 (46) all_56_15 = e1
% 154.55/26.40 (47) ~ (all_52_14 = e1)
% 154.55/26.40 (48) ~ (all_52_12 = all_52_14)
% 154.55/26.40 (49) ~ (all_52_7 = e1)
% 154.55/26.40 (50) op(e0, e2) = all_52_7
% 154.55/26.40 (51) op(e1, e0) = all_52_14
% 154.55/26.40 (52) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.40 (53) ~ (all_52_12 = e1)
% 154.55/26.40 (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.40 (55) all_54_5 = all_8_2
% 154.55/26.40 (56) ~ (all_52_12 = all_4_0)
% 154.55/26.40 (57) ~ (all_52_9 = all_8_2)
% 154.55/26.40 (58) all_54_11 = all_52_14
% 154.55/26.40 (59) ~ (all_52_13 = all_8_2)
% 154.55/26.40 (60) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.40 (61) all_54_12 = all_52_3
% 154.55/26.40 (62) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.40 (63) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.40 (64) ~ (all_52_3 = all_52_7)
% 154.55/26.40
% 154.55/26.40 Begin of proof
% 154.55/26.40 |
% 154.55/26.40 | BETA: splitting (62) gives:
% 154.55/26.40 |
% 154.55/26.40 | Case 1:
% 154.55/26.40 | |
% 154.55/26.40 | | (65) all_54_7 = e2
% 154.55/26.40 | |
% 154.55/26.40 | | COMBINE_EQS: (45), (65) imply:
% 154.55/26.40 | | (66) all_4_0 = e2
% 154.55/26.40 | |
% 154.55/26.40 | | REDUCE: (18), (66) imply:
% 154.55/26.40 | | (67) $false
% 154.55/26.40 | |
% 154.55/26.40 | | CLOSE: (67) is inconsistent.
% 154.55/26.40 | |
% 154.55/26.40 | Case 2:
% 154.55/26.40 | |
% 154.55/26.40 | | (68) all_54_7 = e1 | all_54_7 = e0
% 154.55/26.40 | |
% 154.55/26.40 | | BETA: splitting (68) gives:
% 154.55/26.40 | |
% 154.55/26.40 | | Case 1:
% 154.55/26.40 | | |
% 154.55/26.40 | | | (69) all_54_7 = e1
% 154.55/26.40 | | |
% 154.55/26.40 | | | COMBINE_EQS: (45), (69) imply:
% 154.55/26.40 | | | (70) all_4_0 = e1
% 154.55/26.40 | | |
% 154.55/26.40 | | | REDUCE: (44), (70) imply:
% 154.55/26.40 | | | (71) $false
% 154.55/26.40 | | |
% 154.55/26.40 | | | CLOSE: (71) is inconsistent.
% 154.55/26.40 | | |
% 154.55/26.40 | | Case 2:
% 154.55/26.40 | | |
% 154.55/26.40 | | | (72) all_54_7 = e0
% 154.55/26.40 | | |
% 154.55/26.40 | | | COMBINE_EQS: (45), (72) imply:
% 154.55/26.40 | | | (73) all_4_0 = e0
% 154.55/26.40 | | |
% 154.55/26.40 | | | REDUCE: (56), (73) imply:
% 154.55/26.40 | | | (74) ~ (all_52_12 = e0)
% 154.55/26.40 | | |
% 154.55/26.40 | | | REDUCE: (1), (73) imply:
% 154.55/26.40 | | | (75) ~ (all_52_14 = e0)
% 154.55/26.40 | | |
% 154.55/26.40 | | | REDUCE: (36), (73) imply:
% 154.55/26.40 | | | (76) op(e2, e0) = e0
% 154.55/26.40 | | |
% 154.55/26.40 | | | BETA: splitting (40) gives:
% 154.55/26.40 | | |
% 154.55/26.40 | | | Case 1:
% 154.55/26.40 | | | |
% 154.55/26.40 | | | | (77) all_54_11 = e3
% 154.55/26.40 | | | |
% 154.55/26.40 | | | | COMBINE_EQS: (58), (77) imply:
% 154.55/26.40 | | | | (78) all_52_14 = e3
% 154.55/26.40 | | | |
% 154.55/26.40 | | | | SIMP: (78) implies:
% 154.55/26.40 | | | | (79) all_52_14 = e3
% 154.55/26.40 | | | |
% 154.55/26.40 | | | | REDUCE: (48), (79) imply:
% 154.55/26.40 | | | | (80) ~ (all_52_12 = e3)
% 154.55/26.40 | | | |
% 154.55/26.40 | | | | REDUCE: (75), (79) imply:
% 154.55/26.40 | | | | (81) ~ (e3 = e0)
% 154.55/26.40 | | | |
% 154.55/26.40 | | | | REDUCE: (51), (79) imply:
% 154.55/26.40 | | | | (82) op(e1, e0) = e3
% 154.55/26.40 | | | |
% 154.55/26.40 | | | | BETA: splitting (14) gives:
% 154.55/26.40 | | | |
% 154.55/26.40 | | | | Case 1:
% 154.55/26.40 | | | | |
% 154.55/26.40 | | | | | (83) all_54_3 = e3
% 154.55/26.40 | | | | |
% 154.55/26.40 | | | | | COMBINE_EQS: (37), (83) imply:
% 154.55/26.40 | | | | | (84) all_52_12 = e3
% 154.55/26.40 | | | | |
% 154.55/26.40 | | | | | REDUCE: (80), (84) imply:
% 154.55/26.40 | | | | | (85) $false
% 154.55/26.40 | | | | |
% 154.55/26.40 | | | | | CLOSE: (85) is inconsistent.
% 154.55/26.40 | | | | |
% 154.55/26.40 | | | | Case 2:
% 154.55/26.40 | | | | |
% 154.55/26.40 | | | | | (86) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 154.55/26.40 | | | | |
% 154.55/26.40 | | | | | BETA: splitting (86) gives:
% 154.55/26.40 | | | | |
% 154.55/26.40 | | | | | Case 1:
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | (87) all_54_3 = e2
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | COMBINE_EQS: (37), (87) imply:
% 154.55/26.40 | | | | | | (88) all_52_12 = e2
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | REDUCE: (15), (88) imply:
% 154.55/26.40 | | | | | | (89) ~ (all_52_4 = e2)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | REDUCE: (53), (88) imply:
% 154.55/26.40 | | | | | | (90) ~ (e2 = e1)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | GROUND_INST: instantiating (54) with all_52_4, e0, e2, e3,
% 154.55/26.40 | | | | | | simplifying with (11), (32) gives:
% 154.55/26.40 | | | | | | (91) all_52_4 = e0
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | REDUCE: (39), (91) imply:
% 154.55/26.40 | | | | | | (92) ~ (all_52_7 = e0)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | SIMP: (92) implies:
% 154.55/26.40 | | | | | | (93) ~ (all_52_7 = e0)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | REDUCE: (35), (91) imply:
% 154.55/26.40 | | | | | | (94) ~ (all_8_2 = e0)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | SIMP: (94) implies:
% 154.55/26.40 | | | | | | (95) ~ (all_8_2 = e0)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | REDUCE: (89), (91) imply:
% 154.55/26.40 | | | | | | (96) ~ (e2 = e0)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | SIMP: (96) implies:
% 154.55/26.40 | | | | | | (97) ~ (e2 = e0)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | REDUCE: (33), (91) imply:
% 154.55/26.40 | | | | | | (98) ~ (e1 = e0)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | SIMP: (98) implies:
% 154.55/26.40 | | | | | | (99) ~ (e1 = e0)
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | BETA: splitting (26) gives:
% 154.55/26.40 | | | | | |
% 154.55/26.40 | | | | | | Case 1:
% 154.55/26.40 | | | | | | |
% 154.55/26.40 | | | | | | | (100) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) &
% 154.55/26.40 | | | | | | | op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 &
% 154.55/26.40 | | | | | | | all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 &
% 154.55/26.40 | | | | | | | op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~
% 154.55/26.40 | | | | | | | (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.40 | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) &
% 154.55/26.40 | | | | | | | op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_2 = e3 &
% 154.55/26.40 | | | | | | | all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 &
% 154.55/26.40 | | | | | | | op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 154.55/26.40 | | | | | | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.40 | | | | | | |
% 154.55/26.40 | | | | | | | BETA: splitting (100) gives:
% 154.55/26.40 | | | | | | |
% 154.55/26.40 | | | | | | | Case 1:
% 154.55/26.40 | | | | | | | |
% 154.55/26.40 | | | | | | | | (101) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) &
% 154.55/26.40 | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 &
% 154.55/26.40 | | | | | | | | all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2
% 154.55/26.40 | | | | | | | | & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 &
% 154.55/26.40 | | | | | | | | ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 154.55/26.40 | | | | | | | | e3)
% 154.55/26.40 | | | | | | | |
% 154.55/26.40 | | | | | | | | BETA: splitting (101) gives:
% 154.55/26.40 | | | | | | | |
% 154.55/26.40 | | | | | | | | Case 1:
% 154.55/26.40 | | | | | | | | |
% 154.55/26.40 | | | | | | | | | (102) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) &
% 154.55/26.40 | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = e3
% 154.55/26.40 | | | | | | | | |
% 154.55/26.40 | | | | | | | | | ALPHA: (102) implies:
% 154.55/26.40 | | | | | | | | | (103) op(e3, e2) = e3
% 154.55/26.40 | | | | | | | | |
% 154.55/26.40 | | | | | | | | | REF_CLOSE: (32), (54), (81), (103) are inconsistent by
% 154.55/26.40 | | | | | | | | | sub-proof #1303.
% 154.55/26.40 | | | | | | | | |
% 154.55/26.40 | | | | | | | | Case 2:
% 154.55/26.40 | | | | | | | | |
% 154.55/26.40 | | | | | | | | | (104) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3)
% 154.55/26.40 | | | | | | | | | & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 =
% 154.55/26.40 | | | | | | | | | e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3,
% 154.55/26.40 | | | | | | | | | e1) = e3 & op(e1, e3) = e3)
% 154.55/26.40 | | | | | | | | |
% 154.55/26.40 | | | | | | | | | BETA: splitting (104) gives:
% 154.55/26.40 | | | | | | | | |
% 154.55/26.40 | | | | | | | | | Case 1:
% 154.55/26.40 | | | | | | | | | |
% 154.55/26.40 | | | | | | | | | | (105) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3)
% 154.55/26.40 | | | | | | | | | | & op(e3, e2) = e2 & op(e2, e3) = e2
% 154.55/26.40 | | | | | | | | | |
% 154.55/26.40 | | | | | | | | | | ALPHA: (105) implies:
% 154.55/26.40 | | | | | | | | | | (106) op(e3, e2) = e2
% 154.55/26.40 | | | | | | | | | |
% 154.55/26.40 | | | | | | | | | | REF_CLOSE: (32), (54), (97), (106) are inconsistent by
% 154.55/26.40 | | | | | | | | | | sub-proof #74.
% 154.55/26.40 | | | | | | | | | |
% 154.55/26.40 | | | | | | | | | Case 2:
% 154.55/26.40 | | | | | | | | | |
% 154.55/26.40 | | | | | | | | | | (107) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1)
% 154.55/26.40 | | | | | | | | | | & op(e3, e1) = e3 & op(e1, e3) = e3
% 154.55/26.40 | | | | | | | | | |
% 154.55/26.40 | | | | | | | | | | REF_CLOSE: (19), (29), (38), (54), (81), (82), (97), (99),
% 154.55/26.40 | | | | | | | | | | (107) are inconsistent by sub-proof #15.
% 154.55/26.40 | | | | | | | | | |
% 154.55/26.40 | | | | | | | | | End of split
% 154.55/26.40 | | | | | | | | |
% 154.55/26.40 | | | | | | | | End of split
% 154.55/26.40 | | | | | | | |
% 154.55/26.40 | | | | | | | Case 2:
% 154.55/26.40 | | | | | | | |
% 154.55/26.40 | | | | | | | | (108) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) &
% 154.55/26.40 | | | | | | | | op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_2 = e3 &
% 154.55/26.40 | | | | | | | | all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3
% 154.55/26.40 | | | | | | | | & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 &
% 154.55/26.40 | | | | | | | | ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 154.55/26.40 | | | | | | | | e0)
% 154.55/26.40 | | | | | | | |
% 154.55/26.40 | | | | | | | | REF_CLOSE: (3), (4), (5), (12), (20), (34), (40), (47), (48),
% 154.55/26.40 | | | | | | | | (54), (58), (75), (108) are inconsistent by sub-proof
% 154.55/26.40 | | | | | | | | #14.
% 154.55/26.40 | | | | | | | |
% 154.55/26.40 | | | | | | | End of split
% 154.55/26.40 | | | | | | |
% 154.55/26.40 | | | | | | Case 2:
% 154.55/26.40 | | | | | | |
% 154.55/26.41 | | | | | | | (109) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) &
% 154.55/26.41 | | | | | | | op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 &
% 154.55/26.41 | | | | | | | all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 &
% 154.55/26.41 | | | | | | | op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 154.55/26.41 | | | | | | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.55/26.41 | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) &
% 154.55/26.41 | | | | | | | op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 &
% 154.55/26.41 | | | | | | | all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) = e1
% 154.55/26.41 | | | | | | | & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 &
% 154.55/26.41 | | | | | | | ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | | BETA: splitting (109) gives:
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | (110) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) &
% 154.55/26.41 | | | | | | | | op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 &
% 154.55/26.41 | | | | | | | | all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1
% 154.55/26.41 | | | | | | | | & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2
% 154.55/26.41 | | | | | | | | & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 154.55/26.41 | | | | | | | | = e2)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | BETA: splitting (110) gives:
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | (111) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) &
% 154.55/26.41 | | | | | | | | | op(e2, e1) = e2 & op(e1, e2) = e2
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | ALPHA: (111) implies:
% 154.55/26.41 | | | | | | | | | (112) op(e1, e2) = e2
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | REF_CLOSE: (30), (54), (90), (112) are inconsistent by
% 154.55/26.41 | | | | | | | | | sub-proof #1088.
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | (113) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2)
% 154.55/26.41 | | | | | | | | | & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 =
% 154.55/26.41 | | | | | | | | | e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2,
% 154.55/26.41 | | | | | | | | | e0) = e2 & op(e0, e2) = e2)
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | BETA: splitting (113) gives:
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | (114) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2)
% 154.55/26.41 | | | | | | | | | | & op(e2, e1) = e1 & op(e1, e2) = e1
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | ALPHA: (114) implies:
% 154.55/26.41 | | | | | | | | | | (115) ~ (all_56_13 = e2)
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | REDUCE: (13), (115) imply:
% 154.55/26.41 | | | | | | | | | | (116) ~ (all_8_2 = e2)
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | BETA: splitting (22) gives:
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | (117) all_54_5 = e3
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | COMBINE_EQS: (55), (117) imply:
% 154.55/26.41 | | | | | | | | | | | (118) all_8_2 = e3
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | COMBINE_EQS: (13), (118) imply:
% 154.55/26.41 | | | | | | | | | | | (119) all_56_13 = e3
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | REDUCE: (43), (118) imply:
% 154.55/26.41 | | | | | | | | | | | (120) ~ (all_52_7 = e3)
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | REDUCE: (116), (118) imply:
% 154.55/26.41 | | | | | | | | | | | (121) ~ (e3 = e2)
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (12), (31), (46), (49), (52),
% 154.55/26.41 | | | | | | | | | | | (60), (61), (63), (64), (90), (93), (99), (119),
% 154.55/26.41 | | | | | | | | | | | (120), (121) are inconsistent by sub-proof #12.
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | (122) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11), (12),
% 154.55/26.41 | | | | | | | | | | | (13), (16), (17), (19), (20), (21), (23), (24),
% 154.55/26.41 | | | | | | | | | | | (25), (26), (27), (28), (29), (32), (34), (36),
% 154.55/26.41 | | | | | | | | | | | (38), (39), (40), (41), (42), (43), (44), (45),
% 154.55/26.41 | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (54), (55),
% 154.55/26.41 | | | | | | | | | | | (57), (58), (59), (93), (95), (122) are
% 154.55/26.41 | | | | | | | | | | | inconsistent by sub-proof #6.
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | (123) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | ALPHA: (123) implies:
% 154.55/26.41 | | | | | | | | | | (124) op(e2, e0) = e2
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | REF_CLOSE: (21), (54), (76), (97), (124) are inconsistent by
% 154.55/26.41 | | | | | | | | | | sub-proof #1397.
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | End of split
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | (125) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) &
% 154.55/26.41 | | | | | | | | op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 &
% 154.55/26.41 | | | | | | | | all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) =
% 154.55/26.41 | | | | | | | | e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 =
% 154.55/26.41 | | | | | | | | e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0,
% 154.55/26.41 | | | | | | | | e1) = e0)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | REF_CLOSE: (5), (40), (41), (47), (50), (51), (54), (58), (75),
% 154.55/26.41 | | | | | | | | (93), (99), (125) are inconsistent by sub-proof #8.
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | End of split
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | End of split
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | Case 2:
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | | (126) all_54_3 = e1 | all_54_3 = e0
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | | REF_CLOSE: (37), (53), (74), (126) are inconsistent by sub-proof
% 154.55/26.41 | | | | | | #1289.
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | End of split
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | End of split
% 154.55/26.41 | | | |
% 154.55/26.41 | | | Case 2:
% 154.55/26.41 | | | |
% 154.55/26.41 | | | | (127) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.41 | | | |
% 154.55/26.41 | | | | REF_CLOSE: (5), (47), (58), (75), (127) are inconsistent by sub-proof
% 154.55/26.41 | | | | #1226.
% 154.55/26.41 | | | |
% 154.55/26.41 | | | End of split
% 154.55/26.41 | | |
% 154.55/26.41 | | End of split
% 154.55/26.41 | |
% 154.55/26.41 | End of split
% 154.55/26.41 |
% 154.55/26.41 End of proof
% 154.55/26.41
% 154.55/26.41 Sub-proof #6 shows that the following formulas are inconsistent:
% 154.55/26.41 ----------------------------------------------------------------
% 154.55/26.41 (1) ~ (all_52_14 = all_4_0)
% 154.55/26.41 (2) op(e0, e3) = all_52_3
% 154.55/26.41 (3) op(e3, e0) = all_52_12
% 154.55/26.41 (4) ~ (all_52_14 = e2)
% 154.55/26.41 (5) all_54_13 = all_52_7
% 154.55/26.41 (6) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.41 (7) ~ (all_52_1 = all_8_2)
% 154.55/26.41 (8) op(e3, e2) = all_52_4
% 154.55/26.41 (9) ~ (all_52_3 = e0)
% 154.55/26.41 (10) all_56_13 = all_8_2
% 154.55/26.41 (11) op(e2, e1) = all_52_9
% 154.55/26.41 (12) op(e2, e3) = all_52_1
% 154.55/26.41 (13) ~ (all_8_2 = e0)
% 154.55/26.41 (14) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 154.55/26.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 154.55/26.41 (15) op(e1, e3) = all_52_2
% 154.55/26.41 (16) op(e2, e0) = all_52_13
% 154.55/26.41 (17) ~ (all_4_0 = e3)
% 154.55/26.41 (18) ~ (all_52_6 = all_8_2)
% 154.55/26.41 (19) op(e1, e2) = all_52_6
% 154.55/26.41 (20) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.41 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.41 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.41 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.41 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.41 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.41 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.41 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.41 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.41 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.41 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.41 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.41 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.41 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.41 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.41 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.41 = e0)
% 154.55/26.41 (21) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 154.55/26.41 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 154.55/26.41 (22) ~ (all_8_2 = all_4_0)
% 154.55/26.41 (23) all_58_7 = e1
% 154.55/26.41 (24) ~ (all_52_7 = e0)
% 154.55/26.41 (25) op(e3, e2) = e0
% 154.55/26.41 (26) ~ (all_52_2 = e1)
% 154.55/26.41 (27) op(e2, e0) = all_4_0
% 154.55/26.41 (28) all_58_8 = e2
% 154.55/26.41 (29) ~ (all_52_4 = all_52_7)
% 154.55/26.41 (30) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.41 (31) op(e0, e1) = e0
% 154.55/26.41 (32) ~ (all_8_2 = e1)
% 154.55/26.41 (33) ~ (all_52_7 = all_8_2)
% 154.55/26.41 (34) ~ (all_4_0 = e1)
% 154.55/26.41 (35) all_54_7 = all_4_0
% 154.55/26.41 (36) ~ (all_52_14 = e1)
% 154.55/26.41 (37) ~ (all_52_12 = all_52_14)
% 154.55/26.41 (38) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 154.55/26.41 (39) ~ (all_52_7 = e1)
% 154.55/26.41 (40) op(e0, e2) = all_52_7
% 154.55/26.41 (41) op(e1, e0) = all_52_14
% 154.55/26.41 (42) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.41 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.41 (44) all_54_5 = all_8_2
% 154.55/26.41 (45) ~ (all_52_9 = all_8_2)
% 154.55/26.41 (46) all_54_11 = all_52_14
% 154.55/26.41 (47) ~ (all_52_13 = all_8_2)
% 154.55/26.41
% 154.55/26.41 Begin of proof
% 154.55/26.41 |
% 154.55/26.41 | BETA: splitting (38) gives:
% 154.55/26.41 |
% 154.55/26.41 | Case 1:
% 154.55/26.41 | |
% 154.55/26.41 | | (48) all_54_5 = e2
% 154.55/26.41 | |
% 154.55/26.41 | | COMBINE_EQS: (44), (48) imply:
% 154.55/26.41 | | (49) all_8_2 = e2
% 154.55/26.41 | |
% 154.55/26.41 | | SIMP: (49) implies:
% 154.55/26.41 | | (50) all_8_2 = e2
% 154.55/26.41 | |
% 154.55/26.41 | | COMBINE_EQS: (10), (50) imply:
% 154.55/26.41 | | (51) all_56_13 = e2
% 154.55/26.41 | |
% 154.55/26.41 | | REDUCE: (33), (50) imply:
% 154.55/26.41 | | (52) ~ (all_52_7 = e2)
% 154.55/26.41 | |
% 154.55/26.41 | | REDUCE: (22), (50) imply:
% 154.55/26.41 | | (53) ~ (all_4_0 = e2)
% 154.55/26.41 | |
% 154.55/26.41 | | SIMP: (53) implies:
% 154.55/26.41 | | (54) ~ (all_4_0 = e2)
% 154.55/26.41 | |
% 154.55/26.41 | | BETA: splitting (6) gives:
% 154.55/26.41 | |
% 154.55/26.41 | | Case 1:
% 154.55/26.41 | | |
% 154.55/26.41 | | | (55) all_54_7 = e3
% 154.55/26.41 | | |
% 154.55/26.41 | | | REF_CLOSE: (17), (35), (55) are inconsistent by sub-proof #11.
% 154.55/26.41 | | |
% 154.55/26.41 | | Case 2:
% 154.55/26.41 | | |
% 154.55/26.41 | | | (56) ~ (all_54_7 = e3)
% 154.55/26.41 | | | (57) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.41 | | |
% 154.55/26.41 | | | BETA: splitting (21) gives:
% 154.55/26.41 | | |
% 154.55/26.41 | | | Case 1:
% 154.55/26.41 | | | |
% 154.55/26.41 | | | | (58) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2)
% 154.55/26.41 | | | | = e2)
% 154.55/26.41 | | | |
% 154.55/26.41 | | | | BETA: splitting (58) gives:
% 154.55/26.41 | | | |
% 154.55/26.41 | | | | Case 1:
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | | (59) all_58_2 = e2 & op(e2, e3) = e2
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | | ALPHA: (59) implies:
% 154.55/26.41 | | | | | (60) op(e2, e3) = e2
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | | REF_CLOSE: (7), (12), (13), (32), (38), (43), (44), (60) are
% 154.55/26.41 | | | | | inconsistent by sub-proof #321.
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | Case 2:
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | | (61) all_58_3 = e2 & op(e2, e2) = e2
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | | ALPHA: (61) implies:
% 154.55/26.41 | | | | | (62) all_58_3 = e2
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | | BETA: splitting (42) gives:
% 154.55/26.41 | | | | |
% 154.55/26.41 | | | | | Case 1:
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | | (63) all_54_13 = e3
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | | COMBINE_EQS: (5), (63) imply:
% 154.55/26.41 | | | | | | (64) all_52_7 = e3
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | | SIMP: (64) implies:
% 154.55/26.41 | | | | | | (65) all_52_7 = e3
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | | REDUCE: (29), (65) imply:
% 154.55/26.41 | | | | | | (66) ~ (all_52_4 = e3)
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | | BETA: splitting (57) gives:
% 154.55/26.41 | | | | | |
% 154.55/26.41 | | | | | | Case 1:
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | | (67) all_54_7 = e2
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | | REF_CLOSE: (35), (54), (67) are inconsistent by sub-proof #10.
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | Case 2:
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | | (68) ~ (all_54_7 = e2)
% 154.55/26.41 | | | | | | | (69) all_54_7 = e1 | all_54_7 = e0
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | | BETA: splitting (69) gives:
% 154.55/26.41 | | | | | | |
% 154.55/26.41 | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | (70) all_54_7 = e1
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | REF_CLOSE: (34), (35), (70) are inconsistent by sub-proof #9.
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | (71) all_54_7 = e0
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | COMBINE_EQS: (35), (71) imply:
% 154.55/26.41 | | | | | | | | (72) all_4_0 = e0
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | SIMP: (72) implies:
% 154.55/26.41 | | | | | | | | (73) all_4_0 = e0
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | REDUCE: (1), (73) imply:
% 154.55/26.41 | | | | | | | | (74) ~ (all_52_14 = e0)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | REDUCE: (17), (73) imply:
% 154.55/26.41 | | | | | | | | (75) ~ (e3 = e0)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | SIMP: (75) implies:
% 154.55/26.41 | | | | | | | | (76) ~ (e3 = e0)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | REDUCE: (54), (73) imply:
% 154.55/26.41 | | | | | | | | (77) ~ (e2 = e0)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | SIMP: (77) implies:
% 154.55/26.41 | | | | | | | | (78) ~ (e2 = e0)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | REDUCE: (34), (73) imply:
% 154.55/26.41 | | | | | | | | (79) ~ (e1 = e0)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | SIMP: (79) implies:
% 154.55/26.41 | | | | | | | | (80) ~ (e1 = e0)
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | REDUCE: (27), (73) imply:
% 154.55/26.41 | | | | | | | | (81) op(e2, e0) = e0
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | BETA: splitting (14) gives:
% 154.55/26.41 | | | | | | | |
% 154.55/26.41 | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | (82) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 154.55/26.41 | | | | | | | | | op(e1, e2) = e0)
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | BETA: splitting (82) gives:
% 154.55/26.41 | | | | | | | | |
% 154.55/26.41 | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | (83) all_58_6 = e0 & op(e1, e3) = e0
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | ALPHA: (83) implies:
% 154.55/26.41 | | | | | | | | | | (84) op(e1, e3) = e0
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | BETA: splitting (20) gives:
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | (85) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.55/26.41 | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.41 | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.41 | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.41 | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.41 | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.41 | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.41 | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.41 | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | BETA: splitting (85) gives:
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | (86) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.55/26.41 | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.41 | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.41 | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | BETA: splitting (86) gives:
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | (87) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | ALPHA: (87) implies:
% 154.55/26.41 | | | | | | | | | | | | | (88) op(e3, e2) = e3
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | REF_CLOSE: (8), (43), (66), (88) are inconsistent by
% 154.55/26.41 | | | | | | | | | | | | | sub-proof #1540.
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | (89) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.41 | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.41 | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | BETA: splitting (89) gives:
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | (90) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.41 | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | ALPHA: (90) implies:
% 154.55/26.41 | | | | | | | | | | | | | | (91) op(e3, e2) = e2
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | REF_CLOSE: (25), (43), (78), (91) are inconsistent by
% 154.55/26.41 | | | | | | | | | | | | | | sub-proof #74.
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | (92) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | ALPHA: (92) implies:
% 154.55/26.41 | | | | | | | | | | | | | | (93) op(e1, e3) = e3
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | REF_CLOSE: (43), (76), (84), (93) are inconsistent by
% 154.55/26.41 | | | | | | | | | | | | | | sub-proof #114.
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | (94) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.41 | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.41 | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.41 | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.41 | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (9), (15), (26), (30), (36), (37),
% 154.55/26.41 | | | | | | | | | | | | (43), (46), (74), (94) are inconsistent by
% 154.55/26.41 | | | | | | | | | | | | sub-proof #14.
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | (95) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.55/26.41 | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.41 | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.55/26.41 | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.55/26.41 | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.55/26.41 | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | BETA: splitting (95) gives:
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | (96) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.55/26.41 | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.41 | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | BETA: splitting (96) gives:
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | (97) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | ALPHA: (97) implies:
% 154.55/26.41 | | | | | | | | | | | | | (98) op(e1, e2) = e2
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | REF_CLOSE: (13), (18), (19), (32), (38), (43), (44), (98) are
% 154.55/26.41 | | | | | | | | | | | | | inconsistent by sub-proof #1173.
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | (99) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.41 | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | BETA: splitting (99) gives:
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | Case 1:
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | (100) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | ALPHA: (100) implies:
% 154.55/26.41 | | | | | | | | | | | | | | (101) ~ (all_56_13 = e2)
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | REDUCE: (51), (101) imply:
% 154.55/26.41 | | | | | | | | | | | | | | (102) $false
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | CLOSE: (102) is inconsistent.
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | (103) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | ALPHA: (103) implies:
% 154.55/26.41 | | | | | | | | | | | | | | (104) op(e2, e0) = e2
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | | REF_CLOSE: (16), (43), (78), (81), (104) are inconsistent by
% 154.55/26.41 | | | | | | | | | | | | | | sub-proof #1397.
% 154.55/26.41 | | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | (105) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.55/26.41 | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.55/26.41 | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.41 | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.55/26.41 | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.41 | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | | REF_CLOSE: (4), (24), (30), (31), (36), (40), (41), (43),
% 154.55/26.41 | | | | | | | | | | | | (46), (74), (80), (105) are inconsistent by
% 154.55/26.41 | | | | | | | | | | | | sub-proof #8.
% 154.55/26.41 | | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | End of split
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | Case 2:
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | (106) all_58_7 = e0 & op(e1, e2) = e0
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.41 | | | | | | | | | | ALPHA: (106) implies:
% 154.55/26.41 | | | | | | | | | | (107) all_58_7 = e0
% 154.55/26.41 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | REF_CLOSE: (23), (80), (107) are inconsistent by sub-proof
% 154.55/26.42 | | | | | | | | | | #1072.
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | End of split
% 154.55/26.42 | | | | | | | | |
% 154.55/26.42 | | | | | | | | Case 2:
% 154.55/26.42 | | | | | | | | |
% 154.55/26.42 | | | | | | | | | (108) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 154.55/26.42 | | | | | | | | | op(e1, e0) = e0)
% 154.55/26.42 | | | | | | | | |
% 154.55/26.42 | | | | | | | | | BETA: splitting (108) gives:
% 154.55/26.42 | | | | | | | | |
% 154.55/26.42 | | | | | | | | | Case 1:
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | (109) all_58_8 = e0 & op(e1, e1) = e0
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | ALPHA: (109) implies:
% 154.55/26.42 | | | | | | | | | | (110) all_58_8 = e0
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | COMBINE_EQS: (28), (110) imply:
% 154.55/26.42 | | | | | | | | | | (111) e2 = e0
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | COMBINE_EQS: (62), (111) imply:
% 154.55/26.42 | | | | | | | | | | (112) all_58_3 = e0
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | REF_CLOSE: (7), (11), (12), (13), (16), (21), (32), (38),
% 154.55/26.42 | | | | | | | | | | (43), (44), (45), (47), (112) are inconsistent by
% 154.55/26.42 | | | | | | | | | | sub-proof #324.
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | Case 2:
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | (113) all_58_11 = e0 & op(e1, e0) = e0
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | ALPHA: (113) implies:
% 154.55/26.42 | | | | | | | | | | (114) op(e1, e0) = e0
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | | REF_CLOSE: (4), (30), (36), (41), (43), (46), (74), (114) are
% 154.55/26.42 | | | | | | | | | | inconsistent by sub-proof #111.
% 154.55/26.42 | | | | | | | | | |
% 154.55/26.42 | | | | | | | | | End of split
% 154.55/26.42 | | | | | | | | |
% 154.55/26.42 | | | | | | | | End of split
% 154.55/26.42 | | | | | | | |
% 154.55/26.42 | | | | | | | End of split
% 154.55/26.42 | | | | | | |
% 154.55/26.42 | | | | | | End of split
% 154.55/26.42 | | | | | |
% 154.55/26.42 | | | | | Case 2:
% 154.55/26.42 | | | | | |
% 154.55/26.42 | | | | | | (115) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.42 | | | | | |
% 154.55/26.42 | | | | | | REF_CLOSE: (5), (24), (39), (52), (115) are inconsistent by
% 154.55/26.42 | | | | | | sub-proof #254.
% 154.55/26.42 | | | | | |
% 154.55/26.42 | | | | | End of split
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | End of split
% 154.55/26.42 | | | |
% 154.55/26.42 | | | Case 2:
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | (116) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2,
% 154.55/26.42 | | | | e0) = e2)
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | BETA: splitting (116) gives:
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | Case 1:
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | (117) all_58_5 = e2 & op(e2, e1) = e2
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | REF_CLOSE: (11), (13), (32), (38), (43), (44), (45), (117) are
% 154.55/26.42 | | | | | inconsistent by sub-proof #915.
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | Case 2:
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | (118) all_58_10 = e2 & op(e2, e0) = e2
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | ALPHA: (118) implies:
% 154.55/26.42 | | | | | (119) op(e2, e0) = e2
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | REF_CLOSE: (16), (27), (34), (35), (43), (54), (57), (119) are
% 154.55/26.42 | | | | | inconsistent by sub-proof #7.
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | End of split
% 154.55/26.42 | | | |
% 154.55/26.42 | | | End of split
% 154.55/26.42 | | |
% 154.55/26.42 | | End of split
% 154.55/26.42 | |
% 154.55/26.42 | Case 2:
% 154.55/26.42 | |
% 154.55/26.42 | | (120) all_54_5 = e1 | all_54_5 = e0
% 154.55/26.42 | |
% 154.55/26.42 | | REF_CLOSE: (13), (32), (44), (120) are inconsistent by sub-proof #1239.
% 154.55/26.42 | |
% 154.55/26.42 | End of split
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #7 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) op(e2, e0) = e2
% 154.55/26.42 (2) ~ (all_4_0 = e2)
% 154.55/26.42 (3) op(e2, e0) = all_52_13
% 154.55/26.42 (4) op(e2, e0) = all_4_0
% 154.55/26.42 (5) ~ (all_4_0 = e1)
% 154.55/26.42 (6) all_54_7 = all_4_0
% 154.55/26.42 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.42 (8) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | BETA: splitting (8) gives:
% 154.55/26.42 |
% 154.55/26.42 | Case 1:
% 154.55/26.42 | |
% 154.55/26.42 | | (9) all_54_7 = e2
% 154.55/26.42 | |
% 154.55/26.42 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #10.
% 154.55/26.42 | |
% 154.55/26.42 | Case 2:
% 154.55/26.42 | |
% 154.55/26.42 | | (10) ~ (all_54_7 = e2)
% 154.55/26.42 | | (11) all_54_7 = e1 | all_54_7 = e0
% 154.55/26.42 | |
% 154.55/26.42 | | BETA: splitting (11) gives:
% 154.55/26.42 | |
% 154.55/26.42 | | Case 1:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (12) all_54_7 = e1
% 154.55/26.42 | | |
% 154.55/26.42 | | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #9.
% 154.55/26.42 | | |
% 154.55/26.42 | | Case 2:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (13) all_54_7 = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | COMBINE_EQS: (6), (13) imply:
% 154.55/26.42 | | | (14) all_4_0 = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | SIMP: (14) implies:
% 154.55/26.42 | | | (15) all_4_0 = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | REDUCE: (2), (15) imply:
% 154.55/26.42 | | | (16) ~ (e2 = e0)
% 154.55/26.42 | | |
% 154.55/26.42 | | | SIMP: (16) implies:
% 154.55/26.42 | | | (17) ~ (e2 = e0)
% 154.55/26.42 | | |
% 154.55/26.42 | | | REDUCE: (4), (15) imply:
% 154.55/26.42 | | | (18) op(e2, e0) = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | REF_CLOSE: (1), (3), (7), (17), (18) are inconsistent by sub-proof #1397.
% 154.55/26.42 | | |
% 154.55/26.42 | | End of split
% 154.55/26.42 | |
% 154.55/26.42 | End of split
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #8 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) ~ (all_52_14 = e2)
% 154.55/26.42 (2) ~ (all_52_14 = e0)
% 154.55/26.42 (3) ~ (all_52_7 = e0)
% 154.55/26.42 (4) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.42 (5) ~ (e1 = e0)
% 154.55/26.42 (6) op(e0, e1) = e0
% 154.55/26.42 (7) ~ (all_52_14 = e1)
% 154.55/26.42 (8) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 &
% 154.55/26.42 op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.42 e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11
% 154.55/26.42 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.42 (9) op(e0, e2) = all_52_7
% 154.55/26.42 (10) op(e1, e0) = all_52_14
% 154.55/26.42 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.42 (12) all_54_11 = all_52_14
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | BETA: splitting (8) gives:
% 154.55/26.42 |
% 154.55/26.42 | Case 1:
% 154.55/26.42 | |
% 154.55/26.42 | | (13) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) =
% 154.55/26.42 | | e0 & op(e0, e2) = e0
% 154.55/26.42 | |
% 154.55/26.42 | | ALPHA: (13) implies:
% 154.55/26.42 | | (14) op(e0, e2) = e0
% 154.55/26.42 | |
% 154.55/26.42 | | REF_CLOSE: (3), (9), (11), (14) are inconsistent by sub-proof #1532.
% 154.55/26.42 | |
% 154.55/26.42 | Case 2:
% 154.55/26.42 | |
% 154.55/26.42 | | (15) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) =
% 154.55/26.42 | | e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~
% 154.55/26.42 | | (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.42 | |
% 154.55/26.42 | | BETA: splitting (15) gives:
% 154.55/26.42 | |
% 154.55/26.42 | | Case 1:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (16) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0)
% 154.55/26.42 | | | = e1 & op(e0, e1) = e1
% 154.55/26.42 | | |
% 154.55/26.42 | | | ALPHA: (16) implies:
% 154.55/26.42 | | | (17) op(e0, e1) = e1
% 154.55/26.42 | | |
% 154.55/26.42 | | | REF_CLOSE: (5), (6), (11), (17) are inconsistent by sub-proof #129.
% 154.55/26.42 | | |
% 154.55/26.42 | | Case 2:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (18) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 154.55/26.42 | | | = e0 & op(e0, e1) = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | ALPHA: (18) implies:
% 154.55/26.42 | | | (19) op(e1, e0) = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | REF_CLOSE: (1), (2), (4), (7), (10), (11), (12), (19) are inconsistent by
% 154.55/26.42 | | | sub-proof #111.
% 154.55/26.42 | | |
% 154.55/26.42 | | End of split
% 154.55/26.42 | |
% 154.55/26.42 | End of split
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #9 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) all_54_7 = all_4_0
% 154.55/26.42 (2) all_54_7 = e1
% 154.55/26.42 (3) ~ (all_4_0 = e1)
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | COMBINE_EQS: (1), (2) imply:
% 154.55/26.42 | (4) all_4_0 = e1
% 154.55/26.42 |
% 154.55/26.42 | SIMP: (4) implies:
% 154.55/26.42 | (5) all_4_0 = e1
% 154.55/26.42 |
% 154.55/26.42 | REDUCE: (3), (5) imply:
% 154.55/26.42 | (6) $false
% 154.55/26.42 |
% 154.55/26.42 | CLOSE: (6) is inconsistent.
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #10 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) all_54_7 = all_4_0
% 154.55/26.42 (2) all_54_7 = e2
% 154.55/26.42 (3) ~ (all_4_0 = e2)
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | COMBINE_EQS: (1), (2) imply:
% 154.55/26.42 | (4) all_4_0 = e2
% 154.55/26.42 |
% 154.55/26.42 | SIMP: (4) implies:
% 154.55/26.42 | (5) all_4_0 = e2
% 154.55/26.42 |
% 154.55/26.42 | REDUCE: (3), (5) imply:
% 154.55/26.42 | (6) $false
% 154.55/26.42 |
% 154.55/26.42 | CLOSE: (6) is inconsistent.
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #11 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) all_54_7 = all_4_0
% 154.55/26.42 (2) all_54_7 = e3
% 154.55/26.42 (3) ~ (all_4_0 = e3)
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | COMBINE_EQS: (1), (2) imply:
% 154.55/26.42 | (4) all_4_0 = e3
% 154.55/26.42 |
% 154.55/26.42 | SIMP: (4) implies:
% 154.55/26.42 | (5) all_4_0 = e3
% 154.55/26.42 |
% 154.55/26.42 | REDUCE: (3), (5) imply:
% 154.55/26.42 | (6) $false
% 154.55/26.42 |
% 154.55/26.42 | CLOSE: (6) is inconsistent.
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #12 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) ~ (all_52_3 = e1)
% 154.55/26.42 (2) all_54_13 = all_52_7
% 154.55/26.42 (3) ~ (all_52_7 = e3)
% 154.55/26.42 (4) all_56_12 = all_10_2
% 154.55/26.42 (5) all_56_14 = e2
% 154.55/26.42 (6) ~ (all_52_3 = e0)
% 154.55/26.42 (7) ~ (all_52_7 = e0)
% 154.55/26.42 (8) ~ (all_52_3 = all_10_2)
% 154.55/26.42 (9) ~ (e2 = e1)
% 154.55/26.42 (10) ~ (e1 = e0)
% 154.55/26.42 (11) all_56_15 = e1
% 154.55/26.42 (12) all_56_13 = e3
% 154.55/26.42 (13) ~ (all_52_7 = e1)
% 154.55/26.42 (14) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.42 (15) ~ (e3 = e2)
% 154.55/26.42 (16) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.42 (17) all_54_12 = all_52_3
% 154.55/26.42 (18) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.42 (19) ~ (all_52_3 = all_52_7)
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | BETA: splitting (14) gives:
% 154.55/26.42 |
% 154.55/26.42 | Case 1:
% 154.55/26.42 | |
% 154.55/26.42 | | (20) all_54_13 = e3
% 154.55/26.42 | |
% 154.55/26.42 | | REF_CLOSE: (2), (3), (20) are inconsistent by sub-proof #1435.
% 154.55/26.42 | |
% 154.55/26.42 | Case 2:
% 154.55/26.42 | |
% 154.55/26.42 | | (21) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.42 | |
% 154.55/26.42 | | BETA: splitting (18) gives:
% 154.55/26.42 | |
% 154.55/26.42 | | Case 1:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (22) all_56_12 = e3
% 154.55/26.42 | | |
% 154.55/26.42 | | | COMBINE_EQS: (4), (22) imply:
% 154.55/26.42 | | | (23) all_10_2 = e3
% 154.55/26.42 | | |
% 154.55/26.42 | | | REDUCE: (8), (23) imply:
% 154.55/26.42 | | | (24) ~ (all_52_3 = e3)
% 154.55/26.42 | | |
% 154.55/26.42 | | | BETA: splitting (21) gives:
% 154.55/26.42 | | |
% 154.55/26.42 | | | Case 1:
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | (25) all_54_13 = e2
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | COMBINE_EQS: (2), (25) imply:
% 154.55/26.42 | | | | (26) all_52_7 = e2
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | SIMP: (26) implies:
% 154.55/26.42 | | | | (27) all_52_7 = e2
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | REDUCE: (19), (27) imply:
% 154.55/26.42 | | | | (28) ~ (all_52_3 = e2)
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | BETA: splitting (16) gives:
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | Case 1:
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | (29) all_54_12 = e3
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | REF_CLOSE: (17), (24), (29) are inconsistent by sub-proof #1234.
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | Case 2:
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | (30) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | | REF_CLOSE: (1), (6), (17), (28), (30) are inconsistent by sub-proof
% 154.55/26.42 | | | | | #1098.
% 154.55/26.42 | | | | |
% 154.55/26.42 | | | | End of split
% 154.55/26.42 | | | |
% 154.55/26.42 | | | Case 2:
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | (31) all_54_13 = e1 | all_54_13 = e0
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | REF_CLOSE: (2), (7), (13), (31) are inconsistent by sub-proof #875.
% 154.55/26.42 | | | |
% 154.55/26.42 | | | End of split
% 154.55/26.42 | | |
% 154.55/26.42 | | Case 2:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (32) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | BETA: splitting (32) gives:
% 154.55/26.42 | | |
% 154.55/26.42 | | | Case 1:
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | (33) all_56_13 = e2
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | REF_CLOSE: (12), (15), (33) are inconsistent by sub-proof #674.
% 154.55/26.42 | | | |
% 154.55/26.42 | | | Case 2:
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | (34) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.42 | | | |
% 154.55/26.42 | | | | REF_CLOSE: (5), (9), (10), (11), (34) are inconsistent by sub-proof #13.
% 154.55/26.42 | | | |
% 154.55/26.42 | | | End of split
% 154.55/26.42 | | |
% 154.55/26.42 | | End of split
% 154.55/26.42 | |
% 154.55/26.42 | End of split
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #13 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) all_56_14 = e2
% 154.55/26.42 (2) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.42 (3) ~ (e2 = e1)
% 154.55/26.42 (4) ~ (e1 = e0)
% 154.55/26.42 (5) all_56_15 = e1
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | BETA: splitting (2) gives:
% 154.55/26.42 |
% 154.55/26.42 | Case 1:
% 154.55/26.42 | |
% 154.55/26.42 | | (6) all_56_14 = e1
% 154.55/26.42 | |
% 154.55/26.42 | | COMBINE_EQS: (1), (6) imply:
% 154.55/26.42 | | (7) e2 = e1
% 154.55/26.42 | |
% 154.55/26.42 | | REDUCE: (3), (7) imply:
% 154.55/26.42 | | (8) $false
% 154.55/26.42 | |
% 154.55/26.42 | | CLOSE: (8) is inconsistent.
% 154.55/26.42 | |
% 154.55/26.42 | Case 2:
% 154.55/26.42 | |
% 154.55/26.42 | | (9) all_56_15 = e0
% 154.55/26.42 | |
% 154.55/26.42 | | COMBINE_EQS: (5), (9) imply:
% 154.55/26.42 | | (10) e1 = e0
% 154.55/26.42 | |
% 154.55/26.42 | | REDUCE: (4), (10) imply:
% 154.55/26.42 | | (11) $false
% 154.55/26.42 | |
% 154.55/26.42 | | CLOSE: (11) is inconsistent.
% 154.55/26.42 | |
% 154.55/26.42 | End of split
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #14 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.42 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0)
% 154.55/26.42 & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 &
% 154.55/26.42 ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.42 (2) op(e0, e3) = all_52_3
% 154.55/26.42 (3) op(e3, e0) = all_52_12
% 154.55/26.42 (4) ~ (all_52_14 = e2)
% 154.55/26.42 (5) ~ (all_52_14 = e0)
% 154.55/26.42 (6) ~ (all_52_3 = e0)
% 154.55/26.42 (7) op(e1, e3) = all_52_2
% 154.55/26.42 (8) ~ (all_52_2 = e1)
% 154.55/26.42 (9) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.42 (10) ~ (all_52_14 = e1)
% 154.55/26.42 (11) ~ (all_52_12 = all_52_14)
% 154.55/26.42 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.42 (13) all_54_11 = all_52_14
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | BETA: splitting (1) gives:
% 154.55/26.42 |
% 154.55/26.42 | Case 1:
% 154.55/26.42 | |
% 154.55/26.42 | | (14) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) =
% 154.55/26.42 | | e1 & op(e1, e3) = e1
% 154.55/26.42 | |
% 154.55/26.42 | | ALPHA: (14) implies:
% 154.55/26.42 | | (15) op(e1, e3) = e1
% 154.55/26.42 | |
% 154.55/26.42 | | REF_CLOSE: (7), (8), (12), (15) are inconsistent by sub-proof #1412.
% 154.55/26.42 | |
% 154.55/26.42 | Case 2:
% 154.55/26.42 | |
% 154.55/26.42 | | (16) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 154.55/26.42 | | e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 154.55/26.42 | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.42 | |
% 154.55/26.42 | | BETA: splitting (16) gives:
% 154.55/26.42 | |
% 154.55/26.42 | | Case 1:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (17) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 154.55/26.42 | | | e3 & op(e0, e3) = e3
% 154.55/26.42 | | |
% 154.55/26.42 | | | ALPHA: (17) implies:
% 154.55/26.42 | | | (18) op(e3, e0) = e3
% 154.55/26.42 | | |
% 154.55/26.42 | | | REF_CLOSE: (3), (4), (5), (9), (10), (11), (12), (13), (18) are
% 154.55/26.42 | | | inconsistent by sub-proof #121.
% 154.55/26.42 | | |
% 154.55/26.42 | | Case 2:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (19) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 154.55/26.42 | | | e0 & op(e0, e3) = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | ALPHA: (19) implies:
% 154.55/26.42 | | | (20) op(e0, e3) = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | REF_CLOSE: (2), (6), (12), (20) are inconsistent by sub-proof #89.
% 154.55/26.42 | | |
% 154.55/26.42 | | End of split
% 154.55/26.42 | |
% 154.55/26.42 | End of split
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #15 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) ~ (e3 = e0)
% 154.55/26.42 (2) ~ (e2 = e0)
% 154.55/26.42 (3) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 154.55/26.42 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 154.55/26.42 (4) all_58_7 = e1
% 154.55/26.42 (5) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 &
% 154.55/26.42 op(e1, e3) = e3
% 154.55/26.42 (6) all_58_8 = e2
% 154.55/26.42 (7) ~ (e1 = e0)
% 154.55/26.42 (8) op(e1, e0) = e3
% 154.55/26.42 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.42
% 154.55/26.42 Begin of proof
% 154.55/26.42 |
% 154.55/26.42 | ALPHA: (5) implies:
% 154.55/26.42 | (10) op(e1, e3) = e3
% 154.55/26.42 |
% 154.55/26.42 | BETA: splitting (3) gives:
% 154.55/26.42 |
% 154.55/26.42 | Case 1:
% 154.55/26.42 | |
% 154.55/26.42 | | (11) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 154.55/26.42 | | e0)
% 154.55/26.42 | |
% 154.55/26.42 | | BETA: splitting (11) gives:
% 154.55/26.42 | |
% 154.55/26.42 | | Case 1:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (12) all_58_6 = e0 & op(e1, e3) = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | ALPHA: (12) implies:
% 154.55/26.42 | | | (13) op(e1, e3) = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | REF_CLOSE: (1), (9), (10), (13) are inconsistent by sub-proof #114.
% 154.55/26.42 | | |
% 154.55/26.42 | | Case 2:
% 154.55/26.42 | | |
% 154.55/26.42 | | | (14) all_58_7 = e0 & op(e1, e2) = e0
% 154.55/26.42 | | |
% 154.55/26.42 | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #992.
% 154.55/26.42 | | |
% 154.55/26.42 | | End of split
% 154.55/26.42 | |
% 154.55/26.42 | Case 2:
% 154.55/26.42 | |
% 154.55/26.42 | | (15) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 154.55/26.42 | | e0)
% 154.55/26.42 | |
% 154.55/26.42 | | REF_CLOSE: (1), (2), (6), (8), (9), (15) are inconsistent by sub-proof #117.
% 154.55/26.42 | |
% 154.55/26.42 | End of split
% 154.55/26.42 |
% 154.55/26.42 End of proof
% 154.55/26.42
% 154.55/26.42 Sub-proof #16 shows that the following formulas are inconsistent:
% 154.55/26.42 ----------------------------------------------------------------
% 154.55/26.42 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 154.55/26.42 (2) all_58_5 = e2
% 154.55/26.42 (3) ~ (all_52_3 = e1)
% 154.55/26.42 (4) op(e0, e3) = all_52_3
% 154.55/26.42 (5) op(e3, e0) = all_52_12
% 154.55/26.42 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 154.55/26.42 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 154.55/26.42 (7) op(e3, e3) = all_10_2
% 154.55/26.42 (8) all_54_13 = all_52_7
% 154.55/26.42 (9) ~ (all_52_1 = e2)
% 154.55/26.42 (10) op(e1, e1) = all_6_2
% 154.55/26.42 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 154.55/26.42 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 154.55/26.42 e1)
% 154.55/26.42 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 154.55/26.42 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 154.55/26.42 (13) all_54_10 = all_6_2
% 154.55/26.42 (14) all_56_12 = all_10_2
% 154.55/26.42 (15) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 154.55/26.42 (16) all_58_14 = e0
% 154.55/26.42 (17) all_16_2 = all_10_2
% 154.55/26.42 (18) ~ (all_56_12 = e2) | (all_56_0 = e3 & op(e3, e2) = e3)
% 154.55/26.42 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.42 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.42 (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 154.55/26.42 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 154.55/26.42 (21) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.55/26.42 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.42 (22) all_54_1 = all_52_4
% 154.55/26.42 (23) op(e3, e2) = all_52_4
% 154.55/26.42 (24) ~ (all_52_3 = e0)
% 154.55/26.42 (25) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.42 (26) all_56_13 = all_8_2
% 154.55/26.42 (27) all_54_0 = all_10_2
% 154.55/26.42 (28) op(e2, e3) = all_52_1
% 154.55/26.43 (29) all_54_2 = all_52_8
% 154.55/26.43 (30) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 154.55/26.43 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 154.55/26.43 (31) ~ (all_52_2 = all_6_2)
% 154.55/26.43 (32) ~ (e3 = e0)
% 154.55/26.43 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.43 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.43 (34) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 154.55/26.43 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 154.55/26.43 (35) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 154.55/26.43 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.43 e2)
% 154.55/26.43 (36) ~ (e2 = e0)
% 154.55/26.43 (37) ~ (all_56_12 = e0) | (all_56_2 = e3 & op(e3, e0) = e3)
% 154.55/26.43 (38) ~ (all_52_8 = e0)
% 154.55/26.43 (39) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 &
% 154.55/26.43 op(e3, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 154.55/26.43 e0) & op(e3, e3) = all_28_1 & $i(all_28_1))
% 154.55/26.43 (40) all_56_13 = e1
% 154.55/26.43 (41) op(e1, e3) = all_52_2
% 154.55/26.43 (42) ~ (all_52_6 = all_6_2)
% 154.55/26.43 (43) op(e2, e0) = all_52_13
% 154.55/26.43 (44) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 154.55/26.43 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 154.55/26.43 (45) ~ (all_52_8 = all_52_12)
% 154.55/26.43 (46) all_12_2 = e1
% 154.55/26.43 (47) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.55/26.43 (48) op(e1, e2) = all_52_6
% 154.55/26.43 (49) ~ (all_12_2 = e1) | ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 &
% 154.55/26.43 op(e1, e1) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 =
% 154.55/26.43 e3) & op(e1, e1) = all_12_1 & $i(all_12_1))
% 154.55/26.43 (50) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.43 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.43 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.43 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.43 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.43 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.43 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.43 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.43 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.43 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.43 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.43 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.43 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.43 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.43 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.43 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.43 = e0)
% 154.55/26.43 (51) ~ (all_52_4 = all_10_2)
% 154.55/26.43 (52) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.43 (53) ~ (all_52_8 = e2)
% 154.55/26.43 (54) ~ (all_52_7 = e0)
% 154.55/26.43 (55) ~ (all_52_3 = all_10_2)
% 154.55/26.43 (56) ~ (all_52_8 = all_10_2)
% 154.55/26.43 (57) ~ (all_6_2 = e0)
% 154.55/26.43 (58) ~ (all_52_13 = e2)
% 154.55/26.43 (59) ~ (all_36_2 = e3) | ( ~ (all_36_0 = e0) & op(all_36_1, e1) = all_36_0 &
% 154.55/26.43 op(e3, e3) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 154.55/26.43 e2) & op(e3, e3) = all_36_1 & $i(all_36_1))
% 154.55/26.43 (60) op(e0, e1) = all_52_11
% 154.55/26.43 (61) ~ (all_52_4 = e1)
% 154.55/26.43 (62) all_28_2 = all_6_2
% 154.55/26.43 (63) ~ (all_52_6 = e1)
% 154.55/26.43 (64) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 154.55/26.43 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 154.55/26.43 (65) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 154.55/26.43 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 154.55/26.43 (66) ~ (all_52_8 = all_6_2)
% 154.55/26.43 (67) all_58_15 = e1
% 154.55/26.43 (68) ~ (e2 = e1)
% 154.55/26.43 (69) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.55/26.43 (70) ~ (all_52_12 = all_10_2)
% 154.55/26.43 (71) ~ (e1 = e0)
% 154.55/26.43 (72) op(e0, e1) = e0
% 154.55/26.43 (73) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0 &
% 154.55/26.43 op(e2, e2) = all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 =
% 154.55/26.43 e0) & op(e2, e2) = all_16_1 & $i(all_16_1))
% 154.55/26.43 (74) ~ (all_52_7 = all_8_2)
% 154.55/26.43 (75) ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e1, e1) = all_8_1 &
% 154.55/26.43 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e3) & op(e1, e1) = all_8_1
% 154.55/26.43 & $i(all_8_1))
% 154.55/26.43 (76) op(e3, e1) = all_52_8
% 154.55/26.43 (77) ~ (all_6_2 = e2)
% 154.55/26.43 (78) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 154.55/26.43 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 154.55/26.43 e3)
% 154.55/26.43 (79) all_56_14 = all_6_2
% 154.55/26.43 (80) all_56_15 = e1
% 154.55/26.43 (81) ~ (all_52_1 = all_10_2)
% 154.55/26.43 (82) ~ (all_52_14 = e1)
% 154.55/26.43 (83) ( ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 & op(e1, e1) = all_4_1 &
% 154.55/26.43 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e2) & op(e1, e1) = all_4_1
% 154.55/26.43 & $i(all_4_1))
% 154.55/26.43 (84) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 154.55/26.43 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 154.55/26.43 (85) ~ (all_52_7 = e1)
% 154.55/26.43 (86) op(e0, e2) = all_52_7
% 154.55/26.43 (87) op(e1, e0) = all_52_14
% 154.55/26.43 (88) ~ (all_10_2 = e0) | ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 154.55/26.43 op(e0, e0) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 =
% 154.55/26.43 e1) & op(e0, e0) = all_10_1 & $i(all_10_1))
% 154.55/26.43 (89) op(e0, e0) = e1
% 154.55/26.43 (90) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.43 (91) ~ (all_52_14 = all_6_2)
% 154.55/26.43 (92) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.43 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.43 (93) ~ (all_52_12 = e1)
% 154.55/26.43 (94) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.43 (95) op(e2, e1) = e2
% 154.55/26.43 (96) all_36_2 = all_6_2
% 154.55/26.43 (97) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 154.55/26.43 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.43 (98) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.43 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.43 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.43 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.43 (99) ~ (all_52_4 = all_52_8)
% 154.55/26.43 (100) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.43 (101) all_54_12 = all_52_3
% 154.55/26.43 (102) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.43 (103) all_58_3 = e1
% 154.55/26.43 (104) ~ (all_52_3 = all_52_7)
% 154.55/26.43
% 154.55/26.43 Begin of proof
% 154.55/26.43 |
% 154.55/26.43 | BETA: splitting (88) gives:
% 154.55/26.43 |
% 154.55/26.43 | Case 1:
% 154.55/26.43 | |
% 154.55/26.43 | | (105) ~ (all_10_2 = e0)
% 154.55/26.43 | |
% 154.55/26.43 | | BETA: splitting (49) gives:
% 154.55/26.43 | |
% 154.55/26.43 | | Case 1:
% 154.55/26.43 | | |
% 154.55/26.43 | | | (106) ~ (all_12_2 = e1)
% 154.55/26.43 | | |
% 154.55/26.43 | | | REDUCE: (46), (106) imply:
% 154.55/26.43 | | | (107) $false
% 154.55/26.43 | | |
% 154.55/26.43 | | | CLOSE: (107) is inconsistent.
% 154.55/26.43 | | |
% 154.55/26.43 | | Case 2:
% 154.55/26.43 | | |
% 154.55/26.43 | | | (108) ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e1, e1) =
% 154.55/26.43 | | | all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e3) &
% 154.55/26.43 | | | op(e1, e1) = all_12_1 & $i(all_12_1))
% 154.55/26.43 | | |
% 154.55/26.43 | | | BETA: splitting (73) gives:
% 154.55/26.43 | | |
% 154.55/26.43 | | | Case 1:
% 154.55/26.43 | | | |
% 154.55/26.43 | | | | (109) ~ (all_16_2 = e2)
% 154.55/26.43 | | | |
% 154.55/26.43 | | | | REDUCE: (17), (109) imply:
% 154.55/26.43 | | | | (110) ~ (all_10_2 = e2)
% 154.55/26.43 | | | |
% 154.55/26.43 | | | | BETA: splitting (39) gives:
% 154.55/26.43 | | | |
% 154.55/26.43 | | | | Case 1:
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | (111) ~ (all_28_2 = e3)
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | REDUCE: (62), (111) imply:
% 154.55/26.43 | | | | | (112) ~ (all_6_2 = e3)
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | BETA: splitting (69) gives:
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | Case 1:
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | (113) all_54_10 = e3
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | REF_CLOSE: (13), (112), (113) are inconsistent by sub-proof #1531.
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | Case 2:
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | (114) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | BETA: splitting (114) gives:
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | Case 1:
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | (115) all_54_10 = e2
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | REF_CLOSE: (13), (77), (115) are inconsistent by sub-proof #1530.
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | Case 2:
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | (116) all_54_10 = e1 | all_54_10 = e0
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | BETA: splitting (116) gives:
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | (117) all_54_10 = e1
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | COMBINE_EQS: (13), (117) imply:
% 154.55/26.43 | | | | | | | | (118) all_6_2 = e1
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | SIMP: (118) implies:
% 154.55/26.43 | | | | | | | | (119) all_6_2 = e1
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | COMBINE_EQS: (79), (119) imply:
% 154.55/26.43 | | | | | | | | (120) all_56_14 = e1
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | REDUCE: (31), (119) imply:
% 154.55/26.43 | | | | | | | | (121) ~ (all_52_2 = e1)
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | REDUCE: (66), (119) imply:
% 154.55/26.43 | | | | | | | | (122) ~ (all_52_8 = e1)
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | BETA: splitting (52) gives:
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | (123) all_54_2 = e3
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | COMBINE_EQS: (29), (123) imply:
% 154.55/26.43 | | | | | | | | | (124) all_52_8 = e3
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | SIMP: (124) implies:
% 154.55/26.43 | | | | | | | | | (125) all_52_8 = e3
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | REDUCE: (45), (125) imply:
% 154.55/26.43 | | | | | | | | | (126) ~ (all_52_12 = e3)
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | SIMP: (126) implies:
% 154.55/26.43 | | | | | | | | | (127) ~ (all_52_12 = e3)
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | REDUCE: (76), (125) imply:
% 154.55/26.43 | | | | | | | | | (128) op(e3, e1) = e3
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | BETA: splitting (50) gives:
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | (129) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.43 | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.55/26.43 | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.43 | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.43 | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.43 | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.43 | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.43 | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.43 | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.43 | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.43 | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.43 | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | BETA: splitting (129) gives:
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | (130) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.43 | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.55/26.43 | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.43 | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.43 | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.43 | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | BETA: splitting (130) gives:
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | (131) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.43 | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 154.55/26.43 | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | ALPHA: (131) implies:
% 154.55/26.43 | | | | | | | | | | | | (132) op(e3, e2) = e3
% 154.55/26.43 | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | REF_CLOSE: (23), (29), (52), (76), (94), (99), (128), (132)
% 154.55/26.43 | | | | | | | | | | | | are inconsistent by sub-proof #53.
% 154.55/26.43 | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | Case 2:
% 154.55/26.43 | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | (133) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.43 | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.43 | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.43 | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.43 | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | BETA: splitting (133) gives:
% 154.55/26.43 | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | | (134) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.43 | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | | ALPHA: (134) implies:
% 154.55/26.43 | | | | | | | | | | | | | (135) op(e2, e3) = e2
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | | REF_CLOSE: (9), (28), (94), (135) are inconsistent by
% 154.55/26.43 | | | | | | | | | | | | | sub-proof #1544.
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | Case 2:
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | | (136) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.43 | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | | ALPHA: (136) implies:
% 154.55/26.43 | | | | | | | | | | | | | (137) ~ (all_56_14 = e1)
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | | REDUCE: (120), (137) imply:
% 154.55/26.43 | | | | | | | | | | | | | (138) $false
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 154.55/26.43 | | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | | End of split
% 154.55/26.43 | | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | End of split
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | Case 2:
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | (139) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.43 | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.43 | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.43 | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.43 | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.43 | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | REF_CLOSE: (4), (5), (24), (41), (94), (121), (127), (139)
% 154.55/26.43 | | | | | | | | | | | are inconsistent by sub-proof #88.
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | End of split
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | Case 2:
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | (140) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.43 | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.55/26.43 | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.43 | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.43 | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.43 | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.55/26.43 | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.55/26.43 | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.55/26.43 | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.43 | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.55/26.43 | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.43 | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | BETA: splitting (140) gives:
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | (141) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.43 | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.55/26.43 | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.43 | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.43 | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.43 | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | REF_CLOSE: (43), (48), (58), (63), (94), (120), (141) are
% 154.55/26.43 | | | | | | | | | | | inconsistent by sub-proof #124.
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | Case 2:
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | (142) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.55/26.43 | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.55/26.43 | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.43 | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.55/26.43 | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.43 | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | | REF_CLOSE: (54), (71), (72), (86), (94), (120), (142) are
% 154.55/26.43 | | | | | | | | | | | inconsistent by sub-proof #38.
% 154.55/26.43 | | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | End of split
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | End of split
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | Case 2:
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | (143) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | REF_CLOSE: (29), (38), (53), (122), (143) are inconsistent by
% 154.55/26.43 | | | | | | | | | sub-proof #28.
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | End of split
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | Case 2:
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | (144) all_54_10 = e0
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | REF_CLOSE: (13), (57), (144) are inconsistent by sub-proof
% 154.55/26.43 | | | | | | | | #1528.
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | End of split
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | End of split
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | End of split
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | Case 2:
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | (145) all_28_2 = e3
% 154.55/26.43 | | | | | (146) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3,
% 154.55/26.43 | | | | | e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 154.55/26.43 | | | | | (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1))
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | COMBINE_EQS: (62), (145) imply:
% 154.55/26.43 | | | | | (147) all_6_2 = e3
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | SIMP: (147) implies:
% 154.55/26.43 | | | | | (148) all_6_2 = e3
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | COMBINE_EQS: (96), (148) imply:
% 154.55/26.43 | | | | | (149) all_36_2 = e3
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | COMBINE_EQS: (79), (148) imply:
% 154.55/26.43 | | | | | (150) all_56_14 = e3
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | REDUCE: (66), (148) imply:
% 154.55/26.43 | | | | | (151) ~ (all_52_8 = e3)
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | REDUCE: (10), (148) imply:
% 154.55/26.43 | | | | | (152) op(e1, e1) = e3
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | BETA: splitting (1) gives:
% 154.55/26.43 | | | | |
% 154.55/26.43 | | | | | Case 1:
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | (153) ~ (all_56_12 = e1)
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | REDUCE: (14), (153) imply:
% 154.55/26.43 | | | | | | (154) ~ (all_10_2 = e1)
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | BETA: splitting (59) gives:
% 154.55/26.43 | | | | | |
% 154.55/26.43 | | | | | | Case 1:
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | (155) ~ (all_36_2 = e3)
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | REDUCE: (149), (155) imply:
% 154.55/26.43 | | | | | | | (156) $false
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | CLOSE: (156) is inconsistent.
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | Case 2:
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | (157) ( ~ (all_36_0 = e0) & op(all_36_1, e1) = all_36_0 &
% 154.55/26.43 | | | | | | | op(e3, e3) = all_36_1 & $i(all_36_0) & $i(all_36_1)) |
% 154.55/26.43 | | | | | | | ( ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 &
% 154.55/26.43 | | | | | | | $i(all_36_1))
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | BETA: splitting (65) gives:
% 154.55/26.43 | | | | | | |
% 154.55/26.43 | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | (158) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 &
% 154.55/26.43 | | | | | | | | op(e2, e1) = e1)
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | BETA: splitting (158) gives:
% 154.55/26.43 | | | | | | | |
% 154.55/26.43 | | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | (159) all_58_4 = e1 & op(e3, e1) = e1
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | ALPHA: (159) implies:
% 154.55/26.43 | | | | | | | | | (160) op(e3, e1) = e1
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | BETA: splitting (75) gives:
% 154.55/26.43 | | | | | | | | |
% 154.55/26.43 | | | | | | | | | Case 1:
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | (161) ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 &
% 154.55/26.43 | | | | | | | | | | op(e1, e1) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 154.55/26.43 | | | | | | | | | |
% 154.55/26.43 | | | | | | | | | | ALPHA: (161) implies:
% 154.55/26.43 | | | | | | | | | | (162) ~ (all_8_0 = e0)
% 154.55/26.46 | | | | | | | | | | (163) op(e1, e1) = all_8_1
% 154.55/26.46 | | | | | | | | | | (164) op(all_8_1, e2) = all_8_0
% 154.55/26.46 | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | BETA: splitting (6) gives:
% 154.55/26.46 | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | Case 1:
% 154.55/26.46 | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | (165) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 154.55/26.46 | | | | | | | | | | | & op(e1, e2) = e1)
% 154.55/26.46 | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | BETA: splitting (165) gives:
% 154.55/26.46 | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | Case 1:
% 154.55/26.46 | | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | | (166) all_58_6 = e1 & op(e1, e3) = e1
% 154.55/26.46 | | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | | ALPHA: (166) implies:
% 154.55/26.46 | | | | | | | | | | | | (167) all_58_6 = e1
% 154.55/26.46 | | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | | BETA: splitting (157) gives:
% 154.55/26.46 | | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | | Case 1:
% 154.55/26.46 | | | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | | | (168) ~ (all_36_0 = e0) & op(all_36_1, e1) = all_36_0 &
% 154.55/26.46 | | | | | | | | | | | | | op(e3, e3) = all_36_1 & $i(all_36_0) &
% 154.55/26.46 | | | | | | | | | | | | | $i(all_36_1)
% 154.55/26.46 | | | | | | | | | | | | |
% 154.55/26.46 | | | | | | | | | | | | | ALPHA: (168) implies:
% 154.55/26.46 | | | | | | | | | | | | | (169) op(e3, e3) = all_36_1
% 154.55/26.46 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (7), (10), (14), (15), (19), (21),
% 154.55/26.47 | | | | | | | | | | | | | (22), (23), (24), (25), (27), (28), (30), (33),
% 154.55/26.47 | | | | | | | | | | | | | (35), (41), (43), (44), (47), (48), (50), (51),
% 154.55/26.47 | | | | | | | | | | | | | (54), (55), (58), (60), (61), (63), (67), (71),
% 154.55/26.47 | | | | | | | | | | | | | (72), (77), (81), (83), (86), (89), (92), (94),
% 154.55/26.47 | | | | | | | | | | | | | (97), (98), (100), (101), (102), (103), (104),
% 154.55/26.47 | | | | | | | | | | | | | (105), (108), (110), (146), (150), (152), (154),
% 154.55/26.47 | | | | | | | | | | | | | (160), (162), (163), (164), (167), (169) are
% 154.55/26.47 | | | | | | | | | | | | | inconsistent by sub-proof #20.
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | (170) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 &
% 154.55/26.47 | | | | | | | | | | | | | $i(all_36_1)
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | ALPHA: (170) implies:
% 154.55/26.47 | | | | | | | | | | | | | (171) op(e3, e3) = all_36_1
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (7), (10), (14), (15), (19), (21),
% 154.55/26.47 | | | | | | | | | | | | | (22), (23), (24), (25), (27), (28), (30), (33),
% 154.55/26.47 | | | | | | | | | | | | | (35), (41), (43), (44), (47), (48), (50), (51),
% 154.55/26.47 | | | | | | | | | | | | | (54), (55), (58), (60), (61), (63), (67), (71),
% 154.55/26.47 | | | | | | | | | | | | | (72), (77), (81), (83), (86), (89), (92), (94),
% 154.55/26.47 | | | | | | | | | | | | | (97), (98), (100), (101), (102), (103), (104),
% 154.55/26.47 | | | | | | | | | | | | | (105), (108), (110), (146), (150), (152), (154),
% 154.55/26.47 | | | | | | | | | | | | | (160), (162), (163), (164), (167), (171) are
% 154.55/26.47 | | | | | | | | | | | | | inconsistent by sub-proof #20.
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | (172) all_58_7 = e1 & op(e1, e2) = e1
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | ALPHA: (172) implies:
% 154.55/26.47 | | | | | | | | | | | | (173) op(e1, e2) = e1
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REF_CLOSE: (48), (63), (94), (173) are inconsistent by
% 154.55/26.47 | | | | | | | | | | | | sub-proof #1166.
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | (174) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 154.55/26.47 | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | BETA: splitting (174) gives:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | (175) all_58_8 = e1 & op(e1, e1) = e1
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | ALPHA: (175) implies:
% 154.55/26.47 | | | | | | | | | | | | (176) all_58_8 = e1
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REF_CLOSE: (2), (10), (12), (14), (16), (20), (27), (28),
% 154.55/26.47 | | | | | | | | | | | | (36), (47), (56), (60), (64), (68), (72), (76),
% 154.55/26.47 | | | | | | | | | | | | (77), (81), (94), (102), (103), (105), (110),
% 154.55/26.47 | | | | | | | | | | | | (154), (160), (176) are inconsistent by sub-proof
% 154.55/26.47 | | | | | | | | | | | | #19.
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | (177) all_58_11 = e1 & op(e1, e0) = e1
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | ALPHA: (177) implies:
% 154.55/26.47 | | | | | | | | | | | | (178) op(e1, e0) = e1
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REF_CLOSE: (82), (87), (94), (178) are inconsistent by
% 154.55/26.47 | | | | | | | | | | | | sub-proof #108.
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | (179) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 154.55/26.47 | | | | | | | | | | $i(all_8_1)
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | ALPHA: (179) implies:
% 154.55/26.47 | | | | | | | | | | (180) ~ (all_8_1 = e3)
% 154.55/26.47 | | | | | | | | | | (181) op(e1, e1) = all_8_1
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | BETA: splitting (108) gives:
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | (182) ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 &
% 154.55/26.47 | | | | | | | | | | | op(e1, e1) = all_12_1 & $i(all_12_0) &
% 154.55/26.47 | | | | | | | | | | | $i(all_12_1)
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | ALPHA: (182) implies:
% 154.55/26.47 | | | | | | | | | | | (183) op(e1, e1) = all_12_1
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | BETA: splitting (83) gives:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | (184) ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 154.55/26.47 | | | | | | | | | | | | op(e1, e1) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | ALPHA: (184) implies:
% 154.55/26.47 | | | | | | | | | | | | (185) op(e1, e1) = all_4_1
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REF_CLOSE: (94), (152), (180), (181), (183), (185) are
% 154.55/26.47 | | | | | | | | | | | | inconsistent by sub-proof #18.
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | (186) ~ (all_4_1 = e2) & op(e1, e1) = all_4_1 &
% 154.55/26.47 | | | | | | | | | | | | $i(all_4_1)
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | ALPHA: (186) implies:
% 154.55/26.47 | | | | | | | | | | | | (187) op(e1, e1) = all_4_1
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REF_CLOSE: (94), (152), (180), (181), (183), (187) are
% 154.55/26.47 | | | | | | | | | | | | inconsistent by sub-proof #18.
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | (188) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 154.55/26.47 | | | | | | | | | | | $i(all_12_1)
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | ALPHA: (188) implies:
% 154.55/26.47 | | | | | | | | | | | (189) ~ (all_12_1 = e3)
% 154.55/26.47 | | | | | | | | | | | (190) op(e1, e1) = all_12_1
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | REF_CLOSE: (94), (152), (189), (190) are inconsistent by
% 154.55/26.47 | | | | | | | | | | | sub-proof #21.
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | (191) all_58_5 = e1 & op(e2, e1) = e1
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | ALPHA: (191) implies:
% 154.55/26.47 | | | | | | | | | (192) op(e2, e1) = e1
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | REF_CLOSE: (68), (94), (95), (192) are inconsistent by
% 154.55/26.47 | | | | | | | | | sub-proof #956.
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | End of split
% 154.55/26.47 | | | | | | | |
% 154.55/26.47 | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | |
% 154.55/26.47 | | | | | | | | (193) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 154.55/26.47 | | | | | | | | op(e0, e1) = e1)
% 154.55/26.47 | | | | | | | |
% 154.55/26.47 | | | | | | | | BETA: splitting (193) gives:
% 154.55/26.47 | | | | | | | |
% 154.55/26.47 | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | (194) all_58_8 = e1 & op(e1, e1) = e1
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | ALPHA: (194) implies:
% 154.55/26.47 | | | | | | | | | (195) all_58_8 = e1
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | BETA: splitting (84) gives:
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | (196) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 154.55/26.47 | | | | | | | | | | & op(e3, e2) = e1)
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | BETA: splitting (196) gives:
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | (197) all_58_0 = e1 & op(e3, e3) = e1
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | ALPHA: (197) implies:
% 154.55/26.47 | | | | | | | | | | | (198) all_58_0 = e1
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | BETA: splitting (102) gives:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | (199) all_56_12 = e3
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | COMBINE_EQS: (14), (199) imply:
% 154.55/26.47 | | | | | | | | | | | | (200) all_10_2 = e3
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | SIMP: (200) implies:
% 154.55/26.47 | | | | | | | | | | | | (201) all_10_2 = e3
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REDUCE: (81), (201) imply:
% 154.55/26.47 | | | | | | | | | | | | (202) ~ (all_52_1 = e3)
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REDUCE: (55), (201) imply:
% 154.55/26.47 | | | | | | | | | | | | (203) ~ (all_52_3 = e3)
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REDUCE: (110), (201) imply:
% 154.55/26.47 | | | | | | | | | | | | (204) ~ (e3 = e2)
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REDUCE: (154), (201) imply:
% 154.55/26.47 | | | | | | | | | | | | (205) ~ (e3 = e1)
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | BETA: splitting (100) gives:
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | (206) all_54_12 = e3
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | REF_CLOSE: (101), (203), (206) are inconsistent by sub-proof
% 154.55/26.47 | | | | | | | | | | | | | #1234.
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | (207) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | BETA: splitting (19) gives:
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | (208) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 154.55/26.47 | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 154.55/26.47 | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | REF_CLOSE: (28), (94), (198), (202), (205), (208) are
% 154.55/26.47 | | | | | | | | | | | | | | inconsistent by sub-proof #191.
% 154.55/26.47 | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | (209) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 154.55/26.47 | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 154.55/26.47 | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 154.55/26.47 | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | | (210) all_58_6 = e3 & op(e1, e3) = e3
% 154.55/26.47 | | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 154.55/26.47 | | | | | | | | | | | | | | | (211) op(e1, e3) = e3
% 154.55/26.47 | | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | | REF_CLOSE: (15), (41), (94), (150), (205), (211) are
% 154.55/26.47 | | | | | | | | | | | | | | | inconsistent by sub-proof #144.
% 154.55/26.47 | | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | | (212) all_58_12 = e3 & op(e0, e3) = e3
% 154.55/26.47 | | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 154.55/26.47 | | | | | | | | | | | | | | | (213) all_58_12 = e3
% 154.55/26.47 | | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | | REF_CLOSE: (3), (24), (35), (36), (60), (68), (72), (86),
% 154.55/26.47 | | | | | | | | | | | | | | | (89), (94), (101), (104), (204), (207), (213) are
% 154.55/26.47 | | | | | | | | | | | | | | | inconsistent by sub-proof #17.
% 154.55/26.47 | | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | (214) ~ (all_56_12 = e3)
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | | REF_CLOSE: (14), (27), (47), (105), (110), (154), (214) are
% 154.55/26.47 | | | | | | | | | | | | inconsistent by sub-proof #22.
% 154.55/26.47 | | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | (215) all_58_1 = e1 & op(e3, e2) = e1
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | REF_CLOSE: (23), (61), (94), (215) are inconsistent by
% 154.55/26.47 | | | | | | | | | | | sub-proof #1284.
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | (216) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 154.55/26.47 | | | | | | | | | | & op(e3, e0) = e1)
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | BETA: splitting (216) gives:
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | Case 1:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | (217) all_58_4 = e1 & op(e3, e1) = e1
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | ALPHA: (217) implies:
% 154.55/26.47 | | | | | | | | | | | (218) op(e3, e1) = e1
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | REF_CLOSE: (2), (10), (12), (14), (16), (20), (27), (28),
% 154.55/26.47 | | | | | | | | | | | (36), (47), (56), (60), (64), (68), (72), (76),
% 154.55/26.47 | | | | | | | | | | | (77), (81), (94), (102), (103), (105), (110),
% 154.55/26.47 | | | | | | | | | | | (154), (195), (218) are inconsistent by sub-proof
% 154.55/26.47 | | | | | | | | | | | #19.
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | (219) all_58_9 = e1 & op(e3, e0) = e1
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | | REF_CLOSE: (5), (93), (94), (219) are inconsistent by
% 154.55/26.47 | | | | | | | | | | | sub-proof #67.
% 154.55/26.47 | | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | | |
% 154.55/26.47 | | | | | | | | | End of split
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | Case 2:
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | (220) all_58_14 = e1 & op(e0, e1) = e1
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | ALPHA: (220) implies:
% 154.55/26.47 | | | | | | | | | (221) op(e0, e1) = e1
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | | REF_CLOSE: (71), (72), (94), (221) are inconsistent by
% 154.55/26.47 | | | | | | | | | sub-proof #129.
% 154.55/26.47 | | | | | | | | |
% 154.55/26.47 | | | | | | | | End of split
% 154.55/26.47 | | | | | | | |
% 154.55/26.47 | | | | | | | End of split
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | End of split
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | Case 2:
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | (222) all_56_1 = e3 & op(e3, e1) = e3
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | ALPHA: (222) implies:
% 154.55/26.47 | | | | | | (223) op(e3, e1) = e3
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | REF_CLOSE: (76), (94), (151), (223) are inconsistent by sub-proof
% 154.55/26.47 | | | | | | #1538.
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | End of split
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | End of split
% 154.55/26.47 | | | |
% 154.55/26.47 | | | Case 2:
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | (224) all_16_2 = e2
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | COMBINE_EQS: (17), (224) imply:
% 154.55/26.47 | | | | (225) all_10_2 = e2
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | SIMP: (225) implies:
% 154.55/26.47 | | | | (226) all_10_2 = e2
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | COMBINE_EQS: (14), (226) imply:
% 154.55/26.47 | | | | (227) all_56_12 = e2
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | REDUCE: (55), (226) imply:
% 154.55/26.47 | | | | (228) ~ (all_52_3 = e2)
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | REDUCE: (70), (226) imply:
% 154.55/26.47 | | | | (229) ~ (all_52_12 = e2)
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | REF_CLOSE: (3), (5), (6), (8), (10), (11), (12), (16), (18), (19), (20),
% 154.55/26.47 | | | | (23), (24), (26), (29), (31), (33), (34), (36), (41), (42),
% 154.55/26.47 | | | | (48), (52), (53), (54), (57), (60), (67), (71), (72), (74),
% 154.55/26.47 | | | | (76), (77), (78), (79), (80), (85), (86), (87), (90), (91),
% 154.55/26.47 | | | | (92), (94), (98), (99), (100), (101), (102), (104), (227),
% 154.55/26.47 | | | | (228), (229) are inconsistent by sub-proof #51.
% 154.55/26.47 | | | |
% 154.55/26.47 | | | End of split
% 154.55/26.47 | | |
% 154.55/26.47 | | End of split
% 154.55/26.47 | |
% 154.55/26.47 | Case 2:
% 154.55/26.47 | |
% 154.55/26.47 | | (230) all_10_2 = e0
% 154.55/26.47 | |
% 154.55/26.47 | | COMBINE_EQS: (14), (230) imply:
% 154.55/26.47 | | (231) all_56_12 = e0
% 154.55/26.47 | |
% 154.55/26.47 | | BETA: splitting (102) gives:
% 154.55/26.47 | |
% 154.55/26.47 | | Case 1:
% 154.55/26.47 | | |
% 154.55/26.47 | | | (232) all_56_12 = e3
% 154.55/26.47 | | |
% 154.55/26.47 | | | COMBINE_EQS: (231), (232) imply:
% 154.55/26.47 | | | (233) e3 = e0
% 154.55/26.47 | | |
% 154.55/26.47 | | | REDUCE: (32), (233) imply:
% 154.55/26.47 | | | (234) $false
% 154.55/26.47 | | |
% 154.55/26.47 | | | CLOSE: (234) is inconsistent.
% 154.55/26.47 | | |
% 154.55/26.47 | | Case 2:
% 154.55/26.47 | | |
% 154.55/26.47 | | | (235) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.47 | | |
% 154.55/26.47 | | | BETA: splitting (235) gives:
% 154.55/26.47 | | |
% 154.55/26.47 | | | Case 1:
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | (236) all_56_13 = e2
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | COMBINE_EQS: (40), (236) imply:
% 154.55/26.47 | | | | (237) e2 = e1
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | REDUCE: (68), (237) imply:
% 154.55/26.47 | | | | (238) $false
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | CLOSE: (238) is inconsistent.
% 154.55/26.47 | | | |
% 154.55/26.47 | | | Case 2:
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | (239) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | BETA: splitting (37) gives:
% 154.55/26.47 | | | |
% 154.55/26.47 | | | | Case 1:
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | | (240) ~ (all_56_12 = e0)
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | | REDUCE: (231), (240) imply:
% 154.55/26.47 | | | | | (241) $false
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | | CLOSE: (241) is inconsistent.
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | Case 2:
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | | (242) all_56_2 = e3 & op(e3, e0) = e3
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | | ALPHA: (242) implies:
% 154.55/26.47 | | | | | (243) op(e3, e0) = e3
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | | BETA: splitting (239) gives:
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | | Case 1:
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | (244) all_56_14 = e1
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | COMBINE_EQS: (79), (244) imply:
% 154.55/26.47 | | | | | | (245) all_6_2 = e1
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | SIMP: (245) implies:
% 154.55/26.47 | | | | | | (246) all_6_2 = e1
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | REDUCE: (66), (246) imply:
% 154.55/26.47 | | | | | | (247) ~ (all_52_8 = e1)
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | BETA: splitting (52) gives:
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | Case 1:
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | | (248) all_54_2 = e3
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | | COMBINE_EQS: (29), (248) imply:
% 154.55/26.47 | | | | | | | (249) all_52_8 = e3
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | | REDUCE: (45), (249) imply:
% 154.55/26.47 | | | | | | | (250) ~ (all_52_12 = e3)
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | | SIMP: (250) implies:
% 154.55/26.47 | | | | | | | (251) ~ (all_52_12 = e3)
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | | REF_CLOSE: (5), (94), (243), (251) are inconsistent by sub-proof
% 154.55/26.47 | | | | | | | #210.
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | Case 2:
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | | (252) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | | REF_CLOSE: (29), (38), (53), (247), (252) are inconsistent by
% 154.55/26.47 | | | | | | | sub-proof #28.
% 154.55/26.47 | | | | | | |
% 154.55/26.47 | | | | | | End of split
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | Case 2:
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | (253) all_56_15 = e0
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | | REF_CLOSE: (71), (80), (253) are inconsistent by sub-proof #52.
% 154.55/26.47 | | | | | |
% 154.55/26.47 | | | | | End of split
% 154.55/26.47 | | | | |
% 154.55/26.47 | | | | End of split
% 154.55/26.47 | | | |
% 154.55/26.47 | | | End of split
% 154.55/26.47 | | |
% 154.55/26.47 | | End of split
% 154.55/26.47 | |
% 154.55/26.47 | End of split
% 154.55/26.47 |
% 154.55/26.47 End of proof
% 154.55/26.47
% 154.55/26.47 Sub-proof #17 shows that the following formulas are inconsistent:
% 154.55/26.47 ----------------------------------------------------------------
% 154.55/26.47 (1) ~ (all_52_3 = e1)
% 154.55/26.47 (2) all_58_12 = e3
% 154.55/26.47 (3) ~ (all_52_3 = e0)
% 154.55/26.47 (4) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 154.55/26.47 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.47 (5) ~ (e2 = e0)
% 154.55/26.47 (6) op(e0, e1) = all_52_11
% 154.55/26.47 (7) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.47 (8) ~ (e2 = e1)
% 154.55/26.47 (9) op(e0, e1) = e0
% 154.55/26.47 (10) op(e0, e2) = all_52_7
% 154.55/26.47 (11) op(e0, e0) = e1
% 154.55/26.47 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.47 (13) ~ (e3 = e2)
% 154.55/26.47 (14) all_54_12 = all_52_3
% 154.55/26.47 (15) ~ (all_52_3 = all_52_7)
% 154.55/26.47
% 154.55/26.47 Begin of proof
% 154.55/26.47 |
% 154.55/26.47 | BETA: splitting (4) gives:
% 154.55/26.47 |
% 154.55/26.47 | Case 1:
% 154.55/26.47 | |
% 154.55/26.47 | | (16) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 154.55/26.47 | | e2)
% 154.55/26.47 | |
% 154.55/26.47 | | BETA: splitting (16) gives:
% 154.55/26.47 | |
% 154.55/26.47 | | Case 1:
% 154.55/26.47 | | |
% 154.55/26.47 | | | (17) all_58_12 = e2 & op(e0, e3) = e2
% 154.55/26.47 | | |
% 154.55/26.47 | | | ALPHA: (17) implies:
% 154.55/26.47 | | | (18) all_58_12 = e2
% 154.55/26.47 | | |
% 154.55/26.47 | | | REF_CLOSE: (2), (13), (18) are inconsistent by sub-proof #1490.
% 154.55/26.47 | | |
% 154.55/26.47 | | Case 2:
% 154.55/26.47 | | |
% 154.55/26.47 | | | (19) all_58_13 = e2 & op(e0, e2) = e2
% 154.55/26.47 | | |
% 154.55/26.47 | | | ALPHA: (19) implies:
% 154.55/26.47 | | | (20) op(e0, e2) = e2
% 154.55/26.47 | | |
% 154.55/26.47 | | | REF_CLOSE: (1), (3), (7), (10), (12), (14), (15), (20) are inconsistent by
% 154.55/26.47 | | | sub-proof #55.
% 154.55/26.47 | | |
% 154.55/26.47 | | End of split
% 154.55/26.47 | |
% 154.55/26.47 | Case 2:
% 154.55/26.48 | |
% 154.55/26.48 | | (21) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.48 | | e2)
% 154.55/26.48 | |
% 154.55/26.48 | | REF_CLOSE: (5), (6), (8), (9), (11), (12), (21) are inconsistent by
% 154.55/26.48 | | sub-proof #54.
% 154.55/26.48 | |
% 154.55/26.48 | End of split
% 154.55/26.48 |
% 154.55/26.48 End of proof
% 154.55/26.48
% 154.55/26.48 Sub-proof #18 shows that the following formulas are inconsistent:
% 154.55/26.48 ----------------------------------------------------------------
% 154.55/26.48 (1) op(e1, e1) = e3
% 154.55/26.48 (2) op(e1, e1) = all_8_1
% 154.55/26.48 (3) ~ (all_8_1 = e3)
% 154.55/26.48 (4) op(e1, e1) = all_12_1
% 154.55/26.48 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.48 (6) op(e1, e1) = all_4_1
% 154.55/26.48
% 154.55/26.48 Begin of proof
% 154.55/26.48 |
% 154.55/26.48 | GROUND_INST: instantiating (5) with all_8_1, all_12_1, e1, e1, simplifying
% 154.55/26.48 | with (2), (4) gives:
% 154.55/26.48 | (7) all_12_1 = all_8_1
% 154.55/26.48 |
% 154.55/26.48 | GROUND_INST: instantiating (5) with all_4_1, all_12_1, e1, e1, simplifying
% 154.55/26.48 | with (4), (6) gives:
% 154.55/26.48 | (8) all_12_1 = all_4_1
% 154.55/26.48 |
% 154.55/26.48 | GROUND_INST: instantiating (5) with e3, all_12_1, e1, e1, simplifying with
% 154.55/26.48 | (1), (4) gives:
% 154.55/26.48 | (9) all_12_1 = e3
% 154.55/26.48 |
% 154.55/26.48 | COMBINE_EQS: (7), (9) imply:
% 154.55/26.48 | (10) all_8_1 = e3
% 154.55/26.48 |
% 154.55/26.48 | COMBINE_EQS: (7), (8) imply:
% 154.55/26.48 | (11) all_8_1 = all_4_1
% 154.55/26.48 |
% 154.55/26.48 | COMBINE_EQS: (10), (11) imply:
% 154.55/26.48 | (12) all_4_1 = e3
% 154.55/26.48 |
% 154.55/26.48 | REDUCE: (3), (10) imply:
% 154.55/26.48 | (13) $false
% 154.55/26.48 |
% 154.55/26.48 | CLOSE: (13) is inconsistent.
% 154.55/26.48 |
% 154.55/26.48 End of proof
% 154.55/26.48
% 154.55/26.48 Sub-proof #19 shows that the following formulas are inconsistent:
% 154.55/26.48 ----------------------------------------------------------------
% 154.55/26.48 (1) all_58_5 = e2
% 154.55/26.48 (2) op(e3, e1) = e1
% 154.55/26.48 (3) ~ (all_10_2 = e1)
% 154.55/26.48 (4) op(e1, e1) = all_6_2
% 154.55/26.48 (5) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 154.55/26.48 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 154.55/26.48 (6) all_56_12 = all_10_2
% 154.55/26.48 (7) all_58_14 = e0
% 154.55/26.48 (8) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 154.55/26.48 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 154.55/26.48 (9) all_54_0 = all_10_2
% 154.55/26.48 (10) op(e2, e3) = all_52_1
% 154.55/26.48 (11) ~ (all_10_2 = e0)
% 154.55/26.48 (12) ~ (e2 = e0)
% 154.55/26.48 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.55/26.48 (14) ~ (all_52_8 = all_10_2)
% 154.55/26.48 (15) op(e0, e1) = all_52_11
% 154.55/26.48 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 154.55/26.48 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 154.55/26.48 (17) ~ (all_10_2 = e2)
% 154.55/26.48 (18) ~ (e2 = e1)
% 154.55/26.48 (19) op(e0, e1) = e0
% 154.55/26.48 (20) op(e3, e1) = all_52_8
% 154.55/26.48 (21) ~ (all_6_2 = e2)
% 154.55/26.48 (22) ~ (all_52_1 = all_10_2)
% 154.55/26.48 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.48 (24) all_58_8 = e1
% 154.55/26.48 (25) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.48 (26) all_58_3 = e1
% 154.55/26.48
% 154.55/26.48 Begin of proof
% 154.55/26.48 |
% 154.55/26.48 | BETA: splitting (25) gives:
% 154.55/26.48 |
% 154.55/26.48 | Case 1:
% 154.55/26.48 | |
% 154.55/26.48 | | (27) all_56_12 = e3
% 154.55/26.48 | |
% 154.55/26.48 | | COMBINE_EQS: (6), (27) imply:
% 154.55/26.48 | | (28) all_10_2 = e3
% 154.55/26.48 | |
% 154.55/26.48 | | SIMP: (28) implies:
% 154.55/26.48 | | (29) all_10_2 = e3
% 154.55/26.48 | |
% 154.55/26.48 | | REDUCE: (22), (29) imply:
% 154.55/26.48 | | (30) ~ (all_52_1 = e3)
% 154.55/26.48 | |
% 154.55/26.48 | | REDUCE: (14), (29) imply:
% 154.55/26.48 | | (31) ~ (all_52_8 = e3)
% 154.55/26.48 | |
% 154.55/26.48 | | REDUCE: (17), (29) imply:
% 154.55/26.48 | | (32) ~ (e3 = e2)
% 154.55/26.48 | |
% 154.55/26.48 | | REDUCE: (3), (29) imply:
% 154.55/26.48 | | (33) ~ (e3 = e1)
% 154.55/26.48 | |
% 154.55/26.48 | | REDUCE: (11), (29) imply:
% 154.55/26.48 | | (34) ~ (e3 = e0)
% 154.55/26.48 | |
% 154.55/26.48 | | BETA: splitting (16) gives:
% 154.55/26.48 | |
% 154.55/26.48 | | Case 1:
% 154.55/26.48 | | |
% 154.55/26.48 | | | (35) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 154.55/26.48 | | | e3)
% 154.55/26.48 | | |
% 154.55/26.48 | | | REF_CLOSE: (10), (23), (26), (30), (33), (35) are inconsistent by
% 154.55/26.48 | | | sub-proof #213.
% 154.55/26.48 | | |
% 154.55/26.48 | | Case 2:
% 154.55/26.48 | | |
% 154.55/26.48 | | | (36) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 154.55/26.48 | | | e3)
% 154.55/26.48 | | |
% 154.55/26.48 | | | BETA: splitting (36) gives:
% 154.55/26.48 | | |
% 154.55/26.48 | | | Case 1:
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | (37) all_58_5 = e3 & op(e2, e1) = e3
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | ALPHA: (37) implies:
% 154.55/26.48 | | | | (38) all_58_5 = e3
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | REF_CLOSE: (2), (4), (8), (12), (15), (18), (19), (21), (23), (32), (38)
% 154.55/26.48 | | | | are inconsistent by sub-proof #66.
% 154.55/26.48 | | | |
% 154.55/26.48 | | | Case 2:
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | (39) all_58_10 = e3 & op(e2, e0) = e3
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | ALPHA: (39) implies:
% 154.55/26.48 | | | | (40) all_58_10 = e3
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | BETA: splitting (5) gives:
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | Case 1:
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | (41) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 154.55/26.48 | | | | | e1) = e3)
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | BETA: splitting (41) gives:
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | Case 1:
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | (42) all_58_4 = e3 & op(e3, e1) = e3
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | ALPHA: (42) implies:
% 154.55/26.48 | | | | | | (43) op(e3, e1) = e3
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | REF_CLOSE: (20), (23), (31), (43) are inconsistent by sub-proof
% 154.55/26.48 | | | | | | #1538.
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | Case 2:
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | (44) all_58_5 = e3 & op(e2, e1) = e3
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | ALPHA: (44) implies:
% 154.55/26.48 | | | | | | (45) all_58_5 = e3
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | REF_CLOSE: (2), (4), (8), (12), (15), (18), (19), (21), (23), (32),
% 154.55/26.48 | | | | | | (45) are inconsistent by sub-proof #66.
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | End of split
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | Case 2:
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | (46) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 154.55/26.48 | | | | | e1) = e3)
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | BETA: splitting (46) gives:
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | Case 1:
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | (47) all_58_8 = e3 & op(e1, e1) = e3
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | REF_CLOSE: (24), (33), (47) are inconsistent by sub-proof #870.
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | Case 2:
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | (48) all_58_14 = e3 & op(e0, e1) = e3
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | ALPHA: (48) implies:
% 154.55/26.48 | | | | | | (49) all_58_14 = e3
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | COMBINE_EQS: (7), (49) imply:
% 154.55/26.48 | | | | | | (50) e3 = e0
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | COMBINE_EQS: (40), (50) imply:
% 154.55/26.48 | | | | | | (51) all_58_10 = e0
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | REF_CLOSE: (1), (10), (16), (23), (26), (30), (32), (33), (34), (51)
% 154.55/26.48 | | | | | | are inconsistent by sub-proof #184.
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | End of split
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | End of split
% 154.55/26.48 | | | |
% 154.55/26.48 | | | End of split
% 154.55/26.48 | | |
% 154.55/26.48 | | End of split
% 154.55/26.48 | |
% 154.55/26.48 | Case 2:
% 154.55/26.48 | |
% 154.55/26.48 | | (52) ~ (all_56_12 = e3)
% 154.55/26.48 | |
% 154.55/26.48 | | REDUCE: (6), (52) imply:
% 154.55/26.48 | | (53) ~ (all_10_2 = e3)
% 154.55/26.48 | |
% 154.55/26.48 | | BETA: splitting (13) gives:
% 154.55/26.48 | |
% 154.55/26.48 | | Case 1:
% 154.55/26.48 | | |
% 154.55/26.48 | | | (54) all_54_0 = e3
% 154.55/26.48 | | |
% 154.55/26.48 | | | REF_CLOSE: (9), (53), (54) are inconsistent by sub-proof #50.
% 154.55/26.48 | | |
% 154.55/26.48 | | Case 2:
% 154.55/26.48 | | |
% 154.55/26.48 | | | (55) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.55/26.48 | | |
% 154.55/26.48 | | | REF_CLOSE: (3), (9), (11), (17), (55) are inconsistent by sub-proof #1307.
% 154.55/26.48 | | |
% 154.55/26.48 | | End of split
% 154.55/26.48 | |
% 154.55/26.48 | End of split
% 154.55/26.48 |
% 154.55/26.48 End of proof
% 154.55/26.48
% 154.55/26.48 Sub-proof #20 shows that the following formulas are inconsistent:
% 154.55/26.48 ----------------------------------------------------------------
% 154.55/26.48 (1) op(e1, e1) = e3
% 154.55/26.48 (2) op(e3, e1) = e1
% 154.55/26.48 (3) all_56_14 = e3
% 154.55/26.48 (4) ~ (all_52_3 = e1)
% 154.55/26.48 (5) op(e0, e3) = all_52_3
% 154.55/26.48 (6) op(e3, e0) = all_52_12
% 154.55/26.48 (7) op(e3, e3) = all_10_2
% 154.55/26.48 (8) ~ (all_10_2 = e1)
% 154.55/26.48 (9) op(e1, e1) = all_8_1
% 154.55/26.48 (10) op(e1, e1) = all_6_2
% 154.55/26.48 (11) op(e3, e3) = all_36_1
% 154.55/26.48 (12) all_56_12 = all_10_2
% 154.55/26.48 (13) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 154.55/26.48 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.48 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.48 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.55/26.48 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.48 (16) all_54_1 = all_52_4
% 154.55/26.48 (17) op(e3, e2) = all_52_4
% 154.55/26.48 (18) ~ (all_52_3 = e0)
% 154.55/26.48 (19) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.48 (20) all_58_6 = e1
% 154.55/26.48 (21) all_54_0 = all_10_2
% 154.55/26.48 (22) op(e2, e3) = all_52_1
% 154.55/26.48 (23) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 154.55/26.48 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 154.55/26.48 (24) ~ (all_10_2 = e0)
% 154.55/26.48 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.48 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.48 (26) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 154.55/26.48 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.48 e2)
% 154.55/26.48 (27) op(e1, e3) = all_52_2
% 154.55/26.48 (28) op(e2, e0) = all_52_13
% 154.55/26.48 (29) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 154.55/26.48 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 154.55/26.48 (30) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.55/26.48 (31) op(e1, e2) = all_52_6
% 154.55/26.48 (32) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 154.55/26.48 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3,
% 154.55/26.48 e3) = all_28_1 & $i(all_28_1))
% 154.55/26.48 (33) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.48 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.48 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.48 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.48 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.48 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.48 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.48 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.48 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.48 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.48 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.48 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.48 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.48 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.48 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.48 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.48 = e0)
% 154.55/26.48 (34) ~ (all_8_0 = e0)
% 154.55/26.48 (35) ~ (all_52_4 = all_10_2)
% 154.55/26.48 (36) ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e1, e1) =
% 154.55/26.48 all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e3) & op(e1,
% 154.55/26.48 e1) = all_12_1 & $i(all_12_1))
% 154.55/26.48 (37) ~ (all_52_7 = e0)
% 154.55/26.48 (38) ~ (all_52_3 = all_10_2)
% 154.55/26.48 (39) ~ (all_52_13 = e2)
% 154.55/26.48 (40) op(e0, e1) = all_52_11
% 154.55/26.48 (41) ~ (all_52_4 = e1)
% 154.55/26.48 (42) ~ (all_52_6 = e1)
% 154.55/26.48 (43) ~ (all_10_2 = e2)
% 154.55/26.48 (44) all_58_15 = e1
% 154.55/26.48 (45) ~ (e1 = e0)
% 154.55/26.48 (46) op(e0, e1) = e0
% 154.55/26.48 (47) ~ (all_6_2 = e2)
% 154.55/26.48 (48) ~ (all_52_1 = all_10_2)
% 154.55/26.48 (49) ( ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 & op(e1, e1) = all_4_1 &
% 154.55/26.48 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e2) & op(e1, e1) = all_4_1
% 154.55/26.48 & $i(all_4_1))
% 154.55/26.48 (50) op(e0, e2) = all_52_7
% 154.55/26.48 (51) op(e0, e0) = e1
% 154.55/26.48 (52) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.48 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.48 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.48 (54) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 154.55/26.48 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.48 (55) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.48 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.48 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.48 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.48 (56) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.48 (57) all_54_12 = all_52_3
% 154.55/26.48 (58) op(all_8_1, e2) = all_8_0
% 154.55/26.48 (59) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.48 (60) all_58_3 = e1
% 154.55/26.48 (61) ~ (all_52_3 = all_52_7)
% 154.55/26.48
% 154.55/26.48 Begin of proof
% 154.55/26.48 |
% 154.55/26.48 | BETA: splitting (36) gives:
% 154.55/26.48 |
% 154.55/26.48 | Case 1:
% 154.55/26.48 | |
% 154.55/26.48 | | (62) ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e1, e1) =
% 154.55/26.48 | | all_12_1 & $i(all_12_0) & $i(all_12_1)
% 154.55/26.48 | |
% 154.55/26.48 | | ALPHA: (62) implies:
% 154.55/26.48 | | (63) op(e1, e1) = all_12_1
% 154.55/26.48 | |
% 154.55/26.48 | | BETA: splitting (59) gives:
% 154.55/26.48 | |
% 154.55/26.48 | | Case 1:
% 154.55/26.48 | | |
% 154.55/26.48 | | | (64) all_56_12 = e3
% 154.55/26.48 | | |
% 154.55/26.48 | | | COMBINE_EQS: (12), (64) imply:
% 154.55/26.48 | | | (65) all_10_2 = e3
% 154.55/26.48 | | |
% 154.55/26.48 | | | REDUCE: (48), (65) imply:
% 154.55/26.48 | | | (66) ~ (all_52_1 = e3)
% 154.55/26.48 | | |
% 154.55/26.48 | | | REDUCE: (38), (65) imply:
% 154.55/26.48 | | | (67) ~ (all_52_3 = e3)
% 154.55/26.48 | | |
% 154.55/26.48 | | | REDUCE: (35), (65) imply:
% 154.55/26.48 | | | (68) ~ (all_52_4 = e3)
% 154.55/26.48 | | |
% 154.55/26.48 | | | REDUCE: (8), (65) imply:
% 154.55/26.48 | | | (69) ~ (e3 = e1)
% 154.55/26.48 | | |
% 154.55/26.48 | | | REDUCE: (24), (65) imply:
% 154.55/26.48 | | | (70) ~ (e3 = e0)
% 154.55/26.48 | | |
% 154.55/26.48 | | | REDUCE: (7), (65) imply:
% 154.55/26.48 | | | (71) op(e3, e3) = e3
% 154.55/26.48 | | |
% 154.55/26.48 | | | BETA: splitting (56) gives:
% 154.55/26.48 | | |
% 154.55/26.48 | | | Case 1:
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | (72) all_54_12 = e3
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | REF_CLOSE: (57), (67), (72) are inconsistent by sub-proof #1234.
% 154.55/26.48 | | | |
% 154.55/26.48 | | | Case 2:
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | (73) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | BETA: splitting (73) gives:
% 154.55/26.48 | | | |
% 154.55/26.48 | | | | Case 1:
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | (74) all_54_12 = e2
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | COMBINE_EQS: (57), (74) imply:
% 154.55/26.48 | | | | | (75) all_52_3 = e2
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | SIMP: (75) implies:
% 154.55/26.48 | | | | | (76) all_52_3 = e2
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | REDUCE: (61), (76) imply:
% 154.55/26.48 | | | | | (77) ~ (all_52_7 = e2)
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | SIMP: (77) implies:
% 154.55/26.48 | | | | | (78) ~ (all_52_7 = e2)
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | REDUCE: (4), (76) imply:
% 154.55/26.48 | | | | | (79) ~ (e2 = e1)
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | REDUCE: (18), (76) imply:
% 154.55/26.48 | | | | | (80) ~ (e2 = e0)
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | BETA: splitting (52) gives:
% 154.55/26.48 | | | | |
% 154.55/26.48 | | | | | Case 1:
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | (81) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 154.55/26.48 | | | | | | e3) = e0)
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | BETA: splitting (81) gives:
% 154.55/26.48 | | | | | |
% 154.55/26.48 | | | | | | Case 1:
% 154.55/26.48 | | | | | | |
% 154.55/26.48 | | | | | | | (82) all_58_0 = e0 & op(e3, e3) = e0
% 154.55/26.48 | | | | | | |
% 154.55/26.48 | | | | | | | ALPHA: (82) implies:
% 154.55/26.48 | | | | | | | (83) op(e3, e3) = e0
% 154.55/26.48 | | | | | | |
% 154.55/26.48 | | | | | | | REF_CLOSE: (53), (70), (71), (83) are inconsistent by sub-proof
% 154.55/26.48 | | | | | | | #1521.
% 154.55/26.48 | | | | | | |
% 154.55/26.48 | | | | | | Case 2:
% 154.55/26.48 | | | | | | |
% 154.55/26.48 | | | | | | | (84) all_58_2 = e0 & op(e2, e3) = e0
% 154.55/26.48 | | | | | | |
% 154.55/26.48 | | | | | | | ALPHA: (84) implies:
% 154.55/26.48 | | | | | | | (85) all_58_2 = e0
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | BETA: splitting (26) gives:
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | Case 1:
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | (86) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 154.55/26.49 | | | | | | | | op(e0, e2) = e2)
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | BETA: splitting (86) gives:
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | Case 1:
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | (87) all_58_12 = e2 & op(e0, e3) = e2
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | ALPHA: (87) implies:
% 154.55/26.49 | | | | | | | | | (88) all_58_12 = e2
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | BETA: splitting (49) gives:
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | Case 1:
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | (89) ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 154.55/26.49 | | | | | | | | | | op(e1, e1) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | ALPHA: (89) implies:
% 154.55/26.49 | | | | | | | | | | (90) op(e1, e1) = all_4_1
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (13),
% 154.55/26.49 | | | | | | | | | | (14), (15), (16), (17), (18), (19), (22), (23),
% 154.55/26.49 | | | | | | | | | | (25), (27), (28), (29), (31), (32), (33), (34),
% 154.55/26.49 | | | | | | | | | | (37), (39), (41), (42), (44), (45), (47), (50),
% 154.55/26.49 | | | | | | | | | | (51), (52), (53), (54), (55), (58), (60), (63),
% 154.55/26.49 | | | | | | | | | | (64), (66), (68), (69), (70), (71), (85), (88),
% 154.55/26.49 | | | | | | | | | | (90) are inconsistent by sub-proof #23.
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | Case 2:
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | (91) ~ (all_4_1 = e2) & op(e1, e1) = all_4_1 &
% 154.55/26.49 | | | | | | | | | | $i(all_4_1)
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | ALPHA: (91) implies:
% 154.55/26.49 | | | | | | | | | | (92) op(e1, e1) = all_4_1
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (13),
% 154.55/26.49 | | | | | | | | | | (14), (15), (16), (17), (18), (19), (22), (23),
% 154.55/26.49 | | | | | | | | | | (25), (27), (28), (29), (31), (32), (33), (34),
% 154.55/26.49 | | | | | | | | | | (37), (39), (41), (42), (44), (45), (47), (50),
% 154.55/26.49 | | | | | | | | | | (51), (52), (53), (54), (55), (58), (60), (63),
% 154.55/26.49 | | | | | | | | | | (64), (66), (68), (69), (70), (71), (85), (88),
% 154.55/26.49 | | | | | | | | | | (92) are inconsistent by sub-proof #23.
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | End of split
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | Case 2:
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | (93) all_58_13 = e2 & op(e0, e2) = e2
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | ALPHA: (93) implies:
% 154.55/26.49 | | | | | | | | | (94) op(e0, e2) = e2
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | REF_CLOSE: (50), (53), (78), (94) are inconsistent by
% 154.55/26.49 | | | | | | | | | sub-proof #1479.
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | End of split
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | Case 2:
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | (95) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 154.55/26.49 | | | | | | | | op(e0, e0) = e2)
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | REF_CLOSE: (40), (46), (51), (53), (79), (80), (95) are
% 154.55/26.49 | | | | | | | | inconsistent by sub-proof #54.
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | End of split
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | End of split
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | Case 2:
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | | (96) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 154.55/26.49 | | | | | | e3) = e0)
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | | BETA: splitting (96) gives:
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | | Case 1:
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | (97) all_58_6 = e0 & op(e1, e3) = e0
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | ALPHA: (97) implies:
% 154.55/26.49 | | | | | | | (98) all_58_6 = e0
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | REF_CLOSE: (20), (45), (98) are inconsistent by sub-proof #735.
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | Case 2:
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | (99) all_58_12 = e0 & op(e0, e3) = e0
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | ALPHA: (99) implies:
% 154.55/26.49 | | | | | | | (100) op(e0, e3) = e0
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | REF_CLOSE: (5), (18), (53), (100) are inconsistent by sub-proof
% 154.55/26.49 | | | | | | | #89.
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | End of split
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | End of split
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | Case 2:
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | | (101) all_54_12 = e1 | all_54_12 = e0
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | | REF_CLOSE: (4), (18), (57), (101) are inconsistent by sub-proof #1222.
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | End of split
% 154.55/26.49 | | | |
% 154.55/26.49 | | | End of split
% 154.55/26.49 | | |
% 154.55/26.49 | | Case 2:
% 154.55/26.49 | | |
% 154.55/26.49 | | | (102) ~ (all_56_12 = e3)
% 154.55/26.49 | | |
% 154.55/26.49 | | | REF_CLOSE: (8), (12), (21), (24), (30), (43), (102) are inconsistent by
% 154.55/26.49 | | | sub-proof #22.
% 154.55/26.49 | | |
% 154.55/26.49 | | End of split
% 154.55/26.49 | |
% 154.55/26.49 | Case 2:
% 154.55/26.49 | |
% 154.55/26.49 | | (103) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 & $i(all_12_1)
% 154.55/26.49 | |
% 154.55/26.49 | | ALPHA: (103) implies:
% 154.55/26.49 | | (104) ~ (all_12_1 = e3)
% 154.55/26.49 | | (105) op(e1, e1) = all_12_1
% 154.55/26.49 | |
% 154.55/26.49 | | REF_CLOSE: (1), (53), (104), (105) are inconsistent by sub-proof #21.
% 154.55/26.49 | |
% 154.55/26.49 | End of split
% 154.55/26.49 |
% 154.55/26.49 End of proof
% 154.55/26.49
% 154.55/26.49 Sub-proof #21 shows that the following formulas are inconsistent:
% 154.55/26.49 ----------------------------------------------------------------
% 154.55/26.49 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.49 (2) op(e1, e1) = all_12_1
% 154.55/26.49 (3) op(e1, e1) = e3
% 154.55/26.49 (4) ~ (all_12_1 = e3)
% 154.55/26.49
% 154.55/26.49 Begin of proof
% 154.55/26.49 |
% 154.55/26.49 | GROUND_INST: instantiating (1) with e3, all_12_1, e1, e1, simplifying with
% 154.55/26.49 | (2), (3) gives:
% 154.55/26.49 | (5) all_12_1 = e3
% 154.55/26.49 |
% 154.55/26.49 | REDUCE: (4), (5) imply:
% 154.55/26.49 | (6) $false
% 154.55/26.49 |
% 154.55/26.49 | CLOSE: (6) is inconsistent.
% 154.55/26.49 |
% 154.55/26.49 End of proof
% 154.55/26.49
% 154.55/26.49 Sub-proof #22 shows that the following formulas are inconsistent:
% 154.55/26.49 ----------------------------------------------------------------
% 154.55/26.49 (1) ~ (all_10_2 = e1)
% 154.55/26.49 (2) all_56_12 = all_10_2
% 154.55/26.49 (3) all_54_0 = all_10_2
% 154.55/26.49 (4) ~ (all_10_2 = e0)
% 154.55/26.49 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.55/26.49 (6) ~ (all_56_12 = e3)
% 154.55/26.49 (7) ~ (all_10_2 = e2)
% 154.55/26.49
% 154.55/26.49 Begin of proof
% 154.55/26.49 |
% 154.55/26.49 | REDUCE: (2), (6) imply:
% 154.55/26.49 | (8) ~ (all_10_2 = e3)
% 154.55/26.49 |
% 154.55/26.49 | BETA: splitting (5) gives:
% 154.55/26.49 |
% 154.55/26.49 | Case 1:
% 154.55/26.49 | |
% 154.55/26.49 | | (9) all_54_0 = e3
% 154.55/26.49 | |
% 154.55/26.49 | | REF_CLOSE: (3), (8), (9) are inconsistent by sub-proof #50.
% 154.55/26.49 | |
% 154.55/26.49 | Case 2:
% 154.55/26.49 | |
% 154.55/26.49 | | (10) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.55/26.49 | |
% 154.55/26.49 | | REF_CLOSE: (1), (3), (4), (7), (10) are inconsistent by sub-proof #1307.
% 154.55/26.49 | |
% 154.55/26.49 | End of split
% 154.55/26.49 |
% 154.55/26.49 End of proof
% 154.55/26.49
% 154.55/26.49 Sub-proof #23 shows that the following formulas are inconsistent:
% 154.55/26.49 ----------------------------------------------------------------
% 154.55/26.49 (1) op(e1, e1) = e3
% 154.55/26.49 (2) all_58_12 = e2
% 154.55/26.49 (3) op(e3, e1) = e1
% 154.55/26.49 (4) all_56_14 = e3
% 154.55/26.49 (5) op(e0, e3) = all_52_3
% 154.55/26.49 (6) op(e3, e0) = all_52_12
% 154.55/26.49 (7) op(e1, e1) = all_8_1
% 154.55/26.49 (8) op(e1, e1) = all_6_2
% 154.55/26.49 (9) op(e3, e3) = all_36_1
% 154.55/26.49 (10) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 154.55/26.49 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.49 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.49 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.55/26.49 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.49 (13) all_54_1 = all_52_4
% 154.55/26.49 (14) op(e3, e2) = all_52_4
% 154.55/26.49 (15) ~ (all_52_3 = e0)
% 154.55/26.49 (16) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.49 (17) op(e2, e3) = all_52_1
% 154.55/26.49 (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 154.55/26.49 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 154.55/26.49 (19) ~ (e3 = e0)
% 154.55/26.49 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.49 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.49 (21) op(e1, e3) = all_52_2
% 154.55/26.49 (22) op(e2, e0) = all_52_13
% 154.55/26.49 (23) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 154.55/26.49 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 154.55/26.49 (24) ~ (e3 = e1)
% 154.55/26.49 (25) op(e1, e2) = all_52_6
% 154.55/26.49 (26) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 154.55/26.49 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3,
% 154.55/26.49 e3) = all_28_1 & $i(all_28_1))
% 154.55/26.49 (27) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.49 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.49 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.49 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.49 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.49 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.49 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.49 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.49 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.49 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.49 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.49 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.49 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.49 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.49 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.49 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.49 = e0)
% 154.55/26.49 (28) ~ (all_8_0 = e0)
% 154.55/26.49 (29) ~ (all_52_7 = e0)
% 154.55/26.49 (30) all_56_12 = e3
% 154.55/26.49 (31) ~ (all_52_13 = e2)
% 154.55/26.49 (32) ~ (all_52_4 = e1)
% 154.55/26.49 (33) ~ (all_52_6 = e1)
% 154.55/26.49 (34) ~ (all_52_4 = e3)
% 154.55/26.49 (35) all_58_15 = e1
% 154.55/26.49 (36) op(e3, e3) = e3
% 154.55/26.49 (37) ~ (e1 = e0)
% 154.55/26.49 (38) op(e1, e1) = all_12_1
% 154.55/26.49 (39) ~ (all_6_2 = e2)
% 154.55/26.49 (40) op(e0, e2) = all_52_7
% 154.55/26.49 (41) op(e0, e0) = e1
% 154.55/26.49 (42) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.49 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.49 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.49 (44) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 154.55/26.49 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.49 (45) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.49 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.49 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.49 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.49 (46) op(all_8_1, e2) = all_8_0
% 154.55/26.49 (47) op(e1, e1) = all_4_1
% 154.55/26.49 (48) all_58_2 = e0
% 154.55/26.49 (49) all_58_3 = e1
% 154.55/26.49 (50) ~ (all_52_1 = e3)
% 154.55/26.49
% 154.55/26.49 Begin of proof
% 154.55/26.49 |
% 154.55/26.49 | GROUND_INST: instantiating (43) with all_8_1, all_12_1, e1, e1, simplifying
% 154.55/26.49 | with (7), (38) gives:
% 154.55/26.49 | (51) all_12_1 = all_8_1
% 154.55/26.49 |
% 154.55/26.49 | GROUND_INST: instantiating (43) with all_4_1, all_12_1, e1, e1, simplifying
% 154.55/26.49 | with (38), (47) gives:
% 154.55/26.49 | (52) all_12_1 = all_4_1
% 154.55/26.49 |
% 154.55/26.49 | GROUND_INST: instantiating (43) with e3, all_12_1, e1, e1, simplifying with
% 154.55/26.49 | (1), (38) gives:
% 154.55/26.49 | (53) all_12_1 = e3
% 154.55/26.49 |
% 154.55/26.49 | GROUND_INST: instantiating (43) with e3, all_36_1, e3, e3, simplifying with
% 154.55/26.49 | (9), (36) gives:
% 154.55/26.49 | (54) all_36_1 = e3
% 154.55/26.49 |
% 154.55/26.49 | COMBINE_EQS: (51), (53) imply:
% 154.55/26.49 | (55) all_8_1 = e3
% 154.55/26.49 |
% 154.55/26.49 | COMBINE_EQS: (51), (52) imply:
% 154.55/26.49 | (56) all_8_1 = all_4_1
% 154.55/26.49 |
% 154.55/26.49 | COMBINE_EQS: (55), (56) imply:
% 154.55/26.49 | (57) all_4_1 = e3
% 154.55/26.49 |
% 154.55/26.49 | REDUCE: (46), (55) imply:
% 154.55/26.49 | (58) op(e3, e2) = all_8_0
% 154.55/26.49 |
% 154.55/26.49 | BETA: splitting (26) gives:
% 154.55/26.49 |
% 154.55/26.49 | Case 1:
% 154.55/26.49 | |
% 154.55/26.49 | | (59) ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 154.55/26.49 | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 154.55/26.49 | |
% 154.55/26.49 | | ALPHA: (59) implies:
% 154.55/26.49 | | (60) op(e3, e3) = all_28_1
% 154.55/26.49 | |
% 154.55/26.49 | | GROUND_INST: instantiating (43) with all_52_4, all_8_0, e2, e3, simplifying
% 154.55/26.49 | | with (14), (58) gives:
% 154.55/26.49 | | (61) all_52_4 = all_8_0
% 154.55/26.49 | |
% 154.55/26.49 | | GROUND_INST: instantiating (43) with e3, all_28_1, e3, e3, simplifying with
% 154.55/26.49 | | (36), (60) gives:
% 154.55/26.49 | | (62) all_28_1 = e3
% 154.55/26.49 | |
% 154.55/26.49 | | COMBINE_EQS: (13), (61) imply:
% 154.55/26.49 | | (63) all_54_1 = all_8_0
% 154.55/26.49 | |
% 154.55/26.49 | | REDUCE: (34), (61) imply:
% 154.55/26.49 | | (64) ~ (all_8_0 = e3)
% 154.55/26.49 | |
% 154.55/26.49 | | REDUCE: (32), (61) imply:
% 154.55/26.49 | | (65) ~ (all_8_0 = e1)
% 154.55/26.49 | |
% 154.55/26.49 | | BETA: splitting (16) gives:
% 154.55/26.49 | |
% 154.55/26.49 | | Case 1:
% 154.55/26.49 | | |
% 154.55/26.49 | | | (66) all_54_1 = e3
% 154.55/26.49 | | |
% 154.55/26.49 | | | COMBINE_EQS: (63), (66) imply:
% 154.55/26.49 | | | (67) all_8_0 = e3
% 154.55/26.49 | | |
% 154.55/26.49 | | | REDUCE: (64), (67) imply:
% 154.55/26.49 | | | (68) $false
% 154.55/26.49 | | |
% 154.55/26.49 | | | CLOSE: (68) is inconsistent.
% 154.55/26.49 | | |
% 154.55/26.49 | | Case 2:
% 154.55/26.49 | | |
% 154.55/26.49 | | | (69) ~ (all_54_1 = e3)
% 154.55/26.49 | | | (70) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.49 | | |
% 154.55/26.49 | | | BETA: splitting (70) gives:
% 154.55/26.49 | | |
% 154.55/26.49 | | | Case 1:
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | (71) all_54_1 = e2
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | COMBINE_EQS: (63), (71) imply:
% 154.55/26.49 | | | | (72) all_8_0 = e2
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | REDUCE: (64), (72) imply:
% 154.55/26.49 | | | | (73) ~ (e3 = e2)
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | SIMP: (73) implies:
% 154.55/26.49 | | | | (74) ~ (e3 = e2)
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | REDUCE: (65), (72) imply:
% 154.55/26.49 | | | | (75) ~ (e2 = e1)
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | REDUCE: (28), (72) imply:
% 154.55/26.49 | | | | (76) ~ (e2 = e0)
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | REDUCE: (58), (72) imply:
% 154.55/26.49 | | | | (77) op(e3, e2) = e2
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | BETA: splitting (23) gives:
% 154.55/26.49 | | | |
% 154.55/26.49 | | | | Case 1:
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | | (78) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 154.55/26.49 | | | | | e2) = e0)
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | | REF_CLOSE: (37), (43), (49), (76), (77), (78) are inconsistent by
% 154.55/26.49 | | | | | sub-proof #27.
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | Case 2:
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | | (79) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 154.55/26.49 | | | | | e2) = e0)
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | | BETA: splitting (79) gives:
% 154.55/26.49 | | | | |
% 154.55/26.49 | | | | | Case 1:
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | | (80) all_58_7 = e0 & op(e1, e2) = e0
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | | ALPHA: (80) implies:
% 154.55/26.49 | | | | | | (81) op(e1, e2) = e0
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | | BETA: splitting (18) gives:
% 154.55/26.49 | | | | | |
% 154.55/26.49 | | | | | | Case 1:
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | (82) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 154.55/26.49 | | | | | | | op(e1, e2) = e2)
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | REF_CLOSE: (2), (11), (19), (20), (24), (37), (43), (48), (74),
% 154.55/26.49 | | | | | | | (75), (76), (81), (82) are inconsistent by sub-proof
% 154.55/26.49 | | | | | | | #62.
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | Case 2:
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | (83) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 154.55/26.49 | | | | | | | op(e1, e0) = e2)
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | BETA: splitting (83) gives:
% 154.55/26.49 | | | | | | |
% 154.55/26.49 | | | | | | | Case 1:
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | (84) all_58_8 = e2 & op(e1, e1) = e2
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | REF_CLOSE: (8), (39), (43), (84) are inconsistent by sub-proof
% 154.55/26.49 | | | | | | | | #1440.
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | Case 2:
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | (85) all_58_11 = e2 & op(e1, e0) = e2
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | ALPHA: (85) implies:
% 154.55/26.49 | | | | | | | | (86) op(e1, e0) = e2
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | BETA: splitting (44) gives:
% 154.55/26.49 | | | | | | | |
% 154.55/26.49 | | | | | | | | Case 1:
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | (87) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 154.55/26.49 | | | | | | | | | op(e3, e2) = e0)
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | BETA: splitting (87) gives:
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | Case 1:
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | (88) all_58_0 = e0 & op(e3, e3) = e0
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | ALPHA: (88) implies:
% 154.55/26.49 | | | | | | | | | | (89) op(e3, e3) = e0
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | REF_CLOSE: (19), (36), (43), (89) are inconsistent by
% 154.55/26.49 | | | | | | | | | | sub-proof #1521.
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | Case 2:
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | (90) all_58_1 = e0 & op(e3, e2) = e0
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | ALPHA: (90) implies:
% 154.55/26.49 | | | | | | | | | | (91) op(e3, e2) = e0
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | REF_CLOSE: (43), (76), (77), (91) are inconsistent by
% 154.55/26.49 | | | | | | | | | | sub-proof #74.
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | End of split
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | Case 2:
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | (92) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 154.55/26.49 | | | | | | | | | op(e3, e0) = e0)
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | BETA: splitting (92) gives:
% 154.55/26.49 | | | | | | | | |
% 154.55/26.49 | | | | | | | | | Case 1:
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | (93) all_58_4 = e0 & op(e3, e1) = e0
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | ALPHA: (93) implies:
% 154.55/26.49 | | | | | | | | | | (94) op(e3, e1) = e0
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | | REF_CLOSE: (3), (37), (43), (94) are inconsistent by
% 154.55/26.49 | | | | | | | | | | sub-proof #1281.
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.49 | | | | | | | | | Case 2:
% 154.55/26.49 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | (95) all_58_9 = e0 & op(e3, e0) = e0
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | ALPHA: (95) implies:
% 154.55/26.50 | | | | | | | | | | (96) op(e3, e0) = e0
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (10), (11), (15), (17), (19),
% 154.55/26.50 | | | | | | | | | | (20), (21), (22), (24), (25), (27), (29), (30),
% 154.55/26.50 | | | | | | | | | | (31), (33), (35), (37), (40), (42), (43), (45),
% 154.55/26.50 | | | | | | | | | | (50), (74), (75), (76), (81), (86), (96) are
% 154.55/26.50 | | | | | | | | | | inconsistent by sub-proof #26.
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | End of split
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | End of split
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | End of split
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | End of split
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | Case 2:
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | (97) all_58_13 = e0 & op(e0, e2) = e0
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | ALPHA: (97) implies:
% 154.55/26.50 | | | | | | (98) op(e0, e2) = e0
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | REF_CLOSE: (29), (40), (43), (98) are inconsistent by sub-proof
% 154.55/26.50 | | | | | | #1532.
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | End of split
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | End of split
% 154.55/26.50 | | | |
% 154.55/26.50 | | | Case 2:
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | (99) all_54_1 = e1 | all_54_1 = e0
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | REF_CLOSE: (28), (63), (65), (99) are inconsistent by sub-proof #25.
% 154.55/26.50 | | | |
% 154.55/26.50 | | | End of split
% 154.55/26.50 | | |
% 154.55/26.50 | | End of split
% 154.55/26.50 | |
% 154.55/26.50 | Case 2:
% 154.55/26.50 | |
% 154.55/26.50 | | (100) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1)
% 154.55/26.50 | |
% 154.55/26.50 | | ALPHA: (100) implies:
% 154.55/26.50 | | (101) ~ (all_28_1 = e0)
% 154.55/26.50 | | (102) op(e3, e3) = all_28_1
% 154.55/26.50 | |
% 154.55/26.50 | | GROUND_INST: instantiating (43) with all_52_4, all_8_0, e2, e3, simplifying
% 154.55/26.50 | | with (14), (58) gives:
% 154.55/26.50 | | (103) all_52_4 = all_8_0
% 154.55/26.50 | |
% 154.55/26.50 | | GROUND_INST: instantiating (43) with e3, all_28_1, e3, e3, simplifying with
% 154.55/26.50 | | (36), (102) gives:
% 154.55/26.50 | | (104) all_28_1 = e3
% 154.55/26.50 | |
% 154.55/26.50 | | COMBINE_EQS: (13), (103) imply:
% 154.55/26.50 | | (105) all_54_1 = all_8_0
% 154.55/26.50 | |
% 154.55/26.50 | | REDUCE: (34), (103) imply:
% 154.55/26.50 | | (106) ~ (all_8_0 = e3)
% 154.55/26.50 | |
% 154.55/26.50 | | REDUCE: (32), (103) imply:
% 154.55/26.50 | | (107) ~ (all_8_0 = e1)
% 154.55/26.50 | |
% 154.55/26.50 | | BETA: splitting (16) gives:
% 154.55/26.50 | |
% 154.55/26.50 | | Case 1:
% 154.55/26.50 | | |
% 154.55/26.50 | | | (108) all_54_1 = e3
% 154.55/26.50 | | |
% 154.55/26.50 | | | COMBINE_EQS: (105), (108) imply:
% 154.55/26.50 | | | (109) all_8_0 = e3
% 154.55/26.50 | | |
% 154.55/26.50 | | | REDUCE: (106), (109) imply:
% 154.55/26.50 | | | (110) $false
% 154.55/26.50 | | |
% 154.55/26.50 | | | CLOSE: (110) is inconsistent.
% 154.55/26.50 | | |
% 154.55/26.50 | | Case 2:
% 154.55/26.50 | | |
% 154.55/26.50 | | | (111) ~ (all_54_1 = e3)
% 154.55/26.50 | | | (112) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.50 | | |
% 154.55/26.50 | | | BETA: splitting (112) gives:
% 154.55/26.50 | | |
% 154.55/26.50 | | | Case 1:
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | (113) all_54_1 = e2
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | COMBINE_EQS: (105), (113) imply:
% 154.55/26.50 | | | | (114) all_8_0 = e2
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | REDUCE: (106), (114) imply:
% 154.55/26.50 | | | | (115) ~ (e3 = e2)
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | SIMP: (115) implies:
% 154.55/26.50 | | | | (116) ~ (e3 = e2)
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | REDUCE: (107), (114) imply:
% 154.55/26.50 | | | | (117) ~ (e2 = e1)
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | REDUCE: (28), (114) imply:
% 154.55/26.50 | | | | (118) ~ (e2 = e0)
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | REDUCE: (58), (114) imply:
% 154.55/26.50 | | | | (119) op(e3, e2) = e2
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | BETA: splitting (23) gives:
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | Case 1:
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | (120) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 154.55/26.50 | | | | | e2) = e0)
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | REF_CLOSE: (37), (43), (49), (118), (119), (120) are inconsistent by
% 154.55/26.50 | | | | | sub-proof #27.
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | Case 2:
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | (121) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 154.55/26.50 | | | | | e2) = e0)
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | BETA: splitting (121) gives:
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | Case 1:
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | (122) all_58_7 = e0 & op(e1, e2) = e0
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | ALPHA: (122) implies:
% 154.55/26.50 | | | | | | (123) op(e1, e2) = e0
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | BETA: splitting (12) gives:
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | Case 1:
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | | (124) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 154.55/26.50 | | | | | | | op(e2, e0) = e2)
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | | BETA: splitting (124) gives:
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | | Case 1:
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | (125) all_58_9 = e2 & op(e3, e0) = e2
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | ALPHA: (125) implies:
% 154.55/26.50 | | | | | | | | (126) op(e3, e0) = e2
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | BETA: splitting (44) gives:
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | Case 1:
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | (127) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 154.55/26.50 | | | | | | | | | op(e3, e2) = e0)
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | REF_CLOSE: (43), (101), (102), (118), (119), (127) are
% 154.55/26.50 | | | | | | | | | inconsistent by sub-proof #24.
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | Case 2:
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | (128) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 154.55/26.50 | | | | | | | | | op(e3, e0) = e0)
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | REF_CLOSE: (3), (37), (43), (118), (126), (128) are
% 154.55/26.50 | | | | | | | | | inconsistent by sub-proof #1262.
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | End of split
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | Case 2:
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | (129) all_58_10 = e2 & op(e2, e0) = e2
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | ALPHA: (129) implies:
% 154.55/26.50 | | | | | | | | (130) op(e2, e0) = e2
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | REF_CLOSE: (22), (31), (43), (130) are inconsistent by sub-proof
% 154.55/26.50 | | | | | | | | #1535.
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | End of split
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | Case 2:
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | | (131) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 154.55/26.50 | | | | | | | op(e0, e0) = e2)
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | | BETA: splitting (131) gives:
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | | Case 1:
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | (132) all_58_11 = e2 & op(e1, e0) = e2
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | ALPHA: (132) implies:
% 154.55/26.50 | | | | | | | | (133) op(e1, e0) = e2
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | BETA: splitting (44) gives:
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | Case 1:
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | (134) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 154.55/26.50 | | | | | | | | | op(e3, e2) = e0)
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | REF_CLOSE: (43), (101), (102), (118), (119), (134) are
% 154.55/26.50 | | | | | | | | | inconsistent by sub-proof #24.
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | Case 2:
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | (135) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 154.55/26.50 | | | | | | | | | op(e3, e0) = e0)
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | BETA: splitting (135) gives:
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | | Case 1:
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | (136) all_58_4 = e0 & op(e3, e1) = e0
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | ALPHA: (136) implies:
% 154.55/26.50 | | | | | | | | | | (137) op(e3, e1) = e0
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | REF_CLOSE: (3), (37), (43), (137) are inconsistent by
% 154.55/26.50 | | | | | | | | | | sub-proof #1281.
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | Case 2:
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | (138) all_58_9 = e0 & op(e3, e0) = e0
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | ALPHA: (138) implies:
% 154.55/26.50 | | | | | | | | | | (139) op(e3, e0) = e0
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (10), (11), (15), (17), (19),
% 154.55/26.50 | | | | | | | | | | (20), (21), (22), (24), (25), (27), (29), (30),
% 154.55/26.50 | | | | | | | | | | (31), (33), (35), (37), (40), (42), (43), (45),
% 154.55/26.50 | | | | | | | | | | (50), (116), (117), (118), (123), (133), (139) are
% 154.55/26.50 | | | | | | | | | | inconsistent by sub-proof #26.
% 154.55/26.50 | | | | | | | | | |
% 154.55/26.50 | | | | | | | | | End of split
% 154.55/26.50 | | | | | | | | |
% 154.55/26.50 | | | | | | | | End of split
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | Case 2:
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | (140) all_58_15 = e2 & op(e0, e0) = e2
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | ALPHA: (140) implies:
% 154.55/26.50 | | | | | | | | (141) op(e0, e0) = e2
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | | REF_CLOSE: (41), (43), (117), (141) are inconsistent by
% 154.55/26.50 | | | | | | | | sub-proof #1386.
% 154.55/26.50 | | | | | | | |
% 154.55/26.50 | | | | | | | End of split
% 154.55/26.50 | | | | | | |
% 154.55/26.50 | | | | | | End of split
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | Case 2:
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | (142) all_58_13 = e0 & op(e0, e2) = e0
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | ALPHA: (142) implies:
% 154.55/26.50 | | | | | | (143) op(e0, e2) = e0
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | REF_CLOSE: (29), (40), (43), (143) are inconsistent by sub-proof
% 154.55/26.50 | | | | | | #1532.
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | End of split
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | End of split
% 154.55/26.50 | | | |
% 154.55/26.50 | | | Case 2:
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | (144) all_54_1 = e1 | all_54_1 = e0
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | REF_CLOSE: (28), (105), (107), (144) are inconsistent by sub-proof #25.
% 154.55/26.50 | | | |
% 154.55/26.50 | | | End of split
% 154.55/26.50 | | |
% 154.55/26.50 | | End of split
% 154.55/26.50 | |
% 154.55/26.50 | End of split
% 154.55/26.50 |
% 154.55/26.50 End of proof
% 154.55/26.50
% 154.55/26.50 Sub-proof #24 shows that the following formulas are inconsistent:
% 154.55/26.50 ----------------------------------------------------------------
% 154.55/26.50 (1) ~ (all_28_1 = e0)
% 154.55/26.50 (2) op(e3, e2) = e2
% 154.55/26.50 (3) op(e3, e3) = all_28_1
% 154.55/26.50 (4) ~ (e2 = e0)
% 154.55/26.50 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 154.55/26.50 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.50
% 154.55/26.50 Begin of proof
% 154.55/26.50 |
% 154.55/26.50 | BETA: splitting (5) gives:
% 154.55/26.50 |
% 154.55/26.50 | Case 1:
% 154.55/26.50 | |
% 154.55/26.50 | | (7) all_58_0 = e0 & op(e3, e3) = e0
% 154.55/26.50 | |
% 154.55/26.50 | | ALPHA: (7) implies:
% 154.55/26.50 | | (8) op(e3, e3) = e0
% 154.55/26.50 | |
% 154.55/26.50 | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #227.
% 154.55/26.50 | |
% 154.55/26.50 | Case 2:
% 154.55/26.50 | |
% 154.55/26.50 | | (9) all_58_1 = e0 & op(e3, e2) = e0
% 154.55/26.50 | |
% 154.55/26.50 | | ALPHA: (9) implies:
% 154.55/26.50 | | (10) op(e3, e2) = e0
% 154.55/26.50 | |
% 154.55/26.50 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #74.
% 154.55/26.50 | |
% 154.55/26.50 | End of split
% 154.55/26.50 |
% 154.55/26.50 End of proof
% 154.55/26.50
% 154.55/26.50 Sub-proof #25 shows that the following formulas are inconsistent:
% 154.55/26.50 ----------------------------------------------------------------
% 154.55/26.50 (1) all_54_1 = e1 | all_54_1 = e0
% 154.55/26.50 (2) all_54_1 = all_8_0
% 154.55/26.50 (3) ~ (all_8_0 = e1)
% 154.55/26.50 (4) ~ (all_8_0 = e0)
% 154.55/26.50
% 154.55/26.50 Begin of proof
% 154.55/26.50 |
% 154.55/26.50 | BETA: splitting (1) gives:
% 154.55/26.50 |
% 154.55/26.50 | Case 1:
% 154.55/26.50 | |
% 154.55/26.50 | | (5) all_54_1 = e1
% 154.55/26.50 | |
% 154.55/26.50 | | COMBINE_EQS: (2), (5) imply:
% 154.55/26.50 | | (6) all_8_0 = e1
% 154.55/26.50 | |
% 154.55/26.50 | | REDUCE: (3), (6) imply:
% 154.55/26.50 | | (7) $false
% 154.55/26.50 | |
% 154.55/26.50 | | CLOSE: (7) is inconsistent.
% 154.55/26.50 | |
% 154.55/26.50 | Case 2:
% 154.55/26.50 | |
% 154.55/26.50 | | (8) all_54_1 = e0
% 154.55/26.50 | |
% 154.55/26.50 | | COMBINE_EQS: (2), (8) imply:
% 154.55/26.50 | | (9) all_8_0 = e0
% 154.55/26.50 | |
% 154.55/26.50 | | REDUCE: (4), (9) imply:
% 154.55/26.50 | | (10) $false
% 154.55/26.50 | |
% 154.55/26.50 | | CLOSE: (10) is inconsistent.
% 154.55/26.50 | |
% 154.55/26.50 | End of split
% 154.55/26.50 |
% 154.55/26.50 End of proof
% 154.55/26.50
% 154.55/26.50 Sub-proof #26 shows that the following formulas are inconsistent:
% 154.55/26.50 ----------------------------------------------------------------
% 154.55/26.50 (1) all_58_12 = e2
% 154.55/26.50 (2) all_56_14 = e3
% 154.55/26.50 (3) op(e0, e3) = all_52_3
% 154.55/26.50 (4) op(e3, e0) = all_52_12
% 154.55/26.50 (5) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 154.55/26.50 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.50 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.50 (7) ~ (all_52_3 = e0)
% 154.55/26.50 (8) op(e1, e0) = e2
% 154.55/26.50 (9) op(e1, e2) = e0
% 154.55/26.50 (10) op(e2, e3) = all_52_1
% 154.55/26.50 (11) ~ (e3 = e0)
% 154.55/26.50 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.50 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.50 (13) ~ (e2 = e0)
% 154.55/26.50 (14) op(e3, e0) = e0
% 154.55/26.50 (15) op(e1, e3) = all_52_2
% 154.55/26.50 (16) op(e2, e0) = all_52_13
% 154.55/26.50 (17) ~ (e3 = e1)
% 154.55/26.50 (18) op(e1, e2) = all_52_6
% 154.55/26.50 (19) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.50 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.50 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.50 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.50 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.50 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.50 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.50 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.50 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.50 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.50 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.50 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.50 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.50 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.50 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.50 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.50 = e0)
% 154.55/26.50 (20) ~ (all_52_7 = e0)
% 154.55/26.50 (21) all_56_12 = e3
% 154.55/26.50 (22) ~ (all_52_13 = e2)
% 154.55/26.50 (23) ~ (all_52_6 = e1)
% 154.55/26.50 (24) all_58_15 = e1
% 154.55/26.50 (25) ~ (e2 = e1)
% 154.55/26.50 (26) ~ (e1 = e0)
% 154.55/26.50 (27) op(e0, e2) = all_52_7
% 154.55/26.50 (28) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.50 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.50 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.50 (30) ~ (e3 = e2)
% 154.55/26.50 (31) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.50 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.50 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.50 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.50 (32) ~ (all_52_1 = e3)
% 154.55/26.50
% 154.55/26.50 Begin of proof
% 154.55/26.50 |
% 154.55/26.50 | BETA: splitting (31) gives:
% 154.55/26.50 |
% 154.55/26.50 | Case 1:
% 154.55/26.50 | |
% 154.55/26.50 | | (33) all_58_15 = e0 & op(e0, e0) = e0
% 154.55/26.50 | |
% 154.55/26.50 | | REF_CLOSE: (24), (26), (33) are inconsistent by sub-proof #1410.
% 154.55/26.50 | |
% 154.55/26.50 | Case 2:
% 154.55/26.50 | |
% 154.55/26.50 | | (34) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 154.55/26.50 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 154.55/26.50 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 154.55/26.50 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 154.55/26.50 | |
% 154.55/26.50 | | ALPHA: (34) implies:
% 154.55/26.50 | | (35) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 154.55/26.50 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 154.55/26.50 | |
% 154.55/26.50 | | BETA: splitting (19) gives:
% 154.55/26.50 | |
% 154.55/26.50 | | Case 1:
% 154.55/26.50 | | |
% 154.55/26.50 | | | (36) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2)
% 154.55/26.50 | | | = e3 & op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~
% 154.55/26.50 | | | (all_56_12 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.50 | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1)
% 154.55/26.50 | | | = e3 & op(e1, e3) = e3) | (all_56_1 = e1 & all_56_6 = e1 & ~
% 154.55/26.50 | | | (all_56_12 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.50 | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0)
% 154.55/26.50 | | | = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 154.55/26.50 | | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.50 | | |
% 154.55/26.50 | | | BETA: splitting (36) gives:
% 154.55/26.50 | | |
% 154.55/26.50 | | | Case 1:
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | (37) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3,
% 154.55/26.50 | | | | e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2
% 154.55/26.50 | | | | & ~ (all_56_12 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.50 | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3,
% 154.55/26.50 | | | | e1) = e3 & op(e1, e3) = e3)
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | BETA: splitting (37) gives:
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | Case 1:
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | (38) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3,
% 154.55/26.50 | | | | | e2) = e3 & op(e2, e3) = e3
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | ALPHA: (38) implies:
% 154.55/26.50 | | | | | (39) op(e2, e3) = e3
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | REF_CLOSE: (10), (29), (32), (39) are inconsistent by sub-proof #1183.
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | Case 2:
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | (40) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3,
% 154.55/26.50 | | | | | e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 =
% 154.55/26.50 | | | | | e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 154.55/26.50 | | | | | e3)
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | BETA: splitting (40) gives:
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | Case 1:
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | (41) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3,
% 154.55/26.50 | | | | | | e2) = e2 & op(e2, e3) = e2
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | ALPHA: (41) implies:
% 154.55/26.50 | | | | | | (42) op(e2, e3) = e2
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | REF_CLOSE: (1), (6), (10), (11), (12), (13), (17), (25), (26), (28),
% 154.55/26.50 | | | | | | (29), (30), (42) are inconsistent by sub-proof #1062.
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | Case 2:
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | (43) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3,
% 154.55/26.50 | | | | | | e1) = e3 & op(e1, e3) = e3
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | ALPHA: (43) implies:
% 154.55/26.50 | | | | | | (44) op(e1, e3) = e3
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | | REF_CLOSE: (2), (5), (15), (17), (29), (44) are inconsistent by
% 154.55/26.50 | | | | | | sub-proof #144.
% 154.55/26.50 | | | | | |
% 154.55/26.50 | | | | | End of split
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | End of split
% 154.55/26.50 | | | |
% 154.55/26.50 | | | Case 2:
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | (45) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3,
% 154.55/26.50 | | | | e1) = e1 & op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3
% 154.55/26.50 | | | | & ~ (all_56_15 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.50 | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3,
% 154.55/26.50 | | | | e0) = e0 & op(e0, e3) = e0)
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | BETA: splitting (45) gives:
% 154.55/26.50 | | | |
% 154.55/26.50 | | | | Case 1:
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | (46) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3,
% 154.55/26.50 | | | | | e1) = e1 & op(e1, e3) = e1
% 154.55/26.50 | | | | |
% 154.55/26.50 | | | | | ALPHA: (46) implies:
% 154.55/26.50 | | | | | (47) ~ (all_56_12 = e3)
% 154.55/26.50 | | | | |
% 154.55/26.51 | | | | | REDUCE: (21), (47) imply:
% 154.55/26.51 | | | | | (48) $false
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | CLOSE: (48) is inconsistent.
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | Case 2:
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | (49) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3,
% 154.55/26.51 | | | | | e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 =
% 154.55/26.51 | | | | | e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 154.55/26.51 | | | | | e0)
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | REF_CLOSE: (3), (4), (7), (11), (14), (29), (49) are inconsistent by
% 154.55/26.51 | | | | | sub-proof #64.
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | End of split
% 154.55/26.51 | | | |
% 154.55/26.51 | | | End of split
% 154.55/26.51 | | |
% 154.55/26.51 | | Case 2:
% 154.55/26.51 | | |
% 154.55/26.51 | | | (50) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1)
% 154.55/26.51 | | | = e2 & op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~
% 154.55/26.51 | | | (all_56_13 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.51 | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0)
% 154.55/26.51 | | | = e2 & op(e0, e2) = e2) | (all_56_5 = e0 & all_56_10 = e0 & ~
% 154.55/26.51 | | | (all_56_13 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.55/26.51 | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0)
% 154.55/26.51 | | | = e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~
% 154.55/26.51 | | | (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.51 | | |
% 154.55/26.51 | | | BETA: splitting (50) gives:
% 154.55/26.51 | | |
% 154.55/26.51 | | | Case 1:
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | (51) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2,
% 154.55/26.51 | | | | e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1
% 154.55/26.51 | | | | & ~ (all_56_13 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.51 | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2,
% 154.55/26.51 | | | | e0) = e2 & op(e0, e2) = e2)
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | REF_CLOSE: (9), (13), (16), (18), (22), (23), (29), (51) are
% 154.55/26.51 | | | | inconsistent by sub-proof #132.
% 154.55/26.51 | | | |
% 154.55/26.51 | | | Case 2:
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | (52) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.51 | | | | e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 =
% 154.55/26.51 | | | | e1 & ~ (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 154.55/26.51 | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1,
% 154.55/26.51 | | | | e0) = e0 & op(e0, e1) = e0)
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | REF_CLOSE: (1), (8), (13), (20), (26), (27), (29), (35), (52) are
% 154.55/26.51 | | | | inconsistent by sub-proof #57.
% 154.55/26.51 | | | |
% 154.55/26.51 | | | End of split
% 154.55/26.51 | | |
% 154.55/26.51 | | End of split
% 154.55/26.51 | |
% 154.55/26.51 | End of split
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #27 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) op(e3, e2) = e2
% 154.55/26.51 (2) ~ (e2 = e0)
% 154.55/26.51 (3) ~ (e1 = e0)
% 154.55/26.51 (4) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 154.55/26.51 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.51 (6) all_58_3 = e1
% 154.55/26.51
% 154.55/26.51 Begin of proof
% 154.55/26.51 |
% 154.55/26.51 | BETA: splitting (4) gives:
% 154.55/26.51 |
% 154.55/26.51 | Case 1:
% 154.55/26.51 | |
% 154.55/26.51 | | (7) all_58_1 = e0 & op(e3, e2) = e0
% 154.55/26.51 | |
% 154.55/26.51 | | ALPHA: (7) implies:
% 154.55/26.51 | | (8) op(e3, e2) = e0
% 154.55/26.51 | |
% 154.55/26.51 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #74.
% 154.55/26.51 | |
% 154.55/26.51 | Case 2:
% 154.55/26.51 | |
% 154.55/26.51 | | (9) all_58_3 = e0 & op(e2, e2) = e0
% 154.55/26.51 | |
% 154.55/26.51 | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #203.
% 154.55/26.51 | |
% 154.55/26.51 | End of split
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #28 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) all_54_2 = all_52_8
% 154.55/26.51 (2) ~ (all_52_8 = e0)
% 154.55/26.51 (3) ~ (all_52_8 = e2)
% 154.55/26.51 (4) ~ (all_52_8 = e1)
% 154.55/26.51 (5) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.51
% 154.55/26.51 Begin of proof
% 154.55/26.51 |
% 154.55/26.51 | BETA: splitting (5) gives:
% 154.55/26.51 |
% 154.55/26.51 | Case 1:
% 154.55/26.51 | |
% 154.55/26.51 | | (6) all_54_2 = e2
% 154.55/26.51 | |
% 154.55/26.51 | | COMBINE_EQS: (1), (6) imply:
% 154.55/26.51 | | (7) all_52_8 = e2
% 154.55/26.51 | |
% 154.55/26.51 | | REDUCE: (3), (7) imply:
% 154.55/26.51 | | (8) $false
% 154.55/26.51 | |
% 154.55/26.51 | | CLOSE: (8) is inconsistent.
% 154.55/26.51 | |
% 154.55/26.51 | Case 2:
% 154.55/26.51 | |
% 154.55/26.51 | | (9) all_54_2 = e1 | all_54_2 = e0
% 154.55/26.51 | |
% 154.55/26.51 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #561.
% 154.55/26.51 | |
% 154.55/26.51 | End of split
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #29 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) all_56_14 = e3
% 154.55/26.51 (2) all_58_6 = e1
% 154.55/26.51 (3) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.51 (4) ~ (e3 = e1)
% 154.55/26.51 (5) all_56_13 = e2
% 154.55/26.51 (6) all_54_7 = all_52_13
% 154.55/26.51 (7) ~ (all_52_13 = e2)
% 154.55/26.51 (8) all_56_15 = all_4_2
% 154.55/26.51 (9) ~ (all_52_13 = all_4_2)
% 154.55/26.51 (10) ~ (e2 = e1)
% 154.55/26.51 (11) ~ (all_52_13 = e1)
% 154.55/26.51 (12) all_58_6 = e2 & op(e1, e3) = e2
% 154.55/26.51 (13) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.51
% 154.55/26.51 Begin of proof
% 154.55/26.51 |
% 154.55/26.51 | ALPHA: (12) implies:
% 154.55/26.51 | (14) all_58_6 = e2
% 154.55/26.51 |
% 154.55/26.51 | COMBINE_EQS: (2), (14) imply:
% 154.55/26.51 | (15) e2 = e1
% 154.55/26.51 |
% 154.55/26.51 | COMBINE_EQS: (5), (15) imply:
% 154.55/26.51 | (16) all_56_13 = e1
% 154.55/26.51 |
% 154.55/26.51 | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (13), (16) are
% 154.55/26.51 | inconsistent by sub-proof #136.
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #30 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.51 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.51 (2) all_58_6 = e2
% 154.55/26.51 (3) ~ (e3 = e0)
% 154.55/26.51 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.51 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.51 (5) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 154.55/26.51 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.51 (6) ~ (e2 = e0)
% 154.55/26.51 (7) ~ (e3 = e1)
% 154.55/26.51 (8) all_58_13 = e3
% 154.55/26.51 (9) ~ (all_24_1 = e2)
% 154.55/26.51 (10) op(e0, e1) = all_52_11
% 154.55/26.51 (11) ~ (e2 = e1)
% 154.55/26.51 (12) ~ (e1 = e0)
% 154.55/26.51 (13) op(e0, e1) = e0
% 154.55/26.51 (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.51 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.51 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.51 (16) ~ (e3 = e2)
% 154.55/26.51 (17) op(e0, e0) = all_24_1
% 154.55/26.51
% 154.55/26.51 Begin of proof
% 154.55/26.51 |
% 154.55/26.51 | BETA: splitting (5) gives:
% 154.55/26.51 |
% 154.55/26.51 | Case 1:
% 154.55/26.51 | |
% 154.55/26.51 | | (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 154.55/26.51 | | e2)
% 154.55/26.51 | |
% 154.55/26.51 | | BETA: splitting (18) gives:
% 154.55/26.51 | |
% 154.55/26.51 | | Case 1:
% 154.55/26.51 | | |
% 154.55/26.51 | | | (19) all_58_12 = e2 & op(e0, e3) = e2
% 154.55/26.51 | | |
% 154.55/26.51 | | | ALPHA: (19) implies:
% 154.55/26.51 | | | (20) all_58_12 = e2
% 154.55/26.51 | | |
% 154.55/26.51 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (11), (12), (14), (15), (16),
% 154.55/26.51 | | | (20) are inconsistent by sub-proof #1481.
% 154.55/26.51 | | |
% 154.55/26.51 | | Case 2:
% 154.55/26.51 | | |
% 154.55/26.51 | | | (21) all_58_13 = e2 & op(e0, e2) = e2
% 154.55/26.51 | | |
% 154.55/26.51 | | | ALPHA: (21) implies:
% 154.55/26.51 | | | (22) all_58_13 = e2
% 154.55/26.51 | | |
% 154.55/26.51 | | | REF_CLOSE: (8), (16), (22) are inconsistent by sub-proof #320.
% 154.55/26.51 | | |
% 154.55/26.51 | | End of split
% 154.55/26.51 | |
% 154.55/26.51 | Case 2:
% 154.55/26.51 | |
% 154.55/26.51 | | (23) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.51 | | e2)
% 154.55/26.51 | |
% 154.55/26.51 | | REF_CLOSE: (6), (9), (10), (13), (15), (17), (23) are inconsistent by
% 154.55/26.51 | | sub-proof #312.
% 154.55/26.51 | |
% 154.55/26.51 | End of split
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #31 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) ~ (all_10_0 = e0)
% 154.55/26.51 (2) ~ (all_10_0 = e3)
% 154.55/26.51 (3) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.51 (4) ~ (all_10_0 = e2)
% 154.55/26.51 (5) all_54_8 = all_10_0
% 154.55/26.51 (6) ~ (all_10_0 = e1)
% 154.55/26.51
% 154.55/26.51 Begin of proof
% 154.55/26.51 |
% 154.55/26.51 | BETA: splitting (3) gives:
% 154.55/26.51 |
% 154.55/26.51 | Case 1:
% 154.55/26.51 | |
% 154.55/26.51 | | (7) all_54_8 = e3
% 154.55/26.51 | |
% 154.55/26.51 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #32.
% 154.55/26.51 | |
% 154.55/26.51 | Case 2:
% 154.55/26.51 | |
% 154.55/26.51 | | (8) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.51 | |
% 154.55/26.51 | | REF_CLOSE: (1), (4), (5), (6), (8) are inconsistent by sub-proof #41.
% 154.55/26.51 | |
% 154.55/26.51 | End of split
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #32 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) all_54_8 = all_10_0
% 154.55/26.51 (2) all_54_8 = e3
% 154.55/26.51 (3) ~ (all_10_0 = e3)
% 154.55/26.51
% 154.55/26.51 Begin of proof
% 154.55/26.51 |
% 154.55/26.51 | COMBINE_EQS: (1), (2) imply:
% 154.55/26.51 | (4) all_10_0 = e3
% 154.55/26.51 |
% 154.55/26.51 | SIMP: (4) implies:
% 154.55/26.51 | (5) all_10_0 = e3
% 154.55/26.51 |
% 154.55/26.51 | REDUCE: (3), (5) imply:
% 154.55/26.51 | (6) $false
% 154.55/26.51 |
% 154.55/26.51 | CLOSE: (6) is inconsistent.
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #33 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) all_58_14 = e0
% 154.55/26.51 (2) ~ (e3 = e0)
% 154.55/26.51 (3) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 154.55/26.51 (4) ~ (e3 = e1)
% 154.55/26.51 (5) all_58_15 = e1
% 154.55/26.51
% 154.55/26.51 Begin of proof
% 154.55/26.51 |
% 154.55/26.51 | BETA: splitting (3) gives:
% 154.55/26.51 |
% 154.55/26.51 | Case 1:
% 154.55/26.51 | |
% 154.55/26.51 | | (6) all_58_14 = e3 & op(e0, e1) = e3
% 154.55/26.51 | |
% 154.55/26.51 | | ALPHA: (6) implies:
% 154.55/26.51 | | (7) all_58_14 = e3
% 154.55/26.51 | |
% 154.55/26.51 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #1444.
% 154.55/26.51 | |
% 154.55/26.51 | Case 2:
% 154.55/26.51 | |
% 154.55/26.51 | | (8) all_58_15 = e3 & op(e0, e0) = e3
% 154.55/26.51 | |
% 154.55/26.51 | | ALPHA: (8) implies:
% 154.55/26.51 | | (9) all_58_15 = e3
% 154.55/26.51 | |
% 154.55/26.51 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #1404.
% 154.55/26.51 | |
% 154.55/26.51 | End of split
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #34 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) op(e1, e3) = e0
% 154.55/26.51 (2) op(e3, e0) = all_52_12
% 154.55/26.51 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.51 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.51 (4) op(e3, e2) = all_52_4
% 154.55/26.51 (5) op(e2, e3) = all_52_1
% 154.55/26.51 (6) ~ (e3 = e0)
% 154.55/26.51 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.51 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.51 (8) ~ (e2 = e0)
% 154.55/26.51 (9) op(e3, e3) = e0
% 154.55/26.51 (10) all_58_6 = e0
% 154.55/26.51 (11) ~ (all_52_8 = e0)
% 154.55/26.51 (12) ~ (e3 = e1)
% 154.55/26.51 (13) ~ (all_52_4 = e0)
% 154.55/26.51 (14) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 154.55/26.51 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 154.55/26.51 (15) ~ (e2 = e1)
% 154.55/26.51 (16) ~ (e1 = e0)
% 154.55/26.51 (17) op(e3, e1) = all_52_8
% 154.55/26.51 (18) op(e3, e0) = e3
% 154.55/26.51 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.51 (20) ~ (e3 = e2)
% 154.55/26.51 (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 154.55/26.51 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.51
% 154.55/26.51 Begin of proof
% 154.55/26.51 |
% 154.55/26.51 | BETA: splitting (7) gives:
% 154.55/26.51 |
% 154.55/26.51 | Case 1:
% 154.55/26.51 | |
% 154.55/26.51 | | (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 154.55/26.51 | | e1)
% 154.55/26.51 | |
% 154.55/26.51 | | BETA: splitting (22) gives:
% 154.55/26.51 | |
% 154.55/26.51 | | Case 1:
% 154.55/26.51 | | |
% 154.55/26.51 | | | (23) all_58_0 = e1 & op(e3, e3) = e1
% 154.55/26.51 | | |
% 154.55/26.51 | | | ALPHA: (23) implies:
% 154.55/26.51 | | | (24) all_58_0 = e1
% 154.55/26.51 | | |
% 154.55/26.51 | | | REF_CLOSE: (2), (4), (6), (11), (13), (16), (17), (18), (19), (21), (24)
% 154.55/26.51 | | | are inconsistent by sub-proof #49.
% 154.55/26.51 | | |
% 154.55/26.51 | | Case 2:
% 154.55/26.51 | | |
% 154.55/26.51 | | | (25) all_58_2 = e1 & op(e2, e3) = e1
% 154.55/26.51 | | |
% 154.55/26.51 | | | ALPHA: (25) implies:
% 154.55/26.51 | | | (26) op(e2, e3) = e1
% 154.55/26.51 | | |
% 154.55/26.51 | | | BETA: splitting (3) gives:
% 154.55/26.51 | | |
% 154.55/26.51 | | | Case 1:
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | (27) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 154.55/26.51 | | | | = e3)
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | BETA: splitting (27) gives:
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | Case 1:
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | (28) all_58_0 = e3 & op(e3, e3) = e3
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | ALPHA: (28) implies:
% 154.55/26.51 | | | | | (29) op(e3, e3) = e3
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | REF_CLOSE: (6), (9), (19), (29) are inconsistent by sub-proof #1521.
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | Case 2:
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | (30) all_58_2 = e3 & op(e2, e3) = e3
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | ALPHA: (30) implies:
% 154.55/26.51 | | | | | (31) op(e2, e3) = e3
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | REF_CLOSE: (12), (19), (26), (31) are inconsistent by sub-proof #1494.
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | End of split
% 154.55/26.51 | | | |
% 154.55/26.51 | | | Case 2:
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | (32) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 154.55/26.51 | | | | = e3)
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (12), (13), (14),
% 154.55/26.51 | | | | (15), (16), (17), (18), (19), (20), (21), (32) are
% 154.55/26.51 | | | | inconsistent by sub-proof #35.
% 154.55/26.51 | | | |
% 154.55/26.51 | | | End of split
% 154.55/26.51 | | |
% 154.55/26.51 | | End of split
% 154.55/26.51 | |
% 154.55/26.51 | Case 2:
% 154.55/26.51 | |
% 154.55/26.51 | | (33) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 154.55/26.51 | | e1)
% 154.55/26.51 | |
% 154.55/26.51 | | BETA: splitting (33) gives:
% 154.55/26.51 | |
% 154.55/26.51 | | Case 1:
% 154.55/26.51 | | |
% 154.55/26.51 | | | (34) all_58_6 = e1 & op(e1, e3) = e1
% 154.55/26.51 | | |
% 154.55/26.51 | | | ALPHA: (34) implies:
% 154.55/26.51 | | | (35) all_58_6 = e1
% 154.55/26.51 | | |
% 154.55/26.51 | | | REF_CLOSE: (10), (16), (35) are inconsistent by sub-proof #735.
% 154.55/26.51 | | |
% 154.55/26.51 | | Case 2:
% 154.55/26.51 | | |
% 154.55/26.51 | | | (36) all_58_12 = e1 & op(e0, e3) = e1
% 154.55/26.51 | | |
% 154.55/26.51 | | | ALPHA: (36) implies:
% 154.55/26.51 | | | (37) all_58_12 = e1
% 154.55/26.51 | | |
% 154.55/26.51 | | | BETA: splitting (3) gives:
% 154.55/26.51 | | |
% 154.55/26.51 | | | Case 1:
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | (38) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 154.55/26.51 | | | | = e3)
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | BETA: splitting (38) gives:
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | Case 1:
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | (39) all_58_0 = e3 & op(e3, e3) = e3
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | ALPHA: (39) implies:
% 154.55/26.51 | | | | | (40) op(e3, e3) = e3
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | REF_CLOSE: (6), (9), (19), (40) are inconsistent by sub-proof #1521.
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | Case 2:
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | (41) all_58_2 = e3 & op(e2, e3) = e3
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | ALPHA: (41) implies:
% 154.55/26.51 | | | | | (42) op(e2, e3) = e3
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | BETA: splitting (21) gives:
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | | Case 1:
% 154.55/26.51 | | | | | |
% 154.55/26.51 | | | | | | (43) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 154.55/26.51 | | | | | | e2) = e0)
% 154.55/26.51 | | | | | |
% 154.55/26.51 | | | | | | BETA: splitting (43) gives:
% 154.55/26.51 | | | | | |
% 154.55/26.51 | | | | | | Case 1:
% 154.55/26.51 | | | | | | |
% 154.55/26.51 | | | | | | | (44) all_58_0 = e0 & op(e3, e3) = e0
% 154.55/26.51 | | | | | | |
% 154.55/26.51 | | | | | | | ALPHA: (44) implies:
% 154.55/26.51 | | | | | | | (45) all_58_0 = e0
% 154.55/26.51 | | | | | | |
% 154.55/26.51 | | | | | | | BETA: splitting (14) gives:
% 154.55/26.51 | | | | | | |
% 154.55/26.51 | | | | | | | Case 1:
% 154.55/26.51 | | | | | | | |
% 154.55/26.51 | | | | | | | | (46) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 &
% 154.55/26.51 | | | | | | | | op(e2, e3) = e2)
% 154.55/26.51 | | | | | | | |
% 154.55/26.51 | | | | | | | | REF_CLOSE: (5), (8), (19), (20), (42), (45), (46) are
% 154.55/26.51 | | | | | | | | inconsistent by sub-proof #304.
% 154.55/26.51 | | | | | | | |
% 154.55/26.51 | | | | | | | Case 2:
% 154.55/26.51 | | | | | | | |
% 154.55/26.51 | | | | | | | | (47) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 154.55/26.51 | | | | | | | | op(e0, e3) = e2)
% 154.55/26.51 | | | | | | | |
% 154.55/26.51 | | | | | | | | BETA: splitting (47) gives:
% 154.55/26.51 | | | | | | | |
% 154.55/26.51 | | | | | | | | Case 1:
% 154.55/26.51 | | | | | | | | |
% 154.55/26.51 | | | | | | | | | (48) all_58_6 = e2 & op(e1, e3) = e2
% 154.55/26.51 | | | | | | | | |
% 154.55/26.51 | | | | | | | | | REF_CLOSE: (8), (10), (48) are inconsistent by sub-proof #345.
% 154.55/26.51 | | | | | | | | |
% 154.55/26.51 | | | | | | | | Case 2:
% 154.55/26.51 | | | | | | | | |
% 154.55/26.51 | | | | | | | | | (49) all_58_12 = e2 & op(e0, e3) = e2
% 154.55/26.51 | | | | | | | | |
% 154.55/26.51 | | | | | | | | | REF_CLOSE: (15), (37), (49) are inconsistent by sub-proof
% 154.55/26.51 | | | | | | | | | #1511.
% 154.55/26.51 | | | | | | | | |
% 154.55/26.51 | | | | | | | | End of split
% 154.55/26.51 | | | | | | | |
% 154.55/26.51 | | | | | | | End of split
% 154.55/26.51 | | | | | | |
% 154.55/26.51 | | | | | | Case 2:
% 154.55/26.51 | | | | | | |
% 154.55/26.51 | | | | | | | (50) all_58_1 = e0 & op(e3, e2) = e0
% 154.55/26.51 | | | | | | |
% 154.55/26.51 | | | | | | | REF_CLOSE: (4), (13), (19), (50) are inconsistent by sub-proof
% 154.55/26.51 | | | | | | | #1221.
% 154.55/26.51 | | | | | | |
% 154.55/26.51 | | | | | | End of split
% 154.55/26.51 | | | | | |
% 154.55/26.51 | | | | | Case 2:
% 154.55/26.51 | | | | | |
% 154.55/26.51 | | | | | | (51) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 154.55/26.51 | | | | | | e0) = e0)
% 154.55/26.51 | | | | | |
% 154.55/26.51 | | | | | | REF_CLOSE: (2), (6), (11), (17), (18), (19), (51) are inconsistent
% 154.55/26.51 | | | | | | by sub-proof #257.
% 154.55/26.51 | | | | | |
% 154.55/26.51 | | | | | End of split
% 154.55/26.51 | | | | |
% 154.55/26.51 | | | | End of split
% 154.55/26.51 | | | |
% 154.55/26.51 | | | Case 2:
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | (52) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 154.55/26.51 | | | | = e3)
% 154.55/26.51 | | | |
% 154.55/26.51 | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (12), (13), (14),
% 154.55/26.51 | | | | (15), (16), (17), (18), (19), (20), (21), (52) are
% 154.55/26.51 | | | | inconsistent by sub-proof #35.
% 154.55/26.51 | | | |
% 154.55/26.51 | | | End of split
% 154.55/26.51 | | |
% 154.55/26.51 | | End of split
% 154.55/26.51 | |
% 154.55/26.51 | End of split
% 154.55/26.51 |
% 154.55/26.51 End of proof
% 154.55/26.51
% 154.55/26.51 Sub-proof #35 shows that the following formulas are inconsistent:
% 154.55/26.51 ----------------------------------------------------------------
% 154.55/26.51 (1) op(e1, e3) = e0
% 154.55/26.52 (2) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.52 (3) op(e3, e0) = all_52_12
% 154.55/26.52 (4) op(e3, e2) = all_52_4
% 154.55/26.52 (5) ~ (e3 = e0)
% 154.55/26.52 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.52 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.52 (7) ~ (e2 = e0)
% 154.55/26.52 (8) all_58_6 = e0
% 154.55/26.52 (9) ~ (all_52_8 = e0)
% 154.55/26.52 (10) ~ (e3 = e1)
% 154.55/26.52 (11) ~ (all_52_4 = e0)
% 154.55/26.52 (12) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 154.55/26.52 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 154.55/26.52 (13) ~ (e2 = e1)
% 154.55/26.52 (14) ~ (e1 = e0)
% 154.55/26.52 (15) op(e3, e1) = all_52_8
% 154.55/26.52 (16) op(e3, e0) = e3
% 154.55/26.52 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.52 (18) ~ (e3 = e2)
% 154.55/26.52 (19) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 154.55/26.52 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.52
% 154.55/26.52 Begin of proof
% 154.55/26.52 |
% 154.55/26.52 | BETA: splitting (2) gives:
% 154.55/26.52 |
% 154.55/26.52 | Case 1:
% 154.55/26.52 | |
% 154.55/26.52 | | (20) all_58_6 = e3 & op(e1, e3) = e3
% 154.55/26.52 | |
% 154.55/26.52 | | ALPHA: (20) implies:
% 154.55/26.52 | | (21) op(e1, e3) = e3
% 154.55/26.52 | |
% 154.55/26.52 | | REF_CLOSE: (1), (5), (17), (21) are inconsistent by sub-proof #114.
% 154.55/26.52 | |
% 154.55/26.52 | Case 2:
% 154.55/26.52 | |
% 154.55/26.52 | | (22) all_58_12 = e3 & op(e0, e3) = e3
% 154.55/26.52 | |
% 154.55/26.52 | | ALPHA: (22) implies:
% 154.55/26.52 | | (23) all_58_12 = e3
% 154.55/26.52 | |
% 154.55/26.52 | | BETA: splitting (19) gives:
% 154.55/26.52 | |
% 154.55/26.52 | | Case 1:
% 154.55/26.52 | | |
% 154.55/26.52 | | | (24) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 154.55/26.52 | | | e0)
% 154.55/26.52 | | |
% 154.55/26.52 | | | BETA: splitting (24) gives:
% 154.55/26.52 | | |
% 154.55/26.52 | | | Case 1:
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | (25) all_58_0 = e0 & op(e3, e3) = e0
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | ALPHA: (25) implies:
% 154.55/26.52 | | | | (26) all_58_0 = e0
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | BETA: splitting (12) gives:
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | Case 1:
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | (27) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 154.55/26.52 | | | | | e3) = e2)
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | BETA: splitting (27) gives:
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | Case 1:
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | (28) all_58_0 = e2 & op(e3, e3) = e2
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | REF_CLOSE: (7), (26), (28) are inconsistent by sub-proof #702.
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | Case 2:
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | (29) all_58_2 = e2 & op(e2, e3) = e2
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | ALPHA: (29) implies:
% 154.55/26.52 | | | | | | (30) op(e2, e3) = e2
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | REF_CLOSE: (6), (8), (10), (13), (14), (17), (23), (26), (30) are
% 154.55/26.52 | | | | | | inconsistent by sub-proof #733.
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | End of split
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | Case 2:
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | (31) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0,
% 154.55/26.52 | | | | | e3) = e2)
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | BETA: splitting (31) gives:
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | Case 1:
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | (32) all_58_6 = e2 & op(e1, e3) = e2
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | REF_CLOSE: (7), (8), (32) are inconsistent by sub-proof #345.
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | Case 2:
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | (33) all_58_12 = e2 & op(e0, e3) = e2
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | REF_CLOSE: (18), (23), (33) are inconsistent by sub-proof #1451.
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | End of split
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | End of split
% 154.55/26.52 | | | |
% 154.55/26.52 | | | Case 2:
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | (34) all_58_1 = e0 & op(e3, e2) = e0
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | REF_CLOSE: (4), (11), (17), (34) are inconsistent by sub-proof #1221.
% 154.55/26.52 | | | |
% 154.55/26.52 | | | End of split
% 154.55/26.52 | | |
% 154.55/26.52 | | Case 2:
% 154.55/26.52 | | |
% 154.55/26.52 | | | (35) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 154.55/26.52 | | | e0)
% 154.55/26.52 | | |
% 154.55/26.52 | | | REF_CLOSE: (3), (5), (9), (15), (16), (17), (35) are inconsistent by
% 154.55/26.52 | | | sub-proof #257.
% 154.55/26.52 | | |
% 154.55/26.52 | | End of split
% 154.55/26.52 | |
% 154.55/26.52 | End of split
% 154.55/26.52 |
% 154.55/26.52 End of proof
% 154.55/26.52
% 154.55/26.52 Sub-proof #36 shows that the following formulas are inconsistent:
% 154.55/26.52 ----------------------------------------------------------------
% 154.55/26.52 (1) ~ (all_52_3 = e1)
% 154.55/26.52 (2) op(e0, e3) = all_52_3
% 154.55/26.52 (3) op(e3, e0) = all_52_12
% 154.55/26.52 (4) op(e1, e1) = all_6_2
% 154.55/26.52 (5) all_58_12 = e2 & op(e0, e3) = e2
% 154.55/26.52 (6) all_54_10 = all_6_2
% 154.55/26.52 (7) ~ (all_10_0 = e0)
% 154.55/26.52 (8) all_58_14 = e0
% 154.55/26.52 (9) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.52 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.52 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.52 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.55/26.52 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.52 (12) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 154.55/26.52 (13) all_54_1 = all_52_4
% 154.55/26.52 (14) op(e3, e2) = all_52_4
% 154.55/26.52 (15) ~ (all_52_3 = e0)
% 154.55/26.52 (16) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.52 (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 154.55/26.52 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 154.55/26.52 (18) ~ (all_10_0 = e2)
% 154.55/26.52 (19) op(e2, e1) = all_52_9
% 154.55/26.52 (20) op(e2, e3) = all_52_1
% 154.55/26.52 (21) ~ (all_52_3 = all_10_0)
% 154.55/26.52 (22) ~ (all_52_1 = all_52_3)
% 154.55/26.52 (23) all_54_2 = all_52_8
% 154.55/26.52 (24) ~ (all_52_1 = all_10_0)
% 154.55/26.52 (25) ~ (all_52_8 = all_52_9)
% 154.55/26.52 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.52 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.52 (27) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 154.55/26.52 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.52 e2)
% 154.55/26.52 (28) ~ (e2 = e0)
% 154.55/26.52 (29) all_58_9 = e3
% 154.55/26.52 (30) ~ (all_52_8 = e0)
% 154.55/26.52 (31) ~ (all_52_6 = all_6_2)
% 154.55/26.52 (32) op(e2, e0) = all_52_13
% 154.55/26.52 (33) ~ (all_52_6 = all_10_0)
% 154.55/26.52 (34) op(e1, e2) = all_52_6
% 154.55/26.52 (35) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.52 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.52 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.52 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.52 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.52 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.52 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.52 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.52 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.52 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.52 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.52 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.52 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.52 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.52 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.52 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.52 = e0)
% 154.55/26.52 (36) all_54_4 = all_52_1
% 154.55/26.52 (37) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.52 (38) ~ (all_52_4 = e0)
% 154.55/26.52 (39) ~ (all_52_7 = e0)
% 154.55/26.52 (40) ~ (all_6_2 = e3)
% 154.55/26.52 (41) all_54_8 = all_10_0
% 154.55/26.52 (42) ~ (all_6_2 = e0)
% 154.55/26.52 (43) op(e0, e1) = all_52_11
% 154.55/26.52 (44) ~ (all_52_4 = e3)
% 154.55/26.52 (45) ~ (all_52_8 = all_6_2)
% 154.55/26.52 (46) all_58_15 = e1
% 154.55/26.52 (47) ~ (e2 = e1)
% 154.55/26.52 (48) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.55/26.52 (49) ~ (e1 = e0)
% 154.55/26.52 (50) op(e0, e1) = e0
% 154.55/26.52 (51) ~ (all_52_1 = e0)
% 154.55/26.52 (52) op(e3, e1) = all_52_8
% 154.55/26.52 (53) ~ (all_6_2 = e2)
% 154.55/26.52 (54) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 154.55/26.52 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 154.55/26.52 e3)
% 154.55/26.52 (55) all_56_14 = all_6_2
% 154.55/26.52 (56) op(e3, e0) = e3
% 154.55/26.52 (57) ~ (all_52_8 = e3)
% 154.55/26.52 (58) op(e0, e2) = all_52_7
% 154.55/26.52 (59) ~ (all_10_0 = e1)
% 154.55/26.52 (60) op(e0, e0) = e1
% 154.55/26.52 (61) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.52 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.52 (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.52 (63) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.52 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.52 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.52 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.52 (64) ~ (all_10_0 = all_6_2)
% 154.55/26.52 (65) ~ (all_52_4 = all_52_8)
% 154.55/26.52 (66) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.52 (67) all_54_12 = all_52_3
% 154.55/26.52 (68) ~ (all_52_3 = all_52_7)
% 154.55/26.52
% 154.55/26.52 Begin of proof
% 154.55/26.52 |
% 154.55/26.52 | ALPHA: (5) implies:
% 154.55/26.52 | (69) all_58_12 = e2
% 154.55/26.52 |
% 154.55/26.52 | BETA: splitting (48) gives:
% 154.55/26.52 |
% 154.55/26.52 | Case 1:
% 154.55/26.52 | |
% 154.55/26.52 | | (70) all_54_10 = e3
% 154.55/26.52 | |
% 154.55/26.52 | | REF_CLOSE: (6), (40), (70) are inconsistent by sub-proof #1531.
% 154.55/26.52 | |
% 154.55/26.52 | Case 2:
% 154.55/26.52 | |
% 154.55/26.52 | | (71) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.55/26.52 | |
% 154.55/26.52 | | BETA: splitting (71) gives:
% 154.55/26.52 | |
% 154.55/26.52 | | Case 1:
% 154.55/26.52 | | |
% 154.55/26.52 | | | (72) all_54_10 = e2
% 154.55/26.52 | | |
% 154.55/26.52 | | | REF_CLOSE: (6), (53), (72) are inconsistent by sub-proof #1530.
% 154.55/26.52 | | |
% 154.55/26.52 | | Case 2:
% 154.55/26.52 | | |
% 154.55/26.52 | | | (73) all_54_10 = e1 | all_54_10 = e0
% 154.55/26.52 | | |
% 154.55/26.52 | | | BETA: splitting (9) gives:
% 154.55/26.52 | | |
% 154.55/26.52 | | | Case 1:
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | (74) all_54_8 = e3
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | COMBINE_EQS: (41), (74) imply:
% 154.55/26.52 | | | | (75) all_10_0 = e3
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | SIMP: (75) implies:
% 154.55/26.52 | | | | (76) all_10_0 = e3
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | REDUCE: (24), (76) imply:
% 154.55/26.52 | | | | (77) ~ (all_52_1 = e3)
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | REDUCE: (21), (76) imply:
% 154.55/26.52 | | | | (78) ~ (all_52_3 = e3)
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | REDUCE: (33), (76) imply:
% 154.55/26.52 | | | | (79) ~ (all_52_6 = e3)
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | REDUCE: (64), (76) imply:
% 154.55/26.52 | | | | (80) ~ (all_6_2 = e3)
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | REDUCE: (18), (76) imply:
% 154.55/26.52 | | | | (81) ~ (e3 = e2)
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | REDUCE: (59), (76) imply:
% 154.55/26.52 | | | | (82) ~ (e3 = e1)
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | REDUCE: (7), (76) imply:
% 154.55/26.52 | | | | (83) ~ (e3 = e0)
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | BETA: splitting (54) gives:
% 154.55/26.52 | | | |
% 154.55/26.52 | | | | Case 1:
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | (84) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 154.55/26.52 | | | | | e2) = e3)
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | BETA: splitting (84) gives:
% 154.55/26.52 | | | | |
% 154.55/26.52 | | | | | Case 1:
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | (85) all_58_12 = e3 & op(e0, e3) = e3
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | ALPHA: (85) implies:
% 154.55/26.52 | | | | | | (86) all_58_12 = e3
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | REF_CLOSE: (69), (81), (86) are inconsistent by sub-proof #1490.
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | Case 2:
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | (87) all_58_13 = e3 & op(e0, e2) = e3
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | ALPHA: (87) implies:
% 154.55/26.52 | | | | | | (88) all_58_13 = e3
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | BETA: splitting (17) gives:
% 154.55/26.52 | | | | | |
% 154.55/26.52 | | | | | | Case 1:
% 154.55/26.52 | | | | | | |
% 154.55/26.52 | | | | | | | (89) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 154.55/26.52 | | | | | | | op(e1, e2) = e3)
% 154.55/26.52 | | | | | | |
% 154.55/26.52 | | | | | | | BETA: splitting (89) gives:
% 154.55/26.52 | | | | | | |
% 154.55/26.52 | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | |
% 154.55/26.52 | | | | | | | | (90) all_58_6 = e3 & op(e1, e3) = e3
% 154.55/26.52 | | | | | | | |
% 154.55/26.52 | | | | | | | | ALPHA: (90) implies:
% 154.55/26.52 | | | | | | | | (91) all_58_6 = e3
% 154.55/26.52 | | | | | | | |
% 154.55/26.52 | | | | | | | | BETA: splitting (73) gives:
% 154.55/26.52 | | | | | | | |
% 154.55/26.52 | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | |
% 154.55/26.52 | | | | | | | | | (92) all_54_10 = e1
% 154.55/26.52 | | | | | | | | |
% 154.55/26.52 | | | | | | | | | COMBINE_EQS: (6), (92) imply:
% 154.55/26.52 | | | | | | | | | (93) all_6_2 = e1
% 154.55/26.52 | | | | | | | | |
% 154.55/26.52 | | | | | | | | | SIMP: (93) implies:
% 154.55/26.52 | | | | | | | | | (94) all_6_2 = e1
% 154.55/26.52 | | | | | | | | |
% 154.55/26.52 | | | | | | | | | COMBINE_EQS: (55), (94) imply:
% 154.55/26.52 | | | | | | | | | (95) all_56_14 = e1
% 154.55/26.52 | | | | | | | | |
% 154.55/26.52 | | | | | | | | | REDUCE: (31), (94) imply:
% 154.55/26.52 | | | | | | | | | (96) ~ (all_52_6 = e1)
% 154.55/26.52 | | | | | | | | |
% 154.55/26.52 | | | | | | | | | REDUCE: (45), (94) imply:
% 154.55/26.52 | | | | | | | | | (97) ~ (all_52_8 = e1)
% 154.55/26.52 | | | | | | | | |
% 154.55/26.52 | | | | | | | | | BETA: splitting (37) gives:
% 154.55/26.52 | | | | | | | | |
% 154.55/26.52 | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | (98) all_54_2 = e3
% 154.55/26.52 | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | COMBINE_EQS: (23), (98) imply:
% 154.55/26.52 | | | | | | | | | | (99) all_52_8 = e3
% 154.55/26.52 | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | REDUCE: (57), (99) imply:
% 154.55/26.52 | | | | | | | | | | (100) $false
% 154.55/26.52 | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | CLOSE: (100) is inconsistent.
% 154.55/26.52 | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | Case 2:
% 154.55/26.52 | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | (101) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.52 | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | BETA: splitting (101) gives:
% 154.55/26.52 | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | (102) all_54_2 = e2
% 154.55/26.52 | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | COMBINE_EQS: (23), (102) imply:
% 154.55/26.52 | | | | | | | | | | | (103) all_52_8 = e2
% 154.55/26.52 | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | REDUCE: (65), (103) imply:
% 154.55/26.52 | | | | | | | | | | | (104) ~ (all_52_4 = e2)
% 154.55/26.52 | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | REDUCE: (25), (103) imply:
% 154.55/26.52 | | | | | | | | | | | (105) ~ (all_52_9 = e2)
% 154.55/26.52 | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | SIMP: (105) implies:
% 154.55/26.52 | | | | | | | | | | | (106) ~ (all_52_9 = e2)
% 154.55/26.52 | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | REDUCE: (52), (103) imply:
% 154.55/26.52 | | | | | | | | | | | (107) op(e3, e1) = e2
% 154.55/26.52 | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | BETA: splitting (16) gives:
% 154.55/26.52 | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | (108) all_54_1 = e3
% 154.55/26.52 | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | COMBINE_EQS: (13), (108) imply:
% 154.55/26.52 | | | | | | | | | | | | (109) all_52_4 = e3
% 154.55/26.52 | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | REDUCE: (44), (109) imply:
% 154.55/26.52 | | | | | | | | | | | | (110) $false
% 154.55/26.52 | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | CLOSE: (110) is inconsistent.
% 154.55/26.52 | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | Case 2:
% 154.55/26.52 | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | (111) ~ (all_54_1 = e3)
% 154.55/26.52 | | | | | | | | | | | | (112) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.52 | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | BETA: splitting (112) gives:
% 154.55/26.52 | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | (113) all_54_1 = e2
% 154.55/26.52 | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | COMBINE_EQS: (13), (113) imply:
% 154.55/26.52 | | | | | | | | | | | | | (114) all_52_4 = e2
% 154.55/26.52 | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | REDUCE: (104), (114) imply:
% 154.55/26.52 | | | | | | | | | | | | | (115) $false
% 154.55/26.52 | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 154.55/26.52 | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | Case 2:
% 154.55/26.52 | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | (116) ~ (all_54_1 = e2)
% 154.55/26.52 | | | | | | | | | | | | | (117) all_54_1 = e1 | all_54_1 = e0
% 154.55/26.52 | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | BETA: splitting (66) gives:
% 154.55/26.52 | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | (118) all_54_12 = e3
% 154.55/26.52 | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | REF_CLOSE: (67), (78), (118) are inconsistent by sub-proof
% 154.55/26.52 | | | | | | | | | | | | | | #1234.
% 154.55/26.52 | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | Case 2:
% 154.55/26.52 | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | (119) ~ (all_54_12 = e3)
% 154.55/26.52 | | | | | | | | | | | | | | (120) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.52 | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 154.55/26.52 | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | (121) all_54_12 = e2
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | COMBINE_EQS: (67), (121) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | (122) all_52_3 = e2
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | SIMP: (122) implies:
% 154.55/26.52 | | | | | | | | | | | | | | | (123) all_52_3 = e2
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | REDUCE: (22), (123) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | (124) ~ (all_52_1 = e2)
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | REDUCE: (68), (123) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | (125) ~ (all_52_7 = e2)
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | SIMP: (125) implies:
% 154.55/26.52 | | | | | | | | | | | | | | | (126) ~ (all_52_7 = e2)
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | REDUCE: (78), (123) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | (127) ~ (e3 = e2)
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | REDUCE: (2), (123) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | (128) op(e0, e3) = e2
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 154.55/26.52 | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | (129) all_54_4 = e3
% 154.55/26.52 | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (129) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | | (130) all_52_1 = e3
% 154.55/26.52 | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | REDUCE: (77), (130) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | | (131) $false
% 154.55/26.52 | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 154.55/26.52 | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | Case 2:
% 154.55/26.52 | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | (132) ~ (all_54_4 = e3)
% 154.55/26.52 | | | | | | | | | | | | | | | | (133) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 154.55/26.52 | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 154.55/26.52 | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | (134) all_54_4 = e2
% 154.55/26.52 | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (134) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | | | (135) all_52_1 = e2
% 154.55/26.52 | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | REDUCE: (124), (135) imply:
% 154.55/26.52 | | | | | | | | | | | | | | | | | (136) $false
% 154.55/26.52 | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 154.55/26.52 | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.52 | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | (137) all_54_4 = e1 | all_54_4 = e0
% 154.55/26.52 | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 154.55/26.52 | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | (138) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.52 | | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 154.55/26.52 | | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.52 | | | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | (139) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.52 | | | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (36), (51), (62), (77), (81), (104),
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | (107), (137), (139) are inconsistent by sub-proof
% 154.55/26.52 | | | | | | | | | | | | | | | | | | | #39.
% 154.55/26.52 | | | | | | | | | | | | | | | | | | |
% 154.55/26.52 | | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.52 | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | (140) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.53 | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | (141) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | (142) op(e3, e1) = e1
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (62), (107), (142) are inconsistent by
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | (143) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | (144) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | (145) op(e0, e3) = e3
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (146) all_54_1 = e1
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (146) imply:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (147) all_52_4 = e1
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (147) imply:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (148) ~ (e3 = e1)
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (147) imply:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (149) ~ (e2 = e1)
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with e2, e3, e3, e0,
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | simplifying with (128), (145) gives:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (150) e3 = e2
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (150) imply:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (151) all_58_6 = e2
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (26), (27), (28), (43), (47), (49), (50),
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (60), (61), (62), (81), (82), (83), (88), (151)
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #45.
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (152) all_54_1 = e0
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (152) imply:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (153) all_52_4 = e0
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (153) imply:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | (154) $false
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | (155) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | (156) op(e0, e3) = e0
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (62), (156) are inconsistent by
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | | sub-proof #89.
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.53 | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | (157) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.53 | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.53 | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (34), (39), (49), (50), (58), (62), (95),
% 154.55/26.53 | | | | | | | | | | | | | | | | | | (96), (106), (126), (157) are inconsistent by
% 154.55/26.53 | | | | | | | | | | | | | | | | | | sub-proof #37.
% 154.55/26.53 | | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | Case 2:
% 154.55/26.53 | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | (158) all_54_12 = e1 | all_54_12 = e0
% 154.55/26.53 | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | | REF_CLOSE: (1), (15), (67), (158) are inconsistent by
% 154.55/26.53 | | | | | | | | | | | | | | | sub-proof #1222.
% 154.55/26.53 | | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | Case 2:
% 154.55/26.53 | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | (159) all_54_2 = e1 | all_54_2 = e0
% 154.55/26.53 | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | | REF_CLOSE: (23), (30), (97), (159) are inconsistent by
% 154.55/26.53 | | | | | | | | | | | sub-proof #561.
% 154.55/26.53 | | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | | |
% 154.55/26.53 | | | | | | | | | End of split
% 154.55/26.53 | | | | | | | | |
% 154.55/26.53 | | | | | | | | Case 2:
% 154.55/26.53 | | | | | | | | |
% 154.55/26.53 | | | | | | | | | (160) all_54_10 = e0
% 154.55/26.53 | | | | | | | | |
% 154.55/26.53 | | | | | | | | | REF_CLOSE: (6), (42), (160) are inconsistent by sub-proof
% 154.55/26.53 | | | | | | | | | #1528.
% 154.55/26.53 | | | | | | | | |
% 154.55/26.53 | | | | | | | | End of split
% 154.55/26.53 | | | | | | | |
% 154.55/26.53 | | | | | | | Case 2:
% 154.55/26.53 | | | | | | | |
% 154.55/26.53 | | | | | | | | (161) all_58_7 = e3 & op(e1, e2) = e3
% 154.55/26.53 | | | | | | | |
% 154.55/26.53 | | | | | | | | REF_CLOSE: (34), (62), (79), (161) are inconsistent by sub-proof
% 154.55/26.53 | | | | | | | | #1184.
% 154.55/26.53 | | | | | | | |
% 154.55/26.53 | | | | | | | End of split
% 154.55/26.53 | | | | | | |
% 154.55/26.53 | | | | | | Case 2:
% 154.55/26.53 | | | | | | |
% 154.55/26.53 | | | | | | | (162) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 154.55/26.53 | | | | | | | op(e1, e0) = e3)
% 154.55/26.53 | | | | | | |
% 154.55/26.53 | | | | | | | REF_CLOSE: (3), (4), (11), (28), (29), (32), (40), (46), (47),
% 154.55/26.53 | | | | | | | (49), (56), (60), (62), (63), (81), (83), (162) are
% 154.55/26.53 | | | | | | | inconsistent by sub-proof #46.
% 154.55/26.53 | | | | | | |
% 154.55/26.53 | | | | | | End of split
% 154.55/26.53 | | | | | |
% 154.55/26.53 | | | | | End of split
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | Case 2:
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | | (163) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 154.55/26.53 | | | | | e0) = e3)
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | | REF_CLOSE: (8), (46), (82), (83), (163) are inconsistent by sub-proof
% 154.55/26.53 | | | | | #44.
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | End of split
% 154.55/26.53 | | | |
% 154.55/26.53 | | | Case 2:
% 154.55/26.53 | | | |
% 154.55/26.53 | | | | (164) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.53 | | | |
% 154.55/26.53 | | | | REF_CLOSE: (7), (18), (41), (59), (164) are inconsistent by sub-proof
% 154.55/26.53 | | | | #41.
% 154.55/26.53 | | | |
% 154.55/26.53 | | | End of split
% 154.55/26.53 | | |
% 154.55/26.53 | | End of split
% 154.55/26.53 | |
% 154.55/26.53 | End of split
% 154.55/26.53 |
% 154.55/26.53 End of proof
% 154.55/26.53
% 154.55/26.53 Sub-proof #37 shows that the following formulas are inconsistent:
% 154.55/26.53 ----------------------------------------------------------------
% 154.55/26.53 (1) all_56_14 = e1
% 154.55/26.53 (2) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.53 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2)
% 154.55/26.53 & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2
% 154.55/26.53 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_5
% 154.55/26.53 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 & op(e0,
% 154.55/26.53 e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) &
% 154.55/26.53 op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 &
% 154.55/26.53 ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.53 (3) ~ (all_52_7 = e2)
% 154.55/26.53 (4) op(e2, e1) = all_52_9
% 154.55/26.53 (5) op(e1, e2) = all_52_6
% 154.55/26.53 (6) ~ (all_52_7 = e0)
% 154.55/26.53 (7) ~ (all_52_6 = e1)
% 154.55/26.53 (8) ~ (e1 = e0)
% 154.55/26.53 (9) op(e0, e1) = e0
% 154.55/26.53 (10) ~ (all_52_9 = e2)
% 154.55/26.53 (11) op(e0, e2) = all_52_7
% 154.55/26.53 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.53
% 154.55/26.53 Begin of proof
% 154.55/26.53 |
% 154.55/26.53 | BETA: splitting (2) gives:
% 154.55/26.53 |
% 154.55/26.53 | Case 1:
% 154.55/26.53 | |
% 154.55/26.53 | | (13) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) =
% 154.55/26.53 | | e2 & op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~
% 154.55/26.53 | | (all_56_13 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5
% 154.55/26.53 | | = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 &
% 154.55/26.53 | | op(e0, e2) = e2)
% 154.55/26.53 | |
% 154.55/26.53 | | BETA: splitting (13) gives:
% 154.55/26.53 | |
% 154.55/26.53 | | Case 1:
% 154.55/26.53 | | |
% 154.55/26.53 | | | (14) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) =
% 154.55/26.53 | | | e2 & op(e1, e2) = e2
% 154.55/26.53 | | |
% 154.55/26.53 | | | ALPHA: (14) implies:
% 154.55/26.53 | | | (15) op(e2, e1) = e2
% 154.55/26.53 | | |
% 154.55/26.53 | | | REF_CLOSE: (4), (10), (12), (15) are inconsistent by sub-proof #1441.
% 154.55/26.53 | | |
% 154.55/26.53 | | Case 2:
% 154.55/26.53 | | |
% 154.55/26.53 | | | (16) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1)
% 154.55/26.53 | | | = e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 154.55/26.53 | | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.55/26.53 | | |
% 154.55/26.53 | | | REF_CLOSE: (3), (5), (7), (11), (12), (16) are inconsistent by sub-proof
% 154.55/26.53 | | | #59.
% 154.55/26.53 | | |
% 154.55/26.53 | | End of split
% 154.55/26.53 | |
% 154.55/26.53 | Case 2:
% 154.55/26.53 | |
% 154.55/26.53 | | (17) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) =
% 154.55/26.53 | | e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.53 | | (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8
% 154.55/26.53 | | = e0 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 &
% 154.55/26.53 | | op(e0, e1) = e0)
% 154.55/26.53 | |
% 154.55/26.53 | | REF_CLOSE: (1), (6), (8), (9), (11), (12), (17) are inconsistent by
% 154.55/26.53 | | sub-proof #38.
% 154.55/26.53 | |
% 154.55/26.53 | End of split
% 154.55/26.53 |
% 154.55/26.53 End of proof
% 154.55/26.53
% 154.55/26.53 Sub-proof #38 shows that the following formulas are inconsistent:
% 154.55/26.53 ----------------------------------------------------------------
% 154.55/26.53 (1) all_56_14 = e1
% 154.55/26.53 (2) ~ (all_52_7 = e0)
% 154.55/26.53 (3) ~ (e1 = e0)
% 154.55/26.53 (4) op(e0, e1) = e0
% 154.55/26.53 (5) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 &
% 154.55/26.53 op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.53 e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11
% 154.55/26.53 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.53 (6) op(e0, e2) = all_52_7
% 154.55/26.53 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.53
% 154.55/26.53 Begin of proof
% 154.55/26.53 |
% 154.55/26.53 | BETA: splitting (5) gives:
% 154.55/26.53 |
% 154.55/26.53 | Case 1:
% 154.55/26.53 | |
% 154.55/26.53 | | (8) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) =
% 154.55/26.53 | | e0 & op(e0, e2) = e0
% 154.55/26.53 | |
% 154.55/26.53 | | ALPHA: (8) implies:
% 154.55/26.53 | | (9) op(e0, e2) = e0
% 154.55/26.53 | |
% 154.55/26.53 | | REF_CLOSE: (2), (6), (7), (9) are inconsistent by sub-proof #1532.
% 154.55/26.53 | |
% 154.55/26.53 | Case 2:
% 154.55/26.53 | |
% 154.55/26.53 | | (10) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) =
% 154.55/26.53 | | e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~
% 154.55/26.53 | | (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.53 | |
% 154.55/26.53 | | BETA: splitting (10) gives:
% 154.55/26.53 | |
% 154.55/26.53 | | Case 1:
% 154.55/26.53 | | |
% 154.55/26.53 | | | (11) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0)
% 154.55/26.53 | | | = e1 & op(e0, e1) = e1
% 154.55/26.53 | | |
% 154.55/26.53 | | | ALPHA: (11) implies:
% 154.55/26.53 | | | (12) op(e0, e1) = e1
% 154.55/26.53 | | |
% 154.55/26.53 | | | REF_CLOSE: (3), (4), (7), (12) are inconsistent by sub-proof #129.
% 154.55/26.53 | | |
% 154.55/26.53 | | Case 2:
% 154.55/26.53 | | |
% 154.55/26.53 | | | (13) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 154.55/26.53 | | | = e0 & op(e0, e1) = e0
% 154.55/26.53 | | |
% 154.55/26.53 | | | ALPHA: (13) implies:
% 154.55/26.53 | | | (14) ~ (all_56_14 = e1)
% 154.55/26.53 | | |
% 154.55/26.53 | | | REDUCE: (1), (14) imply:
% 154.55/26.53 | | | (15) $false
% 154.55/26.53 | | |
% 154.55/26.53 | | | CLOSE: (15) is inconsistent.
% 154.55/26.53 | | |
% 154.55/26.53 | | End of split
% 154.55/26.53 | |
% 154.55/26.53 | End of split
% 154.55/26.53 |
% 154.55/26.53 End of proof
% 154.55/26.53
% 154.55/26.53 Sub-proof #39 shows that the following formulas are inconsistent:
% 154.55/26.53 ----------------------------------------------------------------
% 154.55/26.53 (1) op(e3, e2) = all_52_4
% 154.55/26.53 (2) ~ (all_52_4 = e2)
% 154.55/26.53 (3) op(e3, e1) = e2
% 154.55/26.53 (4) op(e2, e3) = all_52_1
% 154.55/26.53 (5) all_54_4 = all_52_1
% 154.55/26.53 (6) ~ (all_52_1 = e0)
% 154.55/26.53 (7) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.53 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3)
% 154.55/26.53 & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 &
% 154.55/26.53 ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.53 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.53 (9) all_54_4 = e1 | all_54_4 = e0
% 154.55/26.53 (10) ~ (e3 = e2)
% 154.55/26.53 (11) ~ (all_52_1 = e3)
% 154.55/26.53
% 154.55/26.53 Begin of proof
% 154.55/26.53 |
% 154.55/26.53 | BETA: splitting (7) gives:
% 154.55/26.53 |
% 154.55/26.53 | Case 1:
% 154.55/26.53 | |
% 154.55/26.53 | | (12) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) =
% 154.55/26.53 | | e3 & op(e2, e3) = e3
% 154.55/26.53 | |
% 154.55/26.53 | | ALPHA: (12) implies:
% 154.55/26.53 | | (13) op(e2, e3) = e3
% 154.55/26.53 | |
% 154.55/26.53 | | REF_CLOSE: (4), (5), (6), (8), (9), (11), (13) are inconsistent by sub-proof
% 154.55/26.53 | | #1236.
% 154.55/26.53 | |
% 154.55/26.53 | Case 2:
% 154.55/26.53 | |
% 154.55/26.53 | | (14) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) =
% 154.55/26.53 | | e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~
% 154.55/26.53 | | (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.53 | |
% 154.55/26.53 | | REF_CLOSE: (1), (2), (3), (8), (10), (14) are inconsistent by sub-proof
% 154.55/26.53 | | #292.
% 154.55/26.53 | |
% 154.55/26.53 | End of split
% 154.55/26.53 |
% 154.55/26.53 End of proof
% 154.55/26.53
% 154.55/26.53 Sub-proof #40 shows that the following formulas are inconsistent:
% 154.55/26.53 ----------------------------------------------------------------
% 154.55/26.53 (1) op(e3, e0) = all_52_12
% 154.55/26.53 (2) op(e1, e1) = all_6_2
% 154.55/26.53 (3) ~ (all_10_0 = e0)
% 154.55/26.53 (4) all_58_14 = e0
% 154.55/26.53 (5) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.53 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.53 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.53 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.55/26.53 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.53 (8) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 154.55/26.53 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 154.55/26.53 (9) ~ (all_10_0 = e2)
% 154.55/26.53 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.53 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.53 (11) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 154.55/26.53 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.53 e2)
% 154.55/26.53 (12) ~ (e2 = e0)
% 154.55/26.53 (13) all_58_9 = e3
% 154.55/26.53 (14) op(e2, e0) = all_52_13
% 154.55/26.53 (15) ~ (all_52_6 = all_10_0)
% 154.55/26.53 (16) op(e1, e2) = all_52_6
% 154.55/26.53 (17) all_54_8 = all_10_0
% 154.55/26.53 (18) op(e0, e1) = all_52_11
% 154.55/26.53 (19) all_58_15 = e1
% 154.55/26.53 (20) ~ (e2 = e1)
% 154.55/26.53 (21) ~ (e1 = e0)
% 154.55/26.53 (22) op(e0, e1) = e0
% 154.55/26.53 (23) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 154.55/26.53 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 154.55/26.53 e3)
% 154.55/26.53 (24) all_58_6 = e2 & op(e1, e3) = e2
% 154.55/26.53 (25) op(e3, e0) = e3
% 154.55/26.53 (26) ~ (all_10_0 = e1)
% 154.55/26.53 (27) op(e0, e0) = e1
% 154.55/26.53 (28) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.53 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.53 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.53 (30) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.53 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.53 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.53 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.53 (31) ~ (all_10_0 = all_6_2)
% 154.55/26.53
% 154.55/26.53 Begin of proof
% 154.55/26.53 |
% 154.55/26.53 | ALPHA: (24) implies:
% 154.55/26.53 | (32) all_58_6 = e2
% 154.55/26.53 |
% 154.55/26.53 | BETA: splitting (5) gives:
% 154.55/26.53 |
% 154.55/26.53 | Case 1:
% 154.55/26.53 | |
% 154.55/26.53 | | (33) all_54_8 = e3
% 154.55/26.53 | |
% 154.55/26.53 | | COMBINE_EQS: (17), (33) imply:
% 154.55/26.53 | | (34) all_10_0 = e3
% 154.55/26.53 | |
% 154.55/26.53 | | SIMP: (34) implies:
% 154.55/26.53 | | (35) all_10_0 = e3
% 154.55/26.53 | |
% 154.55/26.53 | | REDUCE: (15), (35) imply:
% 154.55/26.53 | | (36) ~ (all_52_6 = e3)
% 154.55/26.53 | |
% 154.55/26.53 | | REDUCE: (31), (35) imply:
% 154.55/26.53 | | (37) ~ (all_6_2 = e3)
% 154.55/26.53 | |
% 154.55/26.53 | | SIMP: (37) implies:
% 154.55/26.53 | | (38) ~ (all_6_2 = e3)
% 154.55/26.53 | |
% 154.55/26.53 | | REDUCE: (9), (35) imply:
% 154.55/26.53 | | (39) ~ (e3 = e2)
% 154.55/26.53 | |
% 154.55/26.53 | | REDUCE: (26), (35) imply:
% 154.55/26.53 | | (40) ~ (e3 = e1)
% 154.55/26.53 | |
% 154.55/26.53 | | REDUCE: (3), (35) imply:
% 154.55/26.53 | | (41) ~ (e3 = e0)
% 154.55/26.53 | |
% 154.55/26.53 | | BETA: splitting (23) gives:
% 154.55/26.53 | |
% 154.55/26.53 | | Case 1:
% 154.55/26.53 | | |
% 154.55/26.53 | | | (42) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2)
% 154.55/26.53 | | | = e3)
% 154.55/26.53 | | |
% 154.55/26.53 | | | BETA: splitting (42) gives:
% 154.55/26.53 | | |
% 154.55/26.53 | | | Case 1:
% 154.55/26.53 | | | |
% 154.55/26.53 | | | | (43) all_58_12 = e3 & op(e0, e3) = e3
% 154.55/26.53 | | | |
% 154.55/26.53 | | | | ALPHA: (43) implies:
% 154.55/26.53 | | | | (44) all_58_12 = e3
% 154.55/26.53 | | | |
% 154.55/26.53 | | | | BETA: splitting (8) gives:
% 154.55/26.53 | | | |
% 154.55/26.53 | | | | Case 1:
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | | (45) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 154.55/26.53 | | | | | e2) = e3)
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | | BETA: splitting (45) gives:
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | | Case 1:
% 154.55/26.53 | | | | | |
% 154.55/26.53 | | | | | | (46) all_58_6 = e3 & op(e1, e3) = e3
% 154.55/26.53 | | | | | |
% 154.55/26.53 | | | | | | REF_CLOSE: (6), (10), (12), (20), (21), (28), (29), (32), (39),
% 154.55/26.53 | | | | | | (40), (41), (44), (46) are inconsistent by sub-proof
% 154.55/26.53 | | | | | | #1480.
% 154.55/26.53 | | | | | |
% 154.55/26.53 | | | | | Case 2:
% 154.55/26.53 | | | | | |
% 154.55/26.53 | | | | | | (47) all_58_7 = e3 & op(e1, e2) = e3
% 154.55/26.53 | | | | | |
% 154.55/26.53 | | | | | | REF_CLOSE: (16), (29), (36), (47) are inconsistent by sub-proof
% 154.55/26.53 | | | | | | #1184.
% 154.55/26.53 | | | | | |
% 154.55/26.53 | | | | | End of split
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | Case 2:
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | | (48) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 154.55/26.53 | | | | | e0) = e3)
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | | REF_CLOSE: (1), (2), (7), (12), (13), (14), (19), (20), (21), (25),
% 154.55/26.53 | | | | | (27), (29), (30), (38), (39), (41), (48) are inconsistent
% 154.55/26.53 | | | | | by sub-proof #46.
% 154.55/26.53 | | | | |
% 154.55/26.53 | | | | End of split
% 154.55/26.53 | | | |
% 154.55/26.53 | | | Case 2:
% 154.55/26.53 | | | |
% 154.55/26.53 | | | | (49) all_58_13 = e3 & op(e0, e2) = e3
% 154.55/26.53 | | | |
% 154.55/26.53 | | | | ALPHA: (49) implies:
% 154.55/26.53 | | | | (50) all_58_13 = e3
% 154.55/26.54 | | | |
% 154.55/26.54 | | | | REF_CLOSE: (6), (10), (11), (12), (18), (20), (21), (22), (27), (28),
% 154.55/26.54 | | | | (29), (32), (39), (40), (41), (50) are inconsistent by
% 154.55/26.54 | | | | sub-proof #45.
% 154.55/26.54 | | | |
% 154.55/26.54 | | | End of split
% 154.55/26.54 | | |
% 154.55/26.54 | | Case 2:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (51) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0)
% 154.55/26.54 | | | = e3)
% 154.55/26.54 | | |
% 154.55/26.54 | | | REF_CLOSE: (4), (19), (40), (41), (51) are inconsistent by sub-proof #44.
% 154.55/26.54 | | |
% 154.55/26.54 | | End of split
% 154.55/26.54 | |
% 154.55/26.54 | Case 2:
% 154.55/26.54 | |
% 154.55/26.54 | | (52) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (3), (9), (17), (26), (52) are inconsistent by sub-proof #41.
% 154.55/26.54 | |
% 154.55/26.54 | End of split
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #41 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) ~ (all_10_0 = e0)
% 154.55/26.54 (2) ~ (all_10_0 = e2)
% 154.55/26.54 (3) all_54_8 = all_10_0
% 154.55/26.54 (4) ~ (all_10_0 = e1)
% 154.55/26.54 (5) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | BETA: splitting (5) gives:
% 154.55/26.54 |
% 154.55/26.54 | Case 1:
% 154.55/26.54 | |
% 154.55/26.54 | | (6) all_54_8 = e2
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #43.
% 154.55/26.54 | |
% 154.55/26.54 | Case 2:
% 154.55/26.54 | |
% 154.55/26.54 | | (7) all_54_8 = e1 | all_54_8 = e0
% 154.55/26.54 | |
% 154.55/26.54 | | BETA: splitting (7) gives:
% 154.55/26.54 | |
% 154.55/26.54 | | Case 1:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (8) all_54_8 = e1
% 154.55/26.54 | | |
% 154.55/26.54 | | | COMBINE_EQS: (3), (8) imply:
% 154.55/26.54 | | | (9) all_10_0 = e1
% 154.55/26.54 | | |
% 154.55/26.54 | | | SIMP: (9) implies:
% 154.55/26.54 | | | (10) all_10_0 = e1
% 154.55/26.54 | | |
% 154.55/26.54 | | | REDUCE: (4), (10) imply:
% 154.55/26.54 | | | (11) $false
% 154.55/26.54 | | |
% 154.55/26.54 | | | CLOSE: (11) is inconsistent.
% 154.55/26.54 | | |
% 154.55/26.54 | | Case 2:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (12) all_54_8 = e0
% 154.55/26.54 | | |
% 154.55/26.54 | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #42.
% 154.55/26.54 | | |
% 154.55/26.54 | | End of split
% 154.55/26.54 | |
% 154.55/26.54 | End of split
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #42 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) all_54_8 = all_10_0
% 154.55/26.54 (2) all_54_8 = e0
% 154.55/26.54 (3) ~ (all_10_0 = e0)
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | COMBINE_EQS: (1), (2) imply:
% 154.55/26.54 | (4) all_10_0 = e0
% 154.55/26.54 |
% 154.55/26.54 | SIMP: (4) implies:
% 154.55/26.54 | (5) all_10_0 = e0
% 154.55/26.54 |
% 154.55/26.54 | REDUCE: (3), (5) imply:
% 154.55/26.54 | (6) $false
% 154.55/26.54 |
% 154.55/26.54 | CLOSE: (6) is inconsistent.
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #43 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) all_54_8 = all_10_0
% 154.55/26.54 (2) all_54_8 = e2
% 154.55/26.54 (3) ~ (all_10_0 = e2)
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | COMBINE_EQS: (1), (2) imply:
% 154.55/26.54 | (4) all_10_0 = e2
% 154.55/26.54 |
% 154.55/26.54 | SIMP: (4) implies:
% 154.55/26.54 | (5) all_10_0 = e2
% 154.55/26.54 |
% 154.55/26.54 | REDUCE: (3), (5) imply:
% 154.55/26.54 | (6) $false
% 154.55/26.54 |
% 154.55/26.54 | CLOSE: (6) is inconsistent.
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #44 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) all_58_14 = e0
% 154.55/26.54 (2) ~ (e3 = e0)
% 154.55/26.54 (3) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 154.55/26.54 (4) ~ (e3 = e1)
% 154.55/26.54 (5) all_58_15 = e1
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | BETA: splitting (3) gives:
% 154.55/26.54 |
% 154.55/26.54 | Case 1:
% 154.55/26.54 | |
% 154.55/26.54 | | (6) all_58_14 = e3 & op(e0, e1) = e3
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #314.
% 154.55/26.54 | |
% 154.55/26.54 | Case 2:
% 154.55/26.54 | |
% 154.55/26.54 | | (7) all_58_15 = e3 & op(e0, e0) = e3
% 154.55/26.54 | |
% 154.55/26.54 | | ALPHA: (7) implies:
% 154.55/26.54 | | (8) all_58_15 = e3
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1404.
% 154.55/26.54 | |
% 154.55/26.54 | End of split
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #45 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.54 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.54 (2) all_58_6 = e2
% 154.55/26.54 (3) ~ (e3 = e0)
% 154.55/26.54 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.54 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.54 (5) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 154.55/26.54 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.54 (6) ~ (e2 = e0)
% 154.55/26.54 (7) ~ (e3 = e1)
% 154.55/26.54 (8) all_58_13 = e3
% 154.55/26.54 (9) op(e0, e1) = all_52_11
% 154.55/26.54 (10) ~ (e2 = e1)
% 154.55/26.54 (11) ~ (e1 = e0)
% 154.55/26.54 (12) op(e0, e1) = e0
% 154.55/26.54 (13) op(e0, e0) = e1
% 154.55/26.54 (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.54 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.54 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.54 (16) ~ (e3 = e2)
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | BETA: splitting (5) gives:
% 154.55/26.54 |
% 154.55/26.54 | Case 1:
% 154.55/26.54 | |
% 154.55/26.54 | | (17) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 154.55/26.54 | | e2)
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (14), (15), (16),
% 154.55/26.54 | | (17) are inconsistent by sub-proof #1176.
% 154.55/26.54 | |
% 154.55/26.54 | Case 2:
% 154.55/26.54 | |
% 154.55/26.54 | | (18) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.54 | | e2)
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (6), (9), (10), (12), (13), (15), (18) are inconsistent by
% 154.55/26.54 | | sub-proof #54.
% 154.55/26.54 | |
% 154.55/26.54 | End of split
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #46 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) op(e3, e0) = all_52_12
% 154.55/26.54 (2) op(e1, e1) = all_6_2
% 154.55/26.54 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.55/26.54 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.54 (4) ~ (e3 = e0)
% 154.55/26.54 (5) ~ (e2 = e0)
% 154.55/26.54 (6) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 154.55/26.54 (7) all_58_9 = e3
% 154.55/26.54 (8) op(e2, e0) = all_52_13
% 154.55/26.54 (9) ~ (all_6_2 = e3)
% 154.55/26.54 (10) all_58_15 = e1
% 154.55/26.54 (11) ~ (e2 = e1)
% 154.55/26.54 (12) ~ (e1 = e0)
% 154.55/26.54 (13) op(e3, e0) = e3
% 154.55/26.54 (14) op(e0, e0) = e1
% 154.55/26.54 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.54 (16) ~ (e3 = e2)
% 154.55/26.54 (17) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.54 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.54 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.54 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | BETA: splitting (6) gives:
% 154.55/26.54 |
% 154.55/26.54 | Case 1:
% 154.55/26.54 | |
% 154.55/26.54 | | (18) all_58_8 = e3 & op(e1, e1) = e3
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (2), (9), (15), (18) are inconsistent by sub-proof #1469.
% 154.55/26.54 | |
% 154.55/26.54 | Case 2:
% 154.55/26.54 | |
% 154.55/26.54 | | (19) all_58_11 = e3 & op(e1, e0) = e3
% 154.55/26.54 | |
% 154.55/26.54 | | ALPHA: (19) implies:
% 154.55/26.54 | | (20) all_58_11 = e3
% 154.55/26.54 | | (21) op(e1, e0) = e3
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14), (15),
% 154.55/26.54 | | (16), (17), (20), (21) are inconsistent by sub-proof #47.
% 154.55/26.54 | |
% 154.55/26.54 | End of split
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #47 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) op(e3, e0) = all_52_12
% 154.55/26.54 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.55/26.54 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.54 (3) ~ (e3 = e0)
% 154.55/26.54 (4) ~ (e2 = e0)
% 154.55/26.54 (5) all_58_9 = e3
% 154.55/26.54 (6) op(e2, e0) = all_52_13
% 154.55/26.54 (7) all_58_15 = e1
% 154.55/26.54 (8) ~ (e2 = e1)
% 154.55/26.54 (9) ~ (e1 = e0)
% 154.55/26.54 (10) op(e3, e0) = e3
% 154.55/26.54 (11) op(e1, e0) = e3
% 154.55/26.54 (12) op(e0, e0) = e1
% 154.55/26.54 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.54 (14) ~ (e3 = e2)
% 154.55/26.54 (15) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.54 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.54 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.54 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.54 (16) all_58_11 = e3
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | BETA: splitting (2) gives:
% 154.55/26.54 |
% 154.55/26.54 | Case 1:
% 154.55/26.54 | |
% 154.55/26.54 | | (17) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 154.55/26.54 | | e2)
% 154.55/26.54 | |
% 154.55/26.54 | | BETA: splitting (17) gives:
% 154.55/26.54 | |
% 154.55/26.54 | | Case 1:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (18) all_58_9 = e2 & op(e3, e0) = e2
% 154.55/26.54 | | |
% 154.55/26.54 | | | REF_CLOSE: (5), (14), (18) are inconsistent by sub-proof #1353.
% 154.55/26.54 | | |
% 154.55/26.54 | | Case 2:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (19) all_58_10 = e2 & op(e2, e0) = e2
% 154.55/26.54 | | |
% 154.55/26.54 | | | ALPHA: (19) implies:
% 154.55/26.54 | | | (20) op(e2, e0) = e2
% 154.55/26.54 | | |
% 154.55/26.54 | | | BETA: splitting (15) gives:
% 154.55/26.54 | | |
% 154.55/26.54 | | | Case 1:
% 154.55/26.54 | | | |
% 154.55/26.54 | | | | (21) all_58_15 = e0 & op(e0, e0) = e0
% 154.55/26.54 | | | |
% 154.55/26.54 | | | | REF_CLOSE: (7), (9), (21) are inconsistent by sub-proof #1059.
% 154.55/26.54 | | | |
% 154.55/26.54 | | | Case 2:
% 154.55/26.54 | | | |
% 154.55/26.54 | | | | (22) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 154.55/26.54 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 154.55/26.54 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 154.55/26.54 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 154.55/26.54 | | | |
% 154.55/26.54 | | | | ALPHA: (22) implies:
% 154.55/26.54 | | | | (23) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 154.55/26.54 | | | | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 154.55/26.54 | | | |
% 154.55/26.54 | | | | REF_CLOSE: (1), (3), (4), (6), (10), (11), (13), (20), (23) are
% 154.55/26.54 | | | | inconsistent by sub-proof #48.
% 154.55/26.54 | | | |
% 154.55/26.54 | | | End of split
% 154.55/26.54 | | |
% 154.55/26.54 | | End of split
% 154.55/26.54 | |
% 154.55/26.54 | Case 2:
% 154.55/26.54 | |
% 154.55/26.54 | | (24) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.54 | | e2)
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (8), (12), (13), (14), (16), (24) are inconsistent by sub-proof
% 154.55/26.54 | | #843.
% 154.55/26.54 | |
% 154.55/26.54 | End of split
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #48 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) op(e3, e0) = all_52_12
% 154.55/26.54 (2) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 154.55/26.54 (all_58_11 = e0 & op(e1, e0) = e0)
% 154.55/26.54 (3) op(e2, e0) = e2
% 154.55/26.54 (4) ~ (e3 = e0)
% 154.55/26.54 (5) ~ (e2 = e0)
% 154.55/26.54 (6) op(e2, e0) = all_52_13
% 154.55/26.54 (7) op(e3, e0) = e3
% 154.55/26.54 (8) op(e1, e0) = e3
% 154.55/26.54 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | BETA: splitting (2) gives:
% 154.55/26.54 |
% 154.55/26.54 | Case 1:
% 154.55/26.54 | |
% 154.55/26.54 | | (10) all_58_9 = e0 & op(e3, e0) = e0
% 154.55/26.54 | |
% 154.55/26.54 | | ALPHA: (10) implies:
% 154.55/26.54 | | (11) op(e3, e0) = e0
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (1), (4), (7), (9), (11) are inconsistent by sub-proof #258.
% 154.55/26.54 | |
% 154.55/26.54 | Case 2:
% 154.55/26.54 | |
% 154.55/26.54 | | (12) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 154.55/26.54 | | e0)
% 154.55/26.54 | |
% 154.55/26.54 | | BETA: splitting (12) gives:
% 154.55/26.54 | |
% 154.55/26.54 | | Case 1:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (13) all_58_10 = e0 & op(e2, e0) = e0
% 154.55/26.54 | | |
% 154.55/26.54 | | | ALPHA: (13) implies:
% 154.55/26.54 | | | (14) op(e2, e0) = e0
% 154.55/26.54 | | |
% 154.55/26.54 | | | REF_CLOSE: (3), (5), (6), (9), (14) are inconsistent by sub-proof #1397.
% 154.55/26.54 | | |
% 154.55/26.54 | | Case 2:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (15) all_58_11 = e0 & op(e1, e0) = e0
% 154.55/26.54 | | |
% 154.55/26.54 | | | ALPHA: (15) implies:
% 154.55/26.54 | | | (16) op(e1, e0) = e0
% 154.55/26.54 | | |
% 154.55/26.54 | | | REF_CLOSE: (4), (8), (9), (16) are inconsistent by sub-proof #118.
% 154.55/26.54 | | |
% 154.55/26.54 | | End of split
% 154.55/26.54 | |
% 154.55/26.54 | End of split
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #49 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) op(e3, e0) = all_52_12
% 154.55/26.54 (2) all_58_0 = e1
% 154.55/26.54 (3) op(e3, e2) = all_52_4
% 154.55/26.54 (4) ~ (e3 = e0)
% 154.55/26.54 (5) ~ (all_52_8 = e0)
% 154.55/26.54 (6) ~ (all_52_4 = e0)
% 154.55/26.54 (7) ~ (e1 = e0)
% 154.55/26.54 (8) op(e3, e1) = all_52_8
% 154.55/26.54 (9) op(e3, e0) = e3
% 154.55/26.54 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.54 (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 154.55/26.54 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | BETA: splitting (11) gives:
% 154.55/26.54 |
% 154.55/26.54 | Case 1:
% 154.55/26.54 | |
% 154.55/26.54 | | (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 154.55/26.54 | | e0)
% 154.55/26.54 | |
% 154.55/26.54 | | BETA: splitting (12) gives:
% 154.55/26.54 | |
% 154.55/26.54 | | Case 1:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (13) all_58_0 = e0 & op(e3, e3) = e0
% 154.55/26.54 | | |
% 154.55/26.54 | | | REF_CLOSE: (2), (7), (13) are inconsistent by sub-proof #1520.
% 154.55/26.54 | | |
% 154.55/26.54 | | Case 2:
% 154.55/26.54 | | |
% 154.55/26.54 | | | (14) all_58_1 = e0 & op(e3, e2) = e0
% 154.55/26.54 | | |
% 154.55/26.54 | | | REF_CLOSE: (3), (6), (10), (14) are inconsistent by sub-proof #1221.
% 154.55/26.54 | | |
% 154.55/26.54 | | End of split
% 154.55/26.54 | |
% 154.55/26.54 | Case 2:
% 154.55/26.54 | |
% 154.55/26.54 | | (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 154.55/26.54 | | e0)
% 154.55/26.54 | |
% 154.55/26.54 | | REF_CLOSE: (1), (4), (5), (8), (9), (10), (15) are inconsistent by sub-proof
% 154.55/26.54 | | #257.
% 154.55/26.54 | |
% 154.55/26.54 | End of split
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #50 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) all_54_0 = all_10_2
% 154.55/26.54 (2) all_54_0 = e3
% 154.55/26.54 (3) ~ (all_10_2 = e3)
% 154.55/26.54
% 154.55/26.54 Begin of proof
% 154.55/26.54 |
% 154.55/26.54 | COMBINE_EQS: (1), (2) imply:
% 154.55/26.54 | (4) all_10_2 = e3
% 154.55/26.54 |
% 154.55/26.54 | SIMP: (4) implies:
% 154.55/26.54 | (5) all_10_2 = e3
% 154.55/26.54 |
% 154.55/26.54 | REDUCE: (3), (5) imply:
% 154.55/26.54 | (6) $false
% 154.55/26.54 |
% 154.55/26.54 | CLOSE: (6) is inconsistent.
% 154.55/26.54 |
% 154.55/26.54 End of proof
% 154.55/26.54
% 154.55/26.54 Sub-proof #51 shows that the following formulas are inconsistent:
% 154.55/26.54 ----------------------------------------------------------------
% 154.55/26.54 (1) ~ (all_52_3 = e1)
% 154.55/26.54 (2) op(e3, e0) = all_52_12
% 154.55/26.54 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 154.55/26.54 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 154.55/26.54 (4) ~ (all_52_12 = e2)
% 154.55/26.54 (5) all_54_13 = all_52_7
% 154.55/26.54 (6) op(e1, e1) = all_6_2
% 154.55/26.54 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 154.55/26.54 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 154.55/26.54 (8) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 154.55/26.54 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 154.55/26.54 (9) all_58_14 = e0
% 154.55/26.54 (10) ~ (all_56_12 = e2) | (all_56_0 = e3 & op(e3, e2) = e3)
% 154.55/26.54 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.54 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.54 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 154.55/26.54 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 154.55/26.54 (13) op(e3, e2) = all_52_4
% 154.55/26.54 (14) ~ (all_52_3 = e0)
% 154.55/26.54 (15) all_56_13 = all_8_2
% 154.55/26.54 (16) all_54_2 = all_52_8
% 154.55/26.54 (17) ~ (all_52_2 = all_6_2)
% 154.55/26.54 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.54 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.54 (19) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 154.55/26.54 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 154.55/26.55 (20) ~ (e2 = e0)
% 154.55/26.55 (21) ~ (all_52_3 = e2)
% 154.55/26.55 (22) op(e1, e3) = all_52_2
% 154.55/26.55 (23) ~ (all_52_6 = all_6_2)
% 154.55/26.55 (24) op(e1, e2) = all_52_6
% 154.55/26.55 (25) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.55 (26) ~ (all_52_8 = e2)
% 154.55/26.55 (27) ~ (all_52_7 = e0)
% 154.55/26.55 (28) ~ (all_6_2 = e0)
% 154.55/26.55 (29) op(e0, e1) = all_52_11
% 154.55/26.55 (30) all_56_12 = e2
% 154.55/26.55 (31) all_58_15 = e1
% 154.55/26.55 (32) ~ (e1 = e0)
% 154.55/26.55 (33) op(e0, e1) = e0
% 154.55/26.55 (34) ~ (all_52_7 = all_8_2)
% 154.55/26.55 (35) op(e3, e1) = all_52_8
% 154.55/26.55 (36) ~ (all_6_2 = e2)
% 154.55/26.55 (37) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 154.55/26.55 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 154.55/26.55 e3)
% 154.55/26.55 (38) all_56_14 = all_6_2
% 154.55/26.55 (39) all_56_15 = e1
% 154.55/26.55 (40) ~ (all_52_7 = e1)
% 154.55/26.55 (41) op(e0, e2) = all_52_7
% 154.55/26.55 (42) op(e1, e0) = all_52_14
% 154.55/26.55 (43) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.55 (44) ~ (all_52_14 = all_6_2)
% 154.55/26.55 (45) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.55 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.55 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.55 (47) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.55 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 154.55/26.55 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 154.55/26.55 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 154.55/26.55 (48) ~ (all_52_4 = all_52_8)
% 154.55/26.55 (49) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.55 (50) all_54_12 = all_52_3
% 154.55/26.55 (51) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.55 (52) ~ (all_52_3 = all_52_7)
% 154.55/26.55
% 154.55/26.55 Begin of proof
% 154.55/26.55 |
% 154.55/26.55 | BETA: splitting (10) gives:
% 154.55/26.55 |
% 154.55/26.55 | Case 1:
% 154.55/26.55 | |
% 154.55/26.55 | | (53) ~ (all_56_12 = e2)
% 154.55/26.55 | |
% 154.55/26.55 | | REDUCE: (30), (53) imply:
% 154.55/26.55 | | (54) $false
% 154.55/26.55 | |
% 154.55/26.55 | | CLOSE: (54) is inconsistent.
% 154.55/26.55 | |
% 154.55/26.55 | Case 2:
% 154.55/26.55 | |
% 154.55/26.55 | | (55) all_56_0 = e3 & op(e3, e2) = e3
% 154.55/26.55 | |
% 154.55/26.55 | | ALPHA: (55) implies:
% 154.55/26.55 | | (56) op(e3, e2) = e3
% 154.55/26.55 | |
% 154.55/26.55 | | BETA: splitting (49) gives:
% 154.55/26.55 | |
% 154.55/26.55 | | Case 1:
% 154.55/26.55 | | |
% 154.55/26.55 | | | (57) all_54_12 = e3
% 154.55/26.55 | | |
% 154.55/26.55 | | | COMBINE_EQS: (50), (57) imply:
% 154.55/26.55 | | | (58) all_52_3 = e3
% 154.55/26.55 | | |
% 154.55/26.55 | | | SIMP: (58) implies:
% 154.55/26.55 | | | (59) all_52_3 = e3
% 154.55/26.55 | | |
% 154.55/26.55 | | | REDUCE: (52), (59) imply:
% 154.55/26.55 | | | (60) ~ (all_52_7 = e3)
% 154.55/26.55 | | |
% 154.55/26.55 | | | SIMP: (60) implies:
% 154.55/26.55 | | | (61) ~ (all_52_7 = e3)
% 154.55/26.55 | | |
% 154.55/26.55 | | | REDUCE: (1), (59) imply:
% 154.55/26.55 | | | (62) ~ (e3 = e1)
% 154.55/26.55 | | |
% 154.55/26.55 | | | REDUCE: (14), (59) imply:
% 154.55/26.55 | | | (63) ~ (e3 = e0)
% 154.55/26.55 | | |
% 154.55/26.55 | | | BETA: splitting (37) gives:
% 154.55/26.55 | | |
% 154.55/26.55 | | | Case 1:
% 154.55/26.55 | | | |
% 154.55/26.55 | | | | (64) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 154.55/26.55 | | | | e2) = e3)
% 154.55/26.55 | | | |
% 154.55/26.55 | | | | BETA: splitting (64) gives:
% 154.55/26.55 | | | |
% 154.55/26.55 | | | | Case 1:
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | (65) all_58_12 = e3 & op(e0, e3) = e3
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | ALPHA: (65) implies:
% 154.55/26.55 | | | | | (66) all_58_12 = e3
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | BETA: splitting (12) gives:
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | Case 1:
% 154.55/26.55 | | | | | |
% 154.55/26.55 | | | | | | (67) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 154.55/26.55 | | | | | | e1) = e2)
% 154.55/26.55 | | | | | |
% 154.55/26.55 | | | | | | BETA: splitting (67) gives:
% 154.55/26.55 | | | | | |
% 154.55/26.55 | | | | | | Case 1:
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | | (68) all_58_4 = e2 & op(e3, e1) = e2
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | | ALPHA: (68) implies:
% 154.55/26.55 | | | | | | | (69) op(e3, e1) = e2
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | | REF_CLOSE: (26), (35), (46), (69) are inconsistent by sub-proof
% 154.55/26.55 | | | | | | | #1212.
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | Case 2:
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | | (70) all_58_5 = e2 & op(e2, e1) = e2
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | | ALPHA: (70) implies:
% 154.55/26.55 | | | | | | | (71) all_58_5 = e2
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | | BETA: splitting (43) gives:
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | |
% 154.55/26.55 | | | | | | | | (72) all_54_13 = e3
% 154.55/26.55 | | | | | | | |
% 154.55/26.55 | | | | | | | | REF_CLOSE: (5), (61), (72) are inconsistent by sub-proof #1435.
% 154.55/26.55 | | | | | | | |
% 154.55/26.55 | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | |
% 154.55/26.55 | | | | | | | | (73) ~ (all_54_13 = e3)
% 154.55/26.55 | | | | | | | | (74) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.55 | | | | | | | |
% 154.55/26.55 | | | | | | | | BETA: splitting (74) gives:
% 154.55/26.55 | | | | | | | |
% 154.55/26.55 | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | (75) all_54_13 = e2
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | COMBINE_EQS: (5), (75) imply:
% 154.55/26.55 | | | | | | | | | (76) all_52_7 = e2
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | SIMP: (76) implies:
% 154.55/26.55 | | | | | | | | | (77) all_52_7 = e2
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | REDUCE: (34), (77) imply:
% 154.55/26.55 | | | | | | | | | (78) ~ (all_8_2 = e2)
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | SIMP: (78) implies:
% 154.55/26.55 | | | | | | | | | (79) ~ (all_8_2 = e2)
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | REDUCE: (61), (77) imply:
% 154.55/26.55 | | | | | | | | | (80) ~ (e3 = e2)
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | SIMP: (80) implies:
% 154.55/26.55 | | | | | | | | | (81) ~ (e3 = e2)
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | REDUCE: (40), (77) imply:
% 154.55/26.55 | | | | | | | | | (82) ~ (e2 = e1)
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | REDUCE: (41), (77) imply:
% 154.55/26.55 | | | | | | | | | (83) op(e0, e2) = e2
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | BETA: splitting (51) gives:
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | (84) all_56_12 = e3
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | COMBINE_EQS: (30), (84) imply:
% 154.55/26.55 | | | | | | | | | | (85) e3 = e2
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | SIMP: (85) implies:
% 154.55/26.55 | | | | | | | | | | (86) e3 = e2
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | COMBINE_EQS: (66), (86) imply:
% 154.55/26.55 | | | | | | | | | | (87) all_58_12 = e2
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | REF_CLOSE: (2), (4), (11), (13), (18), (19), (20), (26),
% 154.55/26.55 | | | | | | | | | | (32), (35), (45), (46), (56), (62), (63), (81),
% 154.55/26.55 | | | | | | | | | | (82), (87) are inconsistent by sub-proof #101.
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | (88) ~ (all_56_12 = e3)
% 154.55/26.55 | | | | | | | | | | (89) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | BETA: splitting (89) gives:
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | (90) all_56_13 = e2
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | COMBINE_EQS: (15), (90) imply:
% 154.55/26.55 | | | | | | | | | | | (91) all_8_2 = e2
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | REDUCE: (79), (91) imply:
% 154.55/26.55 | | | | | | | | | | | (92) $false
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | CLOSE: (92) is inconsistent.
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | (93) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | BETA: splitting (93) gives:
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | (94) all_56_14 = e1
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | COMBINE_EQS: (38), (94) imply:
% 154.55/26.55 | | | | | | | | | | | | (95) all_6_2 = e1
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | SIMP: (95) implies:
% 154.55/26.55 | | | | | | | | | | | | (96) all_6_2 = e1
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | REDUCE: (17), (96) imply:
% 154.55/26.55 | | | | | | | | | | | | (97) ~ (all_52_2 = e1)
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | REDUCE: (23), (96) imply:
% 154.55/26.55 | | | | | | | | | | | | (98) ~ (all_52_6 = e1)
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | REDUCE: (44), (96) imply:
% 154.55/26.55 | | | | | | | | | | | | (99) ~ (all_52_14 = e1)
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | REDUCE: (36), (96) imply:
% 154.55/26.55 | | | | | | | | | | | | (100) ~ (e2 = e1)
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | BETA: splitting (3) gives:
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | (101) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 154.55/26.55 | | | | | | | | | | | | | & op(e1, e2) = e1)
% 154.55/26.55 | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | REF_CLOSE: (22), (24), (46), (97), (98), (101) are
% 154.55/26.55 | | | | | | | | | | | | | inconsistent by sub-proof #196.
% 154.55/26.55 | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | (102) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 154.55/26.55 | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 154.55/26.55 | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | BETA: splitting (102) gives:
% 154.55/26.55 | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | (103) all_58_8 = e1 & op(e1, e1) = e1
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | ALPHA: (103) implies:
% 154.55/26.55 | | | | | | | | | | | | | | (104) all_58_8 = e1
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | (105) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 154.55/26.55 | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 154.55/26.55 | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 154.55/26.55 | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | (106) all_58_4 = e3 & op(e3, e1) = e3
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 154.55/26.55 | | | | | | | | | | | | | | | | (107) op(e3, e1) = e3
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (25), (35), (46), (48), (56), (107)
% 154.55/26.55 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #53.
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | (108) all_58_5 = e3 & op(e2, e1) = e3
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 154.55/26.55 | | | | | | | | | | | | | | | | (109) all_58_5 = e3
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (109) imply:
% 154.55/26.55 | | | | | | | | | | | | | | | | (110) e3 = e2
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (110) imply:
% 154.55/26.55 | | | | | | | | | | | | | | | | (111) all_58_12 = e2
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (11), (13), (18), (19), (20), (26),
% 154.55/26.55 | | | | | | | | | | | | | | | | (32), (35), (45), (46), (56), (62), (63), (81),
% 154.55/26.55 | | | | | | | | | | | | | | | | (82), (111) are inconsistent by sub-proof #101.
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | End of split
% 154.55/26.55 | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | (112) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 154.55/26.55 | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 154.55/26.55 | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 154.55/26.55 | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | Case 1:
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | (113) all_58_8 = e3 & op(e1, e1) = e3
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 154.55/26.55 | | | | | | | | | | | | | | | | (114) all_58_8 = e3
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | REF_CLOSE: (62), (104), (114) are inconsistent by sub-proof
% 154.55/26.55 | | | | | | | | | | | | | | | | #950.
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | (115) all_58_14 = e3 & op(e0, e1) = e3
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 154.55/26.55 | | | | | | | | | | | | | | | | (116) all_58_14 = e3
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20), (32), (41), (46), (47), (62), (63),
% 154.55/26.55 | | | | | | | | | | | | | | | | (66), (82), (83), (116) are inconsistent by
% 154.55/26.55 | | | | | | | | | | | | | | | | sub-proof #778.
% 154.55/26.55 | | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | | End of split
% 154.55/26.55 | | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | End of split
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | (117) all_58_11 = e1 & op(e1, e0) = e1
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | ALPHA: (117) implies:
% 154.55/26.55 | | | | | | | | | | | | | | (118) op(e1, e0) = e1
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | | REF_CLOSE: (42), (46), (99), (118) are inconsistent by
% 154.55/26.55 | | | | | | | | | | | | | | sub-proof #108.
% 154.55/26.55 | | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | | End of split
% 154.55/26.55 | | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | End of split
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | (119) all_56_15 = e0
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | | REF_CLOSE: (32), (39), (119) are inconsistent by sub-proof
% 154.55/26.55 | | | | | | | | | | | | #52.
% 154.55/26.55 | | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | | End of split
% 154.55/26.55 | | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | | End of split
% 154.55/26.55 | | | | | | | | | |
% 154.55/26.55 | | | | | | | | | End of split
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | Case 2:
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | (120) all_54_13 = e1 | all_54_13 = e0
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | | REF_CLOSE: (5), (27), (40), (120) are inconsistent by
% 154.55/26.55 | | | | | | | | | sub-proof #875.
% 154.55/26.55 | | | | | | | | |
% 154.55/26.55 | | | | | | | | End of split
% 154.55/26.55 | | | | | | | |
% 154.55/26.55 | | | | | | | End of split
% 154.55/26.55 | | | | | | |
% 154.55/26.55 | | | | | | End of split
% 154.55/26.55 | | | | | |
% 154.55/26.55 | | | | | Case 2:
% 154.55/26.55 | | | | | |
% 154.55/26.55 | | | | | | (121) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 154.55/26.55 | | | | | | op(e0, e1) = e2)
% 154.55/26.55 | | | | | |
% 154.55/26.55 | | | | | | REF_CLOSE: (6), (20), (29), (33), (36), (46), (121) are inconsistent
% 154.55/26.55 | | | | | | by sub-proof #333.
% 154.55/26.55 | | | | | |
% 154.55/26.55 | | | | | End of split
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | Case 2:
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | (122) all_58_13 = e3 & op(e0, e2) = e3
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | REF_CLOSE: (41), (46), (61), (122) are inconsistent by sub-proof
% 154.55/26.55 | | | | | #1449.
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | End of split
% 154.55/26.55 | | | |
% 154.55/26.55 | | | Case 2:
% 154.55/26.55 | | | |
% 154.55/26.55 | | | | (123) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 154.55/26.55 | | | | e0) = e3)
% 154.55/26.55 | | | |
% 154.55/26.55 | | | | BETA: splitting (123) gives:
% 154.55/26.55 | | | |
% 154.55/26.55 | | | | Case 1:
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | (124) all_58_14 = e3 & op(e0, e1) = e3
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | ALPHA: (124) implies:
% 154.55/26.55 | | | | | (125) all_58_14 = e3
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | REF_CLOSE: (9), (63), (125) are inconsistent by sub-proof #1444.
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | Case 2:
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | (126) all_58_15 = e3 & op(e0, e0) = e3
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | | REF_CLOSE: (31), (62), (126) are inconsistent by sub-proof #1054.
% 154.55/26.55 | | | | |
% 154.55/26.55 | | | | End of split
% 154.55/26.55 | | | |
% 154.55/26.55 | | | End of split
% 154.55/26.55 | | |
% 154.55/26.55 | | Case 2:
% 154.55/26.55 | | |
% 154.55/26.55 | | | (127) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.55 | | |
% 154.55/26.55 | | | REF_CLOSE: (1), (14), (21), (50), (127) are inconsistent by sub-proof
% 154.55/26.55 | | | #1098.
% 154.55/26.55 | | |
% 154.55/26.55 | | End of split
% 154.55/26.55 | |
% 154.55/26.55 | End of split
% 154.55/26.55 |
% 154.55/26.55 End of proof
% 154.55/26.55
% 154.55/26.55 Sub-proof #52 shows that the following formulas are inconsistent:
% 154.55/26.55 ----------------------------------------------------------------
% 154.55/26.55 (1) all_56_15 = e1
% 154.55/26.55 (2) all_56_15 = e0
% 154.55/26.55 (3) ~ (e1 = e0)
% 154.55/26.55
% 154.55/26.55 Begin of proof
% 154.55/26.55 |
% 154.55/26.55 | COMBINE_EQS: (1), (2) imply:
% 154.55/26.55 | (4) e1 = e0
% 154.55/26.55 |
% 154.55/26.55 | SIMP: (4) implies:
% 154.55/26.55 | (5) e1 = e0
% 154.55/26.55 |
% 154.55/26.55 | REDUCE: (3), (5) imply:
% 154.55/26.55 | (6) $false
% 154.55/26.55 |
% 154.55/26.55 | CLOSE: (6) is inconsistent.
% 154.55/26.55 |
% 154.55/26.55 End of proof
% 154.55/26.55
% 154.55/26.55 Sub-proof #53 shows that the following formulas are inconsistent:
% 154.55/26.55 ----------------------------------------------------------------
% 154.55/26.55 (1) op(e3, e1) = e3
% 154.55/26.55 (2) op(e3, e2) = all_52_4
% 154.55/26.55 (3) all_54_2 = all_52_8
% 154.55/26.55 (4) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.55 (5) op(e3, e2) = e3
% 154.55/26.55 (6) op(e3, e1) = all_52_8
% 154.55/26.55 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.55 (8) ~ (all_52_4 = all_52_8)
% 154.55/26.55
% 154.55/26.55 Begin of proof
% 154.55/26.55 |
% 154.55/26.55 | BETA: splitting (4) gives:
% 154.55/26.55 |
% 154.55/26.55 | Case 1:
% 154.55/26.55 | |
% 154.55/26.55 | | (9) all_54_2 = e3
% 154.55/26.55 | |
% 154.55/26.55 | | COMBINE_EQS: (3), (9) imply:
% 154.55/26.55 | | (10) all_52_8 = e3
% 154.55/26.55 | |
% 154.55/26.55 | | REDUCE: (8), (10) imply:
% 154.55/26.55 | | (11) ~ (all_52_4 = e3)
% 154.55/26.55 | |
% 154.55/26.55 | | REF_CLOSE: (2), (5), (7), (11) are inconsistent by sub-proof #1540.
% 154.55/26.55 | |
% 154.55/26.55 | Case 2:
% 154.55/26.55 | |
% 154.55/26.55 | | (12) ~ (all_54_2 = e3)
% 154.55/26.55 | |
% 154.55/26.55 | | REDUCE: (3), (12) imply:
% 154.55/26.55 | | (13) ~ (all_52_8 = e3)
% 154.55/26.55 | |
% 154.55/26.55 | | REF_CLOSE: (1), (6), (7), (13) are inconsistent by sub-proof #1538.
% 154.55/26.55 | |
% 154.55/26.55 | End of split
% 154.55/26.55 |
% 154.55/26.55 End of proof
% 154.55/26.55
% 154.55/26.55 Sub-proof #54 shows that the following formulas are inconsistent:
% 154.55/26.55 ----------------------------------------------------------------
% 154.55/26.55 (1) ~ (e2 = e0)
% 154.55/26.55 (2) op(e0, e1) = all_52_11
% 154.55/26.55 (3) ~ (e2 = e1)
% 154.55/26.55 (4) op(e0, e1) = e0
% 154.55/26.55 (5) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.55 (6) op(e0, e0) = e1
% 154.55/26.55 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.55
% 154.55/26.55 Begin of proof
% 154.55/26.55 |
% 154.55/26.55 | BETA: splitting (5) gives:
% 154.55/26.55 |
% 154.55/26.55 | Case 1:
% 154.55/26.55 | |
% 154.55/26.55 | | (8) all_58_14 = e2 & op(e0, e1) = e2
% 154.55/26.55 | |
% 154.55/26.55 | | ALPHA: (8) implies:
% 154.55/26.55 | | (9) op(e0, e1) = e2
% 154.55/26.55 | |
% 154.55/26.55 | | REF_CLOSE: (1), (2), (4), (7), (9) are inconsistent by sub-proof #1372.
% 154.55/26.55 | |
% 154.55/26.55 | Case 2:
% 154.55/26.55 | |
% 154.55/26.55 | | (10) all_58_15 = e2 & op(e0, e0) = e2
% 154.55/26.55 | |
% 154.55/26.55 | | ALPHA: (10) implies:
% 154.55/26.55 | | (11) op(e0, e0) = e2
% 154.55/26.55 | |
% 154.55/26.55 | | REF_CLOSE: (3), (6), (7), (11) are inconsistent by sub-proof #1386.
% 154.55/26.55 | |
% 154.55/26.55 | End of split
% 154.55/26.55 |
% 154.55/26.55 End of proof
% 154.55/26.55
% 154.55/26.55 Sub-proof #55 shows that the following formulas are inconsistent:
% 154.55/26.55 ----------------------------------------------------------------
% 154.55/26.55 (1) ~ (all_52_3 = e1)
% 154.55/26.55 (2) ~ (all_52_3 = e0)
% 154.55/26.55 (3) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.55/26.55 (4) op(e0, e2) = e2
% 154.55/26.55 (5) op(e0, e2) = all_52_7
% 154.55/26.55 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.55 (7) all_54_12 = all_52_3
% 154.55/26.55 (8) ~ (all_52_3 = all_52_7)
% 154.55/26.55
% 154.55/26.55 Begin of proof
% 154.55/26.55 |
% 154.55/26.55 | BETA: splitting (3) gives:
% 154.55/26.55 |
% 154.55/26.55 | Case 1:
% 154.55/26.55 | |
% 154.55/26.55 | | (9) all_54_12 = e2
% 154.55/26.55 | |
% 154.55/26.55 | | COMBINE_EQS: (7), (9) imply:
% 154.55/26.55 | | (10) all_52_3 = e2
% 154.55/26.55 | |
% 154.55/26.55 | | SIMP: (10) implies:
% 154.55/26.55 | | (11) all_52_3 = e2
% 154.55/26.55 | |
% 154.55/26.55 | | REDUCE: (8), (11) imply:
% 154.55/26.55 | | (12) ~ (all_52_7 = e2)
% 154.55/26.55 | |
% 154.55/26.55 | | SIMP: (12) implies:
% 154.55/26.55 | | (13) ~ (all_52_7 = e2)
% 154.55/26.55 | |
% 154.55/26.55 | | REF_CLOSE: (4), (5), (6), (13) are inconsistent by sub-proof #1479.
% 154.55/26.55 | |
% 154.55/26.55 | Case 2:
% 154.55/26.55 | |
% 154.55/26.55 | | (14) all_54_12 = e1 | all_54_12 = e0
% 154.55/26.55 | |
% 154.55/26.55 | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #1222.
% 154.55/26.55 | |
% 154.55/26.55 | End of split
% 154.55/26.55 |
% 154.55/26.55 End of proof
% 154.55/26.55
% 154.55/26.55 Sub-proof #56 shows that the following formulas are inconsistent:
% 154.55/26.55 ----------------------------------------------------------------
% 154.55/26.55 (1) op(e3, e0) = all_52_12
% 154.55/26.55 (2) op(e3, e1) = e2
% 154.55/26.55 (3) ~ (e2 = e1)
% 154.55/26.55 (4) ~ (all_52_12 = e1)
% 154.55/26.55 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.55 (6) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 154.55/26.55
% 154.55/26.55 Begin of proof
% 154.55/26.55 |
% 154.55/26.55 | BETA: splitting (6) gives:
% 154.55/26.55 |
% 154.55/26.55 | Case 1:
% 154.55/26.55 | |
% 154.55/26.55 | | (7) all_58_4 = e1 & op(e3, e1) = e1
% 154.55/26.55 | |
% 154.55/26.55 | | ALPHA: (7) implies:
% 154.55/26.55 | | (8) op(e3, e1) = e1
% 154.55/26.55 | |
% 154.55/26.55 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #338.
% 154.55/26.55 | |
% 154.55/26.55 | Case 2:
% 154.55/26.55 | |
% 154.55/26.56 | | (9) all_58_9 = e1 & op(e3, e0) = e1
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #67.
% 154.55/26.56 | |
% 154.55/26.56 | End of split
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #57 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) all_58_12 = e2
% 154.55/26.56 (2) op(e1, e0) = e2
% 154.55/26.56 (3) ~ (e2 = e0)
% 154.55/26.56 (4) ~ (all_52_7 = e0)
% 154.55/26.56 (5) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 154.55/26.56 (all_58_14 = e0 & op(e0, e1) = e0)
% 154.55/26.56 (6) ~ (e1 = e0)
% 154.55/26.56 (7) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 &
% 154.55/26.56 op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.56 e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11
% 154.55/26.56 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.56 (8) op(e0, e2) = all_52_7
% 154.55/26.56 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | BETA: splitting (7) gives:
% 154.55/26.56 |
% 154.55/26.56 | Case 1:
% 154.55/26.56 | |
% 154.55/26.56 | | (10) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) =
% 154.55/26.56 | | e0 & op(e0, e2) = e0
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (10) implies:
% 154.55/26.56 | | (11) op(e0, e2) = e0
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (4), (8), (9), (11) are inconsistent by sub-proof #1532.
% 154.55/26.56 | |
% 154.55/26.56 | Case 2:
% 154.55/26.56 | |
% 154.55/26.56 | | (12) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) =
% 154.55/26.56 | | e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~
% 154.55/26.56 | | (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.56 | |
% 154.55/26.56 | | BETA: splitting (12) gives:
% 154.55/26.56 | |
% 154.55/26.56 | | Case 1:
% 154.55/26.56 | | |
% 154.55/26.56 | | | (13) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0)
% 154.55/26.56 | | | = e1 & op(e0, e1) = e1
% 154.55/26.56 | | |
% 154.55/26.56 | | | ALPHA: (13) implies:
% 154.55/26.56 | | | (14) op(e0, e1) = e1
% 154.55/26.56 | | |
% 154.55/26.56 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (14) are inconsistent by
% 154.55/26.56 | | | sub-proof #97.
% 154.55/26.56 | | |
% 154.55/26.56 | | Case 2:
% 154.55/26.56 | | |
% 154.55/26.56 | | | (15) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 154.55/26.56 | | | = e0 & op(e0, e1) = e0
% 154.55/26.56 | | |
% 154.55/26.56 | | | ALPHA: (15) implies:
% 154.55/26.56 | | | (16) op(e1, e0) = e0
% 154.55/26.56 | | |
% 154.55/26.56 | | | REF_CLOSE: (2), (3), (9), (16) are inconsistent by sub-proof #58.
% 154.55/26.56 | | |
% 154.55/26.56 | | End of split
% 154.55/26.56 | |
% 154.55/26.56 | End of split
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #58 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.56 (2) op(e1, e0) = e2
% 154.55/26.56 (3) op(e1, e0) = e0
% 154.55/26.56 (4) ~ (e2 = e0)
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | GROUND_INST: instantiating (1) with e0, e2, e0, e1, simplifying with (2), (3)
% 154.55/26.56 | gives:
% 154.55/26.56 | (5) e2 = e0
% 154.55/26.56 |
% 154.55/26.56 | REDUCE: (4), (5) imply:
% 154.55/26.56 | (6) $false
% 154.55/26.56 |
% 154.55/26.56 | CLOSE: (6) is inconsistent.
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #59 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) ~ (all_52_7 = e2)
% 154.55/26.56 (2) op(e1, e2) = all_52_6
% 154.55/26.56 (3) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 &
% 154.55/26.56 op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.56 e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.55/26.56 (4) ~ (all_52_6 = e1)
% 154.55/26.56 (5) op(e0, e2) = all_52_7
% 154.55/26.56 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | BETA: splitting (3) gives:
% 154.55/26.56 |
% 154.55/26.56 | Case 1:
% 154.55/26.56 | |
% 154.55/26.56 | | (7) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1
% 154.55/26.56 | | & op(e1, e2) = e1
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (7) implies:
% 154.55/26.56 | | (8) op(e1, e2) = e1
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1166.
% 154.55/26.56 | |
% 154.55/26.56 | Case 2:
% 154.55/26.56 | |
% 154.55/26.56 | | (9) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) =
% 154.55/26.56 | | e2 & op(e0, e2) = e2
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (9) implies:
% 154.55/26.56 | | (10) op(e0, e2) = e2
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #1479.
% 154.55/26.56 | |
% 154.55/26.56 | End of split
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #60 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.56 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0)
% 154.55/26.56 & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 &
% 154.55/26.56 ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.56 (2) op(e0, e3) = all_52_3
% 154.55/26.56 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 154.55/26.56 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 154.55/26.56 (4) all_58_8 = e3
% 154.55/26.56 (5) ~ (all_52_3 = e0)
% 154.55/26.56 (6) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 154.55/26.56 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 154.55/26.56 (7) op(e3, e1) = e2
% 154.55/26.56 (8) ~ (e3 = e0)
% 154.55/26.56 (9) ~ (e2 = e0)
% 154.55/26.56 (10) ~ (all_52_9 = e3)
% 154.55/26.56 (11) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 154.55/26.56 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 154.55/26.56 (12) op(e0, e3) = e2
% 154.55/26.56 (13) op(e1, e2) = all_52_6
% 154.55/26.56 (14) all_58_11 = e2
% 154.55/26.56 (15) all_54_6 = all_52_9
% 154.55/26.56 (16) ~ (e2 = e1)
% 154.55/26.56 (17) ~ (all_52_9 = e0)
% 154.55/26.56 (18) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 154.55/26.56 (19) ~ (all_52_9 = e2)
% 154.55/26.56 (20) ~ (all_52_6 = e3)
% 154.55/26.56 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.56 (22) ~ (e3 = e2)
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | BETA: splitting (1) gives:
% 154.55/26.56 |
% 154.55/26.56 | Case 1:
% 154.55/26.56 | |
% 154.55/26.56 | | (23) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) =
% 154.55/26.56 | | e1 & op(e1, e3) = e1
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (23) implies:
% 154.55/26.56 | | (24) op(e3, e1) = e1
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (7), (16), (21), (24) are inconsistent by sub-proof #338.
% 154.55/26.56 | |
% 154.55/26.56 | Case 2:
% 154.55/26.56 | |
% 154.55/26.56 | | (25) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 154.55/26.56 | | e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 154.55/26.56 | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.56 | |
% 154.55/26.56 | | BETA: splitting (25) gives:
% 154.55/26.56 | |
% 154.55/26.56 | | Case 1:
% 154.55/26.56 | | |
% 154.55/26.56 | | | (26) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 154.55/26.56 | | | e3 & op(e0, e3) = e3
% 154.55/26.56 | | |
% 154.55/26.56 | | | ALPHA: (26) implies:
% 154.55/26.56 | | | (27) op(e0, e3) = e3
% 154.55/26.56 | | |
% 154.55/26.56 | | | BETA: splitting (18) gives:
% 154.55/26.56 | | |
% 154.55/26.56 | | | Case 1:
% 154.55/26.56 | | | |
% 154.55/26.56 | | | | (28) all_54_6 = e2
% 154.55/26.56 | | | |
% 154.55/26.56 | | | | REF_CLOSE: (15), (19), (28) are inconsistent by sub-proof #1192.
% 154.55/26.56 | | | |
% 154.55/26.56 | | | Case 2:
% 154.55/26.56 | | | |
% 154.55/26.56 | | | | (29) ~ (all_54_6 = e2)
% 154.55/26.56 | | | | (30) all_54_6 = e1 | all_54_6 = e0
% 154.55/26.56 | | | |
% 154.55/26.56 | | | | BETA: splitting (30) gives:
% 154.55/26.56 | | | |
% 154.55/26.56 | | | | Case 1:
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | (31) all_54_6 = e1
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | COMBINE_EQS: (15), (31) imply:
% 154.55/26.56 | | | | | (32) all_52_9 = e1
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | SIMP: (32) implies:
% 154.55/26.56 | | | | | (33) all_52_9 = e1
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | REDUCE: (10), (33) imply:
% 154.55/26.56 | | | | | (34) ~ (e3 = e1)
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | SIMP: (34) implies:
% 154.55/26.56 | | | | | (35) ~ (e3 = e1)
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | REDUCE: (19), (33) imply:
% 154.55/26.56 | | | | | (36) ~ (e2 = e1)
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | REDUCE: (17), (33) imply:
% 154.55/26.56 | | | | | (37) ~ (e1 = e0)
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | GROUND_INST: instantiating (21) with e2, e3, e3, e0, simplifying with
% 154.55/26.56 | | | | | (12), (27) gives:
% 154.55/26.56 | | | | | (38) e3 = e2
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | COMBINE_EQS: (4), (38) imply:
% 154.55/26.56 | | | | | (39) all_58_8 = e2
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | REF_CLOSE: (3), (6), (8), (9), (11), (13), (14), (16), (20), (21),
% 154.55/26.56 | | | | | (22), (35), (37), (39) are inconsistent by sub-proof #1068.
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | Case 2:
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | (40) all_54_6 = e0
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | | REF_CLOSE: (15), (17), (40) are inconsistent by sub-proof #1113.
% 154.55/26.56 | | | | |
% 154.55/26.56 | | | | End of split
% 154.55/26.56 | | | |
% 154.55/26.56 | | | End of split
% 154.55/26.56 | | |
% 154.55/26.56 | | Case 2:
% 154.55/26.56 | | |
% 154.55/26.56 | | | (41) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 154.55/26.56 | | | e0 & op(e0, e3) = e0
% 154.55/26.56 | | |
% 154.55/26.56 | | | ALPHA: (41) implies:
% 154.55/26.56 | | | (42) op(e0, e3) = e0
% 154.55/26.56 | | |
% 154.55/26.56 | | | REF_CLOSE: (2), (5), (21), (42) are inconsistent by sub-proof #89.
% 154.55/26.56 | | |
% 154.55/26.56 | | End of split
% 154.55/26.56 | |
% 154.55/26.56 | End of split
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #61 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) op(e3, e2) = all_52_4
% 154.55/26.56 (2) ~ (all_52_4 = e2)
% 154.55/26.56 (3) op(e1, e3) = all_52_2
% 154.55/26.56 (4) ~ (e3 = e1)
% 154.55/26.56 (5) op(e1, e3) = e1
% 154.55/26.56 (6) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 &
% 154.55/26.56 op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1)
% 154.55/26.56 & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.56 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | BETA: splitting (6) gives:
% 154.55/26.56 |
% 154.55/26.56 | Case 1:
% 154.55/26.56 | |
% 154.55/26.56 | | (8) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2
% 154.55/26.56 | | & op(e2, e3) = e2
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (8) implies:
% 154.55/26.56 | | (9) op(e3, e2) = e2
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (1), (2), (7), (9) are inconsistent by sub-proof #1539.
% 154.55/26.56 | |
% 154.55/26.56 | Case 2:
% 154.55/26.56 | |
% 154.55/26.56 | | (10) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) =
% 154.55/26.56 | | e3 & op(e1, e3) = e3
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (10) implies:
% 154.55/26.56 | | (11) op(e1, e3) = e3
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (3), (4), (5), (7), (11) are inconsistent by sub-proof #1164.
% 154.55/26.56 | |
% 154.55/26.56 | End of split
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #62 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) all_58_12 = e2
% 154.55/26.56 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.56 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.56 (3) op(e1, e2) = e0
% 154.55/26.56 (4) ~ (e3 = e0)
% 154.55/26.56 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.56 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.56 (6) ~ (e2 = e0)
% 154.55/26.56 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 154.55/26.56 (8) ~ (e3 = e1)
% 154.55/26.56 (9) ~ (e2 = e1)
% 154.55/26.56 (10) ~ (e1 = e0)
% 154.55/26.56 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.56 (12) ~ (e3 = e2)
% 154.55/26.56 (13) all_58_2 = e0
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | BETA: splitting (7) gives:
% 154.55/26.56 |
% 154.55/26.56 | Case 1:
% 154.55/26.56 | |
% 154.55/26.56 | | (14) all_58_6 = e2 & op(e1, e3) = e2
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (14) implies:
% 154.55/26.56 | | (15) all_58_6 = e2
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (12), (13), (15) are
% 154.55/26.56 | | inconsistent by sub-proof #1484.
% 154.55/26.56 | |
% 154.55/26.56 | Case 2:
% 154.55/26.56 | |
% 154.55/26.56 | | (16) all_58_7 = e2 & op(e1, e2) = e2
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (16) implies:
% 154.55/26.56 | | (17) op(e1, e2) = e2
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (3), (6), (11), (17) are inconsistent by sub-proof #139.
% 154.55/26.56 | |
% 154.55/26.56 | End of split
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #63 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) ~ (e3 = e0)
% 154.55/26.56 (2) ~ (e2 = e0)
% 154.55/26.56 (3) all_58_5 = e3
% 154.55/26.56 (4) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 154.55/26.56 (5) ~ (e3 = e1)
% 154.55/26.56 (6) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 154.55/26.56 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 154.55/26.56 (7) all_58_4 = e2
% 154.55/26.56 (8) all_58_15 = e1
% 154.55/26.56 (9) ~ (e1 = e0)
% 154.55/26.56 (10) all_58_8 = e1
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | BETA: splitting (4) gives:
% 154.55/26.56 |
% 154.55/26.56 | Case 1:
% 154.55/26.56 | |
% 154.55/26.56 | | (11) all_58_14 = e3 & op(e0, e1) = e3
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (11) implies:
% 154.55/26.56 | | (12) all_58_14 = e3
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (10), (12) are inconsistent by
% 154.55/26.56 | | sub-proof #1442.
% 154.55/26.56 | |
% 154.55/26.56 | Case 2:
% 154.55/26.56 | |
% 154.55/26.56 | | (13) all_58_15 = e3 & op(e0, e0) = e3
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #1054.
% 154.55/26.56 | |
% 154.55/26.56 | End of split
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #64 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) op(e0, e3) = all_52_3
% 154.55/26.56 (2) op(e3, e0) = all_52_12
% 154.55/26.56 (3) ~ (all_52_3 = e0)
% 154.55/26.56 (4) ~ (e3 = e0)
% 154.55/26.56 (5) op(e3, e0) = e0
% 154.55/26.56 (6) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 &
% 154.55/26.56 op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3)
% 154.55/26.56 & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.56 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | BETA: splitting (6) gives:
% 154.55/26.56 |
% 154.55/26.56 | Case 1:
% 154.55/26.56 | |
% 154.55/26.56 | | (8) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3
% 154.55/26.56 | | & op(e0, e3) = e3
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (8) implies:
% 154.55/26.56 | | (9) op(e3, e0) = e3
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (2), (4), (5), (7), (9) are inconsistent by sub-proof #258.
% 154.55/26.56 | |
% 154.55/26.56 | Case 2:
% 154.55/26.56 | |
% 154.55/26.56 | | (10) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 154.55/26.56 | | e0 & op(e0, e3) = e0
% 154.55/26.56 | |
% 154.55/26.56 | | ALPHA: (10) implies:
% 154.55/26.56 | | (11) op(e0, e3) = e0
% 154.55/26.56 | |
% 154.55/26.56 | | REF_CLOSE: (1), (3), (7), (11) are inconsistent by sub-proof #89.
% 154.55/26.56 | |
% 154.55/26.56 | End of split
% 154.55/26.56 |
% 154.55/26.56 End of proof
% 154.55/26.56
% 154.55/26.56 Sub-proof #65 shows that the following formulas are inconsistent:
% 154.55/26.56 ----------------------------------------------------------------
% 154.55/26.56 (1) op(e1, e1) = all_6_2
% 154.55/26.56 (2) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 154.55/26.56 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 154.55/26.56 (3) all_58_14 = e0
% 154.55/26.56 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 154.55/26.56 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 154.55/26.56 (5) ~ (e3 = e0)
% 154.55/26.56 (6) ~ (e2 = e0)
% 154.55/26.56 (7) ~ (e3 = e1)
% 154.55/26.56 (8) ~ (all_6_2 = e3)
% 154.55/26.56 (9) op(e0, e1) = all_52_11
% 154.55/26.56 (10) ~ (e2 = e1)
% 154.55/26.56 (11) op(e0, e1) = e0
% 154.55/26.56 (12) ~ (all_6_2 = e2)
% 154.55/26.56 (13) all_58_5 = e1 & op(e2, e1) = e1
% 154.55/26.56 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.56 (15) ~ (e3 = e2)
% 154.55/26.56
% 154.55/26.56 Begin of proof
% 154.55/26.56 |
% 154.55/26.56 | ALPHA: (13) implies:
% 154.55/26.56 | (16) op(e2, e1) = e1
% 154.55/26.56 |
% 154.55/26.56 | BETA: splitting (2) gives:
% 154.55/26.56 |
% 154.55/26.56 | Case 1:
% 154.55/26.56 | |
% 154.55/26.57 | | (17) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 154.55/26.57 | | e3)
% 154.55/26.57 | |
% 154.55/26.57 | | BETA: splitting (17) gives:
% 154.55/26.57 | |
% 154.55/26.57 | | Case 1:
% 154.55/26.57 | | |
% 154.55/26.57 | | | (18) all_58_4 = e3 & op(e3, e1) = e3
% 154.55/26.57 | | |
% 154.55/26.57 | | | ALPHA: (18) implies:
% 154.55/26.57 | | | (19) op(e3, e1) = e3
% 154.55/26.57 | | |
% 154.55/26.57 | | | BETA: splitting (4) gives:
% 154.55/26.57 | | |
% 154.55/26.57 | | | Case 1:
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 154.55/26.57 | | | | = e2)
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | BETA: splitting (20) gives:
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | Case 1:
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | (21) all_58_4 = e2 & op(e3, e1) = e2
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | ALPHA: (21) implies:
% 154.55/26.57 | | | | | (22) op(e3, e1) = e2
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | REF_CLOSE: (14), (15), (19), (22) are inconsistent by sub-proof #1502.
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | Case 2:
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | (23) all_58_5 = e2 & op(e2, e1) = e2
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | ALPHA: (23) implies:
% 154.55/26.57 | | | | | (24) op(e2, e1) = e2
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | REF_CLOSE: (10), (14), (16), (24) are inconsistent by sub-proof #956.
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | End of split
% 154.55/26.57 | | | |
% 154.55/26.57 | | | Case 2:
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | (25) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 154.55/26.57 | | | | = e2)
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | REF_CLOSE: (1), (6), (9), (11), (12), (14), (25) are inconsistent by
% 154.55/26.57 | | | | sub-proof #333.
% 154.55/26.57 | | | |
% 154.55/26.57 | | | End of split
% 154.55/26.57 | | |
% 154.55/26.57 | | Case 2:
% 154.55/26.57 | | |
% 154.55/26.57 | | | (26) all_58_5 = e3 & op(e2, e1) = e3
% 154.55/26.57 | | |
% 154.55/26.57 | | | ALPHA: (26) implies:
% 154.55/26.57 | | | (27) op(e2, e1) = e3
% 154.55/26.57 | | |
% 154.55/26.57 | | | REF_CLOSE: (7), (14), (16), (27) are inconsistent by sub-proof #352.
% 154.55/26.57 | | |
% 154.55/26.57 | | End of split
% 154.55/26.57 | |
% 154.55/26.57 | Case 2:
% 154.55/26.57 | |
% 154.55/26.57 | | (28) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 154.55/26.57 | | e3)
% 154.55/26.57 | |
% 154.55/26.57 | | REF_CLOSE: (1), (3), (5), (8), (14), (28) are inconsistent by sub-proof
% 154.55/26.57 | | #245.
% 154.55/26.57 | |
% 154.55/26.57 | End of split
% 154.55/26.57 |
% 154.55/26.57 End of proof
% 154.55/26.57
% 154.55/26.57 Sub-proof #66 shows that the following formulas are inconsistent:
% 154.55/26.57 ----------------------------------------------------------------
% 154.55/26.57 (1) op(e3, e1) = e1
% 154.55/26.57 (2) op(e1, e1) = all_6_2
% 154.55/26.57 (3) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 154.55/26.57 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 154.55/26.57 (4) ~ (e2 = e0)
% 154.55/26.57 (5) all_58_5 = e3
% 154.55/26.57 (6) op(e0, e1) = all_52_11
% 154.55/26.57 (7) ~ (e2 = e1)
% 154.55/26.57 (8) op(e0, e1) = e0
% 154.55/26.57 (9) ~ (all_6_2 = e2)
% 154.55/26.57 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.57 (11) ~ (e3 = e2)
% 154.55/26.57
% 154.55/26.57 Begin of proof
% 154.55/26.57 |
% 154.55/26.57 | BETA: splitting (3) gives:
% 154.55/26.57 |
% 154.55/26.57 | Case 1:
% 154.55/26.57 | |
% 154.55/26.57 | | (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 154.55/26.57 | | e2)
% 154.55/26.57 | |
% 154.55/26.57 | | BETA: splitting (12) gives:
% 154.55/26.57 | |
% 154.55/26.57 | | Case 1:
% 154.55/26.57 | | |
% 154.55/26.57 | | | (13) all_58_4 = e2 & op(e3, e1) = e2
% 154.55/26.57 | | |
% 154.55/26.57 | | | ALPHA: (13) implies:
% 154.55/26.57 | | | (14) op(e3, e1) = e2
% 154.55/26.57 | | |
% 154.55/26.57 | | | REF_CLOSE: (1), (7), (10), (14) are inconsistent by sub-proof #338.
% 154.55/26.57 | | |
% 154.55/26.57 | | Case 2:
% 154.55/26.57 | | |
% 154.55/26.57 | | | (15) all_58_5 = e2 & op(e2, e1) = e2
% 154.55/26.57 | | |
% 154.55/26.57 | | | REF_CLOSE: (5), (11), (15) are inconsistent by sub-proof #250.
% 154.55/26.57 | | |
% 154.55/26.57 | | End of split
% 154.55/26.57 | |
% 154.55/26.57 | Case 2:
% 154.55/26.57 | |
% 154.55/26.57 | | (16) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 154.55/26.57 | | e2)
% 154.55/26.57 | |
% 154.55/26.57 | | REF_CLOSE: (2), (4), (6), (8), (9), (10), (16) are inconsistent by sub-proof
% 154.55/26.57 | | #333.
% 154.55/26.57 | |
% 154.55/26.57 | End of split
% 154.55/26.57 |
% 154.55/26.57 End of proof
% 154.55/26.57
% 154.55/26.57 Sub-proof #67 shows that the following formulas are inconsistent:
% 154.55/26.57 ----------------------------------------------------------------
% 154.55/26.57 (1) all_58_9 = e1 & op(e3, e0) = e1
% 154.55/26.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.57 (3) op(e3, e0) = all_52_12
% 154.55/26.57 (4) ~ (all_52_12 = e1)
% 154.55/26.57
% 154.55/26.57 Begin of proof
% 154.55/26.57 |
% 154.55/26.57 | ALPHA: (1) implies:
% 154.55/26.57 | (5) op(e3, e0) = e1
% 154.55/26.57 |
% 154.55/26.57 | GROUND_INST: instantiating (2) with all_52_12, e1, e0, e3, simplifying with
% 154.55/26.57 | (3), (5) gives:
% 154.55/26.57 | (6) all_52_12 = e1
% 154.55/26.57 |
% 154.55/26.57 | REDUCE: (4), (6) imply:
% 154.55/26.57 | (7) $false
% 154.55/26.57 |
% 154.55/26.57 | CLOSE: (7) is inconsistent.
% 154.55/26.57 |
% 154.55/26.57 End of proof
% 154.55/26.57
% 154.55/26.57 Sub-proof #68 shows that the following formulas are inconsistent:
% 154.55/26.57 ----------------------------------------------------------------
% 154.55/26.57 (1) op(e3, e0) = all_52_12
% 154.55/26.57 (2) ~ (all_52_14 = e2)
% 154.55/26.57 (3) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.57 (4) all_56_14 = e2
% 154.55/26.57 (5) all_54_1 = all_52_4
% 154.55/26.57 (6) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.57 (7) all_56_13 = all_8_2
% 154.55/26.57 (8) ~ (all_52_4 = all_52_12)
% 154.55/26.57 (9) all_56_12 = e0
% 154.55/26.57 (10) ~ (all_56_12 = e0) | (all_56_2 = e3 & op(e3, e0) = e3)
% 154.55/26.57 (11) ~ (all_52_2 = e0)
% 154.55/26.57 (12) ~ (all_52_4 = e0)
% 154.55/26.57 (13) all_54_8 = all_52_2
% 154.55/26.57 (14) all_56_15 = all_4_2
% 154.55/26.57 (15) ~ (all_52_4 = e1)
% 154.55/26.57 (16) ~ (all_52_2 = e1)
% 154.55/26.57 (17) ~ (all_52_4 = all_8_2)
% 154.55/26.57 (18) ~ (all_52_2 = all_52_14)
% 154.55/26.57 (19) ~ (e2 = e1)
% 154.55/26.57 (20) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.57 (21) ~ (all_52_2 = e2)
% 154.55/26.57 (22) ~ (all_52_14 = e1)
% 154.55/26.57 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.57 (24) all_54_11 = all_52_14
% 154.55/26.57 (25) ~ (all_52_14 = all_4_2)
% 154.55/26.57 (26) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.57
% 154.55/26.57 Begin of proof
% 154.55/26.57 |
% 154.55/26.57 | BETA: splitting (3) gives:
% 154.55/26.57 |
% 154.55/26.57 | Case 1:
% 154.55/26.57 | |
% 154.55/26.57 | | (27) all_54_8 = e3
% 154.55/26.57 | |
% 154.55/26.57 | | COMBINE_EQS: (13), (27) imply:
% 154.55/26.57 | | (28) all_52_2 = e3
% 154.55/26.57 | |
% 154.55/26.57 | | REDUCE: (18), (28) imply:
% 154.55/26.57 | | (29) ~ (all_52_14 = e3)
% 154.55/26.57 | |
% 154.55/26.57 | | SIMP: (29) implies:
% 154.55/26.57 | | (30) ~ (all_52_14 = e3)
% 154.55/26.57 | |
% 154.55/26.57 | | BETA: splitting (10) gives:
% 154.55/26.57 | |
% 154.55/26.57 | | Case 1:
% 154.55/26.57 | | |
% 154.55/26.57 | | | (31) ~ (all_56_12 = e0)
% 154.55/26.57 | | |
% 154.55/26.57 | | | REDUCE: (9), (31) imply:
% 154.55/26.57 | | | (32) $false
% 154.55/26.57 | | |
% 154.55/26.57 | | | CLOSE: (32) is inconsistent.
% 154.55/26.57 | | |
% 154.55/26.57 | | Case 2:
% 154.55/26.57 | | |
% 154.55/26.57 | | | (33) all_56_2 = e3 & op(e3, e0) = e3
% 154.55/26.57 | | |
% 154.55/26.57 | | | ALPHA: (33) implies:
% 154.55/26.57 | | | (34) op(e3, e0) = e3
% 154.55/26.57 | | |
% 154.55/26.57 | | | BETA: splitting (20) gives:
% 154.55/26.57 | | |
% 154.55/26.57 | | | Case 1:
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | (35) all_54_11 = e3
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | REF_CLOSE: (24), (30), (35) are inconsistent by sub-proof #1415.
% 154.55/26.57 | | | |
% 154.55/26.57 | | | Case 2:
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | (36) ~ (all_54_11 = e3)
% 154.55/26.57 | | | | (37) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | BETA: splitting (37) gives:
% 154.55/26.57 | | | |
% 154.55/26.57 | | | | Case 1:
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | (38) all_54_11 = e2
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | REF_CLOSE: (2), (24), (38) are inconsistent by sub-proof #1414.
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | Case 2:
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | (39) all_54_11 = e1 | all_54_11 = e0
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | BETA: splitting (39) gives:
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | | Case 1:
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | (40) all_54_11 = e1
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | REF_CLOSE: (22), (24), (40) are inconsistent by sub-proof #1228.
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | Case 2:
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | (41) all_54_11 = e0
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | COMBINE_EQS: (24), (41) imply:
% 154.55/26.57 | | | | | | (42) all_52_14 = e0
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | SIMP: (42) implies:
% 154.55/26.57 | | | | | | (43) all_52_14 = e0
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | REDUCE: (25), (43) imply:
% 154.55/26.57 | | | | | | (44) ~ (all_4_2 = e0)
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | SIMP: (44) implies:
% 154.55/26.57 | | | | | | (45) ~ (all_4_2 = e0)
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | REDUCE: (30), (43) imply:
% 154.55/26.57 | | | | | | (46) ~ (e3 = e0)
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | SIMP: (46) implies:
% 154.55/26.57 | | | | | | (47) ~ (e3 = e0)
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | BETA: splitting (26) gives:
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | | Case 1:
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | | (48) all_56_12 = e3
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | | COMBINE_EQS: (9), (48) imply:
% 154.55/26.57 | | | | | | | (49) e3 = e0
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | | REDUCE: (47), (49) imply:
% 154.55/26.57 | | | | | | | (50) $false
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | | CLOSE: (50) is inconsistent.
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | Case 2:
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | | (51) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | | BETA: splitting (51) gives:
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | | Case 1:
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | | (52) all_56_13 = e2
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | | COMBINE_EQS: (7), (52) imply:
% 154.55/26.57 | | | | | | | | (53) all_8_2 = e2
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | | REDUCE: (17), (53) imply:
% 154.55/26.57 | | | | | | | | (54) ~ (all_52_4 = e2)
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | | BETA: splitting (6) gives:
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | | Case 1:
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | | (55) all_54_1 = e3
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | | COMBINE_EQS: (5), (55) imply:
% 154.55/26.57 | | | | | | | | | (56) all_52_4 = e3
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | | SIMP: (56) implies:
% 154.55/26.57 | | | | | | | | | (57) all_52_4 = e3
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | | REDUCE: (8), (57) imply:
% 154.55/26.57 | | | | | | | | | (58) ~ (all_52_12 = e3)
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | | SIMP: (58) implies:
% 154.55/26.57 | | | | | | | | | (59) ~ (all_52_12 = e3)
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | | REF_CLOSE: (1), (23), (34), (59) are inconsistent by sub-proof
% 154.55/26.57 | | | | | | | | | #210.
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | Case 2:
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | | (60) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | | REF_CLOSE: (5), (12), (15), (54), (60) are inconsistent by
% 154.55/26.57 | | | | | | | | | sub-proof #1107.
% 154.55/26.57 | | | | | | | | |
% 154.55/26.57 | | | | | | | | End of split
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | Case 2:
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | | (61) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | | REF_CLOSE: (4), (14), (19), (45), (61) are inconsistent by
% 154.55/26.57 | | | | | | | | sub-proof #73.
% 154.55/26.57 | | | | | | | |
% 154.55/26.57 | | | | | | | End of split
% 154.55/26.57 | | | | | | |
% 154.55/26.57 | | | | | | End of split
% 154.55/26.57 | | | | | |
% 154.55/26.57 | | | | | End of split
% 154.55/26.57 | | | | |
% 154.55/26.57 | | | | End of split
% 154.55/26.57 | | | |
% 154.55/26.57 | | | End of split
% 154.55/26.57 | | |
% 154.55/26.57 | | End of split
% 154.55/26.57 | |
% 154.55/26.57 | Case 2:
% 154.55/26.57 | |
% 154.55/26.57 | | (62) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.57 | |
% 154.55/26.57 | | REF_CLOSE: (11), (13), (16), (21), (62) are inconsistent by sub-proof #1006.
% 154.55/26.57 | |
% 154.55/26.57 | End of split
% 154.55/26.57 |
% 154.55/26.57 End of proof
% 154.55/26.57
% 154.55/26.57 Sub-proof #69 shows that the following formulas are inconsistent:
% 154.55/26.57 ----------------------------------------------------------------
% 154.55/26.57 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 154.55/26.57 (2) op(e3, e0) = all_52_12
% 154.55/26.57 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 154.55/26.57 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 154.55/26.57 (4) ~ (all_52_14 = e2)
% 154.55/26.57 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 154.55/26.57 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 154.55/26.57 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 154.55/26.57 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 154.55/26.57 (7) all_54_13 = all_52_7
% 154.55/26.57 (8) all_52_1 = e2
% 154.55/26.57 (9) ~ (all_52_7 = e3)
% 154.55/26.57 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 154.55/26.57 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 154.55/26.57 e1)
% 154.55/26.57 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 154.55/26.57 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 154.55/26.57 (12) all_56_12 = all_10_2
% 154.55/26.57 (13) ~ (all_52_2 = all_10_2)
% 154.55/26.57 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.57 (15) ~ (all_52_7 = all_52_11)
% 154.55/26.57 (16) ~ (all_52_12 = all_4_2)
% 154.55/26.57 (17) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.57 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.57 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.57 (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 154.55/26.57 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 154.55/26.57 (20) all_56_14 = e2
% 154.55/26.57 (21) op(e3, e2) = all_52_4
% 154.55/26.57 (22) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 154.55/26.57 (23) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 154.55/26.57 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 154.55/26.57 (24) op(e2, e1) = all_52_9
% 154.55/26.57 (25) op(e2, e3) = all_52_1
% 154.55/26.57 (26) ~ (all_52_13 = e3)
% 154.55/26.57 (27) ~ (all_6_0 = e0)
% 154.55/26.57 (28) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 154.55/26.57 op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 154.55/26.57 e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 154.55/26.57 (29) all_54_2 = all_52_8
% 154.55/26.57 (30) ~ (all_52_8 = all_52_9)
% 154.55/26.57 (31) ~ (all_10_2 = e0)
% 154.55/26.57 (32) ~ (e3 = e0)
% 154.55/26.57 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.57 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.57 (34) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 154.55/26.57 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 154.55/26.57 (35) ~ (all_52_9 = all_52_13)
% 154.55/26.57 (36) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 154.55/26.57 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 154.55/26.57 e2)
% 154.55/26.57 (37) ~ (e2 = e0)
% 154.55/26.57 (38) ~ (all_52_9 = e3)
% 154.55/26.57 (39) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 154.55/26.57 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 154.55/26.57 (40) op(e1, e3) = all_52_2
% 154.55/26.57 (41) op(e2, e0) = all_52_13
% 154.55/26.57 (42) ~ (all_52_8 = all_52_12)
% 154.55/26.57 (43) ~ (e3 = e1)
% 154.55/26.57 (44) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 154.55/26.57 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 154.55/26.57 (45) all_6_1 = e3
% 154.55/26.57 (46) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.57 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.57 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.57 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.57 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.57 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.57 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.57 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.57 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.57 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.57 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.57 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.57 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.57 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.57 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.57 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.57 = e0)
% 154.55/26.57 (47) ~ (all_4_2 = e1)
% 154.55/26.57 (48) ~ (all_52_4 = all_10_2)
% 154.55/26.57 (49) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.57 (50) ~ (all_52_8 = e2)
% 154.55/26.57 (51) ~ (all_52_11 = e2)
% 154.55/26.57 (52) all_58_7 = e1
% 154.55/26.57 (53) op(e1, e2) = e1
% 154.55/26.57 (54) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 154.55/26.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 154.55/26.57 (55) op(e3, e3) = all_14_1
% 154.55/26.57 (56) op(e0, e0) = all_4_2
% 154.55/26.57 (57) all_54_8 = all_52_2
% 154.55/26.57 (58) all_54_7 = all_52_13
% 154.55/26.57 (59) ~ (all_52_8 = all_10_2)
% 154.55/26.57 (60) ~ (all_52_13 = e2)
% 154.55/26.57 (61) all_14_1 = all_10_2
% 154.55/26.57 (62) all_56_15 = all_4_2
% 154.55/26.57 (63) op(e0, e1) = all_52_11
% 154.55/26.57 (64) ~ (all_52_4 = e1)
% 154.55/26.57 (65) ~ (all_52_9 = all_52_11)
% 154.55/26.57 (66) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 154.55/26.57 (67) ~ (all_52_13 = all_4_2)
% 154.55/26.57 (68) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0 &
% 154.55/26.57 op(e2, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 154.55/26.57 e1) & op(e2, e2) = all_20_1 & $i(all_20_1))
% 154.55/26.57 (69) ~ (all_52_2 = e1)
% 154.55/26.57 (70) ~ (all_52_2 = all_52_14)
% 154.55/26.57 (71) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 154.55/26.57 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 154.55/26.57 (72) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 154.55/26.57 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 154.55/26.57 (73) all_54_6 = all_52_9
% 154.55/26.57 (74) ~ (all_10_2 = e2)
% 154.55/26.57 (75) ~ (e2 = e1)
% 154.55/26.57 (76) all_58_8 = e2
% 154.55/26.57 (77) ~ (all_52_12 = all_10_2)
% 154.55/26.57 (78) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.57 (79) ~ (e1 = e0)
% 154.55/26.57 (80) ~ (all_52_2 = e2)
% 154.55/26.57 (81) ~ (all_8_2 = e1)
% 154.55/26.57 (82) all_58_3 = e3
% 154.55/26.57 (83) op(e3, e1) = all_52_8
% 154.55/26.58 (84) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 154.55/26.58 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 154.55/26.58 e3)
% 154.55/26.58 (85) all_56_13 = e3
% 154.55/26.58 (86) ~ (all_52_14 = e1)
% 154.55/26.58 (87) op(all_6_1, e1) = all_6_0
% 154.55/26.58 (88) ~ (all_52_12 = all_52_14)
% 154.55/26.58 (89) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 154.55/26.58 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 154.55/26.58 (90) ~ (all_52_9 = e2)
% 154.55/26.58 (91) all_22_2 = e3
% 154.55/26.58 (92) ~ (all_52_7 = all_4_2)
% 154.55/26.58 (93) ~ (all_52_7 = e1)
% 154.55/26.58 (94) op(e0, e2) = all_52_7
% 154.55/26.58 (95) op(e1, e0) = all_52_14
% 154.55/26.58 (96) all_54_15 = all_4_2
% 154.55/26.58 (97) all_20_2 = all_4_2
% 154.55/26.58 (98) op(e2, e2) = all_8_2
% 154.55/26.58 (99) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.58 (100) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.58 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.58 (101) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.58 (102) all_54_11 = all_52_14
% 154.55/26.58 (103) ~ (all_52_13 = all_52_14)
% 154.55/26.58 (104) ~ (e3 = e2)
% 154.55/26.58 (105) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 154.55/26.58 (106) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 154.55/26.58 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.58 (107) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 154.55/26.58 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 154.55/26.58 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 154.55/26.58 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 154.55/26.58 e0)))
% 154.55/26.58 (108) ~ (all_52_14 = all_4_2)
% 154.55/26.58 (109) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.58 (110) ~ (all_52_1 = e3)
% 154.55/26.58
% 154.55/26.58 Begin of proof
% 154.55/26.58 |
% 154.55/26.58 | REDUCE: (45), (87) imply:
% 154.55/26.58 | (111) op(e3, e1) = all_6_0
% 154.55/26.58 |
% 154.55/26.58 | REDUCE: (55), (61) imply:
% 154.55/26.58 | (112) op(e3, e3) = all_10_2
% 154.55/26.58 |
% 154.55/26.58 | REDUCE: (8), (25) imply:
% 154.55/26.58 | (113) op(e2, e3) = e2
% 154.55/26.58 |
% 154.55/26.58 | GROUND_INST: instantiating (101) with all_52_8, all_6_0, e1, e3, simplifying
% 154.55/26.58 | with (83), (111) gives:
% 154.55/26.58 | (114) all_52_8 = all_6_0
% 154.55/26.58 |
% 154.55/26.58 | COMBINE_EQS: (29), (114) imply:
% 154.55/26.58 | (115) all_54_2 = all_6_0
% 154.55/26.58 |
% 154.55/26.58 | REDUCE: (30), (114) imply:
% 154.55/26.58 | (116) ~ (all_52_9 = all_6_0)
% 154.55/26.58 |
% 154.55/26.58 | SIMP: (116) implies:
% 154.55/26.58 | (117) ~ (all_52_9 = all_6_0)
% 154.55/26.58 |
% 154.55/26.58 | REDUCE: (42), (114) imply:
% 154.55/26.58 | (118) ~ (all_52_12 = all_6_0)
% 154.55/26.58 |
% 154.55/26.58 | SIMP: (118) implies:
% 154.55/26.58 | (119) ~ (all_52_12 = all_6_0)
% 154.55/26.58 |
% 154.55/26.58 | REDUCE: (59), (114) imply:
% 154.55/26.58 | (120) ~ (all_10_2 = all_6_0)
% 154.55/26.58 |
% 154.55/26.58 | SIMP: (120) implies:
% 154.55/26.58 | (121) ~ (all_10_2 = all_6_0)
% 154.55/26.58 |
% 154.55/26.58 | REDUCE: (50), (114) imply:
% 154.55/26.58 | (122) ~ (all_6_0 = e2)
% 154.55/26.58 |
% 154.55/26.58 | BETA: splitting (68) gives:
% 154.55/26.58 |
% 154.55/26.58 | Case 1:
% 154.55/26.58 | |
% 154.55/26.58 | | (123) ~ (all_20_2 = e2)
% 154.55/26.58 | |
% 154.55/26.58 | | REDUCE: (97), (123) imply:
% 154.55/26.58 | | (124) ~ (all_4_2 = e2)
% 154.55/26.58 | |
% 154.55/26.58 | | BETA: splitting (19) gives:
% 154.55/26.58 | |
% 154.55/26.58 | | Case 1:
% 154.55/26.58 | | |
% 154.55/26.58 | | | (125) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 154.55/26.58 | | | = e2)
% 154.55/26.58 | | |
% 154.55/26.58 | | | BETA: splitting (125) gives:
% 154.55/26.58 | | |
% 154.55/26.58 | | | Case 1:
% 154.55/26.58 | | | |
% 154.55/26.58 | | | | (126) all_58_9 = e2 & op(e3, e0) = e2
% 154.55/26.58 | | | |
% 154.55/26.58 | | | | ALPHA: (126) implies:
% 154.55/26.58 | | | | (127) all_58_9 = e2
% 154.55/26.58 | | | | (128) op(e3, e0) = e2
% 154.55/26.58 | | | |
% 154.55/26.58 | | | | BETA: splitting (5) gives:
% 154.55/26.58 | | | |
% 154.55/26.58 | | | | Case 1:
% 154.55/26.58 | | | | |
% 154.55/26.58 | | | | | (129) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 154.55/26.58 | | | | | e0) = e1)
% 154.55/26.58 | | | | |
% 154.55/26.58 | | | | | BETA: splitting (129) gives:
% 154.55/26.58 | | | | |
% 154.55/26.58 | | | | | Case 1:
% 154.55/26.58 | | | | | |
% 154.55/26.58 | | | | | | (130) all_58_9 = e1 & op(e3, e0) = e1
% 154.55/26.58 | | | | | |
% 154.55/26.58 | | | | | | REF_CLOSE: (75), (127), (130) are inconsistent by sub-proof #1325.
% 154.55/26.58 | | | | | |
% 154.55/26.58 | | | | | Case 2:
% 154.55/26.58 | | | | | |
% 154.55/26.58 | | | | | | (131) all_58_10 = e1 & op(e2, e0) = e1
% 154.55/26.58 | | | | | |
% 154.55/26.58 | | | | | | ALPHA: (131) implies:
% 154.55/26.58 | | | | | | (132) all_58_10 = e1
% 154.55/26.58 | | | | | | (133) op(e2, e0) = e1
% 154.55/26.58 | | | | | |
% 154.55/26.58 | | | | | | BETA: splitting (36) gives:
% 154.55/26.58 | | | | | |
% 154.55/26.58 | | | | | | Case 1:
% 154.55/26.58 | | | | | | |
% 154.55/26.58 | | | | | | | (134) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 154.55/26.58 | | | | | | | op(e0, e2) = e2)
% 154.55/26.58 | | | | | | |
% 154.55/26.58 | | | | | | | BETA: splitting (134) gives:
% 154.55/26.58 | | | | | | |
% 154.55/26.58 | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | |
% 154.55/26.58 | | | | | | | | (135) all_58_12 = e2 & op(e0, e3) = e2
% 154.55/26.58 | | | | | | | |
% 154.55/26.58 | | | | | | | | ALPHA: (135) implies:
% 154.55/26.58 | | | | | | | | (136) all_58_12 = e2
% 154.55/26.58 | | | | | | | |
% 154.55/26.58 | | | | | | | | REF_CLOSE: (18), (25), (32), (33), (37), (43), (75), (79),
% 154.55/26.58 | | | | | | | | (100), (101), (104), (113), (136) are inconsistent by
% 154.55/26.58 | | | | | | | | sub-proof #1062.
% 154.55/26.58 | | | | | | | |
% 154.55/26.58 | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | |
% 154.55/26.58 | | | | | | | | (137) all_58_13 = e2 & op(e0, e2) = e2
% 154.55/26.58 | | | | | | | |
% 154.55/26.58 | | | | | | | | ALPHA: (137) implies:
% 154.55/26.58 | | | | | | | | (138) all_58_13 = e2
% 154.55/26.58 | | | | | | | | (139) op(e0, e2) = e2
% 154.55/26.58 | | | | | | | |
% 154.55/26.58 | | | | | | | | BETA: splitting (106) gives:
% 154.55/26.58 | | | | | | | |
% 154.55/26.58 | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | |
% 154.55/26.58 | | | | | | | | | (140) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 154.55/26.58 | | | | | | | | | op(e3, e2) = e0)
% 154.55/26.58 | | | | | | | | |
% 154.55/26.58 | | | | | | | | | BETA: splitting (140) gives:
% 154.55/26.58 | | | | | | | | |
% 154.55/26.58 | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | (141) all_58_0 = e0 & op(e3, e3) = e0
% 154.55/26.58 | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | REF_CLOSE: (31), (101), (112), (141) are inconsistent by
% 154.55/26.58 | | | | | | | | | | sub-proof #165.
% 154.55/26.58 | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | (142) all_58_1 = e0 & op(e3, e2) = e0
% 154.55/26.58 | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | ALPHA: (142) implies:
% 154.55/26.58 | | | | | | | | | | (143) all_58_1 = e0
% 154.55/26.58 | | | | | | | | | | (144) op(e3, e2) = e0
% 154.55/26.58 | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | BETA: splitting (54) gives:
% 154.55/26.58 | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | (145) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 154.55/26.58 | | | | | | | | | | | & op(e2, e2) = e0)
% 154.55/26.58 | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | REF_CLOSE: (32), (37), (82), (101), (113), (145) are
% 154.55/26.58 | | | | | | | | | | | inconsistent by sub-proof #755.
% 154.55/26.58 | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | (146) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 154.55/26.58 | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 154.55/26.58 | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | BETA: splitting (146) gives:
% 154.55/26.58 | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | (147) all_58_5 = e0 & op(e2, e1) = e0
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | ALPHA: (147) implies:
% 154.55/26.58 | | | | | | | | | | | | (148) op(e2, e1) = e0
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_52_7, e2, e2, e0,
% 154.55/26.58 | | | | | | | | | | | | simplifying with (94), (139) gives:
% 154.55/26.58 | | | | | | | | | | | | (149) all_52_7 = e2
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_52_13, e1, e0, e2,
% 154.55/26.58 | | | | | | | | | | | | simplifying with (41), (133) gives:
% 154.55/26.58 | | | | | | | | | | | | (150) all_52_13 = e1
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_52_9, e0, e1, e2,
% 154.55/26.58 | | | | | | | | | | | | simplifying with (24), (148) gives:
% 154.55/26.58 | | | | | | | | | | | | (151) all_52_9 = e0
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_52_12, e2, e0, e3,
% 154.55/26.58 | | | | | | | | | | | | simplifying with (2), (128) gives:
% 154.55/26.58 | | | | | | | | | | | | (152) all_52_12 = e2
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_52_4, e0, e2, e3,
% 154.55/26.58 | | | | | | | | | | | | simplifying with (21), (144) gives:
% 154.55/26.58 | | | | | | | | | | | | (153) all_52_4 = e0
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (48), (153) imply:
% 154.55/26.58 | | | | | | | | | | | | (154) ~ (all_10_2 = e0)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (9), (149) imply:
% 154.55/26.58 | | | | | | | | | | | | (155) ~ (e3 = e2)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (65), (151) imply:
% 154.55/26.58 | | | | | | | | | | | | (156) ~ (all_52_11 = e0)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | SIMP: (156) implies:
% 154.55/26.58 | | | | | | | | | | | | (157) ~ (all_52_11 = e0)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (35), (150), (151) imply:
% 154.55/26.58 | | | | | | | | | | | | (158) ~ (e1 = e0)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (90), (151) imply:
% 154.55/26.58 | | | | | | | | | | | | (159) ~ (e2 = e0)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (88), (152) imply:
% 154.55/26.58 | | | | | | | | | | | | (160) ~ (all_52_14 = e2)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (77), (152) imply:
% 154.55/26.58 | | | | | | | | | | | | (161) ~ (all_10_2 = e2)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (119), (152) imply:
% 154.55/26.58 | | | | | | | | | | | | (162) ~ (all_6_0 = e2)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (16), (152) imply:
% 154.55/26.58 | | | | | | | | | | | | (163) ~ (all_4_2 = e2)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (103), (150) imply:
% 154.55/26.58 | | | | | | | | | | | | (164) ~ (all_52_14 = e1)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (67), (150) imply:
% 154.55/26.58 | | | | | | | | | | | | (165) ~ (all_4_2 = e1)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (26), (150) imply:
% 154.55/26.58 | | | | | | | | | | | | (166) ~ (e3 = e1)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | REDUCE: (60), (150) imply:
% 154.55/26.58 | | | | | | | | | | | | (167) ~ (e2 = e1)
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | BETA: splitting (46) gives:
% 154.55/26.58 | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | (168) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.58 | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.58 | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.58 | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.58 | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.58 | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | BETA: splitting (168) gives:
% 154.55/26.58 | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | (169) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 154.55/26.58 | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.58 | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.58 | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | (170) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | (171) op(e2, e3) = e3
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | REF_CLOSE: (25), (101), (110), (171) are inconsistent by
% 154.55/26.58 | | | | | | | | | | | | | | | sub-proof #1183.
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | (172) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.58 | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 154.55/26.58 | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | (173) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.58 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | | (174) op(e3, e2) = e2
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | REF_CLOSE: (37), (101), (144), (174) are inconsistent by
% 154.55/26.58 | | | | | | | | | | | | | | | | sub-proof #74.
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | (175) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | | (176) ~ (all_56_14 = e1)
% 154.55/26.58 | | | | | | | | | | | | | | | | (177) op(e1, e3) = e3
% 154.55/26.58 | | | | | | | | | | | | | | | | (178) op(e3, e1) = e3
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_52_2, e3, e3, e1,
% 154.55/26.58 | | | | | | | | | | | | | | | | simplifying with (40), (177) gives:
% 154.55/26.58 | | | | | | | | | | | | | | | | (179) all_52_2 = e3
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_6_0, e3, e1, e3,
% 154.55/26.58 | | | | | | | | | | | | | | | | simplifying with (111), (178) gives:
% 154.55/26.58 | | | | | | | | | | | | | | | | (180) all_6_0 = e3
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | REDUCE: (70), (179) imply:
% 154.55/26.58 | | | | | | | | | | | | | | | | (181) ~ (all_52_14 = e3)
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | SIMP: (181) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | | (182) ~ (all_52_14 = e3)
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | REDUCE: (121), (180) imply:
% 154.55/26.58 | | | | | | | | | | | | | | | | (183) ~ (all_10_2 = e3)
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | (184) all_54_11 = e3
% 154.55/26.58 | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (102), (182), (184) are inconsistent by sub-proof
% 154.55/26.58 | | | | | | | | | | | | | | | | | #1415.
% 154.55/26.58 | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | (185) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 154.55/26.58 | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | (186) all_54_11 = e2
% 154.55/26.58 | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (102), (186) are inconsistent by sub-proof
% 154.55/26.58 | | | | | | | | | | | | | | | | | | #1414.
% 154.55/26.58 | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | (187) all_54_11 = e1 | all_54_11 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 154.55/26.58 | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | (188) all_56_12 = e3
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (188) imply:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | (189) all_10_2 = e3
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | REDUCE: (183), (189) imply:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | (190) $false
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | (191) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | (192) all_54_11 = e1
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (102), (192) are inconsistent by sub-proof
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | #1228.
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | (193) all_54_11 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (193) imply:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | (194) all_52_14 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | SIMP: (194) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | (195) all_52_14 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (195) imply:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | (196) ~ (all_4_2 = e0)
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | (197) ~ (all_4_2 = e0)
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | | (198) all_56_13 = e2
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (104), (198) are inconsistent by sub-proof
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | | #674.
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | | (199) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (62), (75), (197), (199) are inconsistent by
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | | sub-proof #73.
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | (200) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 154.55/26.58 | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 154.55/26.58 | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.58 | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 154.55/26.58 | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 154.55/26.58 | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | REF_CLOSE: (37), (40), (47), (62), (66), (69), (96), (101),
% 154.55/26.58 | | | | | | | | | | | | | | (105), (124), (128), (200) are inconsistent by
% 154.55/26.58 | | | | | | | | | | | | | | sub-proof #110.
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | (201) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.58 | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.58 | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.55/26.58 | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.58 | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | BETA: splitting (201) gives:
% 154.55/26.58 | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | (202) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 154.55/26.58 | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.58 | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.58 | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | (203) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | (204) op(e1, e2) = e2
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | REF_CLOSE: (53), (75), (101), (204) are inconsistent by
% 154.55/26.58 | | | | | | | | | | | | | | | sub-proof #1088.
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | (205) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 154.55/26.58 | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.58 | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | (206) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | | (207) op(e2, e1) = e1
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with e0, e1, e1, e2,
% 154.55/26.58 | | | | | | | | | | | | | | | | simplifying with (148), (207) gives:
% 154.55/26.58 | | | | | | | | | | | | | | | | (208) e1 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (208) imply:
% 154.55/26.58 | | | | | | | | | | | | | | | | (209) all_58_7 = e0
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (43), (75), (79), (82), (138), (143), (209)
% 154.55/26.58 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #752.
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | (210) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 154.55/26.58 | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | | (211) op(e2, e0) = e2
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | | REF_CLOSE: (41), (60), (101), (211) are inconsistent by
% 154.55/26.58 | | | | | | | | | | | | | | | | sub-proof #1535.
% 154.55/26.58 | | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | End of split
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | Case 2:
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | (212) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 154.55/26.58 | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.58 | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.55/26.58 | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.58 | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 154.55/26.58 | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | Case 1:
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | (213) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 154.55/26.58 | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 154.55/26.58 | | | | | | | | | | | | | | |
% 154.55/26.58 | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 154.55/26.58 | | | | | | | | | | | | | | | (214) op(e0, e2) = e0
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | REF_CLOSE: (37), (94), (101), (139), (214) are inconsistent
% 154.55/26.59 | | | | | | | | | | | | | | | by sub-proof #1040.
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | (215) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.59 | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 154.55/26.59 | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.59 | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | (216) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 154.55/26.59 | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 154.55/26.59 | | | | | | | | | | | | | | | | (217) ~ (all_56_15 = e0)
% 154.55/26.59 | | | | | | | | | | | | | | | | (218) op(e1, e0) = e1
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | REDUCE: (62), (217) imply:
% 154.55/26.59 | | | | | | | | | | | | | | | | (219) ~ (all_4_2 = e0)
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | (220) all_56_12 = e3
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (220) imply:
% 154.55/26.59 | | | | | | | | | | | | | | | | | (221) all_10_2 = e3
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | SIMP: (221) implies:
% 154.55/26.59 | | | | | | | | | | | | | | | | | (222) all_10_2 = e3
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | REDUCE: (112), (222) imply:
% 154.55/26.59 | | | | | | | | | | | | | | | | | (223) op(e3, e3) = e3
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | (224) ~ (all_22_2 = e3)
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | REDUCE: (91), (224) imply:
% 154.55/26.59 | | | | | | | | | | | | | | | | | | (225) $false
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | (226) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0
% 154.55/26.59 | | | | | | | | | | | | | | | | | | & op(e3, e3) = all_22_1 & $i(all_22_0) &
% 154.55/26.59 | | | | | | | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3, e3)
% 154.55/26.59 | | | | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | (227) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 154.55/26.59 | | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | (228) op(e3, e3) = all_22_1
% 154.55/26.59 | | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (32), (33), (37), (43), (52), (75), (76),
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | (79), (100), (101), (104), (113), (218), (223),
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | (228) are inconsistent by sub-proof #72.
% 154.55/26.59 | | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | (229) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 154.55/26.59 | | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | (230) op(e3, e3) = all_22_1
% 154.55/26.59 | | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (32), (33), (37), (43), (52), (75), (76),
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | (79), (100), (101), (104), (113), (218), (223),
% 154.55/26.59 | | | | | | | | | | | | | | | | | | | (230) are inconsistent by sub-proof #72.
% 154.55/26.59 | | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | (231) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | (232) all_56_13 = e2
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (104), (232) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | | | | | | | | | | | | | #674.
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | (233) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (62), (75), (219), (233) are inconsistent by
% 154.55/26.59 | | | | | | | | | | | | | | | | | | sub-proof #73.
% 154.55/26.59 | | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | (234) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 154.55/26.59 | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 154.55/26.59 | | | | | | | | | | | | | | | | (235) op(e0, e1) = e0
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_52_11, e0, e1, e0,
% 154.55/26.59 | | | | | | | | | | | | | | | | simplifying with (63), (235) gives:
% 154.55/26.59 | | | | | | | | | | | | | | | | (236) all_52_11 = e0
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | REDUCE: (157), (236) imply:
% 154.55/26.59 | | | | | | | | | | | | | | | | (237) $false
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | CLOSE: (237) is inconsistent.
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | (238) all_58_10 = e0 & op(e2, e0) = e0
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | ALPHA: (238) implies:
% 154.55/26.59 | | | | | | | | | | | | (239) all_58_10 = e0
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | COMBINE_EQS: (132), (239) imply:
% 154.55/26.59 | | | | | | | | | | | | (240) e1 = e0
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | SIMP: (240) implies:
% 154.55/26.59 | | | | | | | | | | | | (241) e1 = e0
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | COMBINE_EQS: (52), (241) imply:
% 154.55/26.59 | | | | | | | | | | | | (242) all_58_7 = e0
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | REF_CLOSE: (3), (43), (75), (79), (82), (138), (143), (242)
% 154.55/26.59 | | | | | | | | | | | | are inconsistent by sub-proof #752.
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | (243) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 154.55/26.59 | | | | | | | | | op(e3, e0) = e0)
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | BETA: splitting (243) gives:
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | (244) all_58_4 = e0 & op(e3, e1) = e0
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | ALPHA: (244) implies:
% 154.55/26.59 | | | | | | | | | | (245) all_58_4 = e0
% 154.55/26.59 | | | | | | | | | | (246) op(e3, e1) = e0
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | BETA: splitting (11) gives:
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | (247) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 154.55/26.59 | | | | | | | | | | | & op(e2, e1) = e3)
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | BETA: splitting (247) gives:
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | (248) all_58_4 = e3 & op(e3, e1) = e3
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | ALPHA: (248) implies:
% 154.55/26.59 | | | | | | | | | | | | (249) all_58_4 = e3
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | REF_CLOSE: (32), (245), (249) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | | | | | | | #1501.
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | (250) all_58_5 = e3 & op(e2, e1) = e3
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | ALPHA: (250) implies:
% 154.55/26.59 | | | | | | | | | | | | (251) op(e2, e1) = e3
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | REF_CLOSE: (24), (38), (101), (251) are inconsistent by
% 154.55/26.59 | | | | | | | | | | | | sub-proof #1196.
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | (252) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 154.55/26.59 | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | BETA: splitting (252) gives:
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | (253) all_58_8 = e3 & op(e1, e1) = e3
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | REF_CLOSE: (76), (104), (253) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | | | | | | | #1069.
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | (254) all_58_14 = e3 & op(e0, e1) = e3
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | ALPHA: (254) implies:
% 154.55/26.59 | | | | | | | | | | | | (255) all_58_14 = e3
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | BETA: splitting (72) gives:
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | (256) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 154.55/26.59 | | | | | | | | | | | | | & op(e2, e1) = e1)
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | BETA: splitting (256) gives:
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | (257) all_58_4 = e1 & op(e3, e1) = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | ALPHA: (257) implies:
% 154.55/26.59 | | | | | | | | | | | | | | (258) op(e3, e1) = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | REF_CLOSE: (79), (101), (246), (258) are inconsistent by
% 154.55/26.59 | | | | | | | | | | | | | | sub-proof #1281.
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | (259) all_58_5 = e1 & op(e2, e1) = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | ALPHA: (259) implies:
% 154.55/26.59 | | | | | | | | | | | | | | (260) all_58_5 = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | REF_CLOSE: (6), (32), (37), (43), (54), (75), (79), (82),
% 154.55/26.59 | | | | | | | | | | | | | | (101), (113), (132), (260) are inconsistent by
% 154.55/26.59 | | | | | | | | | | | | | | sub-proof #754.
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | (261) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 154.55/26.59 | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | BETA: splitting (261) gives:
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | (262) all_58_8 = e1 & op(e1, e1) = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | ALPHA: (262) implies:
% 154.55/26.59 | | | | | | | | | | | | | | (263) all_58_8 = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | COMBINE_EQS: (76), (263) imply:
% 154.55/26.59 | | | | | | | | | | | | | | (264) e2 = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | SIMP: (264) implies:
% 154.55/26.59 | | | | | | | | | | | | | | (265) e2 = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | REDUCE: (75), (265) imply:
% 154.55/26.59 | | | | | | | | | | | | | | (266) $false
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | CLOSE: (266) is inconsistent.
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | (267) all_58_14 = e1 & op(e0, e1) = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | ALPHA: (267) implies:
% 154.55/26.59 | | | | | | | | | | | | | | (268) all_58_14 = e1
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | REF_CLOSE: (43), (255), (268) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | | | | | | | | | #1147.
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | (269) all_58_9 = e0 & op(e3, e0) = e0
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | ALPHA: (269) implies:
% 154.55/26.59 | | | | | | | | | | (270) op(e3, e0) = e0
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | REF_CLOSE: (37), (101), (128), (270) are inconsistent by
% 154.55/26.59 | | | | | | | | | | sub-proof #1500.
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | End of split
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | End of split
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | End of split
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | Case 2:
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | (271) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 154.55/26.59 | | | | | | | op(e0, e0) = e2)
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | BETA: splitting (271) gives:
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | (272) all_58_14 = e2 & op(e0, e1) = e2
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | REF_CLOSE: (51), (63), (101), (272) are inconsistent by
% 154.55/26.59 | | | | | | | | sub-proof #1175.
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | (273) all_58_15 = e2 & op(e0, e0) = e2
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | REF_CLOSE: (56), (101), (124), (273) are inconsistent by
% 154.55/26.59 | | | | | | | | sub-proof #1452.
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | End of split
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | End of split
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | End of split
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | Case 2:
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | | (274) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 154.55/26.59 | | | | | e0) = e1)
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | | REF_CLOSE: (23), (32), (37), (39), (43), (47), (52), (56), (76), (79),
% 154.55/26.59 | | | | | (101), (104), (274) are inconsistent by sub-proof #104.
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | End of split
% 154.55/26.59 | | | |
% 154.55/26.59 | | | Case 2:
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | (275) all_58_10 = e2 & op(e2, e0) = e2
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | ALPHA: (275) implies:
% 154.55/26.59 | | | | (276) all_58_10 = e2
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | REF_CLOSE: (6), (25), (32), (37), (43), (54), (71), (75), (79), (81),
% 154.55/26.59 | | | | (98), (101), (104), (113), (276) are inconsistent by
% 154.55/26.59 | | | | sub-proof #905.
% 154.55/26.59 | | | |
% 154.55/26.59 | | | End of split
% 154.55/26.59 | | |
% 154.55/26.59 | | Case 2:
% 154.55/26.59 | | |
% 154.55/26.59 | | | (277) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0)
% 154.55/26.59 | | | = e2)
% 154.55/26.59 | | |
% 154.55/26.59 | | | REF_CLOSE: (4), (56), (95), (101), (124), (277) are inconsistent by
% 154.55/26.59 | | | sub-proof #1185.
% 154.55/26.59 | | |
% 154.55/26.59 | | End of split
% 154.55/26.59 | |
% 154.55/26.59 | Case 2:
% 154.55/26.59 | |
% 154.55/26.59 | | (278) all_20_2 = e2
% 154.55/26.59 | |
% 154.55/26.59 | | COMBINE_EQS: (97), (278) imply:
% 154.55/26.59 | | (279) all_4_2 = e2
% 154.55/26.59 | |
% 154.55/26.59 | | COMBINE_EQS: (62), (279) imply:
% 154.55/26.59 | | (280) all_56_15 = e2
% 154.55/26.59 | |
% 154.55/26.59 | | REDUCE: (92), (279) imply:
% 154.55/26.59 | | (281) ~ (all_52_7 = e2)
% 154.55/26.59 | |
% 154.55/26.59 | | REDUCE: (16), (279) imply:
% 154.55/26.59 | | (282) ~ (all_52_12 = e2)
% 154.55/26.59 | |
% 154.55/26.59 | | BETA: splitting (109) gives:
% 154.55/26.59 | |
% 154.55/26.59 | | Case 1:
% 154.55/26.59 | | |
% 154.55/26.59 | | | (283) all_56_12 = e3
% 154.55/26.59 | | |
% 154.55/26.59 | | | COMBINE_EQS: (12), (283) imply:
% 154.55/26.59 | | | (284) all_10_2 = e3
% 154.55/26.59 | | |
% 154.55/26.59 | | | REDUCE: (13), (284) imply:
% 154.55/26.59 | | | (285) ~ (all_52_2 = e3)
% 154.55/26.59 | | |
% 154.55/26.59 | | | REDUCE: (121), (284) imply:
% 154.55/26.59 | | | (286) ~ (all_6_0 = e3)
% 154.55/26.59 | | |
% 154.55/26.59 | | | SIMP: (286) implies:
% 154.55/26.59 | | | (287) ~ (all_6_0 = e3)
% 154.55/26.59 | | |
% 154.55/26.59 | | | REDUCE: (112), (284) imply:
% 154.55/26.59 | | | (288) op(e3, e3) = e3
% 154.55/26.59 | | |
% 154.55/26.59 | | | BETA: splitting (28) gives:
% 154.55/26.59 | | |
% 154.55/26.59 | | | Case 1:
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | (289) ~ (all_22_2 = e3)
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | REDUCE: (91), (289) imply:
% 154.55/26.59 | | | | (290) $false
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | CLOSE: (290) is inconsistent.
% 154.55/26.59 | | | |
% 154.55/26.59 | | | Case 2:
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | (291) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3)
% 154.55/26.59 | | | | = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 154.55/26.59 | | | | e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | BETA: splitting (19) gives:
% 154.55/26.59 | | | |
% 154.55/26.59 | | | | Case 1:
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | | (292) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 154.55/26.59 | | | | | e0) = e2)
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | | BETA: splitting (292) gives:
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | | Case 1:
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | (293) all_58_9 = e2 & op(e3, e0) = e2
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | REF_CLOSE: (2), (101), (282), (293) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | #1238.
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | Case 2:
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | (294) all_58_10 = e2 & op(e2, e0) = e2
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | ALPHA: (294) implies:
% 154.55/26.59 | | | | | | (295) all_58_10 = e2
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | REF_CLOSE: (6), (25), (32), (37), (43), (54), (71), (75), (79),
% 154.55/26.59 | | | | | | (81), (98), (101), (104), (113), (295) are inconsistent
% 154.55/26.59 | | | | | | by sub-proof #905.
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | End of split
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | Case 2:
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | | (296) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 154.55/26.59 | | | | | e0) = e2)
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | | BETA: splitting (296) gives:
% 154.55/26.59 | | | | |
% 154.55/26.59 | | | | | Case 1:
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | (297) all_58_11 = e2 & op(e1, e0) = e2
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | ALPHA: (297) implies:
% 154.55/26.59 | | | | | | (298) op(e1, e0) = e2
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | REF_CLOSE: (4), (95), (101), (298) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | #1389.
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | Case 2:
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | (299) all_58_15 = e2 & op(e0, e0) = e2
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | ALPHA: (299) implies:
% 154.55/26.59 | | | | | | (300) all_58_15 = e2
% 154.55/26.59 | | | | | | (301) op(e0, e0) = e2
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | BETA: splitting (11) gives:
% 154.55/26.59 | | | | | |
% 154.55/26.59 | | | | | | Case 1:
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | (302) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 154.55/26.59 | | | | | | | op(e2, e1) = e3)
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | BETA: splitting (302) gives:
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | (303) all_58_4 = e3 & op(e3, e1) = e3
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | ALPHA: (303) implies:
% 154.55/26.59 | | | | | | | | (304) all_58_4 = e3
% 154.55/26.59 | | | | | | | | (305) op(e3, e1) = e3
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | BETA: splitting (291) gives:
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | (306) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 154.55/26.59 | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | ALPHA: (306) implies:
% 154.55/26.59 | | | | | | | | | (307) op(e3, e3) = all_22_1
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | REF_CLOSE: (18), (21), (25), (31), (32), (33), (34), (37),
% 154.55/26.59 | | | | | | | | | (40), (43), (64), (69), (74), (75), (79), (89),
% 154.55/26.59 | | | | | | | | | (100), (101), (104), (106), (110), (112), (113),
% 154.55/26.59 | | | | | | | | | (288), (304), (305), (307) are inconsistent by
% 154.55/26.59 | | | | | | | | | sub-proof #71.
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | (308) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 154.55/26.59 | | | | | | | | | $i(all_22_1)
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | ALPHA: (308) implies:
% 154.55/26.59 | | | | | | | | | (309) op(e3, e3) = all_22_1
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | REF_CLOSE: (18), (21), (25), (31), (32), (33), (34), (37),
% 154.55/26.59 | | | | | | | | | (40), (43), (64), (69), (74), (75), (79), (89),
% 154.55/26.59 | | | | | | | | | (100), (101), (104), (106), (110), (112), (113),
% 154.55/26.59 | | | | | | | | | (288), (304), (305), (309) are inconsistent by
% 154.55/26.59 | | | | | | | | | sub-proof #71.
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | End of split
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | (310) all_58_5 = e3 & op(e2, e1) = e3
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | ALPHA: (310) implies:
% 154.55/26.59 | | | | | | | | (311) op(e2, e1) = e3
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | REF_CLOSE: (24), (38), (101), (311) are inconsistent by
% 154.55/26.59 | | | | | | | | sub-proof #1196.
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | End of split
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | Case 2:
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | (312) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 154.55/26.59 | | | | | | | op(e0, e1) = e3)
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | BETA: splitting (312) gives:
% 154.55/26.59 | | | | | | |
% 154.55/26.59 | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | (313) all_58_8 = e3 & op(e1, e1) = e3
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | REF_CLOSE: (76), (104), (313) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | | | #112.
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | (314) all_58_14 = e3 & op(e0, e1) = e3
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | ALPHA: (314) implies:
% 154.55/26.59 | | | | | | | | (315) all_58_14 = e3
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | BETA: splitting (22) gives:
% 154.55/26.59 | | | | | | | |
% 154.55/26.59 | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | (316) ~ (all_56_15 = e2)
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | REDUCE: (280), (316) imply:
% 154.55/26.59 | | | | | | | | | (317) $false
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | CLOSE: (317) is inconsistent.
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | (318) all_56_10 = e0 & op(e0, e2) = e0
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | ALPHA: (318) implies:
% 154.55/26.59 | | | | | | | | | (319) op(e0, e2) = e0
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | BETA: splitting (99) gives:
% 154.55/26.59 | | | | | | | | |
% 154.55/26.59 | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | (320) all_54_13 = e3
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | REF_CLOSE: (7), (9), (320) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | | | | | #1435.
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | (321) ~ (all_54_13 = e3)
% 154.55/26.59 | | | | | | | | | | (322) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | BETA: splitting (10) gives:
% 154.55/26.59 | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | (323) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 154.55/26.59 | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | BETA: splitting (323) gives:
% 154.55/26.59 | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | (324) all_58_12 = e1 & op(e0, e3) = e1
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | ALPHA: (324) implies:
% 154.55/26.59 | | | | | | | | | | | | (325) op(e0, e3) = e1
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | BETA: splitting (49) gives:
% 154.55/26.59 | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | (326) all_54_2 = e3
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | REF_CLOSE: (115), (287), (326) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | | | | | | | | #81.
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | (327) ~ (all_54_2 = e3)
% 154.55/26.59 | | | | | | | | | | | | | (328) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | BETA: splitting (328) gives:
% 154.55/26.59 | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | (329) all_54_2 = e2
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | REF_CLOSE: (115), (122), (329) are inconsistent by sub-proof
% 154.55/26.59 | | | | | | | | | | | | | | #77.
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | Case 2:
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | (330) ~ (all_54_2 = e2)
% 154.55/26.59 | | | | | | | | | | | | | | (331) all_54_2 = e1 | all_54_2 = e0
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 154.55/26.59 | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | (332) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 154.55/26.59 | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 154.55/26.59 | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | (333) all_58_6 = e3 & op(e1, e3) = e3
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 154.55/26.59 | | | | | | | | | | | | | | | | (334) all_58_6 = e3
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 154.55/26.59 | | | | | | | | | | | | | | | |
% 154.55/26.59 | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.59 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | (335) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 154.55/26.60 | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | (336) all_58_0 = e0 & op(e3, e3) = e0
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 154.55/26.60 | | | | | | | | | | | | | | | | | | (337) op(e3, e3) = e0
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (101), (288), (337) are inconsistent by
% 154.55/26.60 | | | | | | | | | | | | | | | | | | sub-proof #1521.
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | (338) all_58_2 = e0 & op(e2, e3) = e0
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 154.55/26.60 | | | | | | | | | | | | | | | | | | (339) op(e2, e3) = e0
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (101), (113), (339) are inconsistent by
% 154.55/26.60 | | | | | | | | | | | | | | | | | | sub-proof #1156.
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | (340) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 154.55/26.60 | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | (341) all_58_6 = e0 & op(e1, e3) = e0
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (334), (341) are inconsistent by sub-proof
% 154.55/26.60 | | | | | | | | | | | | | | | | | | #1350.
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | (342) all_58_12 = e0 & op(e0, e3) = e0
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 154.55/26.60 | | | | | | | | | | | | | | | | | | (343) op(e0, e3) = e0
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (79), (101), (325), (343) are inconsistent by
% 154.55/26.60 | | | | | | | | | | | | | | | | | | sub-proof #83.
% 154.55/26.60 | | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | (344) all_58_7 = e3 & op(e1, e2) = e3
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 154.55/26.60 | | | | | | | | | | | | | | | | (345) all_58_7 = e3
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | REF_CLOSE: (43), (52), (345) are inconsistent by sub-proof
% 154.55/26.60 | | | | | | | | | | | | | | | | #1330.
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | (346) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 154.55/26.60 | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 154.55/26.60 | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | BETA: splitting (346) gives:
% 154.55/26.60 | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | Case 1:
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | (347) all_58_8 = e3 & op(e1, e1) = e3
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | ALPHA: (347) implies:
% 154.55/26.60 | | | | | | | | | | | | | | | | (348) all_58_8 = e3
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (348) imply:
% 154.55/26.60 | | | | | | | | | | | | | | | | (349) e3 = e2
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (349) imply:
% 154.55/26.60 | | | | | | | | | | | | | | | | (350) all_58_14 = e2
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (32), (37), (43), (75), (79), (84),
% 154.55/26.60 | | | | | | | | | | | | | | | | (94), (101), (104), (107), (300), (301), (350) are
% 154.55/26.60 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1380.
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | (351) all_58_11 = e3 & op(e1, e0) = e3
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | ALPHA: (351) implies:
% 154.55/26.60 | | | | | | | | | | | | | | | | (352) op(e1, e0) = e3
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | Case 1:
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | (353) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 154.55/26.60 | | | | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 154.55/26.60 | | | | | | | | | | | | | | | | | $i(all_22_1)
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 154.55/26.60 | | | | | | | | | | | | | | | | | (354) op(e3, e3) = all_22_1
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (14), (15), (17),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (23), (24), (25), (26), (27), (35), (38), (40),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (41), (44), (46), (52), (53), (57), (58), (60),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (63), (69), (70), (73), (76), (78), (80), (81),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (82), (86), (88), (90), (93), (98), (100), (101),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (102), (104), (110), (111), (113), (115), (117),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (122), (281), (283), (285), (287), (288), (322),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (325), (328), (331), (352), (354) are inconsistent
% 154.55/26.60 | | | | | | | | | | | | | | | | | by sub-proof #70.
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | (355) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 154.55/26.60 | | | | | | | | | | | | | | | | | $i(all_22_1)
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | ALPHA: (355) implies:
% 154.55/26.60 | | | | | | | | | | | | | | | | | (356) op(e3, e3) = all_22_1
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (14), (15), (17),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (23), (24), (25), (26), (27), (35), (38), (40),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (41), (44), (46), (52), (53), (57), (58), (60),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (63), (69), (70), (73), (76), (78), (80), (81),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (82), (86), (88), (90), (93), (98), (100), (101),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (102), (104), (110), (111), (113), (115), (117),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (122), (281), (283), (285), (287), (288), (322),
% 154.55/26.60 | | | | | | | | | | | | | | | | | (325), (328), (331), (352), (356) are inconsistent
% 154.55/26.60 | | | | | | | | | | | | | | | | | by sub-proof #70.
% 154.55/26.60 | | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | (357) all_58_13 = e1 & op(e0, e2) = e1
% 154.55/26.60 | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | ALPHA: (357) implies:
% 154.55/26.60 | | | | | | | | | | | | (358) op(e0, e2) = e1
% 154.55/26.60 | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | | REF_CLOSE: (79), (94), (101), (319), (358) are inconsistent
% 154.55/26.60 | | | | | | | | | | | | by sub-proof #1396.
% 154.55/26.60 | | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | Case 2:
% 154.55/26.60 | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | (359) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 154.55/26.60 | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 154.55/26.60 | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | | REF_CLOSE: (43), (75), (101), (301), (315), (359) are
% 154.55/26.60 | | | | | | | | | | | inconsistent by sub-proof #776.
% 154.55/26.60 | | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | | |
% 154.55/26.60 | | | | | | | | | End of split
% 154.55/26.60 | | | | | | | | |
% 154.55/26.60 | | | | | | | | End of split
% 154.55/26.60 | | | | | | | |
% 154.55/26.60 | | | | | | | End of split
% 154.55/26.60 | | | | | | |
% 154.55/26.60 | | | | | | End of split
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | End of split
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | End of split
% 154.55/26.60 | | | |
% 154.55/26.60 | | | End of split
% 154.55/26.60 | | |
% 154.55/26.60 | | Case 2:
% 154.55/26.60 | | |
% 154.55/26.60 | | | (360) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 154.55/26.60 | | |
% 154.55/26.60 | | | BETA: splitting (360) gives:
% 154.55/26.60 | | |
% 154.55/26.60 | | | Case 1:
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | (361) all_56_13 = e2
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | COMBINE_EQS: (85), (361) imply:
% 154.55/26.60 | | | | (362) e3 = e2
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | REDUCE: (104), (362) imply:
% 154.55/26.60 | | | | (363) $false
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | CLOSE: (363) is inconsistent.
% 154.55/26.60 | | | |
% 154.55/26.60 | | | Case 2:
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | (364) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | BETA: splitting (364) gives:
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | Case 1:
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | (365) all_56_14 = e1
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | REF_CLOSE: (20), (75), (365) are inconsistent by sub-proof #93.
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | Case 2:
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | (366) all_56_15 = e0
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | COMBINE_EQS: (280), (366) imply:
% 154.55/26.60 | | | | | (367) e2 = e0
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | SIMP: (367) implies:
% 154.55/26.60 | | | | | (368) e2 = e0
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | COMBINE_EQS: (20), (368) imply:
% 154.55/26.60 | | | | | (369) all_56_14 = e0
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | REF_CLOSE: (37), (79), (280), (364), (369) are inconsistent by
% 154.55/26.60 | | | | | sub-proof #149.
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | End of split
% 154.55/26.60 | | | |
% 154.55/26.60 | | | End of split
% 154.55/26.60 | | |
% 154.55/26.60 | | End of split
% 154.55/26.60 | |
% 154.55/26.60 | End of split
% 154.55/26.60 |
% 154.55/26.60 End of proof
% 154.55/26.60
% 154.55/26.60 Sub-proof #70 shows that the following formulas are inconsistent:
% 154.55/26.60 ----------------------------------------------------------------
% 154.55/26.60 (1) op(e0, e3) = e1
% 154.55/26.60 (2) ~ (all_52_9 = all_6_0)
% 154.55/26.60 (3) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 154.55/26.60 (4) op(e3, e0) = all_52_12
% 154.55/26.60 (5) ~ (all_52_14 = e2)
% 154.55/26.60 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 154.55/26.60 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 154.55/26.60 (7) all_54_13 = all_52_7
% 154.55/26.60 (8) ~ (all_52_7 = e3)
% 154.55/26.60 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.60 (10) ~ (all_52_7 = all_52_11)
% 154.55/26.60 (11) ~ (all_52_7 = e2)
% 154.55/26.60 (12) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.60 (13) ~ (all_6_0 = e3)
% 154.55/26.60 (14) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 154.55/26.60 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 154.55/26.60 (15) op(e2, e1) = all_52_9
% 154.55/26.60 (16) op(e2, e3) = all_52_1
% 154.55/26.60 (17) ~ (all_52_13 = e3)
% 154.55/26.60 (18) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.55/26.60 (19) ~ (all_6_0 = e0)
% 154.55/26.60 (20) ~ (all_52_9 = all_52_13)
% 154.55/26.60 (21) ~ (all_52_9 = e3)
% 154.55/26.60 (22) op(e1, e3) = all_52_2
% 154.55/26.60 (23) op(e2, e0) = all_52_13
% 154.55/26.60 (24) op(e2, e3) = e2
% 154.55/26.60 (25) ~ (all_6_0 = e2)
% 154.55/26.60 (26) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 154.55/26.60 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 154.55/26.60 (27) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.60 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.60 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.60 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.60 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.60 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.60 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.60 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.60 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.60 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.60 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.60 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.60 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.60 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.60 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.60 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.60 = e0)
% 154.55/26.60 (28) all_58_7 = e1
% 154.55/26.60 (29) op(e1, e2) = e1
% 154.55/26.60 (30) all_54_8 = all_52_2
% 154.55/26.60 (31) all_54_7 = all_52_13
% 154.55/26.60 (32) all_56_12 = e3
% 154.55/26.60 (33) ~ (all_52_2 = e3)
% 154.55/26.60 (34) ~ (all_52_13 = e2)
% 154.55/26.60 (35) op(e0, e1) = all_52_11
% 154.55/26.60 (36) ~ (all_52_2 = e1)
% 154.55/26.60 (37) all_54_2 = e1 | all_54_2 = e0
% 154.55/26.60 (38) ~ (all_52_2 = all_52_14)
% 154.55/26.60 (39) all_54_6 = all_52_9
% 154.55/26.60 (40) op(e3, e3) = e3
% 154.55/26.60 (41) all_58_8 = e2
% 154.55/26.60 (42) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.60 (43) ~ (all_52_2 = e2)
% 154.55/26.60 (44) ~ (all_8_2 = e1)
% 154.55/26.60 (45) all_54_2 = all_6_0
% 154.55/26.60 (46) all_58_3 = e3
% 154.55/26.60 (47) ~ (all_52_14 = e1)
% 154.55/26.60 (48) ~ (all_52_12 = all_52_14)
% 154.55/26.60 (49) ~ (all_52_9 = e2)
% 154.55/26.60 (50) ~ (all_52_7 = e1)
% 154.55/26.60 (51) op(e1, e0) = e3
% 154.55/26.60 (52) op(e3, e3) = all_22_1
% 154.55/26.60 (53) op(e3, e1) = all_6_0
% 154.55/26.60 (54) op(e2, e2) = all_8_2
% 154.55/26.60 (55) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.60 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.60 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.60 (57) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.60 (58) all_54_11 = all_52_14
% 154.55/26.60 (59) ~ (e3 = e2)
% 154.55/26.60 (60) ~ (all_52_1 = e3)
% 154.55/26.60
% 154.55/26.60 Begin of proof
% 154.55/26.60 |
% 154.55/26.60 | BETA: splitting (37) gives:
% 154.55/26.60 |
% 154.55/26.60 | Case 1:
% 154.55/26.60 | |
% 154.55/26.60 | | (61) all_54_2 = e1
% 154.55/26.60 | |
% 154.55/26.60 | | COMBINE_EQS: (45), (61) imply:
% 154.55/26.60 | | (62) all_6_0 = e1
% 154.55/26.60 | |
% 154.55/26.60 | | SIMP: (62) implies:
% 154.55/26.60 | | (63) all_6_0 = e1
% 154.55/26.60 | |
% 154.55/26.60 | | REDUCE: (25), (63) imply:
% 154.55/26.60 | | (64) ~ (e2 = e1)
% 154.55/26.60 | |
% 154.55/26.60 | | SIMP: (64) implies:
% 154.55/26.60 | | (65) ~ (e2 = e1)
% 154.55/26.60 | |
% 154.55/26.60 | | REDUCE: (53), (63) imply:
% 154.55/26.60 | | (66) op(e3, e1) = e1
% 154.55/26.60 | |
% 154.55/26.60 | | BETA: splitting (18) gives:
% 154.55/26.60 | |
% 154.55/26.60 | | Case 1:
% 154.55/26.60 | | |
% 154.55/26.60 | | | (67) all_54_13 = e2
% 154.55/26.60 | | |
% 154.55/26.60 | | | REF_CLOSE: (7), (11), (67) are inconsistent by sub-proof #1370.
% 154.55/26.60 | | |
% 154.55/26.60 | | Case 2:
% 154.55/26.60 | | |
% 154.55/26.60 | | | (68) ~ (all_54_13 = e2)
% 154.55/26.60 | | | (69) all_54_13 = e1 | all_54_13 = e0
% 154.55/26.60 | | |
% 154.55/26.60 | | | BETA: splitting (69) gives:
% 154.55/26.60 | | |
% 154.55/26.60 | | | Case 1:
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | (70) all_54_13 = e1
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | REF_CLOSE: (7), (50), (70) are inconsistent by sub-proof #876.
% 154.55/26.60 | | | |
% 154.55/26.60 | | | Case 2:
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | (71) all_54_13 = e0
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | COMBINE_EQS: (7), (71) imply:
% 154.55/26.60 | | | | (72) all_52_7 = e0
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | SIMP: (72) implies:
% 154.55/26.60 | | | | (73) all_52_7 = e0
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | REDUCE: (10), (73) imply:
% 154.55/26.60 | | | | (74) ~ (all_52_11 = e0)
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | SIMP: (74) implies:
% 154.55/26.60 | | | | (75) ~ (all_52_11 = e0)
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | REDUCE: (8), (73) imply:
% 154.55/26.60 | | | | (76) ~ (e3 = e0)
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | SIMP: (76) implies:
% 154.55/26.60 | | | | (77) ~ (e3 = e0)
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | REDUCE: (11), (73) imply:
% 154.55/26.60 | | | | (78) ~ (e2 = e0)
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | SIMP: (78) implies:
% 154.55/26.60 | | | | (79) ~ (e2 = e0)
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | REDUCE: (50), (73) imply:
% 154.55/26.60 | | | | (80) ~ (e1 = e0)
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | SIMP: (80) implies:
% 154.55/26.60 | | | | (81) ~ (e1 = e0)
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | BETA: splitting (26) gives:
% 154.55/26.60 | | | |
% 154.55/26.60 | | | | Case 1:
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | (82) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 154.55/26.60 | | | | | e1) = e0)
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | BETA: splitting (82) gives:
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | Case 1:
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | (83) all_58_4 = e0 & op(e3, e1) = e0
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | ALPHA: (83) implies:
% 154.55/26.60 | | | | | | (84) op(e3, e1) = e0
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | REF_CLOSE: (56), (66), (81), (84) are inconsistent by sub-proof
% 154.55/26.60 | | | | | | #1281.
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | Case 2:
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | (85) all_58_5 = e0 & op(e2, e1) = e0
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | ALPHA: (85) implies:
% 154.55/26.60 | | | | | | (86) all_58_5 = e0
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (12), (13), (14),
% 154.55/26.60 | | | | | | (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 154.55/26.60 | | | | | | (25), (27), (28), (29), (30), (31), (32), (33), (34),
% 154.55/26.60 | | | | | | (36), (38), (39), (40), (41), (42), (43), (44), (45),
% 154.55/26.60 | | | | | | (46), (47), (48), (49), (51), (52), (53), (54), (55),
% 154.55/26.60 | | | | | | (56), (57), (58), (59), (60), (65), (77), (79), (81),
% 154.55/26.60 | | | | | | (86) are inconsistent by sub-proof #79.
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | End of split
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | Case 2:
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | (87) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 154.55/26.60 | | | | | e1) = e0)
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | BETA: splitting (87) gives:
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | | Case 1:
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | (88) all_58_8 = e0 & op(e1, e1) = e0
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | REF_CLOSE: (41), (79), (88) are inconsistent by sub-proof #1071.
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | Case 2:
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | (89) all_58_14 = e0 & op(e0, e1) = e0
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | ALPHA: (89) implies:
% 154.55/26.60 | | | | | | (90) op(e0, e1) = e0
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | | REF_CLOSE: (35), (56), (75), (90) are inconsistent by sub-proof #87.
% 154.55/26.60 | | | | | |
% 154.55/26.60 | | | | | End of split
% 154.55/26.60 | | | | |
% 154.55/26.60 | | | | End of split
% 154.55/26.60 | | | |
% 154.55/26.60 | | | End of split
% 154.55/26.60 | | |
% 154.55/26.60 | | End of split
% 154.55/26.60 | |
% 154.55/26.60 | Case 2:
% 154.55/26.60 | |
% 154.55/26.60 | | (91) all_54_2 = e0
% 154.55/26.60 | |
% 154.55/26.60 | | REF_CLOSE: (19), (45), (91) are inconsistent by sub-proof #76.
% 154.55/26.60 | |
% 154.55/26.60 | End of split
% 154.55/26.60 |
% 154.55/26.60 End of proof
% 154.55/26.60
% 154.55/26.60 Sub-proof #71 shows that the following formulas are inconsistent:
% 154.55/26.60 ----------------------------------------------------------------
% 154.55/26.60 (1) op(e3, e1) = e3
% 154.55/26.60 (2) op(e3, e3) = all_10_2
% 154.55/26.60 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.60 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.60 (4) op(e3, e2) = all_52_4
% 154.55/26.60 (5) op(e2, e3) = all_52_1
% 154.55/26.60 (6) ~ (all_10_2 = e0)
% 154.55/26.60 (7) ~ (e3 = e0)
% 154.55/26.60 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.60 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.60 (9) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 154.55/26.60 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 154.55/26.60 (10) ~ (e2 = e0)
% 154.55/26.60 (11) op(e1, e3) = all_52_2
% 154.55/26.60 (12) op(e2, e3) = e2
% 154.55/26.60 (13) ~ (e3 = e1)
% 154.55/26.60 (14) ~ (all_52_4 = e1)
% 154.55/26.60 (15) ~ (all_52_2 = e1)
% 154.55/26.60 (16) ~ (all_10_2 = e2)
% 154.55/26.60 (17) ~ (e2 = e1)
% 154.55/26.60 (18) op(e3, e3) = e3
% 154.55/26.60 (19) ~ (e1 = e0)
% 154.55/26.60 (20) all_58_4 = e3
% 154.55/26.60 (21) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 154.55/26.60 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 154.55/26.60 (22) op(e3, e3) = all_22_1
% 154.55/26.60 (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.60 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.60 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.60 (25) ~ (e3 = e2)
% 154.55/26.60 (26) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 154.55/26.60 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 154.55/26.60 (27) ~ (all_52_1 = e3)
% 154.55/26.60
% 154.55/26.60 Begin of proof
% 154.55/26.60 |
% 154.55/26.60 | BETA: splitting (8) gives:
% 154.55/26.60 |
% 154.55/26.60 | Case 1:
% 154.55/26.60 | |
% 154.55/26.61 | | (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 154.55/26.61 | | e1)
% 154.55/26.61 | |
% 154.55/26.61 | | REF_CLOSE: (12), (13), (17), (18), (22), (24), (28) are inconsistent by
% 154.55/26.61 | | sub-proof #863.
% 154.55/26.61 | |
% 154.55/26.61 | Case 2:
% 154.55/26.61 | |
% 154.55/26.61 | | (29) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 154.55/26.61 | | e1)
% 154.55/26.61 | |
% 154.55/26.61 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 154.55/26.61 | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 154.55/26.61 | | (26), (27), (29) are inconsistent by sub-proof #82.
% 154.55/26.61 | |
% 154.55/26.61 | End of split
% 154.55/26.61 |
% 154.55/26.61 End of proof
% 154.55/26.61
% 154.55/26.61 Sub-proof #72 shows that the following formulas are inconsistent:
% 154.55/26.61 ----------------------------------------------------------------
% 154.55/26.61 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 154.55/26.61 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 154.55/26.61 (2) ~ (e3 = e0)
% 154.55/26.61 (3) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.61 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.61 (4) ~ (e2 = e0)
% 154.55/26.61 (5) op(e2, e3) = e2
% 154.55/26.61 (6) ~ (e3 = e1)
% 154.55/26.61 (7) all_58_7 = e1
% 154.55/26.61 (8) op(e1, e0) = e1
% 154.55/26.61 (9) ~ (e2 = e1)
% 154.55/26.61 (10) op(e3, e3) = e3
% 154.55/26.61 (11) all_58_8 = e2
% 154.55/26.61 (12) ~ (e1 = e0)
% 154.55/26.61 (13) op(e3, e3) = all_22_1
% 154.55/26.61 (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 154.55/26.61 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 154.55/26.61 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.61 (16) ~ (e3 = e2)
% 154.55/26.61
% 154.55/26.61 Begin of proof
% 154.55/26.61 |
% 154.55/26.61 | BETA: splitting (1) gives:
% 154.55/26.61 |
% 154.55/26.61 | Case 1:
% 154.55/26.61 | |
% 154.55/26.61 | | (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 154.55/26.61 | | e3)
% 154.55/26.61 | |
% 154.55/26.61 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), (15),
% 154.55/26.61 | | (17) are inconsistent by sub-proof #80.
% 154.55/26.61 | |
% 154.55/26.61 | Case 2:
% 154.55/26.61 | |
% 154.55/26.61 | | (18) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 154.55/26.61 | | e3)
% 154.55/26.61 | |
% 154.55/26.61 | | REF_CLOSE: (6), (8), (11), (15), (16), (18) are inconsistent by sub-proof
% 154.55/26.61 | | #107.
% 154.55/26.61 | |
% 154.55/26.61 | End of split
% 154.55/26.61 |
% 154.55/26.61 End of proof
% 154.55/26.61
% 154.55/26.61 Sub-proof #73 shows that the following formulas are inconsistent:
% 154.55/26.61 ----------------------------------------------------------------
% 154.55/26.61 (1) all_56_14 = e2
% 154.55/26.61 (2) all_56_14 = e1 | all_56_15 = e0
% 154.55/26.61 (3) ~ (all_4_2 = e0)
% 154.55/26.61 (4) all_56_15 = all_4_2
% 154.55/26.61 (5) ~ (e2 = e1)
% 154.55/26.61
% 154.55/26.61 Begin of proof
% 154.55/26.61 |
% 154.55/26.61 | BETA: splitting (2) gives:
% 154.55/26.61 |
% 154.55/26.61 | Case 1:
% 154.55/26.61 | |
% 154.55/26.61 | | (6) all_56_14 = e1
% 154.55/26.61 | |
% 154.55/26.61 | | COMBINE_EQS: (1), (6) imply:
% 154.55/26.61 | | (7) e2 = e1
% 154.55/26.61 | |
% 154.55/26.61 | | REDUCE: (5), (7) imply:
% 154.55/26.61 | | (8) $false
% 154.55/26.61 | |
% 154.55/26.61 | | CLOSE: (8) is inconsistent.
% 154.55/26.61 | |
% 154.55/26.61 | Case 2:
% 154.55/26.61 | |
% 154.55/26.61 | | (9) all_56_15 = e0
% 154.55/26.61 | |
% 154.55/26.61 | | COMBINE_EQS: (4), (9) imply:
% 154.55/26.61 | | (10) all_4_2 = e0
% 154.55/26.61 | |
% 154.55/26.61 | | REDUCE: (3), (10) imply:
% 154.55/26.61 | | (11) $false
% 154.55/26.61 | |
% 154.55/26.61 | | CLOSE: (11) is inconsistent.
% 154.55/26.61 | |
% 154.55/26.61 | End of split
% 154.55/26.61 |
% 154.55/26.61 End of proof
% 154.55/26.61
% 154.55/26.61 Sub-proof #74 shows that the following formulas are inconsistent:
% 154.55/26.61 ----------------------------------------------------------------
% 154.55/26.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 154.55/26.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 154.55/26.61 (2) op(e3, e2) = e2
% 154.55/26.61 (3) op(e3, e2) = e0
% 154.55/26.61 (4) ~ (e2 = e0)
% 154.55/26.61
% 154.55/26.61 Begin of proof
% 154.55/26.61 |
% 154.55/26.61 | GROUND_INST: instantiating (1) with e0, e2, e2, e3, simplifying with (2), (3)
% 154.55/26.61 | gives:
% 154.55/26.61 | (5) e2 = e0
% 154.55/26.61 |
% 154.55/26.61 | REDUCE: (4), (5) imply:
% 154.55/26.61 | (6) $false
% 154.55/26.61 |
% 154.55/26.61 | CLOSE: (6) is inconsistent.
% 154.55/26.61 |
% 154.55/26.61 End of proof
% 154.55/26.61
% 154.55/26.61 Sub-proof #75 shows that the following formulas are inconsistent:
% 154.55/26.61 ----------------------------------------------------------------
% 154.55/26.61 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 154.55/26.61 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 154.55/26.61 (3) op(e3, e0) = all_52_12
% 154.55/26.61 (4) ~ (all_52_14 = e2)
% 154.55/26.61 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 154.55/26.61 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 154.55/26.61 (6) all_52_1 = e2
% 154.55/26.61 (7) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 154.55/26.61 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 154.55/26.61 (8) all_56_12 = all_10_2
% 154.55/26.61 (9) ~ (all_52_2 = all_10_2)
% 154.55/26.61 (10) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.55/26.61 (11) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 154.55/26.61 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 154.55/26.61 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 154.55/26.61 (13) op(e3, e2) = all_52_4
% 154.55/26.61 (14) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 154.55/26.61 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 154.55/26.61 (15) all_54_0 = all_10_2
% 154.55/26.61 (16) op(e2, e1) = all_52_9
% 154.55/26.61 (17) op(e2, e3) = all_52_1
% 154.55/26.61 (18) ~ (all_52_13 = e3)
% 154.55/26.61 (19) ~ (all_6_0 = e0)
% 154.55/26.61 (20) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 154.55/26.61 op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 154.55/26.61 e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 154.55/26.61 (21) all_54_2 = all_52_8
% 154.55/26.61 (22) ~ (all_52_8 = all_52_9)
% 154.55/26.61 (23) ~ (all_10_2 = e0)
% 154.55/26.61 (24) ~ (e3 = e0)
% 154.55/26.61 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 154.55/26.61 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 154.55/26.61 (26) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 154.55/26.61 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 154.55/26.61 (27) ~ (all_52_9 = all_52_13)
% 154.55/26.61 (28) ~ (e2 = e0)
% 154.55/26.61 (29) ~ (all_52_9 = e3)
% 154.55/26.61 (30) op(e1, e3) = all_52_2
% 154.55/26.61 (31) op(e2, e0) = all_52_13
% 154.55/26.61 (32) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.55/26.61 (33) ~ (e3 = e1)
% 154.55/26.61 (34) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 154.55/26.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 154.55/26.61 (35) all_6_1 = e3
% 154.55/26.61 (36) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 154.55/26.61 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 154.55/26.61 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 154.55/26.61 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 154.55/26.61 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 154.55/26.61 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 154.55/26.61 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 154.55/26.61 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 154.55/26.61 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 154.55/26.61 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 154.55/26.61 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 154.55/26.61 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 154.55/26.61 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 154.55/26.61 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 154.55/26.61 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 154.55/26.61 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 154.55/26.61 = e0)
% 154.55/26.61 (37) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 154.55/26.61 (38) all_18_1 = e3
% 154.55/26.61 (39) ~ (all_52_8 = e2)
% 154.55/26.61 (40) all_58_7 = e1
% 154.55/26.61 (41) op(e1, e2) = e1
% 154.55/26.61 (42) op(e3, e3) = all_14_1
% 154.55/26.61 (43) all_54_8 = all_52_2
% 154.55/26.61 (44) all_54_7 = all_52_13
% 154.55/26.61 (45) ~ (all_52_8 = all_10_2)
% 154.55/26.61 (46) ~ (all_52_13 = e2)
% 154.55/26.61 (47) all_14_1 = all_10_2
% 154.55/26.61 (48) ~ (all_52_4 = e1)
% 154.55/26.61 (49) ~ (all_52_2 = e1)
% 154.55/26.61 (50) ~ (all_52_2 = all_52_14)
% 154.55/26.61 (51) all_54_6 = all_52_9
% 154.55/26.61 (52) ~ (all_10_2 = e2)
% 154.55/26.61 (53) ~ (e2 = e1)
% 154.55/26.61 (54) all_58_8 = e2
% 154.55/26.61 (55) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 154.55/26.61 (56) ~ (e1 = e0)
% 154.55/26.61 (57) ~ (all_52_2 = e2)
% 154.55/26.61 (58) ~ (all_8_2 = e1)
% 154.55/26.61 (59) all_58_3 = e3
% 154.55/26.61 (60) op(e3, e1) = all_52_8
% 154.55/26.61 (61) ~ (all_18_0 = e3)
% 154.55/26.61 (62) ~ (all_52_14 = e1)
% 154.55/26.61 (63) op(all_6_1, e1) = all_6_0
% 154.55/26.61 (64) ~ (all_52_12 = all_52_14)
% 154.55/26.61 (65) op(all_18_1, e1) = all_18_0
% 154.55/26.61 (66) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 154.55/26.61 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 154.55/26.61 (67) ~ (all_52_9 = e2)
% 154.55/26.61 (68) all_22_2 = e3
% 154.55/26.61 (69) op(e2, e2) = all_8_2
% 155.22/26.61 (70) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.22/26.61 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.22/26.61 (71) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.61 (72) all_54_11 = all_52_14
% 155.22/26.61 (73) ~ (e3 = e2)
% 155.22/26.61 (74) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 155.22/26.61 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 155.22/26.61 (75) ~ (all_52_1 = e3)
% 155.22/26.61
% 155.22/26.61 Begin of proof
% 155.22/26.61 |
% 155.22/26.61 | REDUCE: (38), (65) imply:
% 155.22/26.61 | (76) op(e3, e1) = all_18_0
% 155.22/26.61 |
% 155.22/26.61 | REDUCE: (35), (63) imply:
% 155.22/26.61 | (77) op(e3, e1) = all_6_0
% 155.22/26.61 |
% 155.22/26.61 | REDUCE: (42), (47) imply:
% 155.22/26.61 | (78) op(e3, e3) = all_10_2
% 155.22/26.61 |
% 155.22/26.61 | REDUCE: (6), (17) imply:
% 155.22/26.61 | (79) op(e2, e3) = e2
% 155.22/26.61 |
% 155.22/26.61 | GROUND_INST: instantiating (71) with all_52_8, all_6_0, e1, e3, simplifying
% 155.22/26.61 | with (60), (77) gives:
% 155.22/26.61 | (80) all_52_8 = all_6_0
% 155.22/26.61 |
% 155.22/26.61 | GROUND_INST: instantiating (71) with all_52_8, all_18_0, e1, e3, simplifying
% 155.22/26.61 | with (60), (76) gives:
% 155.22/26.61 | (81) all_52_8 = all_18_0
% 155.22/26.61 |
% 155.22/26.61 | COMBINE_EQS: (80), (81) imply:
% 155.22/26.61 | (82) all_18_0 = all_6_0
% 155.22/26.61 |
% 155.22/26.61 | SIMP: (82) implies:
% 155.22/26.61 | (83) all_18_0 = all_6_0
% 155.22/26.61 |
% 155.22/26.61 | COMBINE_EQS: (21), (80) imply:
% 155.22/26.61 | (84) all_54_2 = all_6_0
% 155.22/26.61 |
% 155.22/26.61 | REDUCE: (22), (80) imply:
% 155.22/26.61 | (85) ~ (all_52_9 = all_6_0)
% 155.22/26.61 |
% 155.22/26.61 | SIMP: (85) implies:
% 155.22/26.61 | (86) ~ (all_52_9 = all_6_0)
% 155.22/26.61 |
% 155.22/26.61 | REDUCE: (45), (80) imply:
% 155.22/26.61 | (87) ~ (all_10_2 = all_6_0)
% 155.22/26.61 |
% 155.22/26.61 | SIMP: (87) implies:
% 155.22/26.61 | (88) ~ (all_10_2 = all_6_0)
% 155.22/26.61 |
% 155.22/26.61 | REDUCE: (39), (80) imply:
% 155.22/26.61 | (89) ~ (all_6_0 = e2)
% 155.22/26.61 |
% 155.22/26.61 | REDUCE: (61), (83) imply:
% 155.22/26.61 | (90) ~ (all_6_0 = e3)
% 155.22/26.61 |
% 155.22/26.61 | BETA: splitting (1) gives:
% 155.22/26.61 |
% 155.22/26.61 | Case 1:
% 155.22/26.61 | |
% 155.22/26.61 | | (91) ~ (all_56_12 = e1)
% 155.22/26.61 | |
% 155.22/26.61 | | REDUCE: (8), (91) imply:
% 155.22/26.61 | | (92) ~ (all_10_2 = e1)
% 155.22/26.61 | |
% 155.22/26.61 | | BETA: splitting (7) gives:
% 155.22/26.61 | |
% 155.22/26.61 | | Case 1:
% 155.22/26.61 | | |
% 155.22/26.61 | | | (93) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 155.22/26.61 | | | e3)
% 155.22/26.61 | | |
% 155.22/26.61 | | | BETA: splitting (93) gives:
% 155.22/26.61 | | |
% 155.22/26.61 | | | Case 1:
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | (94) all_58_4 = e3 & op(e3, e1) = e3
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | ALPHA: (94) implies:
% 155.22/26.61 | | | | (95) all_58_4 = e3
% 155.22/26.61 | | | | (96) op(e3, e1) = e3
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | BETA: splitting (20) gives:
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | Case 1:
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | (97) ~ (all_22_2 = e3)
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | REDUCE: (68), (97) imply:
% 155.22/26.61 | | | | | (98) $false
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | CLOSE: (98) is inconsistent.
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | Case 2:
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | (99) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3)
% 155.22/26.61 | | | | | = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 155.22/26.61 | | | | | e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | BETA: splitting (99) gives:
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | Case 1:
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | (100) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3,
% 155.22/26.61 | | | | | | e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | ALPHA: (100) implies:
% 155.22/26.61 | | | | | | (101) op(e3, e3) = all_22_1
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | BETA: splitting (25) gives:
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | Case 1:
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | (102) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 155.22/26.61 | | | | | | | op(e2, e3) = e1)
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | REF_CLOSE: (15), (23), (32), (52), (53), (71), (78), (79), (92),
% 155.22/26.61 | | | | | | | (101), (102) are inconsistent by sub-proof #85.
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | Case 2:
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | (103) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 155.22/26.61 | | | | | | | op(e0, e3) = e1)
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | REF_CLOSE: (12), (13), (17), (23), (24), (26), (28), (30), (33),
% 155.22/26.61 | | | | | | | (48), (49), (52), (53), (56), (66), (70), (71), (73),
% 155.22/26.61 | | | | | | | (74), (75), (78), (79), (95), (96), (101), (103) are
% 155.22/26.61 | | | | | | | inconsistent by sub-proof #82.
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | End of split
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | Case 2:
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | (104) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | ALPHA: (104) implies:
% 155.22/26.61 | | | | | | (105) op(e3, e3) = all_22_1
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | BETA: splitting (25) gives:
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | Case 1:
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | (106) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 155.22/26.61 | | | | | | | op(e2, e3) = e1)
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | REF_CLOSE: (15), (23), (32), (52), (53), (71), (78), (79), (92),
% 155.22/26.61 | | | | | | | (105), (106) are inconsistent by sub-proof #85.
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | Case 2:
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | (107) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 155.22/26.61 | | | | | | | op(e0, e3) = e1)
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | REF_CLOSE: (12), (13), (17), (23), (24), (26), (28), (30), (33),
% 155.22/26.61 | | | | | | | (48), (49), (52), (53), (56), (66), (70), (71), (73),
% 155.22/26.61 | | | | | | | (74), (75), (78), (79), (95), (96), (105), (107) are
% 155.22/26.61 | | | | | | | inconsistent by sub-proof #82.
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | End of split
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | End of split
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | End of split
% 155.22/26.61 | | | |
% 155.22/26.61 | | | Case 2:
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | (108) all_58_5 = e3 & op(e2, e1) = e3
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | ALPHA: (108) implies:
% 155.22/26.61 | | | | (109) op(e2, e1) = e3
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | REF_CLOSE: (16), (29), (71), (109) are inconsistent by sub-proof #1196.
% 155.22/26.61 | | | |
% 155.22/26.61 | | | End of split
% 155.22/26.61 | | |
% 155.22/26.61 | | Case 2:
% 155.22/26.61 | | |
% 155.22/26.61 | | | (110) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 155.22/26.61 | | | = e3)
% 155.22/26.61 | | |
% 155.22/26.61 | | | BETA: splitting (110) gives:
% 155.22/26.61 | | |
% 155.22/26.61 | | | Case 1:
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | (111) all_58_8 = e3 & op(e1, e1) = e3
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | REF_CLOSE: (54), (73), (111) are inconsistent by sub-proof #112.
% 155.22/26.61 | | | |
% 155.22/26.61 | | | Case 2:
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | (112) all_58_14 = e3 & op(e0, e1) = e3
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | ALPHA: (112) implies:
% 155.22/26.61 | | | | (113) all_58_14 = e3
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | BETA: splitting (20) gives:
% 155.22/26.61 | | | |
% 155.22/26.61 | | | | Case 1:
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | (114) ~ (all_22_2 = e3)
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | REDUCE: (68), (114) imply:
% 155.22/26.61 | | | | | (115) $false
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | CLOSE: (115) is inconsistent.
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | Case 2:
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | (116) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3,
% 155.22/26.61 | | | | | e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 155.22/26.61 | | | | | (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | BETA: splitting (116) gives:
% 155.22/26.61 | | | | |
% 155.22/26.61 | | | | | Case 1:
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | (117) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3,
% 155.22/26.61 | | | | | | e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | ALPHA: (117) implies:
% 155.22/26.61 | | | | | | (118) op(e3, e3) = all_22_1
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | BETA: splitting (25) gives:
% 155.22/26.61 | | | | | |
% 155.22/26.61 | | | | | | Case 1:
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | (119) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 155.22/26.61 | | | | | | | op(e2, e3) = e1)
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | REF_CLOSE: (15), (23), (32), (52), (53), (71), (78), (79), (92),
% 155.22/26.61 | | | | | | | (118), (119) are inconsistent by sub-proof #85.
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | Case 2:
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | (120) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 155.22/26.61 | | | | | | | op(e0, e3) = e1)
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | BETA: splitting (120) gives:
% 155.22/26.61 | | | | | | |
% 155.22/26.61 | | | | | | | Case 1:
% 155.22/26.61 | | | | | | | |
% 155.22/26.61 | | | | | | | | (121) all_58_6 = e1 & op(e1, e3) = e1
% 155.22/26.61 | | | | | | | |
% 155.22/26.61 | | | | | | | | ALPHA: (121) implies:
% 155.22/26.62 | | | | | | | | (122) op(e1, e3) = e1
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | REF_CLOSE: (30), (49), (71), (122) are inconsistent by sub-proof
% 155.22/26.62 | | | | | | | | #1412.
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | Case 2:
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | (123) all_58_12 = e1 & op(e0, e3) = e1
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | ALPHA: (123) implies:
% 155.22/26.62 | | | | | | | | (124) op(e0, e3) = e1
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (11), (14), (15),
% 155.22/26.62 | | | | | | | | (16), (17), (18), (19), (23), (24), (25), (27), (28),
% 155.22/26.62 | | | | | | | | (29), (30), (31), (32), (34), (36), (37), (40), (41),
% 155.22/26.62 | | | | | | | | (43), (44), (46), (49), (50), (51), (52), (53), (54),
% 155.22/26.62 | | | | | | | | (55), (56), (57), (58), (59), (62), (64), (67), (69),
% 155.22/26.62 | | | | | | | | (70), (71), (72), (75), (77), (78), (79), (84), (86),
% 155.22/26.62 | | | | | | | | (88), (89), (90), (92), (113), (118), (124) are
% 155.22/26.62 | | | | | | | | inconsistent by sub-proof #78.
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | End of split
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | End of split
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | Case 2:
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | (125) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | ALPHA: (125) implies:
% 155.22/26.62 | | | | | | (126) ~ (all_22_1 = e1)
% 155.22/26.62 | | | | | | (127) op(e3, e3) = all_22_1
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | BETA: splitting (25) gives:
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | Case 1:
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | (128) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 155.22/26.62 | | | | | | | op(e2, e3) = e1)
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | REF_CLOSE: (53), (71), (79), (126), (127), (128) are inconsistent
% 155.22/26.62 | | | | | | | by sub-proof #278.
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | Case 2:
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | (129) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 155.22/26.62 | | | | | | | op(e0, e3) = e1)
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | BETA: splitting (129) gives:
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | Case 1:
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | (130) all_58_6 = e1 & op(e1, e3) = e1
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | ALPHA: (130) implies:
% 155.22/26.62 | | | | | | | | (131) op(e1, e3) = e1
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | REF_CLOSE: (30), (49), (71), (131) are inconsistent by sub-proof
% 155.22/26.62 | | | | | | | | #1412.
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | Case 2:
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | (132) all_58_12 = e1 & op(e0, e3) = e1
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | ALPHA: (132) implies:
% 155.22/26.62 | | | | | | | | (133) op(e0, e3) = e1
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (11), (14), (15),
% 155.22/26.62 | | | | | | | | (16), (17), (18), (19), (23), (24), (25), (27), (28),
% 155.22/26.62 | | | | | | | | (29), (30), (31), (32), (34), (36), (37), (40), (41),
% 155.22/26.62 | | | | | | | | (43), (44), (46), (49), (50), (51), (52), (53), (54),
% 155.22/26.62 | | | | | | | | (55), (56), (57), (58), (59), (62), (64), (67), (69),
% 155.22/26.62 | | | | | | | | (70), (71), (72), (75), (77), (78), (79), (84), (86),
% 155.22/26.62 | | | | | | | | (88), (89), (90), (92), (113), (127), (133) are
% 155.22/26.62 | | | | | | | | inconsistent by sub-proof #78.
% 155.22/26.62 | | | | | | | |
% 155.22/26.62 | | | | | | | End of split
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | End of split
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | End of split
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | End of split
% 155.22/26.62 | | | |
% 155.22/26.62 | | | End of split
% 155.22/26.62 | | |
% 155.22/26.62 | | End of split
% 155.22/26.62 | |
% 155.22/26.62 | Case 2:
% 155.22/26.62 | |
% 155.22/26.62 | | (134) all_56_12 = e1
% 155.22/26.62 | |
% 155.22/26.62 | | COMBINE_EQS: (8), (134) imply:
% 155.22/26.62 | | (135) all_10_2 = e1
% 155.22/26.62 | |
% 155.22/26.62 | | SIMP: (135) implies:
% 155.22/26.62 | | (136) all_10_2 = e1
% 155.22/26.62 | |
% 155.22/26.62 | | REDUCE: (88), (136) imply:
% 155.22/26.62 | | (137) ~ (all_6_0 = e1)
% 155.22/26.62 | |
% 155.22/26.62 | | SIMP: (137) implies:
% 155.22/26.62 | | (138) ~ (all_6_0 = e1)
% 155.22/26.62 | |
% 155.22/26.62 | | BETA: splitting (37) gives:
% 155.22/26.62 | |
% 155.22/26.62 | | Case 1:
% 155.22/26.62 | | |
% 155.22/26.62 | | | (139) all_54_2 = e3
% 155.22/26.62 | | |
% 155.22/26.62 | | | COMBINE_EQS: (84), (139) imply:
% 155.22/26.62 | | | (140) all_6_0 = e3
% 155.22/26.62 | | |
% 155.22/26.62 | | | REDUCE: (90), (140) imply:
% 155.22/26.62 | | | (141) $false
% 155.22/26.62 | | |
% 155.22/26.62 | | | CLOSE: (141) is inconsistent.
% 155.22/26.62 | | |
% 155.22/26.62 | | Case 2:
% 155.22/26.62 | | |
% 155.22/26.62 | | | (142) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 155.22/26.62 | | |
% 155.22/26.62 | | | BETA: splitting (142) gives:
% 155.22/26.62 | | |
% 155.22/26.62 | | | Case 1:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | (143) all_54_2 = e2
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | REF_CLOSE: (84), (89), (143) are inconsistent by sub-proof #77.
% 155.22/26.62 | | | |
% 155.22/26.62 | | | Case 2:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | (144) all_54_2 = e1 | all_54_2 = e0
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | BETA: splitting (144) gives:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | Case 1:
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | (145) all_54_2 = e1
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | COMBINE_EQS: (84), (145) imply:
% 155.22/26.62 | | | | | (146) all_6_0 = e1
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | SIMP: (146) implies:
% 155.22/26.62 | | | | | (147) all_6_0 = e1
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REDUCE: (138), (147) imply:
% 155.22/26.62 | | | | | (148) $false
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | CLOSE: (148) is inconsistent.
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | Case 2:
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | (149) all_54_2 = e0
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REF_CLOSE: (19), (84), (149) are inconsistent by sub-proof #76.
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | End of split
% 155.22/26.62 | | | |
% 155.22/26.62 | | | End of split
% 155.22/26.62 | | |
% 155.22/26.62 | | End of split
% 155.22/26.62 | |
% 155.22/26.62 | End of split
% 155.22/26.62 |
% 155.22/26.62 End of proof
% 155.22/26.62
% 155.22/26.62 Sub-proof #76 shows that the following formulas are inconsistent:
% 155.22/26.62 ----------------------------------------------------------------
% 155.22/26.62 (1) all_54_2 = all_6_0
% 155.22/26.62 (2) all_54_2 = e0
% 155.22/26.62 (3) ~ (all_6_0 = e0)
% 155.22/26.62
% 155.22/26.62 Begin of proof
% 155.22/26.62 |
% 155.22/26.62 | COMBINE_EQS: (1), (2) imply:
% 155.22/26.62 | (4) all_6_0 = e0
% 155.22/26.62 |
% 155.22/26.62 | SIMP: (4) implies:
% 155.22/26.62 | (5) all_6_0 = e0
% 155.22/26.62 |
% 155.22/26.62 | REDUCE: (3), (5) imply:
% 155.22/26.62 | (6) $false
% 155.22/26.62 |
% 155.22/26.62 | CLOSE: (6) is inconsistent.
% 155.22/26.62 |
% 155.22/26.62 End of proof
% 155.22/26.62
% 155.22/26.62 Sub-proof #77 shows that the following formulas are inconsistent:
% 155.22/26.62 ----------------------------------------------------------------
% 155.22/26.62 (1) all_54_2 = all_6_0
% 155.22/26.62 (2) all_54_2 = e2
% 155.22/26.62 (3) ~ (all_6_0 = e2)
% 155.22/26.62
% 155.22/26.62 Begin of proof
% 155.22/26.62 |
% 155.22/26.62 | COMBINE_EQS: (1), (2) imply:
% 155.22/26.62 | (4) all_6_0 = e2
% 155.22/26.62 |
% 155.22/26.62 | SIMP: (4) implies:
% 155.22/26.62 | (5) all_6_0 = e2
% 155.22/26.62 |
% 155.22/26.62 | REDUCE: (3), (5) imply:
% 155.22/26.62 | (6) $false
% 155.22/26.62 |
% 155.22/26.62 | CLOSE: (6) is inconsistent.
% 155.22/26.62 |
% 155.22/26.62 End of proof
% 155.22/26.62
% 155.22/26.62 Sub-proof #78 shows that the following formulas are inconsistent:
% 155.22/26.62 ----------------------------------------------------------------
% 155.22/26.62 (1) op(e0, e3) = e1
% 155.22/26.62 (2) ~ (all_52_9 = all_6_0)
% 155.22/26.62 (3) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 155.22/26.62 (4) op(e3, e0) = all_52_12
% 155.22/26.62 (5) ~ (all_52_14 = e2)
% 155.22/26.62 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.62 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 155.22/26.62 (7) op(e3, e3) = all_10_2
% 155.22/26.62 (8) ~ (all_10_2 = e1)
% 155.22/26.62 (9) all_58_14 = e3
% 155.22/26.62 (10) all_56_12 = all_10_2
% 155.22/26.62 (11) ~ (all_52_2 = all_10_2)
% 155.22/26.62 (12) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 155.22/26.62 (13) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.22/26.62 (14) ~ (all_6_0 = e3)
% 155.22/26.62 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.22/26.62 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.22/26.62 (16) all_54_0 = all_10_2
% 155.22/26.62 (17) op(e2, e1) = all_52_9
% 155.22/26.62 (18) op(e2, e3) = all_52_1
% 155.22/26.62 (19) ~ (all_52_13 = e3)
% 155.22/26.62 (20) ~ (all_6_0 = e0)
% 155.22/26.62 (21) ~ (all_10_2 = e0)
% 155.22/26.62 (22) ~ (e3 = e0)
% 155.22/26.62 (23) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.22/26.62 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.22/26.62 (24) ~ (all_52_9 = all_52_13)
% 155.22/26.62 (25) ~ (e2 = e0)
% 155.22/26.62 (26) ~ (all_52_9 = e3)
% 155.22/26.62 (27) ~ (all_10_2 = all_6_0)
% 155.22/26.62 (28) op(e1, e3) = all_52_2
% 155.22/26.62 (29) op(e2, e0) = all_52_13
% 155.22/26.62 (30) op(e2, e3) = e2
% 155.22/26.62 (31) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 155.22/26.62 (32) ~ (all_6_0 = e2)
% 155.22/26.62 (33) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 155.22/26.62 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 155.22/26.62 (34) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 155.22/26.62 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.62 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 155.22/26.62 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.22/26.62 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 155.22/26.62 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.62 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 155.22/26.62 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 155.22/26.62 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.22/26.62 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.62 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 155.22/26.62 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 155.22/26.62 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 155.22/26.62 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 155.22/26.62 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 155.22/26.62 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 155.22/26.62 = e0)
% 155.22/26.62 (35) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 155.22/26.62 (36) all_58_7 = e1
% 155.22/26.62 (37) op(e1, e2) = e1
% 155.22/26.62 (38) all_54_8 = all_52_2
% 155.22/26.62 (39) all_54_7 = all_52_13
% 155.22/26.62 (40) ~ (all_52_13 = e2)
% 155.22/26.62 (41) ~ (all_52_2 = e1)
% 155.22/26.62 (42) ~ (all_52_2 = all_52_14)
% 155.22/26.62 (43) all_54_6 = all_52_9
% 155.22/26.62 (44) ~ (all_10_2 = e2)
% 155.22/26.62 (45) ~ (e2 = e1)
% 155.22/26.62 (46) all_58_8 = e2
% 155.22/26.62 (47) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.22/26.62 (48) ~ (e1 = e0)
% 155.22/26.62 (49) ~ (all_52_2 = e2)
% 155.22/26.62 (50) ~ (all_8_2 = e1)
% 155.22/26.62 (51) all_54_2 = all_6_0
% 155.22/26.62 (52) all_58_3 = e3
% 155.22/26.62 (53) ~ (all_52_14 = e1)
% 155.22/26.62 (54) ~ (all_52_12 = all_52_14)
% 155.22/26.62 (55) ~ (all_52_9 = e2)
% 155.22/26.62 (56) op(e3, e3) = all_22_1
% 155.22/26.62 (57) op(e3, e1) = all_6_0
% 155.22/26.62 (58) op(e2, e2) = all_8_2
% 155.22/26.62 (59) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.22/26.62 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.22/26.62 (60) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.62 (61) all_54_11 = all_52_14
% 155.22/26.62 (62) ~ (all_52_1 = e3)
% 155.22/26.62
% 155.22/26.62 Begin of proof
% 155.22/26.62 |
% 155.22/26.62 | BETA: splitting (35) gives:
% 155.22/26.62 |
% 155.22/26.62 | Case 1:
% 155.22/26.62 | |
% 155.22/26.62 | | (63) all_54_2 = e3
% 155.22/26.62 | |
% 155.22/26.62 | | REF_CLOSE: (14), (51), (63) are inconsistent by sub-proof #81.
% 155.22/26.62 | |
% 155.22/26.62 | Case 2:
% 155.22/26.62 | |
% 155.22/26.62 | | (64) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 155.22/26.62 | |
% 155.22/26.62 | | BETA: splitting (33) gives:
% 155.22/26.62 | |
% 155.22/26.62 | | Case 1:
% 155.22/26.62 | | |
% 155.22/26.62 | | | (65) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 155.22/26.62 | | | e0)
% 155.22/26.62 | | |
% 155.22/26.62 | | | BETA: splitting (65) gives:
% 155.22/26.62 | | |
% 155.22/26.62 | | | Case 1:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | (66) all_58_4 = e0 & op(e3, e1) = e0
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | ALPHA: (66) implies:
% 155.22/26.62 | | | | (67) op(e3, e1) = e0
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | BETA: splitting (64) gives:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | Case 1:
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | (68) all_54_2 = e2
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | COMBINE_EQS: (51), (68) imply:
% 155.22/26.62 | | | | | (69) all_6_0 = e2
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REDUCE: (32), (69) imply:
% 155.22/26.62 | | | | | (70) $false
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | CLOSE: (70) is inconsistent.
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | Case 2:
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | (71) all_54_2 = e1 | all_54_2 = e0
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | BETA: splitting (71) gives:
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | Case 1:
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | (72) all_54_2 = e1
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | COMBINE_EQS: (51), (72) imply:
% 155.22/26.62 | | | | | | (73) all_6_0 = e1
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | REDUCE: (57), (73) imply:
% 155.22/26.62 | | | | | | (74) op(e3, e1) = e1
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | REF_CLOSE: (48), (60), (67), (74) are inconsistent by sub-proof
% 155.22/26.62 | | | | | | #1281.
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | Case 2:
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | (75) all_54_2 = e0
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | COMBINE_EQS: (51), (75) imply:
% 155.22/26.62 | | | | | | (76) all_6_0 = e0
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | REDUCE: (20), (76) imply:
% 155.22/26.62 | | | | | | (77) $false
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | CLOSE: (77) is inconsistent.
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | End of split
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | End of split
% 155.22/26.62 | | | |
% 155.22/26.62 | | | Case 2:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | (78) all_58_5 = e0 & op(e2, e1) = e0
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | ALPHA: (78) implies:
% 155.22/26.62 | | | | (79) all_58_5 = e0
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | BETA: splitting (31) gives:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | Case 1:
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | (80) all_54_0 = e3
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | COMBINE_EQS: (16), (80) imply:
% 155.22/26.62 | | | | | (81) all_10_2 = e3
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | SIMP: (81) implies:
% 155.22/26.62 | | | | | (82) all_10_2 = e3
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | COMBINE_EQS: (10), (82) imply:
% 155.22/26.62 | | | | | (83) all_56_12 = e3
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REDUCE: (11), (82) imply:
% 155.22/26.62 | | | | | (84) ~ (all_52_2 = e3)
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REDUCE: (27), (82) imply:
% 155.22/26.62 | | | | | (85) ~ (all_6_0 = e3)
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REDUCE: (44), (82) imply:
% 155.22/26.62 | | | | | (86) ~ (e3 = e2)
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REDUCE: (8), (82) imply:
% 155.22/26.62 | | | | | (87) ~ (e3 = e1)
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REDUCE: (7), (82) imply:
% 155.22/26.62 | | | | | (88) op(e3, e3) = e3
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | BETA: splitting (15) gives:
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | Case 1:
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | (89) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 155.22/26.62 | | | | | | e2) = e3)
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | REF_CLOSE: (22), (23), (25), (30), (36), (45), (48), (56), (59),
% 155.22/26.62 | | | | | | (60), (87), (88), (89) are inconsistent by sub-proof #80.
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | Case 2:
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | (90) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 155.22/26.62 | | | | | | e0) = e3)
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | BETA: splitting (90) gives:
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | | Case 1:
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | (91) all_58_8 = e3 & op(e1, e1) = e3
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | REF_CLOSE: (46), (86), (91) are inconsistent by sub-proof #112.
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | Case 2:
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | (92) all_58_11 = e3 & op(e1, e0) = e3
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | ALPHA: (92) implies:
% 155.22/26.62 | | | | | | | (93) op(e1, e0) = e3
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (12), (13), (14), (15),
% 155.22/26.62 | | | | | | | (17), (18), (19), (20), (22), (24), (25), (26), (28),
% 155.22/26.62 | | | | | | | (29), (30), (32), (34), (36), (37), (38), (39), (40),
% 155.22/26.62 | | | | | | | (41), (42), (43), (45), (46), (47), (48), (49), (50),
% 155.22/26.62 | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 155.22/26.62 | | | | | | | (60), (61), (62), (64), (79), (83), (84), (86), (88),
% 155.22/26.62 | | | | | | | (93) are inconsistent by sub-proof #79.
% 155.22/26.62 | | | | | | |
% 155.22/26.62 | | | | | | End of split
% 155.22/26.62 | | | | | |
% 155.22/26.62 | | | | | End of split
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | Case 2:
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | (94) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | | REF_CLOSE: (8), (16), (21), (44), (94) are inconsistent by sub-proof
% 155.22/26.62 | | | | | #1307.
% 155.22/26.62 | | | | |
% 155.22/26.62 | | | | End of split
% 155.22/26.62 | | | |
% 155.22/26.62 | | | End of split
% 155.22/26.62 | | |
% 155.22/26.62 | | Case 2:
% 155.22/26.62 | | |
% 155.22/26.62 | | | (95) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 155.22/26.62 | | | e0)
% 155.22/26.62 | | |
% 155.22/26.62 | | | BETA: splitting (95) gives:
% 155.22/26.62 | | |
% 155.22/26.62 | | | Case 1:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | (96) all_58_8 = e0 & op(e1, e1) = e0
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | REF_CLOSE: (25), (46), (96) are inconsistent by sub-proof #1071.
% 155.22/26.62 | | | |
% 155.22/26.62 | | | Case 2:
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | (97) all_58_14 = e0 & op(e0, e1) = e0
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | ALPHA: (97) implies:
% 155.22/26.62 | | | | (98) all_58_14 = e0
% 155.22/26.62 | | | |
% 155.22/26.62 | | | | REF_CLOSE: (9), (22), (98) are inconsistent by sub-proof #1444.
% 155.22/26.62 | | | |
% 155.22/26.62 | | | End of split
% 155.22/26.62 | | |
% 155.22/26.62 | | End of split
% 155.22/26.62 | |
% 155.22/26.62 | End of split
% 155.22/26.62 |
% 155.22/26.62 End of proof
% 155.22/26.62
% 155.22/26.62 Sub-proof #79 shows that the following formulas are inconsistent:
% 155.22/26.62 ----------------------------------------------------------------
% 155.22/26.62 (1) op(e0, e3) = e1
% 155.22/26.62 (2) ~ (all_52_9 = all_6_0)
% 155.22/26.62 (3) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 155.22/26.62 (4) op(e3, e0) = all_52_12
% 155.22/26.62 (5) ~ (all_52_14 = e2)
% 155.22/26.62 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.62 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 155.22/26.62 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 155.22/26.62 (8) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.22/26.62 (9) ~ (all_6_0 = e3)
% 155.22/26.62 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.22/26.62 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.22/26.62 (11) op(e2, e1) = all_52_9
% 155.22/26.62 (12) op(e2, e3) = all_52_1
% 155.22/26.62 (13) ~ (all_52_13 = e3)
% 155.22/26.62 (14) ~ (all_6_0 = e0)
% 155.22/26.62 (15) ~ (e3 = e0)
% 155.22/26.62 (16) ~ (all_52_9 = all_52_13)
% 155.22/26.62 (17) ~ (e2 = e0)
% 155.22/26.62 (18) ~ (all_52_9 = e3)
% 155.22/26.62 (19) op(e1, e3) = all_52_2
% 155.22/26.62 (20) op(e2, e0) = all_52_13
% 155.22/26.62 (21) op(e2, e3) = e2
% 155.22/26.62 (22) ~ (all_6_0 = e2)
% 155.22/26.63 (23) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 155.22/26.63 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.63 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 155.22/26.63 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.22/26.63 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 155.22/26.63 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.63 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 155.22/26.63 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 155.22/26.63 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.22/26.63 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.63 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 155.22/26.63 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 155.22/26.63 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 155.22/26.63 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 155.22/26.63 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 155.22/26.63 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 155.22/26.63 = e0)
% 155.22/26.63 (24) all_58_7 = e1
% 155.22/26.63 (25) op(e1, e2) = e1
% 155.22/26.63 (26) all_54_8 = all_52_2
% 155.22/26.63 (27) all_54_7 = all_52_13
% 155.22/26.63 (28) all_56_12 = e3
% 155.22/26.63 (29) ~ (all_52_2 = e3)
% 155.22/26.63 (30) ~ (all_52_13 = e2)
% 155.22/26.63 (31) all_58_5 = e0
% 155.22/26.63 (32) ~ (all_52_2 = e1)
% 155.22/26.63 (33) ~ (all_52_2 = all_52_14)
% 155.22/26.63 (34) all_54_6 = all_52_9
% 155.22/26.63 (35) ~ (e2 = e1)
% 155.22/26.63 (36) op(e3, e3) = e3
% 155.22/26.63 (37) all_58_8 = e2
% 155.22/26.63 (38) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.22/26.63 (39) ~ (e1 = e0)
% 155.22/26.63 (40) ~ (all_52_2 = e2)
% 155.22/26.63 (41) ~ (all_8_2 = e1)
% 155.22/26.63 (42) all_54_2 = all_6_0
% 155.22/26.63 (43) all_58_3 = e3
% 155.22/26.63 (44) ~ (all_52_14 = e1)
% 155.22/26.63 (45) ~ (all_52_12 = all_52_14)
% 155.22/26.63 (46) ~ (all_52_9 = e2)
% 155.22/26.63 (47) op(e1, e0) = e3
% 155.22/26.63 (48) op(e3, e3) = all_22_1
% 155.22/26.63 (49) op(e3, e1) = all_6_0
% 155.22/26.63 (50) op(e2, e2) = all_8_2
% 155.22/26.63 (51) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.22/26.63 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.22/26.63 (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.63 (53) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 155.22/26.63 (54) all_54_11 = all_52_14
% 155.22/26.63 (55) ~ (e3 = e2)
% 155.22/26.63 (56) ~ (all_52_1 = e3)
% 155.22/26.63
% 155.22/26.63 Begin of proof
% 155.22/26.63 |
% 155.22/26.63 | BETA: splitting (6) gives:
% 155.22/26.63 |
% 155.22/26.63 | Case 1:
% 155.22/26.63 | |
% 155.22/26.63 | | (57) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 155.22/26.63 | | e1)
% 155.22/26.63 | |
% 155.22/26.63 | | REF_CLOSE: (21), (35), (41), (50), (52), (57) are inconsistent by sub-proof
% 155.22/26.63 | | #1074.
% 155.22/26.63 | |
% 155.22/26.63 | Case 2:
% 155.22/26.63 | |
% 155.22/26.63 | | (58) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 155.22/26.63 | | e1)
% 155.22/26.63 | |
% 155.22/26.63 | | BETA: splitting (58) gives:
% 155.22/26.63 | |
% 155.22/26.63 | | Case 1:
% 155.22/26.63 | | |
% 155.22/26.63 | | | (59) all_58_5 = e1 & op(e2, e1) = e1
% 155.22/26.63 | | |
% 155.22/26.63 | | | ALPHA: (59) implies:
% 155.22/26.63 | | | (60) all_58_5 = e1
% 155.22/26.63 | | |
% 155.22/26.63 | | | REF_CLOSE: (31), (39), (60) are inconsistent by sub-proof #935.
% 155.22/26.63 | | |
% 155.22/26.63 | | Case 2:
% 155.22/26.63 | | |
% 155.22/26.63 | | | (61) all_58_10 = e1 & op(e2, e0) = e1
% 155.22/26.63 | | |
% 155.22/26.63 | | | ALPHA: (61) implies:
% 155.22/26.63 | | | (62) all_58_10 = e1
% 155.22/26.63 | | |
% 155.22/26.63 | | | BETA: splitting (8) gives:
% 155.22/26.63 | | |
% 155.22/26.63 | | | Case 1:
% 155.22/26.63 | | | |
% 155.22/26.63 | | | | (63) all_54_8 = e3
% 155.22/26.63 | | | |
% 155.22/26.63 | | | | COMBINE_EQS: (26), (63) imply:
% 155.22/26.63 | | | | (64) all_52_2 = e3
% 155.22/26.63 | | | |
% 155.22/26.63 | | | | REDUCE: (29), (64) imply:
% 155.22/26.63 | | | | (65) $false
% 155.22/26.63 | | | |
% 155.22/26.63 | | | | CLOSE: (65) is inconsistent.
% 155.22/26.63 | | | |
% 155.22/26.63 | | | Case 2:
% 155.22/26.63 | | | |
% 155.22/26.63 | | | | (66) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.22/26.63 | | | |
% 155.22/26.63 | | | | BETA: splitting (51) gives:
% 155.22/26.63 | | | |
% 155.22/26.63 | | | | Case 1:
% 155.22/26.63 | | | | |
% 155.22/26.63 | | | | | (67) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 155.22/26.63 | | | | | e3) = e0)
% 155.22/26.63 | | | | |
% 155.22/26.63 | | | | | REF_CLOSE: (15), (17), (21), (36), (48), (52), (67) are inconsistent
% 155.22/26.63 | | | | | by sub-proof #865.
% 155.22/26.63 | | | | |
% 155.22/26.63 | | | | Case 2:
% 155.22/26.63 | | | | |
% 155.22/26.63 | | | | | (68) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 155.22/26.63 | | | | | e3) = e0)
% 155.22/26.63 | | | | |
% 155.22/26.63 | | | | | BETA: splitting (68) gives:
% 155.22/26.63 | | | | |
% 155.22/26.63 | | | | | Case 1:
% 155.22/26.63 | | | | | |
% 155.22/26.63 | | | | | | (69) all_58_6 = e0 & op(e1, e3) = e0
% 155.22/26.63 | | | | | |
% 155.22/26.63 | | | | | | ALPHA: (69) implies:
% 155.22/26.63 | | | | | | (70) all_58_6 = e0
% 155.22/26.63 | | | | | |
% 155.22/26.63 | | | | | | BETA: splitting (53) gives:
% 155.22/26.63 | | | | | |
% 155.22/26.63 | | | | | | Case 1:
% 155.22/26.63 | | | | | | |
% 155.22/26.63 | | | | | | | (71) all_54_2 = e2
% 155.22/26.63 | | | | | | |
% 155.22/26.63 | | | | | | | COMBINE_EQS: (42), (71) imply:
% 155.22/26.63 | | | | | | | (72) all_6_0 = e2
% 155.22/26.63 | | | | | | |
% 155.22/26.63 | | | | | | | REDUCE: (22), (72) imply:
% 155.22/26.63 | | | | | | | (73) $false
% 155.22/26.63 | | | | | | |
% 155.22/26.63 | | | | | | | CLOSE: (73) is inconsistent.
% 155.22/26.63 | | | | | | |
% 155.22/26.63 | | | | | | Case 2:
% 155.22/26.63 | | | | | | |
% 155.22/26.63 | | | | | | | (74) ~ (all_54_2 = e2)
% 155.22/26.63 | | | | | | | (75) all_54_2 = e1 | all_54_2 = e0
% 155.22/26.63 | | | | | | |
% 155.22/26.63 | | | | | | | BETA: splitting (75) gives:
% 155.22/26.63 | | | | | | |
% 155.22/26.63 | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | (76) all_54_2 = e1
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | COMBINE_EQS: (42), (76) imply:
% 155.22/26.63 | | | | | | | | (77) all_6_0 = e1
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | REDUCE: (2), (77) imply:
% 155.22/26.63 | | | | | | | | (78) ~ (all_52_9 = e1)
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | REDUCE: (9), (77) imply:
% 155.22/26.63 | | | | | | | | (79) ~ (e3 = e1)
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | SIMP: (79) implies:
% 155.22/26.63 | | | | | | | | (80) ~ (e3 = e1)
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | REDUCE: (22), (77) imply:
% 155.22/26.63 | | | | | | | | (81) ~ (e2 = e1)
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | REDUCE: (49), (77) imply:
% 155.22/26.63 | | | | | | | | (82) op(e3, e1) = e1
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | BETA: splitting (3) gives:
% 155.22/26.63 | | | | | | | |
% 155.22/26.63 | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | |
% 155.22/26.63 | | | | | | | | | (83) all_54_6 = e3
% 155.22/26.63 | | | | | | | | |
% 155.22/26.63 | | | | | | | | | COMBINE_EQS: (34), (83) imply:
% 155.22/26.63 | | | | | | | | | (84) all_52_9 = e3
% 155.22/26.63 | | | | | | | | |
% 155.22/26.63 | | | | | | | | | REDUCE: (18), (84) imply:
% 155.22/26.63 | | | | | | | | | (85) $false
% 155.22/26.63 | | | | | | | | |
% 155.22/26.63 | | | | | | | | | CLOSE: (85) is inconsistent.
% 155.22/26.63 | | | | | | | | |
% 155.22/26.63 | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | |
% 155.22/26.63 | | | | | | | | | (86) ~ (all_54_6 = e3)
% 155.22/26.63 | | | | | | | | | (87) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 155.22/26.63 | | | | | | | | |
% 155.22/26.63 | | | | | | | | | BETA: splitting (87) gives:
% 155.22/26.63 | | | | | | | | |
% 155.22/26.63 | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | (88) all_54_6 = e2
% 155.22/26.63 | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | COMBINE_EQS: (34), (88) imply:
% 155.22/26.63 | | | | | | | | | | (89) all_52_9 = e2
% 155.22/26.63 | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | REDUCE: (46), (89) imply:
% 155.22/26.63 | | | | | | | | | | (90) $false
% 155.22/26.63 | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | CLOSE: (90) is inconsistent.
% 155.22/26.63 | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | (91) all_54_6 = e1 | all_54_6 = e0
% 155.22/26.63 | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | BETA: splitting (66) gives:
% 155.22/26.63 | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | (92) all_54_8 = e2
% 155.22/26.63 | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | REF_CLOSE: (26), (40), (92) are inconsistent by sub-proof
% 155.22/26.63 | | | | | | | | | | | #1231.
% 155.22/26.63 | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | (93) all_54_8 = e1 | all_54_8 = e0
% 155.22/26.63 | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | BETA: splitting (93) gives:
% 155.22/26.63 | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | (94) all_54_8 = e1
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | REF_CLOSE: (26), (32), (94) are inconsistent by sub-proof
% 155.22/26.63 | | | | | | | | | | | | #1379.
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | (95) all_54_8 = e0
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | COMBINE_EQS: (26), (95) imply:
% 155.22/26.63 | | | | | | | | | | | | (96) all_52_2 = e0
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | SIMP: (96) implies:
% 155.22/26.63 | | | | | | | | | | | | (97) all_52_2 = e0
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | REDUCE: (33), (97) imply:
% 155.22/26.63 | | | | | | | | | | | | (98) ~ (all_52_14 = e0)
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | SIMP: (98) implies:
% 155.22/26.63 | | | | | | | | | | | | (99) ~ (all_52_14 = e0)
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | REDUCE: (19), (97) imply:
% 155.22/26.63 | | | | | | | | | | | | (100) op(e1, e3) = e0
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | BETA: splitting (91) gives:
% 155.22/26.63 | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | (101) all_54_6 = e1
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | COMBINE_EQS: (34), (101) imply:
% 155.22/26.63 | | | | | | | | | | | | | (102) all_52_9 = e1
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | REDUCE: (78), (102) imply:
% 155.22/26.63 | | | | | | | | | | | | | (103) $false
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | CLOSE: (103) is inconsistent.
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | (104) all_54_6 = e0
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | COMBINE_EQS: (34), (104) imply:
% 155.22/26.63 | | | | | | | | | | | | | (105) all_52_9 = e0
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | REDUCE: (16), (105) imply:
% 155.22/26.63 | | | | | | | | | | | | | (106) ~ (all_52_13 = e0)
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | SIMP: (106) implies:
% 155.22/26.63 | | | | | | | | | | | | | (107) ~ (all_52_13 = e0)
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | REDUCE: (18), (105) imply:
% 155.22/26.63 | | | | | | | | | | | | | (108) ~ (e3 = e0)
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | REDUCE: (78), (105) imply:
% 155.22/26.63 | | | | | | | | | | | | | (109) ~ (e1 = e0)
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | REDUCE: (11), (105) imply:
% 155.22/26.63 | | | | | | | | | | | | | (110) op(e2, e1) = e0
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | BETA: splitting (7) gives:
% 155.22/26.63 | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | (111) all_54_7 = e3
% 155.22/26.63 | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | COMBINE_EQS: (27), (111) imply:
% 155.22/26.63 | | | | | | | | | | | | | | (112) all_52_13 = e3
% 155.22/26.63 | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | REDUCE: (13), (112) imply:
% 155.22/26.63 | | | | | | | | | | | | | | (113) $false
% 155.22/26.63 | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | CLOSE: (113) is inconsistent.
% 155.22/26.63 | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | (114) ~ (all_54_7 = e3)
% 155.22/26.63 | | | | | | | | | | | | | | (115) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 155.22/26.63 | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 155.22/26.63 | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | (116) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.22/26.63 | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.22/26.63 | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.63 | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.22/26.63 | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 155.22/26.63 | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | (117) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 155.22/26.63 | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.22/26.63 | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (118) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 155.22/26.63 | | | | | | | | | | | | | | | | | (119) op(e2, e3) = e3
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (52), (56), (119) are inconsistent by
% 155.22/26.63 | | | | | | | | | | | | | | | | | sub-proof #1183.
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (120) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (121) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (122) ~ (all_56_12 = e3)
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | REDUCE: (28), (122) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (123) $false
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | CLOSE: (123) is inconsistent.
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (124) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (125) op(e1, e3) = e3
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (126) op(e3, e1) = e3
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (127) all_54_7 = e2
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (127) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (128) all_52_13 = e2
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | REDUCE: (30), (128) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (129) $false
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (130) ~ (all_54_7 = e2)
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (131) all_54_7 = e1 | all_54_7 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (132) all_54_7 = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (132) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (133) all_52_13 = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e0, e3, e3, e1,
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | simplifying with (100), (125) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (134) e3 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e1, e3, e1, e3,
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | simplifying with (82), (126) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (135) e3 = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (135) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (136) e1 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (136) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (137) all_58_10 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (31), (35), (39), (43), (52), (80),
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (137) are inconsistent by sub-proof #839.
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (138) all_54_7 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (138) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (139) all_52_13 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (139) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (140) $false
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | End of split
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | End of split
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | (141) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 155.22/26.63 | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.22/26.63 | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (142) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 155.22/26.63 | | | | | | | | | | | | | | | | | (143) op(e1, e3) = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (32), (52), (143) are inconsistent by
% 155.22/26.63 | | | | | | | | | | | | | | | | | sub-proof #1412.
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (144) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (145) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (146) op(e3, e0) = e3
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (38), (44), (45), (52), (54), (99),
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (146) are inconsistent by sub-proof #121.
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (147) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (148) op(e0, e3) = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (39), (52), (148) are inconsistent by
% 155.22/26.63 | | | | | | | | | | | | | | | | | | sub-proof #83.
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | End of split
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | End of split
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | End of split
% 155.22/26.63 | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | (149) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 155.22/26.63 | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.63 | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 155.22/26.63 | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.22/26.63 | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.63 | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.22/26.63 | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.63 | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.22/26.63 | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 155.22/26.63 | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | (150) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 155.22/26.63 | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 155.22/26.63 | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 155.22/26.63 | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (151) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 155.22/26.63 | | | | | | | | | | | | | | | | | (152) op(e1, e2) = e2
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (35), (52), (152) are inconsistent by
% 155.22/26.63 | | | | | | | | | | | | | | | | | sub-proof #1088.
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (153) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 155.22/26.63 | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (154) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.63 | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | (155) op(e2, e1) = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (156) all_54_7 = e2
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (156) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (157) all_52_13 = e2
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | REDUCE: (30), (157) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (158) $false
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (159) ~ (all_54_7 = e2)
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | (160) all_54_7 = e1 | all_54_7 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (161) all_54_7 = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (161) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (162) all_52_13 = e1
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e0, e1, e1, e2,
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | simplifying with (110), (155) gives:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (163) e1 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (163) imply:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (164) all_58_10 = e0
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (31), (35), (39), (43), (52), (80),
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | | (164) are inconsistent by sub-proof #839.
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.63 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | | (165) all_54_7 = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (165) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | | (166) all_52_13 = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (166) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | | (167) $false
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (168) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 155.22/26.64 | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (169) op(e2, e0) = e2
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (30), (52), (169) are inconsistent by
% 155.22/26.64 | | | | | | | | | | | | | | | | | | sub-proof #1535.
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | (170) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.22/26.64 | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 155.22/26.64 | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.64 | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.22/26.64 | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.64 | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.22/26.64 | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 155.22/26.64 | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | (171) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.22/26.64 | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 155.22/26.64 | | | | | | | | | | | | | | | | | (172) op(e2, e0) = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (173) all_54_7 = e2
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (173) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (174) all_52_13 = e2
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | REDUCE: (30), (174) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (175) $false
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (176) ~ (all_54_7 = e2)
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (177) all_54_7 = e1 | all_54_7 = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (178) all_54_7 = e1
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (178) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (179) all_52_13 = e1
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | REDUCE: (20), (179) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (180) op(e2, e0) = e1
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e0, e1, e0, e2,
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | simplifying with (172), (180) gives:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (181) e1 = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (181) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (182) all_58_10 = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (31), (35), (39), (43), (52), (80),
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (182) are inconsistent by sub-proof #839.
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (183) all_54_7 = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (183) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (184) all_52_13 = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | REDUCE: (107), (184) imply:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | (185) $false
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 155.22/26.64 | | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | (186) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.64 | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.22/26.64 | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.64 | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (187) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.64 | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (188) op(e1, e0) = e1
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (15), (24), (37), (52), (55), (70), (80),
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (188) are inconsistent by sub-proof #106.
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (189) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.64 | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 155.22/26.64 | | | | | | | | | | | | | | | | | | (190) op(e1, e0) = e0
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (47), (52), (190) are inconsistent by
% 155.22/26.64 | | | | | | | | | | | | | | | | | | sub-proof #118.
% 155.22/26.64 | | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | |
% 155.22/26.64 | | | | | | | | End of split
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | (191) all_54_2 = e0
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | COMBINE_EQS: (42), (191) imply:
% 155.22/26.64 | | | | | | | | (192) all_6_0 = e0
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | REDUCE: (14), (192) imply:
% 155.22/26.64 | | | | | | | | (193) $false
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | CLOSE: (193) is inconsistent.
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | End of split
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | End of split
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | Case 2:
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | (194) all_58_12 = e0 & op(e0, e3) = e0
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | ALPHA: (194) implies:
% 155.22/26.64 | | | | | | (195) op(e0, e3) = e0
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | REF_CLOSE: (1), (39), (52), (195) are inconsistent by sub-proof #83.
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | End of split
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | End of split
% 155.22/26.64 | | | |
% 155.22/26.64 | | | End of split
% 155.22/26.64 | | |
% 155.22/26.64 | | End of split
% 155.22/26.64 | |
% 155.22/26.64 | End of split
% 155.22/26.64 |
% 155.22/26.64 End of proof
% 155.22/26.64
% 155.22/26.64 Sub-proof #80 shows that the following formulas are inconsistent:
% 155.22/26.64 ----------------------------------------------------------------
% 155.22/26.64 (1) ~ (e3 = e0)
% 155.22/26.64 (2) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.22/26.64 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.22/26.64 (3) ~ (e2 = e0)
% 155.22/26.64 (4) op(e2, e3) = e2
% 155.22/26.64 (5) ~ (e3 = e1)
% 155.22/26.64 (6) all_58_7 = e1
% 155.22/26.64 (7) ~ (e2 = e1)
% 155.22/26.64 (8) op(e3, e3) = e3
% 155.22/26.64 (9) ~ (e1 = e0)
% 155.22/26.64 (10) op(e3, e3) = all_22_1
% 155.22/26.64 (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.22/26.64 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.22/26.64 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.64 (13) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 155.22/26.64
% 155.22/26.64 Begin of proof
% 155.22/26.64 |
% 155.22/26.64 | BETA: splitting (13) gives:
% 155.22/26.64 |
% 155.22/26.64 | Case 1:
% 155.22/26.64 | |
% 155.22/26.64 | | (14) all_58_6 = e3 & op(e1, e3) = e3
% 155.22/26.64 | |
% 155.22/26.64 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14)
% 155.22/26.64 | | are inconsistent by sub-proof #861.
% 155.22/26.64 | |
% 155.22/26.64 | Case 2:
% 155.22/26.64 | |
% 155.22/26.64 | | (15) all_58_7 = e3 & op(e1, e2) = e3
% 155.22/26.64 | |
% 155.22/26.64 | | ALPHA: (15) implies:
% 155.22/26.64 | | (16) all_58_7 = e3
% 155.22/26.64 | |
% 155.22/26.64 | | REF_CLOSE: (5), (6), (16) are inconsistent by sub-proof #1330.
% 155.22/26.64 | |
% 155.22/26.64 | End of split
% 155.22/26.64 |
% 155.22/26.64 End of proof
% 155.22/26.64
% 155.22/26.64 Sub-proof #81 shows that the following formulas are inconsistent:
% 155.22/26.64 ----------------------------------------------------------------
% 155.22/26.64 (1) all_54_2 = all_6_0
% 155.22/26.64 (2) all_54_2 = e3
% 155.22/26.64 (3) ~ (all_6_0 = e3)
% 155.22/26.64
% 155.22/26.64 Begin of proof
% 155.22/26.64 |
% 155.22/26.64 | COMBINE_EQS: (1), (2) imply:
% 155.22/26.64 | (4) all_6_0 = e3
% 155.22/26.64 |
% 155.22/26.64 | SIMP: (4) implies:
% 155.22/26.64 | (5) all_6_0 = e3
% 155.22/26.64 |
% 155.22/26.64 | REDUCE: (3), (5) imply:
% 155.22/26.64 | (6) $false
% 155.22/26.64 |
% 155.22/26.64 | CLOSE: (6) is inconsistent.
% 155.22/26.64 |
% 155.22/26.64 End of proof
% 155.22/26.64
% 155.22/26.64 Sub-proof #82 shows that the following formulas are inconsistent:
% 155.22/26.64 ----------------------------------------------------------------
% 155.22/26.64 (1) op(e3, e1) = e3
% 155.22/26.64 (2) op(e3, e3) = all_10_2
% 155.22/26.64 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 155.22/26.64 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 155.22/26.64 (4) op(e3, e2) = all_52_4
% 155.22/26.64 (5) op(e2, e3) = all_52_1
% 155.22/26.64 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.22/26.64 (7) ~ (all_10_2 = e0)
% 155.22/26.64 (8) ~ (e3 = e0)
% 155.22/26.64 (9) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 155.22/26.64 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 155.22/26.64 (10) ~ (e2 = e0)
% 155.22/26.64 (11) op(e1, e3) = all_52_2
% 155.22/26.64 (12) op(e2, e3) = e2
% 155.22/26.64 (13) ~ (e3 = e1)
% 155.22/26.64 (14) ~ (all_52_4 = e1)
% 155.22/26.64 (15) ~ (all_52_2 = e1)
% 155.22/26.64 (16) ~ (all_10_2 = e2)
% 155.22/26.64 (17) ~ (e2 = e1)
% 155.22/26.64 (18) ~ (e1 = e0)
% 155.22/26.64 (19) all_58_4 = e3
% 155.22/26.64 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 155.22/26.64 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 155.22/26.64 (21) op(e3, e3) = all_22_1
% 155.22/26.64 (22) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.22/26.64 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.22/26.64 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.64 (24) ~ (e3 = e2)
% 155.22/26.64 (25) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 155.22/26.64 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 155.22/26.64 (26) ~ (all_52_1 = e3)
% 155.22/26.64
% 155.22/26.64 Begin of proof
% 155.22/26.64 |
% 155.22/26.64 | BETA: splitting (6) gives:
% 155.22/26.64 |
% 155.22/26.64 | Case 1:
% 155.22/26.64 | |
% 155.22/26.64 | | (27) all_58_6 = e1 & op(e1, e3) = e1
% 155.22/26.64 | |
% 155.22/26.64 | | ALPHA: (27) implies:
% 155.22/26.64 | | (28) op(e1, e3) = e1
% 155.22/26.64 | |
% 155.22/26.64 | | REF_CLOSE: (11), (15), (23), (28) are inconsistent by sub-proof #1412.
% 155.22/26.64 | |
% 155.22/26.64 | Case 2:
% 155.22/26.64 | |
% 155.22/26.64 | | (29) all_58_12 = e1 & op(e0, e3) = e1
% 155.22/26.64 | |
% 155.22/26.64 | | ALPHA: (29) implies:
% 155.22/26.64 | | (30) all_58_12 = e1
% 155.22/26.64 | | (31) op(e0, e3) = e1
% 155.22/26.64 | |
% 155.22/26.64 | | BETA: splitting (22) gives:
% 155.22/26.64 | |
% 155.22/26.64 | | Case 1:
% 155.22/26.64 | | |
% 155.22/26.64 | | | (32) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 155.22/26.64 | | | e0)
% 155.22/26.64 | | |
% 155.22/26.64 | | | BETA: splitting (32) gives:
% 155.22/26.64 | | |
% 155.22/26.64 | | | Case 1:
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | (33) all_58_0 = e0 & op(e3, e3) = e0
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | REF_CLOSE: (2), (7), (23), (33) are inconsistent by sub-proof #165.
% 155.22/26.64 | | | |
% 155.22/26.64 | | | Case 2:
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | (34) all_58_2 = e0 & op(e2, e3) = e0
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | ALPHA: (34) implies:
% 155.22/26.64 | | | | (35) op(e2, e3) = e0
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | REF_CLOSE: (10), (12), (23), (35) are inconsistent by sub-proof #1156.
% 155.22/26.64 | | | |
% 155.22/26.64 | | | End of split
% 155.22/26.64 | | |
% 155.22/26.64 | | Case 2:
% 155.22/26.64 | | |
% 155.22/26.64 | | | (36) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 155.22/26.64 | | | e0)
% 155.22/26.64 | | |
% 155.22/26.64 | | | BETA: splitting (36) gives:
% 155.22/26.64 | | |
% 155.22/26.64 | | | Case 1:
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | (37) all_58_6 = e0 & op(e1, e3) = e0
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | ALPHA: (37) implies:
% 155.22/26.64 | | | | (38) all_58_6 = e0
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | BETA: splitting (20) gives:
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | Case 1:
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | | (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3,
% 155.22/26.64 | | | | | e2) = e1)
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | | BETA: splitting (39) gives:
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | | Case 1:
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | (40) all_58_0 = e1 & op(e3, e3) = e1
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | ALPHA: (40) implies:
% 155.22/26.64 | | | | | | (41) op(e3, e3) = e1
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | BETA: splitting (3) gives:
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | Case 1:
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | (42) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 155.22/26.64 | | | | | | | op(e2, e3) = e3)
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | BETA: splitting (42) gives:
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | (43) all_58_0 = e3 & op(e3, e3) = e3
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | ALPHA: (43) implies:
% 155.22/26.64 | | | | | | | | (44) op(e3, e3) = e3
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | REF_CLOSE: (13), (21), (23), (41), (44) are inconsistent by
% 155.22/26.64 | | | | | | | | sub-proof #864.
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | (45) all_58_2 = e3 & op(e2, e3) = e3
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | ALPHA: (45) implies:
% 155.22/26.64 | | | | | | | | (46) op(e2, e3) = e3
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | REF_CLOSE: (5), (23), (26), (46) are inconsistent by sub-proof
% 155.22/26.64 | | | | | | | | #1183.
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | End of split
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | Case 2:
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | (47) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 155.22/26.64 | | | | | | | op(e0, e3) = e3)
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | REF_CLOSE: (8), (13), (30), (38), (47) are inconsistent by
% 155.22/26.64 | | | | | | | sub-proof #84.
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | End of split
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | Case 2:
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | (48) all_58_1 = e1 & op(e3, e2) = e1
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | REF_CLOSE: (4), (14), (23), (48) are inconsistent by sub-proof
% 155.22/26.64 | | | | | | #1284.
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | End of split
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | Case 2:
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | | (49) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3,
% 155.22/26.64 | | | | | e0) = e1)
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | | BETA: splitting (49) gives:
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | | Case 1:
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | (50) all_58_4 = e1 & op(e3, e1) = e1
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | REF_CLOSE: (13), (19), (50) are inconsistent by sub-proof #1345.
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | Case 2:
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | (51) all_58_9 = e1 & op(e3, e0) = e1
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | ALPHA: (51) implies:
% 155.22/26.64 | | | | | | (52) all_58_9 = e1
% 155.22/26.64 | | | | | | (53) op(e3, e0) = e1
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | BETA: splitting (9) gives:
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | | Case 1:
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | (54) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 155.22/26.64 | | | | | | | op(e3, e2) = e2)
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | BETA: splitting (54) gives:
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | (55) all_58_0 = e2 & op(e3, e3) = e2
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | REF_CLOSE: (2), (16), (23), (55) are inconsistent by sub-proof
% 155.22/26.64 | | | | | | | | #1523.
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | (56) all_58_1 = e2 & op(e3, e2) = e2
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | ALPHA: (56) implies:
% 155.22/26.64 | | | | | | | | (57) all_58_1 = e2
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | BETA: splitting (3) gives:
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | |
% 155.22/26.64 | | | | | | | | | (58) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 155.22/26.64 | | | | | | | | | op(e2, e3) = e3)
% 155.22/26.64 | | | | | | | | |
% 155.22/26.64 | | | | | | | | | BETA: splitting (58) gives:
% 155.22/26.64 | | | | | | | | |
% 155.22/26.64 | | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | (59) all_58_0 = e3 & op(e3, e3) = e3
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | ALPHA: (59) implies:
% 155.22/26.64 | | | | | | | | | | (60) op(e3, e3) = e3
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | BETA: splitting (25) gives:
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | (61) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 155.22/26.64 | | | | | | | | | | | & op(e3, e2) = e0)
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | BETA: splitting (61) gives:
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | (62) all_58_0 = e0 & op(e3, e3) = e0
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | ALPHA: (62) implies:
% 155.22/26.64 | | | | | | | | | | | | (63) op(e3, e3) = e0
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | REF_CLOSE: (8), (21), (23), (60), (63) are inconsistent by
% 155.22/26.64 | | | | | | | | | | | | sub-proof #866.
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | (64) all_58_1 = e0 & op(e3, e2) = e0
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | REF_CLOSE: (10), (57), (64) are inconsistent by sub-proof
% 155.22/26.64 | | | | | | | | | | | | #796.
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | (65) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 155.22/26.64 | | | | | | | | | | | & op(e3, e0) = e0)
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | BETA: splitting (65) gives:
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | (66) all_58_4 = e0 & op(e3, e1) = e0
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | REF_CLOSE: (8), (19), (66) are inconsistent by sub-proof
% 155.22/26.64 | | | | | | | | | | | | #1344.
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | (67) all_58_9 = e0 & op(e3, e0) = e0
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | ALPHA: (67) implies:
% 155.22/26.64 | | | | | | | | | | | | (68) op(e3, e0) = e0
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | | REF_CLOSE: (18), (23), (53), (68) are inconsistent by
% 155.22/26.64 | | | | | | | | | | | | sub-proof #140.
% 155.22/26.64 | | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | (69) all_58_2 = e3 & op(e2, e3) = e3
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | ALPHA: (69) implies:
% 155.22/26.64 | | | | | | | | | | (70) op(e2, e3) = e3
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | | REF_CLOSE: (5), (23), (26), (70) are inconsistent by
% 155.22/26.64 | | | | | | | | | | sub-proof #1183.
% 155.22/26.64 | | | | | | | | | |
% 155.22/26.64 | | | | | | | | | End of split
% 155.22/26.64 | | | | | | | | |
% 155.22/26.64 | | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | | |
% 155.22/26.64 | | | | | | | | | (71) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 155.22/26.64 | | | | | | | | | op(e0, e3) = e3)
% 155.22/26.64 | | | | | | | | |
% 155.22/26.64 | | | | | | | | | REF_CLOSE: (8), (13), (30), (38), (71) are inconsistent by
% 155.22/26.64 | | | | | | | | | sub-proof #84.
% 155.22/26.64 | | | | | | | | |
% 155.22/26.64 | | | | | | | | End of split
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | End of split
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | Case 2:
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | (72) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 155.22/26.64 | | | | | | | op(e3, e0) = e2)
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | BETA: splitting (72) gives:
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | | Case 1:
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | (73) all_58_4 = e2 & op(e3, e1) = e2
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | ALPHA: (73) implies:
% 155.22/26.64 | | | | | | | | (74) op(e3, e1) = e2
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | REF_CLOSE: (1), (23), (24), (74) are inconsistent by sub-proof
% 155.22/26.64 | | | | | | | | #1502.
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | Case 2:
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | (75) all_58_9 = e2 & op(e3, e0) = e2
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | | REF_CLOSE: (17), (52), (75) are inconsistent by sub-proof #931.
% 155.22/26.64 | | | | | | | |
% 155.22/26.64 | | | | | | | End of split
% 155.22/26.64 | | | | | | |
% 155.22/26.64 | | | | | | End of split
% 155.22/26.64 | | | | | |
% 155.22/26.64 | | | | | End of split
% 155.22/26.64 | | | | |
% 155.22/26.64 | | | | End of split
% 155.22/26.64 | | | |
% 155.22/26.64 | | | Case 2:
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | (76) all_58_12 = e0 & op(e0, e3) = e0
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | ALPHA: (76) implies:
% 155.22/26.64 | | | | (77) op(e0, e3) = e0
% 155.22/26.64 | | | |
% 155.22/26.64 | | | | REF_CLOSE: (18), (23), (31), (77) are inconsistent by sub-proof #83.
% 155.22/26.64 | | | |
% 155.22/26.64 | | | End of split
% 155.22/26.64 | | |
% 155.22/26.64 | | End of split
% 155.22/26.64 | |
% 155.22/26.64 | End of split
% 155.22/26.64 |
% 155.22/26.64 End of proof
% 155.22/26.64
% 155.22/26.64 Sub-proof #83 shows that the following formulas are inconsistent:
% 155.22/26.64 ----------------------------------------------------------------
% 155.22/26.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.64 (2) op(e0, e3) = e1
% 155.22/26.64 (3) op(e0, e3) = e0
% 155.22/26.64 (4) ~ (e1 = e0)
% 155.22/26.64
% 155.22/26.64 Begin of proof
% 155.22/26.64 |
% 155.22/26.64 | GROUND_INST: instantiating (1) with e1, e0, e3, e0, simplifying with (2), (3)
% 155.22/26.64 | gives:
% 155.22/26.64 | (5) e1 = e0
% 155.22/26.64 |
% 155.22/26.64 | REDUCE: (4), (5) imply:
% 155.22/26.64 | (6) $false
% 155.22/26.64 |
% 155.22/26.64 | CLOSE: (6) is inconsistent.
% 155.22/26.64 |
% 155.22/26.64 End of proof
% 155.22/26.64
% 155.22/26.64 Sub-proof #84 shows that the following formulas are inconsistent:
% 155.22/26.64 ----------------------------------------------------------------
% 155.22/26.64 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 155.22/26.64 (2) ~ (e3 = e0)
% 155.22/26.64 (3) all_58_6 = e0
% 155.22/26.64 (4) ~ (e3 = e1)
% 155.22/26.65 (5) all_58_12 = e1
% 155.22/26.65
% 155.22/26.65 Begin of proof
% 155.22/26.65 |
% 155.22/26.65 | BETA: splitting (1) gives:
% 155.22/26.65 |
% 155.22/26.65 | Case 1:
% 155.22/26.65 | |
% 155.22/26.65 | | (6) all_58_6 = e3 & op(e1, e3) = e3
% 155.22/26.65 | |
% 155.22/26.65 | | ALPHA: (6) implies:
% 155.22/26.65 | | (7) all_58_6 = e3
% 155.22/26.65 | |
% 155.22/26.65 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #1321.
% 155.22/26.65 | |
% 155.22/26.65 | Case 2:
% 155.22/26.65 | |
% 155.22/26.65 | | (8) all_58_12 = e3 & op(e0, e3) = e3
% 155.22/26.65 | |
% 155.22/26.65 | | ALPHA: (8) implies:
% 155.22/26.65 | | (9) all_58_12 = e3
% 155.22/26.65 | |
% 155.22/26.65 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #1516.
% 155.22/26.65 | |
% 155.22/26.65 | End of split
% 155.22/26.65 |
% 155.22/26.65 End of proof
% 155.22/26.65
% 155.22/26.65 Sub-proof #85 shows that the following formulas are inconsistent:
% 155.22/26.65 ----------------------------------------------------------------
% 155.22/26.65 (1) op(e3, e3) = all_10_2
% 155.22/26.65 (2) ~ (all_10_2 = e1)
% 155.22/26.65 (3) all_54_0 = all_10_2
% 155.22/26.65 (4) ~ (all_10_2 = e0)
% 155.22/26.65 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 155.22/26.65 (6) op(e2, e3) = e2
% 155.22/26.65 (7) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 155.22/26.65 (8) ~ (all_10_2 = e2)
% 155.22/26.65 (9) ~ (e2 = e1)
% 155.22/26.65 (10) op(e3, e3) = all_22_1
% 155.22/26.65 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.65
% 155.22/26.65 Begin of proof
% 155.22/26.65 |
% 155.22/26.65 | BETA: splitting (5) gives:
% 155.22/26.65 |
% 155.22/26.65 | Case 1:
% 155.22/26.65 | |
% 155.22/26.65 | | (12) all_58_0 = e1 & op(e3, e3) = e1
% 155.22/26.65 | |
% 155.22/26.65 | | ALPHA: (12) implies:
% 155.22/26.65 | | (13) op(e3, e3) = e1
% 155.22/26.65 | |
% 155.22/26.65 | | BETA: splitting (7) gives:
% 155.22/26.65 | |
% 155.22/26.65 | | Case 1:
% 155.22/26.65 | | |
% 155.22/26.65 | | | (14) all_54_0 = e3
% 155.22/26.65 | | |
% 155.22/26.65 | | | COMBINE_EQS: (3), (14) imply:
% 155.22/26.65 | | | (15) all_10_2 = e3
% 155.22/26.65 | | |
% 155.22/26.65 | | | REDUCE: (2), (15) imply:
% 155.22/26.65 | | | (16) ~ (e3 = e1)
% 155.22/26.65 | | |
% 155.22/26.65 | | | REDUCE: (1), (15) imply:
% 155.22/26.65 | | | (17) op(e3, e3) = e3
% 155.22/26.65 | | |
% 155.22/26.65 | | | REF_CLOSE: (10), (11), (13), (16), (17) are inconsistent by sub-proof
% 155.22/26.65 | | | #864.
% 155.22/26.65 | | |
% 155.22/26.65 | | Case 2:
% 155.22/26.65 | | |
% 155.22/26.65 | | | (18) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 155.22/26.65 | | |
% 155.22/26.65 | | | REF_CLOSE: (2), (3), (4), (8), (18) are inconsistent by sub-proof #1307.
% 155.22/26.65 | | |
% 155.22/26.65 | | End of split
% 155.22/26.65 | |
% 155.22/26.65 | Case 2:
% 155.22/26.65 | |
% 155.22/26.65 | | (19) all_58_2 = e1 & op(e2, e3) = e1
% 155.22/26.65 | |
% 155.22/26.65 | | ALPHA: (19) implies:
% 155.22/26.65 | | (20) op(e2, e3) = e1
% 155.22/26.65 | |
% 155.22/26.65 | | REF_CLOSE: (6), (9), (11), (20) are inconsistent by sub-proof #1430.
% 155.22/26.65 | |
% 155.22/26.65 | End of split
% 155.22/26.65 |
% 155.22/26.65 End of proof
% 155.22/26.65
% 155.22/26.65 Sub-proof #86 shows that the following formulas are inconsistent:
% 155.22/26.65 ----------------------------------------------------------------
% 155.22/26.65 (1) ~ (all_52_12 = e3)
% 155.22/26.65 (2) op(e0, e3) = all_52_3
% 155.22/26.65 (3) all_58_0 = e2
% 155.22/26.65 (4) op(e3, e0) = all_52_12
% 155.22/26.65 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.65 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 155.22/26.65 (6) ~ (all_52_14 = e2)
% 155.22/26.65 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 155.22/26.65 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.22/26.65 (8) ~ (all_52_12 = e2)
% 155.22/26.65 (9) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.65 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 155.22/26.65 (10) op(e3, e3) = all_10_2
% 155.22/26.65 (11) all_54_13 = all_52_7
% 155.22/26.65 (12) ~ (all_52_7 = e3)
% 155.22/26.65 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 155.22/26.65 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 155.22/26.65 e1)
% 155.22/26.65 (14) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 155.22/26.65 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 155.22/26.65 (15) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 155.22/26.65 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 155.22/26.65 (16) ~ (all_52_7 = all_52_11)
% 155.22/26.65 (17) ~ (all_52_12 = all_4_2)
% 155.22/26.65 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 155.22/26.65 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 155.22/26.65 (19) ~ (all_52_1 = all_8_2)
% 155.22/26.65 (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 155.22/26.65 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 155.22/26.65 (21) all_56_14 = e2
% 155.22/26.65 (22) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 155.22/26.65 (23) op(e3, e2) = all_52_4
% 155.22/26.65 (24) ~ (all_52_1 = all_52_13)
% 155.22/26.65 (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.22/26.65 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.22/26.65 (26) all_56_13 = all_8_2
% 155.22/26.65 (27) op(e2, e3) = all_52_1
% 155.22/26.65 (28) ~ (all_52_1 = all_52_3)
% 155.22/26.65 (29) op(e2, e2) = all_38_1
% 155.22/26.65 (30) ~ (all_10_2 = e0)
% 155.22/26.65 (31) ( ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0 & op(e2, e2) =
% 155.22/26.65 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e0) & op(e2,
% 155.22/26.65 e2) = all_16_1 & $i(all_16_1))
% 155.22/26.65 (32) ~ (e3 = e0)
% 155.22/26.65 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.22/26.65 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.22/26.65 (34) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 155.22/26.65 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 155.22/26.65 e2)
% 155.22/26.65 (35) ~ (e2 = e0)
% 155.22/26.65 (36) ~ (all_8_2 = e3)
% 155.22/26.65 (37) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 155.22/26.65 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.22/26.65 (38) all_30_2 = all_8_2
% 155.22/26.65 (39) op(e1, e3) = all_52_2
% 155.22/26.65 (40) op(e2, e0) = all_52_13
% 155.22/26.65 (41) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.22/26.65 (42) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 155.22/26.65 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 155.22/26.65 (43) ~ (all_52_6 = all_8_2)
% 155.22/26.65 (44) ~ (e3 = e1)
% 155.22/26.65 (45) op(e1, e2) = all_52_6
% 155.22/26.65 (46) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 155.22/26.65 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.65 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 155.22/26.65 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.22/26.65 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 155.22/26.65 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.65 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 155.22/26.65 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 155.22/26.65 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.22/26.65 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.65 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 155.22/26.65 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 155.22/26.65 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 155.22/26.65 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 155.22/26.65 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 155.22/26.65 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 155.22/26.65 = e0)
% 155.22/26.65 (47) ~ (all_4_2 = e1)
% 155.22/26.65 (48) all_54_4 = all_52_1
% 155.22/26.65 (49) ~ (all_52_11 = e2)
% 155.22/26.65 (50) ~ (all_52_3 = all_4_2)
% 155.22/26.65 (51) all_58_7 = e1
% 155.22/26.65 (52) op(e1, e2) = e1
% 155.22/26.65 (53) op(e0, e0) = all_4_2
% 155.22/26.65 (54) all_56_15 = all_4_2
% 155.22/26.65 (55) op(e0, e1) = all_52_11
% 155.22/26.65 (56) ~ (all_52_13 = all_4_2)
% 155.22/26.65 (57) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0 &
% 155.22/26.65 op(e2, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 155.22/26.65 e1) & op(e2, e2) = all_20_1 & $i(all_20_1))
% 155.22/26.65 (58) ~ (all_52_2 = e1)
% 155.22/26.65 (59) all_56_12 = e2
% 155.22/26.65 (60) all_52_4 = e3
% 155.22/26.65 (61) ~ (e2 = e1)
% 155.22/26.65 (62) all_58_8 = e2
% 155.22/26.65 (63) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.22/26.65 (64) ~ (e1 = e0)
% 155.22/26.65 (65) ~ (all_8_2 = e1)
% 155.22/26.65 (66) ~ (all_52_7 = all_8_2)
% 155.22/26.65 (67) op(e3, e1) = all_52_8
% 155.22/26.65 (68) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 155.22/26.65 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 155.22/26.65 e3)
% 155.22/26.65 (69) ~ (all_52_14 = e1)
% 155.22/26.65 (70) ~ (all_52_12 = all_52_14)
% 155.22/26.65 (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 155.22/26.65 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 155.22/26.65 (72) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0 &
% 155.22/26.65 op(e0, e0) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 155.22/26.65 e1) & op(e0, e0) = all_30_1 & $i(all_30_1))
% 155.22/26.65 (73) ~ (all_52_8 = e3)
% 155.22/26.65 (74) ~ (all_52_7 = all_4_2)
% 155.22/26.65 (75) ~ (all_52_7 = e1)
% 155.22/26.65 (76) op(e0, e2) = all_52_7
% 155.22/26.65 (77) op(e1, e0) = all_52_14
% 155.22/26.65 (78) all_38_1 = all_8_2
% 155.22/26.65 (79) all_20_2 = all_4_2
% 155.22/26.65 (80) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 155.22/26.65 (81) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.22/26.65 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.22/26.65 (82) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.65 (83) all_54_5 = all_8_2
% 155.22/26.65 (84) all_54_11 = all_52_14
% 155.22/26.65 (85) ~ (all_52_13 = all_52_14)
% 155.22/26.65 (86) ~ (e3 = e2)
% 155.22/26.65 (87) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 155.22/26.65 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 155.22/26.65 (88) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 155.22/26.65 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 155.22/26.65 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 155.22/26.65 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 155.22/26.65 (89) ~ (all_52_13 = all_8_2)
% 155.22/26.65 (90) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 155.22/26.65 (91) all_54_12 = all_52_3
% 155.22/26.65 (92) ~ (all_52_14 = all_4_2)
% 155.22/26.65 (93) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 155.22/26.65 (94) ~ (all_52_3 = all_52_7)
% 155.22/26.65
% 155.22/26.65 Begin of proof
% 155.22/26.65 |
% 155.22/26.65 | REDUCE: (23), (60) imply:
% 155.22/26.65 | (95) op(e3, e2) = e3
% 155.22/26.65 |
% 155.22/26.65 | REDUCE: (29), (78) imply:
% 155.22/26.65 | (96) op(e2, e2) = all_8_2
% 155.22/26.65 |
% 155.22/26.65 | BETA: splitting (57) gives:
% 155.22/26.65 |
% 155.22/26.65 | Case 1:
% 155.22/26.65 | |
% 155.22/26.65 | | (97) ~ (all_20_2 = e2)
% 155.22/26.65 | |
% 155.22/26.65 | | REDUCE: (79), (97) imply:
% 155.22/26.65 | | (98) ~ (all_4_2 = e2)
% 155.22/26.65 | |
% 155.22/26.65 | | BETA: splitting (20) gives:
% 155.22/26.65 | |
% 155.22/26.65 | | Case 1:
% 155.22/26.65 | | |
% 155.22/26.65 | | | (99) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 155.22/26.65 | | | e2)
% 155.22/26.65 | | |
% 155.22/26.65 | | | BETA: splitting (99) gives:
% 155.22/26.65 | | |
% 155.22/26.65 | | | Case 1:
% 155.22/26.65 | | | |
% 155.22/26.65 | | | | (100) all_58_9 = e2 & op(e3, e0) = e2
% 155.22/26.65 | | | |
% 155.22/26.65 | | | | ALPHA: (100) implies:
% 155.22/26.65 | | | | (101) all_58_9 = e2
% 155.22/26.65 | | | |
% 155.22/26.65 | | | | REF_CLOSE: (3), (32), (35), (44), (61), (64), (71), (82), (87), (95),
% 155.22/26.65 | | | | (101) are inconsistent by sub-proof #1251.
% 155.22/26.65 | | | |
% 155.22/26.65 | | | Case 2:
% 155.22/26.65 | | | |
% 155.22/26.65 | | | | (102) all_58_10 = e2 & op(e2, e0) = e2
% 155.22/26.65 | | | |
% 155.22/26.65 | | | | ALPHA: (102) implies:
% 155.22/26.65 | | | | (103) all_58_10 = e2
% 155.22/26.65 | | | | (104) op(e2, e0) = e2
% 155.22/26.65 | | | |
% 155.22/26.65 | | | | BETA: splitting (7) gives:
% 155.22/26.65 | | | |
% 155.22/26.65 | | | | Case 1:
% 155.22/26.65 | | | | |
% 155.22/26.65 | | | | | (105) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 155.22/26.65 | | | | | e0) = e1)
% 155.22/26.65 | | | | |
% 155.22/26.65 | | | | | BETA: splitting (105) gives:
% 155.22/26.65 | | | | |
% 155.22/26.65 | | | | | Case 1:
% 155.22/26.65 | | | | | |
% 155.22/26.65 | | | | | | (106) all_58_9 = e1 & op(e3, e0) = e1
% 155.22/26.65 | | | | | |
% 155.22/26.65 | | | | | | ALPHA: (106) implies:
% 155.22/26.65 | | | | | | (107) all_58_9 = e1
% 155.22/26.65 | | | | | | (108) op(e3, e0) = e1
% 155.22/26.65 | | | | | |
% 155.22/26.65 | | | | | | BETA: splitting (87) gives:
% 155.22/26.65 | | | | | |
% 155.22/26.65 | | | | | | Case 1:
% 155.22/26.65 | | | | | | |
% 155.22/26.65 | | | | | | | (109) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 155.22/26.65 | | | | | | | op(e3, e2) = e0)
% 155.22/26.65 | | | | | | |
% 155.22/26.65 | | | | | | | REF_CLOSE: (10), (30), (32), (82), (95), (109) are inconsistent by
% 155.22/26.65 | | | | | | | sub-proof #135.
% 155.22/26.65 | | | | | | |
% 155.22/26.65 | | | | | | Case 2:
% 155.22/26.65 | | | | | | |
% 155.22/26.65 | | | | | | | (110) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 155.22/26.65 | | | | | | | op(e3, e0) = e0)
% 155.22/26.65 | | | | | | |
% 155.22/26.65 | | | | | | | BETA: splitting (110) gives:
% 155.22/26.65 | | | | | | |
% 155.22/26.65 | | | | | | | Case 1:
% 155.22/26.65 | | | | | | | |
% 155.22/26.65 | | | | | | | | (111) all_58_4 = e0 & op(e3, e1) = e0
% 155.22/26.65 | | | | | | | |
% 155.22/26.65 | | | | | | | | ALPHA: (111) implies:
% 155.22/26.65 | | | | | | | | (112) op(e3, e1) = e0
% 155.22/26.65 | | | | | | | |
% 155.22/26.65 | | | | | | | | BETA: splitting (34) gives:
% 155.22/26.65 | | | | | | | |
% 155.22/26.65 | | | | | | | | Case 1:
% 155.22/26.65 | | | | | | | | |
% 155.22/26.65 | | | | | | | | | (113) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2
% 155.22/26.65 | | | | | | | | | & op(e0, e2) = e2)
% 155.22/26.65 | | | | | | | | |
% 155.22/26.65 | | | | | | | | | BETA: splitting (113) gives:
% 155.22/26.65 | | | | | | | | |
% 155.22/26.65 | | | | | | | | | Case 1:
% 155.22/26.65 | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | (114) all_58_12 = e2 & op(e0, e3) = e2
% 155.22/26.65 | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | ALPHA: (114) implies:
% 155.22/26.65 | | | | | | | | | | (115) all_58_12 = e2
% 155.22/26.65 | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | REF_CLOSE: (3), (18), (32), (33), (35), (44), (61), (64),
% 155.22/26.65 | | | | | | | | | | (81), (86), (115) are inconsistent by sub-proof
% 155.22/26.65 | | | | | | | | | | #999.
% 155.22/26.65 | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | Case 2:
% 155.22/26.65 | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | (116) all_58_13 = e2 & op(e0, e2) = e2
% 155.22/26.65 | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | ALPHA: (116) implies:
% 155.22/26.65 | | | | | | | | | | (117) op(e0, e2) = e2
% 155.22/26.65 | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | BETA: splitting (42) gives:
% 155.22/26.65 | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | Case 1:
% 155.22/26.65 | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | (118) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 155.22/26.65 | | | | | | | | | | | & op(e2, e2) = e0)
% 155.22/26.65 | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | BETA: splitting (118) gives:
% 155.22/26.65 | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | Case 1:
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | (119) all_58_1 = e0 & op(e3, e2) = e0
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | ALPHA: (119) implies:
% 155.22/26.65 | | | | | | | | | | | | (120) op(e3, e2) = e0
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REF_CLOSE: (32), (82), (95), (120) are inconsistent by
% 155.22/26.65 | | | | | | | | | | | | sub-proof #1303.
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | Case 2:
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | (121) all_58_3 = e0 & op(e2, e2) = e0
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | ALPHA: (121) implies:
% 155.22/26.65 | | | | | | | | | | | | (122) op(e2, e2) = e0
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | GROUND_INST: instantiating (82) with all_52_7, e2, e2, e0,
% 155.22/26.65 | | | | | | | | | | | | simplifying with (76), (117) gives:
% 155.22/26.65 | | | | | | | | | | | | (123) all_52_7 = e2
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | GROUND_INST: instantiating (82) with all_52_13, e2, e0, e2,
% 155.22/26.65 | | | | | | | | | | | | simplifying with (40), (104) gives:
% 155.22/26.65 | | | | | | | | | | | | (124) all_52_13 = e2
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | GROUND_INST: instantiating (82) with all_8_2, e0, e2, e2,
% 155.22/26.65 | | | | | | | | | | | | simplifying with (96), (122) gives:
% 155.22/26.65 | | | | | | | | | | | | (125) all_8_2 = e0
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | GROUND_INST: instantiating (82) with all_52_12, e1, e0, e3,
% 155.22/26.65 | | | | | | | | | | | | simplifying with (4), (108) gives:
% 155.22/26.65 | | | | | | | | | | | | (126) all_52_12 = e1
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | GROUND_INST: instantiating (82) with all_52_8, e0, e1, e3,
% 155.22/26.65 | | | | | | | | | | | | simplifying with (67), (112) gives:
% 155.22/26.65 | | | | | | | | | | | | (127) all_52_8 = e0
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | COMBINE_EQS: (38), (125) imply:
% 155.22/26.65 | | | | | | | | | | | | (128) all_30_2 = e0
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | COMBINE_EQS: (26), (125) imply:
% 155.22/26.65 | | | | | | | | | | | | (129) all_56_13 = e0
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (24), (124) imply:
% 155.22/26.65 | | | | | | | | | | | | (130) ~ (all_52_1 = e2)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (19), (125) imply:
% 155.22/26.65 | | | | | | | | | | | | (131) ~ (all_52_1 = e0)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (94), (123) imply:
% 155.22/26.65 | | | | | | | | | | | | (132) ~ (all_52_3 = e2)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (12), (123) imply:
% 155.22/26.65 | | | | | | | | | | | | (133) ~ (e3 = e2)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (70), (126) imply:
% 155.22/26.65 | | | | | | | | | | | | (134) ~ (all_52_14 = e1)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (17), (126) imply:
% 155.22/26.65 | | | | | | | | | | | | (135) ~ (all_4_2 = e1)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (1), (126) imply:
% 155.22/26.65 | | | | | | | | | | | | (136) ~ (e3 = e1)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (8), (126) imply:
% 155.22/26.65 | | | | | | | | | | | | (137) ~ (e2 = e1)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (85), (124) imply:
% 155.22/26.65 | | | | | | | | | | | | (138) ~ (all_52_14 = e2)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (56), (124) imply:
% 155.22/26.65 | | | | | | | | | | | | (139) ~ (all_4_2 = e2)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | REDUCE: (36), (125) imply:
% 155.22/26.65 | | | | | | | | | | | | (140) ~ (e3 = e0)
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | BETA: splitting (72) gives:
% 155.22/26.65 | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | Case 1:
% 155.22/26.65 | | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | | (141) ~ (all_30_2 = e0)
% 155.22/26.65 | | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | | REDUCE: (128), (141) imply:
% 155.22/26.65 | | | | | | | | | | | | | (142) $false
% 155.22/26.65 | | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 155.22/26.65 | | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | Case 2:
% 155.22/26.65 | | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | | (143) ( ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0
% 155.22/26.65 | | | | | | | | | | | | | & op(e0, e0) = all_30_1 & $i(all_30_0) &
% 155.22/26.65 | | | | | | | | | | | | | $i(all_30_1)) | ( ~ (all_30_1 = e1) & op(e0, e0)
% 155.22/26.65 | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 155.22/26.65 | | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | | BETA: splitting (143) gives:
% 155.22/26.65 | | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | | Case 1:
% 155.22/26.65 | | | | | | | | | | | | | |
% 155.22/26.65 | | | | | | | | | | | | | | (144) ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0 &
% 155.22/26.65 | | | | | | | | | | | | | | op(e0, e0) = all_30_1 & $i(all_30_0) &
% 155.22/26.65 | | | | | | | | | | | | | | $i(all_30_1)
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | ALPHA: (144) implies:
% 155.22/26.66 | | | | | | | | | | | | | | (145) op(e0, e0) = all_30_1
% 155.22/26.66 | | | | | | | | | | | | | | (146) op(all_30_1, e2) = all_30_0
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | (147) all_56_12 = e3
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | COMBINE_EQS: (59), (147) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | (148) e3 = e2
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | REDUCE: (86), (148) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | (149) $false
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | (150) ~ (all_56_12 = e3)
% 155.22/26.66 | | | | | | | | | | | | | | | (151) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | (152) all_56_13 = e2
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (152) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | (153) e2 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | REDUCE: (35), (153) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | (154) $false
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | (155) all_56_14 = e1 | all_56_15 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | (156) all_56_14 = e1
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (61), (156) are inconsistent by sub-proof
% 155.22/26.66 | | | | | | | | | | | | | | | | | #93.
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | (157) all_56_15 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | | (158) ~ (all_56_14 = e1)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (157) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (159) all_4_2 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (160) all_4_2 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (50), (160) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (161) ~ (all_52_3 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (92), (160) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (162) ~ (all_52_14 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (98), (160) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (163) ~ (e2 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (47), (160) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (164) ~ (e1 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (53), (160) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (165) op(e0, e0) = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | (166) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 155.22/26.66 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (167) all_58_9 = e3 & op(e3, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (32), (35), (44), (61), (64), (71), (82),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (87), (95), (167) are inconsistent by sub-proof
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | #1077.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (168) all_58_10 = e3 & op(e2, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (103), (168) are inconsistent by sub-proof
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | #1218.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | (169) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 155.22/26.66 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (170) all_58_11 = e3 & op(e1, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (171) all_58_11 = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (172) op(e1, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (173) ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0 &
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_16_1 & $i(all_16_0) &
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | $i(all_16_1)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (174) ~ (all_16_0 = e1)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (175) op(e2, e2) = all_16_1
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (176) op(all_16_1, e3) = all_16_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with e0, all_30_1, e0, e0,
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | simplifying with (145), (165) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (177) all_30_1 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with e0, all_16_1, e2, e2,
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | simplifying with (122), (175) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (178) all_16_1 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (177) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (179) op(e0, e2) = all_30_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (178) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (180) op(e0, e3) = all_16_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with e2, all_30_0, e2, e0,
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | simplifying with (117), (179) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (181) all_30_0 = e2
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with all_52_3, all_16_0, e3,
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | e0, simplifying with (2), (180) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (182) all_52_3 = all_16_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (182) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (183) all_54_12 = all_16_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (182) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (184) ~ (all_52_1 = all_16_0)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (182) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (185) ~ (all_16_0 = e2)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (182) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (186) ~ (all_16_0 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (12), (13), (14),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (15), (18), (20), (22), (23), (25), (27), (35),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (37), (40), (46), (47), (48), (51), (52), (53),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (61), (62), (63), (64), (65), (67), (68), (69),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (70), (71), (73), (76), (77), (82), (84), (87),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (88), (90), (95), (96), (103), (107), (108),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (112), (117), (130), (131), (157), (162), (171),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (172), (174), (183), (184), (185), (186) are
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #90.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (187) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | $i(all_16_1)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (188) ~ (all_16_1 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (189) op(e2, e2) = all_16_1
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (122), (188), (189) are inconsistent by
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | sub-proof #966.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (190) all_58_15 = e3 & op(e0, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (191) all_58_15 = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (192) op(e0, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (20), (25), (35), (37), (40), (47),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (51), (53), (61), (62), (63), (64), (65), (69),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (76), (77), (82), (84), (88), (95), (96), (117),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (162), (191), (192) are inconsistent by sub-proof
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | #91.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | (193) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 &
% 155.22/26.66 | | | | | | | | | | | | | | $i(all_30_1)
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | ALPHA: (193) implies:
% 155.22/26.66 | | | | | | | | | | | | | | (194) ~ (all_30_1 = e1)
% 155.22/26.66 | | | | | | | | | | | | | | (195) op(e0, e0) = all_30_1
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | (196) all_56_12 = e3
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | COMBINE_EQS: (59), (196) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | (197) e3 = e2
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | REDUCE: (86), (197) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | (198) $false
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent.
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | (199) ~ (all_56_12 = e3)
% 155.22/26.66 | | | | | | | | | | | | | | | (200) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | (201) all_56_13 = e2
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (201) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | (202) e2 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | REDUCE: (35), (202) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | (203) $false
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | (204) all_56_14 = e1 | all_56_15 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | (205) all_56_14 = e1
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (61), (205) are inconsistent by sub-proof
% 155.22/26.66 | | | | | | | | | | | | | | | | | #93.
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | (206) all_56_15 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | | (207) ~ (all_56_14 = e1)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (206) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (208) all_4_2 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | SIMP: (208) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (209) all_4_2 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (50), (209) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (210) ~ (all_52_3 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (92), (209) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (211) ~ (all_52_14 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (98), (209) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (212) ~ (e2 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (47), (209) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (213) ~ (e1 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | REDUCE: (53), (209) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | (214) op(e0, e0) = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | (215) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 155.22/26.66 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (216) all_58_9 = e3 & op(e3, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (32), (35), (44), (61), (64), (71), (82),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (87), (95), (216) are inconsistent by sub-proof
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | #1077.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (217) all_58_10 = e3 & op(e2, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (103), (217) are inconsistent by sub-proof
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | #1218.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | (218) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 155.22/26.66 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (219) all_58_11 = e3 & op(e1, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (220) all_58_11 = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (221) op(e1, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (222) ~ (all_16_0 = e1) & op(all_16_1, e3) = all_16_0 &
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_16_1 & $i(all_16_0) &
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | $i(all_16_1)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (223) ~ (all_16_0 = e1)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (224) op(e2, e2) = all_16_1
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (225) op(all_16_1, e3) = all_16_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with e0, all_30_1, e0, e0,
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | simplifying with (195), (214) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (226) all_30_1 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with e0, all_16_1, e2, e2,
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | simplifying with (122), (224) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (227) all_16_1 = e0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (225), (227) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (228) op(e0, e3) = all_16_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with all_52_3, all_16_0, e3,
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | e0, simplifying with (2), (228) gives:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (229) all_52_3 = all_16_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (229) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (230) all_54_12 = all_16_0
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (229) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (231) ~ (all_52_1 = all_16_0)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (229) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (232) ~ (all_16_0 = e2)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REDUCE: (210), (229) imply:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (233) ~ (all_16_0 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (12), (13), (14),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (15), (18), (20), (22), (23), (25), (27), (35),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (37), (40), (46), (47), (48), (51), (52), (53),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (61), (62), (63), (64), (65), (67), (68), (69),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (70), (71), (73), (76), (77), (82), (84), (87),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (88), (90), (95), (96), (103), (107), (108),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (112), (117), (130), (131), (206), (211), (220),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (221), (223), (230), (231), (232), (233) are
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #90.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (234) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | $i(all_16_1)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (235) ~ (all_16_1 = e0)
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | (236) op(e2, e2) = all_16_1
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (122), (235), (236) are inconsistent by
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | | sub-proof #966.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (237) all_58_15 = e3 & op(e0, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (238) all_58_15 = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (239) op(e0, e0) = e3
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (20), (25), (35), (37), (40), (47),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (51), (53), (61), (62), (63), (64), (65), (69),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (76), (77), (82), (84), (88), (95), (96), (117),
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | (211), (238), (239) are inconsistent by sub-proof
% 155.22/26.66 | | | | | | | | | | | | | | | | | | | #91.
% 155.22/26.66 | | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | (240) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 155.22/26.66 | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 155.22/26.66 | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | | REF_CLOSE: (5), (35), (44), (61), (64), (65), (76), (82),
% 155.22/26.66 | | | | | | | | | | | (95), (96), (117), (240) are inconsistent by
% 155.22/26.66 | | | | | | | | | | | sub-proof #1032.
% 155.22/26.66 | | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | |
% 155.22/26.66 | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | |
% 155.22/26.66 | | | | | | | | | (241) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2
% 155.22/26.66 | | | | | | | | | & op(e0, e0) = e2)
% 155.22/26.66 | | | | | | | | |
% 155.22/26.66 | | | | | | | | | BETA: splitting (241) gives:
% 155.22/26.66 | | | | | | | | |
% 155.22/26.66 | | | | | | | | | Case 1:
% 155.22/26.66 | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | (242) all_58_14 = e2 & op(e0, e1) = e2
% 155.22/26.66 | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | REF_CLOSE: (49), (55), (82), (242) are inconsistent by
% 155.22/26.66 | | | | | | | | | | sub-proof #1175.
% 155.22/26.66 | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | (243) all_58_15 = e2 & op(e0, e0) = e2
% 155.22/26.66 | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | | REF_CLOSE: (53), (82), (98), (243) are inconsistent by
% 155.22/26.66 | | | | | | | | | | sub-proof #1452.
% 155.22/26.66 | | | | | | | | | |
% 155.22/26.66 | | | | | | | | | End of split
% 155.22/26.66 | | | | | | | | |
% 155.22/26.66 | | | | | | | | End of split
% 155.22/26.66 | | | | | | | |
% 155.22/26.66 | | | | | | | Case 2:
% 155.22/26.66 | | | | | | | |
% 155.22/26.66 | | | | | | | | (244) all_58_9 = e0 & op(e3, e0) = e0
% 155.22/26.66 | | | | | | | |
% 155.22/26.66 | | | | | | | | ALPHA: (244) implies:
% 155.22/26.66 | | | | | | | | (245) op(e3, e0) = e0
% 155.22/26.66 | | | | | | | |
% 155.22/26.66 | | | | | | | | REF_CLOSE: (64), (82), (108), (245) are inconsistent by
% 155.22/26.66 | | | | | | | | sub-proof #140.
% 155.22/26.66 | | | | | | | |
% 155.22/26.66 | | | | | | | End of split
% 155.22/26.66 | | | | | | |
% 155.22/26.66 | | | | | | End of split
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | Case 2:
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | | (246) all_58_10 = e1 & op(e2, e0) = e1
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | | REF_CLOSE: (61), (103), (246) are inconsistent by sub-proof #1199.
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | End of split
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | Case 2:
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | (247) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 155.22/26.66 | | | | | e0) = e1)
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | REF_CLOSE: (25), (32), (35), (37), (44), (47), (51), (53), (62), (64),
% 155.22/26.66 | | | | | (82), (86), (247) are inconsistent by sub-proof #104.
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | End of split
% 155.22/26.66 | | | |
% 155.22/26.66 | | | End of split
% 155.22/26.66 | | |
% 155.22/26.66 | | Case 2:
% 155.22/26.66 | | |
% 155.22/26.66 | | | (248) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0)
% 155.22/26.66 | | | = e2)
% 155.22/26.66 | | |
% 155.22/26.66 | | | REF_CLOSE: (6), (53), (77), (82), (98), (248) are inconsistent by
% 155.22/26.66 | | | sub-proof #1185.
% 155.22/26.66 | | |
% 155.22/26.66 | | End of split
% 155.22/26.66 | |
% 155.22/26.66 | Case 2:
% 155.22/26.66 | |
% 155.22/26.66 | | (249) all_20_2 = e2
% 155.22/26.66 | |
% 155.22/26.66 | | COMBINE_EQS: (79), (249) imply:
% 155.22/26.66 | | (250) all_4_2 = e2
% 155.22/26.66 | |
% 155.22/26.66 | | SIMP: (250) implies:
% 155.22/26.66 | | (251) all_4_2 = e2
% 155.22/26.66 | |
% 155.22/26.66 | | REDUCE: (74), (251) imply:
% 155.22/26.66 | | (252) ~ (all_52_7 = e2)
% 155.22/26.66 | |
% 155.22/26.66 | | BETA: splitting (80) gives:
% 155.22/26.66 | |
% 155.22/26.66 | | Case 1:
% 155.22/26.66 | | |
% 155.22/26.66 | | | (253) all_54_13 = e3
% 155.22/26.66 | | |
% 155.22/26.66 | | | REF_CLOSE: (11), (12), (253) are inconsistent by sub-proof #1435.
% 155.22/26.66 | | |
% 155.22/26.66 | | Case 2:
% 155.22/26.66 | | |
% 155.22/26.66 | | | (254) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 155.22/26.66 | | |
% 155.22/26.66 | | | BETA: splitting (254) gives:
% 155.22/26.66 | | |
% 155.22/26.66 | | | Case 1:
% 155.22/26.66 | | | |
% 155.22/26.66 | | | | (255) all_54_13 = e2
% 155.22/26.66 | | | |
% 155.22/26.66 | | | | REF_CLOSE: (11), (252), (255) are inconsistent by sub-proof #1370.
% 155.22/26.66 | | | |
% 155.22/26.66 | | | Case 2:
% 155.22/26.66 | | | |
% 155.22/26.66 | | | | (256) all_54_13 = e1 | all_54_13 = e0
% 155.22/26.66 | | | |
% 155.22/26.66 | | | | BETA: splitting (256) gives:
% 155.22/26.66 | | | |
% 155.22/26.66 | | | | Case 1:
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | (257) all_54_13 = e1
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | REF_CLOSE: (11), (75), (257) are inconsistent by sub-proof #876.
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | Case 2:
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | (258) all_54_13 = e0
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | COMBINE_EQS: (11), (258) imply:
% 155.22/26.66 | | | | | (259) all_52_7 = e0
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | SIMP: (259) implies:
% 155.22/26.66 | | | | | (260) all_52_7 = e0
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | REDUCE: (94), (260) imply:
% 155.22/26.66 | | | | | (261) ~ (all_52_3 = e0)
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | REDUCE: (16), (260) imply:
% 155.22/26.66 | | | | | (262) ~ (all_52_11 = e0)
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | SIMP: (262) implies:
% 155.22/26.66 | | | | | (263) ~ (all_52_11 = e0)
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | REDUCE: (66), (260) imply:
% 155.22/26.66 | | | | | (264) ~ (all_8_2 = e0)
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | SIMP: (264) implies:
% 155.22/26.66 | | | | | (265) ~ (all_8_2 = e0)
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | BETA: splitting (41) gives:
% 155.22/26.66 | | | | |
% 155.22/26.66 | | | | | Case 1:
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | | (266) all_54_5 = e3
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | | REF_CLOSE: (36), (83), (266) are inconsistent by sub-proof #1161.
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | Case 2:
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | | (267) ~ (all_54_5 = e3)
% 155.22/26.66 | | | | | | (268) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | | BETA: splitting (268) gives:
% 155.22/26.66 | | | | | |
% 155.22/26.66 | | | | | | Case 1:
% 155.22/26.66 | | | | | | |
% 155.22/26.66 | | | | | | | (269) all_54_5 = e2
% 155.22/26.66 | | | | | | |
% 155.22/26.66 | | | | | | | COMBINE_EQS: (83), (269) imply:
% 155.22/26.66 | | | | | | | (270) all_8_2 = e2
% 155.22/26.66 | | | | | | |
% 155.22/26.67 | | | | | | | SIMP: (270) implies:
% 155.22/26.67 | | | | | | | (271) all_8_2 = e2
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | COMBINE_EQS: (26), (271) imply:
% 155.22/26.67 | | | | | | | (272) all_56_13 = e2
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | REDUCE: (89), (271) imply:
% 155.22/26.67 | | | | | | | (273) ~ (all_52_13 = e2)
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | REDUCE: (36), (271) imply:
% 155.22/26.67 | | | | | | | (274) ~ (e3 = e2)
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | BETA: splitting (46) gives:
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | Case 1:
% 155.22/26.67 | | | | | | | |
% 155.22/26.67 | | | | | | | | (275) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) &
% 155.22/26.67 | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 &
% 155.22/26.67 | | | | | | | | all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2
% 155.22/26.67 | | | | | | | | & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 &
% 155.22/26.67 | | | | | | | | ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 155.22/26.67 | | | | | | | | e3) | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12
% 155.22/26.67 | | | | | | | | = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 155.22/26.67 | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) &
% 155.22/26.67 | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 &
% 155.22/26.67 | | | | | | | | all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0
% 155.22/26.67 | | | | | | | | & op(e0, e3) = e0)
% 155.22/26.67 | | | | | | | |
% 155.22/26.67 | | | | | | | | BETA: splitting (275) gives:
% 155.22/26.67 | | | | | | | |
% 155.22/26.67 | | | | | | | | Case 1:
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | (276) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2)
% 155.22/26.67 | | | | | | | | | & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0 =
% 155.22/26.67 | | | | | | | | | e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3,
% 155.22/26.67 | | | | | | | | | e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 &
% 155.22/26.67 | | | | | | | | | all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) =
% 155.22/26.67 | | | | | | | | | e3 & op(e1, e3) = e3)
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | BETA: splitting (276) gives:
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | Case 1:
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | (277) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2)
% 155.22/26.67 | | | | | | | | | | & op(e3, e2) = e3 & op(e2, e3) = e3
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | ALPHA: (277) implies:
% 155.22/26.67 | | | | | | | | | | (278) ~ (all_56_13 = e2)
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | REDUCE: (272), (278) imply:
% 155.22/26.67 | | | | | | | | | | (279) $false
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | CLOSE: (279) is inconsistent.
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | Case 2:
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | (280) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.67 | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.22/26.67 | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.22/26.67 | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | REF_CLOSE: (23), (67), (73), (82), (86), (95), (280) are
% 155.22/26.67 | | | | | | | | | | inconsistent by sub-proof #146.
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | End of split
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | Case 2:
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | (281) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3)
% 155.22/26.67 | | | | | | | | | & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_2 =
% 155.22/26.67 | | | | | | | | | e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3,
% 155.22/26.67 | | | | | | | | | e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 &
% 155.22/26.67 | | | | | | | | | all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 155.22/26.67 | | | | | | | | | e0 & op(e0, e3) = e0)
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | REF_CLOSE: (1), (2), (4), (39), (58), (82), (261), (281) are
% 155.22/26.67 | | | | | | | | | inconsistent by sub-proof #88.
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | End of split
% 155.22/26.67 | | | | | | | |
% 155.22/26.67 | | | | | | | Case 2:
% 155.22/26.67 | | | | | | | |
% 155.22/26.67 | | | | | | | | (282) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) &
% 155.22/26.67 | | | | | | | | op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 &
% 155.22/26.67 | | | | | | | | all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1
% 155.22/26.67 | | | | | | | | & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2
% 155.22/26.67 | | | | | | | | & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 155.22/26.67 | | | | | | | | = e2) | (all_56_5 = e0 & all_56_10 = e0 & ~
% 155.22/26.67 | | | | | | | | (all_56_13 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 155.22/26.67 | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0)
% 155.22/26.67 | | | | | | | | & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 155.22/26.67 | | | | | | | | & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) =
% 155.22/26.67 | | | | | | | | e0 & op(e0, e1) = e0)
% 155.22/26.67 | | | | | | | |
% 155.22/26.67 | | | | | | | | BETA: splitting (282) gives:
% 155.22/26.67 | | | | | | | |
% 155.22/26.67 | | | | | | | | Case 1:
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | (283) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1)
% 155.22/26.67 | | | | | | | | | & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 =
% 155.22/26.67 | | | | | | | | | e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2,
% 155.22/26.67 | | | | | | | | | e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 155.22/26.67 | | | | | | | | | all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) =
% 155.22/26.67 | | | | | | | | | e2 & op(e0, e2) = e2)
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | REF_CLOSE: (40), (43), (45), (65), (82), (83), (265), (268),
% 155.22/26.67 | | | | | | | | | (272), (273), (283) are inconsistent by sub-proof
% 155.22/26.67 | | | | | | | | | #109.
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | Case 2:
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | (284) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2)
% 155.22/26.67 | | | | | | | | | & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_8 =
% 155.22/26.67 | | | | | | | | | e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1,
% 155.22/26.67 | | | | | | | | | e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 &
% 155.22/26.67 | | | | | | | | | all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) =
% 155.22/26.67 | | | | | | | | | e0 & op(e0, e1) = e0)
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | BETA: splitting (284) gives:
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | | Case 1:
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | (285) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.22/26.67 | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | ALPHA: (285) implies:
% 155.22/26.67 | | | | | | | | | | (286) ~ (all_56_13 = e2)
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | REDUCE: (272), (286) imply:
% 155.22/26.67 | | | | | | | | | | (287) $false
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | CLOSE: (287) is inconsistent.
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | Case 2:
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | (288) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.67 | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.22/26.67 | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.67 | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | BETA: splitting (288) gives:
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | Case 1:
% 155.22/26.67 | | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | | (289) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.67 | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 155.22/26.67 | | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | | ALPHA: (289) implies:
% 155.22/26.67 | | | | | | | | | | | (290) op(e1, e0) = e1
% 155.22/26.67 | | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | | REF_CLOSE: (69), (77), (82), (290) are inconsistent by
% 155.22/26.67 | | | | | | | | | | | sub-proof #108.
% 155.22/26.67 | | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | Case 2:
% 155.22/26.67 | | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | | (291) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.67 | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 155.22/26.67 | | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | | ALPHA: (291) implies:
% 155.22/26.67 | | | | | | | | | | | (292) op(e0, e1) = e0
% 155.22/26.67 | | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | | REF_CLOSE: (55), (82), (263), (292) are inconsistent by
% 155.22/26.67 | | | | | | | | | | | sub-proof #87.
% 155.22/26.67 | | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | | End of split
% 155.22/26.67 | | | | | | | | | |
% 155.22/26.67 | | | | | | | | | End of split
% 155.22/26.67 | | | | | | | | |
% 155.22/26.67 | | | | | | | | End of split
% 155.22/26.67 | | | | | | | |
% 155.22/26.67 | | | | | | | End of split
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | Case 2:
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | (293) all_54_5 = e1 | all_54_5 = e0
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | REF_CLOSE: (65), (83), (265), (293) are inconsistent by sub-proof
% 155.22/26.67 | | | | | | | #1239.
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | End of split
% 155.22/26.67 | | | | | |
% 155.22/26.67 | | | | | End of split
% 155.22/26.67 | | | | |
% 155.22/26.67 | | | | End of split
% 155.22/26.67 | | | |
% 155.22/26.67 | | | End of split
% 155.22/26.67 | | |
% 155.22/26.67 | | End of split
% 155.22/26.67 | |
% 155.22/26.67 | End of split
% 155.22/26.67 |
% 155.22/26.67 End of proof
% 155.22/26.67
% 155.22/26.67 Sub-proof #87 shows that the following formulas are inconsistent:
% 155.22/26.67 ----------------------------------------------------------------
% 155.22/26.67 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.67 (2) op(e0, e1) = all_52_11
% 155.22/26.67 (3) op(e0, e1) = e0
% 155.22/26.67 (4) ~ (all_52_11 = e0)
% 155.22/26.67
% 155.22/26.67 Begin of proof
% 155.22/26.67 |
% 155.22/26.67 | GROUND_INST: instantiating (1) with all_52_11, e0, e1, e0, simplifying with
% 155.22/26.67 | (2), (3) gives:
% 155.22/26.67 | (5) all_52_11 = e0
% 155.22/26.67 |
% 155.22/26.67 | REDUCE: (4), (5) imply:
% 155.22/26.67 | (6) $false
% 155.22/26.67 |
% 155.22/26.67 | CLOSE: (6) is inconsistent.
% 155.22/26.67 |
% 155.22/26.67 End of proof
% 155.22/26.67
% 155.22/26.67 Sub-proof #88 shows that the following formulas are inconsistent:
% 155.22/26.67 ----------------------------------------------------------------
% 155.22/26.67 (1) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 155.22/26.67 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0)
% 155.22/26.67 & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 &
% 155.22/26.67 ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.22/26.67 (2) ~ (all_52_12 = e3)
% 155.22/26.67 (3) op(e0, e3) = all_52_3
% 155.22/26.67 (4) op(e3, e0) = all_52_12
% 155.22/26.67 (5) ~ (all_52_3 = e0)
% 155.22/26.67 (6) op(e1, e3) = all_52_2
% 155.22/26.67 (7) ~ (all_52_2 = e1)
% 155.22/26.67 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.67
% 155.22/26.67 Begin of proof
% 155.22/26.67 |
% 155.22/26.67 | BETA: splitting (1) gives:
% 155.22/26.67 |
% 155.22/26.67 | Case 1:
% 155.22/26.67 | |
% 155.22/26.67 | | (9) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1
% 155.22/26.67 | | & op(e1, e3) = e1
% 155.22/26.67 | |
% 155.22/26.67 | | ALPHA: (9) implies:
% 155.22/26.67 | | (10) op(e1, e3) = e1
% 155.22/26.67 | |
% 155.22/26.67 | | REF_CLOSE: (6), (7), (8), (10) are inconsistent by sub-proof #1412.
% 155.22/26.67 | |
% 155.22/26.67 | Case 2:
% 155.22/26.67 | |
% 155.22/26.67 | | (11) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 155.22/26.67 | | e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 155.22/26.67 | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.22/26.67 | |
% 155.22/26.67 | | BETA: splitting (11) gives:
% 155.22/26.67 | |
% 155.22/26.67 | | Case 1:
% 155.22/26.67 | | |
% 155.22/26.67 | | | (12) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 155.22/26.67 | | | e3 & op(e0, e3) = e3
% 155.22/26.67 | | |
% 155.22/26.67 | | | ALPHA: (12) implies:
% 155.22/26.67 | | | (13) op(e3, e0) = e3
% 155.22/26.67 | | |
% 155.22/26.67 | | | REF_CLOSE: (2), (4), (8), (13) are inconsistent by sub-proof #210.
% 155.22/26.67 | | |
% 155.22/26.67 | | Case 2:
% 155.22/26.67 | | |
% 155.22/26.67 | | | (14) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 155.22/26.67 | | | e0 & op(e0, e3) = e0
% 155.22/26.67 | | |
% 155.22/26.67 | | | ALPHA: (14) implies:
% 155.22/26.67 | | | (15) op(e0, e3) = e0
% 155.22/26.67 | | |
% 155.22/26.67 | | | REF_CLOSE: (3), (5), (8), (15) are inconsistent by sub-proof #89.
% 155.22/26.67 | | |
% 155.22/26.67 | | End of split
% 155.22/26.67 | |
% 155.22/26.67 | End of split
% 155.22/26.67 |
% 155.22/26.67 End of proof
% 155.22/26.67
% 155.22/26.67 Sub-proof #89 shows that the following formulas are inconsistent:
% 155.22/26.67 ----------------------------------------------------------------
% 155.22/26.67 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.67 (2) op(e0, e3) = all_52_3
% 155.22/26.67 (3) op(e0, e3) = e0
% 155.22/26.67 (4) ~ (all_52_3 = e0)
% 155.22/26.67
% 155.22/26.67 Begin of proof
% 155.22/26.67 |
% 155.22/26.67 | GROUND_INST: instantiating (1) with all_52_3, e0, e3, e0, simplifying with
% 155.22/26.67 | (2), (3) gives:
% 155.22/26.67 | (5) all_52_3 = e0
% 155.22/26.67 |
% 155.22/26.67 | REDUCE: (4), (5) imply:
% 155.22/26.67 | (6) $false
% 155.22/26.67 |
% 155.22/26.67 | CLOSE: (6) is inconsistent.
% 155.22/26.67 |
% 155.22/26.67 End of proof
% 155.22/26.67
% 155.22/26.67 Sub-proof #90 shows that the following formulas are inconsistent:
% 155.22/26.67 ----------------------------------------------------------------
% 155.22/26.67 (1) op(e3, e0) = e1
% 155.22/26.67 (2) all_58_0 = e2
% 155.22/26.67 (3) op(e3, e0) = all_52_12
% 155.22/26.67 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.67 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 155.22/26.67 (5) ~ (all_52_1 = all_16_0)
% 155.22/26.67 (6) ~ (all_52_14 = e2)
% 155.22/26.67 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 155.22/26.67 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.22/26.67 (8) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.67 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 155.22/26.67 (9) ~ (all_52_1 = e2)
% 155.22/26.67 (10) ~ (all_52_7 = e3)
% 155.22/26.67 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 155.22/26.67 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 155.22/26.67 e1)
% 155.22/26.67 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 155.22/26.67 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 155.22/26.67 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 155.22/26.67 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 155.22/26.67 (14) ~ (all_52_14 = e0)
% 155.22/26.67 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 155.22/26.67 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 155.22/26.67 (16) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 155.22/26.67 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 155.22/26.67 (17) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 155.22/26.67 (18) op(e3, e2) = all_52_4
% 155.22/26.67 (19) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.22/26.67 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.22/26.67 (20) op(e2, e3) = all_52_1
% 155.22/26.67 (21) all_58_10 = e2
% 155.22/26.67 (22) ~ (e2 = e0)
% 155.22/26.67 (23) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 155.22/26.67 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.22/26.67 (24) ~ (all_16_0 = e1)
% 155.22/26.67 (25) op(e2, e0) = all_52_13
% 155.22/26.67 (26) all_56_15 = e0
% 155.22/26.67 (27) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 155.22/26.67 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.67 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 155.22/26.67 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.22/26.67 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 155.22/26.67 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.67 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 155.22/26.67 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 155.22/26.67 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.22/26.67 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.67 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 155.22/26.67 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 155.22/26.67 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 155.22/26.67 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 155.22/26.67 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 155.22/26.67 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 155.22/26.67 = e0)
% 155.22/26.67 (28) ~ (all_4_2 = e1)
% 155.22/26.67 (29) all_54_4 = all_52_1
% 155.22/26.67 (30) all_58_7 = e1
% 155.22/26.67 (31) ~ (all_16_0 = e2)
% 155.22/26.67 (32) op(e1, e2) = e1
% 155.22/26.67 (33) op(e0, e0) = all_4_2
% 155.22/26.67 (34) op(e3, e1) = e0
% 155.22/26.67 (35) op(e3, e2) = e3
% 155.22/26.67 (36) ~ (e2 = e1)
% 155.22/26.67 (37) ~ (all_16_0 = e0)
% 155.22/26.67 (38) all_58_8 = e2
% 155.22/26.67 (39) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.22/26.67 (40) ~ (e1 = e0)
% 155.22/26.67 (41) ~ (all_8_2 = e1)
% 155.22/26.67 (42) ~ (all_52_1 = e0)
% 155.22/26.67 (43) op(e0, e2) = e2
% 155.22/26.67 (44) all_58_9 = e1
% 155.22/26.67 (45) op(e3, e1) = all_52_8
% 155.22/26.67 (46) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 155.22/26.67 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 155.22/26.67 e3)
% 155.22/26.67 (47) ~ (all_52_14 = e1)
% 155.22/26.67 (48) ~ (all_52_12 = all_52_14)
% 155.22/26.67 (49) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 155.22/26.67 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 155.22/26.67 (50) ~ (all_52_8 = e3)
% 155.22/26.67 (51) op(e1, e0) = e3
% 155.22/26.67 (52) op(e0, e2) = all_52_7
% 155.22/26.67 (53) op(e1, e0) = all_52_14
% 155.22/26.67 (54) op(e2, e2) = all_8_2
% 155.22/26.67 (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.67 (56) all_54_11 = all_52_14
% 155.22/26.67 (57) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 155.22/26.67 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 155.22/26.67 (58) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 155.22/26.67 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 155.22/26.67 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 155.22/26.67 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 155.22/26.67 (59) all_58_11 = e3
% 155.22/26.67 (60) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 155.22/26.67 (61) all_54_12 = all_16_0
% 155.22/26.67
% 155.22/26.67 Begin of proof
% 155.22/26.67 |
% 155.22/26.67 | BETA: splitting (60) gives:
% 155.22/26.67 |
% 155.22/26.67 | Case 1:
% 155.22/26.67 | |
% 155.22/26.67 | | (62) all_54_12 = e3
% 155.22/26.67 | |
% 155.22/26.67 | | COMBINE_EQS: (61), (62) imply:
% 155.22/26.67 | | (63) all_16_0 = e3
% 155.22/26.67 | |
% 155.22/26.67 | | SIMP: (63) implies:
% 155.22/26.67 | | (64) all_16_0 = e3
% 155.22/26.67 | |
% 155.22/26.67 | | REDUCE: (5), (64) imply:
% 155.22/26.67 | | (65) ~ (all_52_1 = e3)
% 155.22/26.67 | |
% 155.22/26.67 | | REDUCE: (31), (64) imply:
% 155.22/26.67 | | (66) ~ (e3 = e2)
% 155.22/26.67 | |
% 155.22/26.67 | | REDUCE: (24), (64) imply:
% 155.22/26.67 | | (67) ~ (e3 = e1)
% 155.22/26.67 | |
% 155.22/26.67 | | REDUCE: (37), (64) imply:
% 155.22/26.67 | | (68) ~ (e3 = e0)
% 155.22/26.67 | |
% 155.22/26.67 | | BETA: splitting (17) gives:
% 155.22/26.67 | |
% 155.22/26.67 | | Case 1:
% 155.22/26.67 | | |
% 155.22/26.67 | | | (69) all_54_4 = e3
% 155.22/26.67 | | |
% 155.22/26.67 | | | COMBINE_EQS: (29), (69) imply:
% 155.22/26.67 | | | (70) all_52_1 = e3
% 155.22/26.67 | | |
% 155.22/26.67 | | | REDUCE: (65), (70) imply:
% 155.22/26.67 | | | (71) $false
% 155.22/26.67 | | |
% 155.22/26.67 | | | CLOSE: (71) is inconsistent.
% 155.22/26.67 | | |
% 155.22/26.67 | | Case 2:
% 155.22/26.67 | | |
% 155.22/26.67 | | | (72) ~ (all_54_4 = e3)
% 155.22/26.67 | | | (73) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 155.22/26.67 | | |
% 155.22/26.67 | | | BETA: splitting (46) gives:
% 155.22/26.67 | | |
% 155.22/26.67 | | | Case 1:
% 155.22/26.67 | | | |
% 155.22/26.67 | | | | (74) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 155.22/26.67 | | | | e2) = e3)
% 155.22/26.67 | | | |
% 155.22/26.67 | | | | BETA: splitting (74) gives:
% 155.22/26.67 | | | |
% 155.22/26.67 | | | | Case 1:
% 155.22/26.67 | | | | |
% 155.22/26.67 | | | | | (75) all_58_12 = e3 & op(e0, e3) = e3
% 155.22/26.67 | | | | |
% 155.22/26.67 | | | | | ALPHA: (75) implies:
% 155.22/26.67 | | | | | (76) all_58_12 = e3
% 155.22/26.67 | | | | |
% 155.22/26.67 | | | | | BETA: splitting (13) gives:
% 155.22/26.67 | | | | |
% 155.22/26.67 | | | | | Case 1:
% 155.22/26.67 | | | | | |
% 155.22/26.67 | | | | | | (77) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 155.22/26.67 | | | | | | e1) = e3)
% 155.22/26.67 | | | | | |
% 155.22/26.67 | | | | | | BETA: splitting (77) gives:
% 155.22/26.67 | | | | | |
% 155.22/26.67 | | | | | | Case 1:
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | (78) all_58_4 = e3 & op(e3, e1) = e3
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | | REF_CLOSE: (2), (22), (35), (36), (40), (49), (55), (57), (67),
% 155.22/26.67 | | | | | | | (68), (78) are inconsistent by sub-proof #1093.
% 155.22/26.67 | | | | | | |
% 155.22/26.67 | | | | | | Case 2:
% 155.22/26.67 | | | | | | |
% 155.22/26.68 | | | | | | | (79) all_58_5 = e3 & op(e2, e1) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | ALPHA: (79) implies:
% 155.22/26.68 | | | | | | | (80) op(e2, e1) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | BETA: splitting (8) gives:
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | |
% 155.22/26.68 | | | | | | | | (81) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 155.22/26.68 | | | | | | | | op(e2, e2) = e1)
% 155.22/26.68 | | | | | | | |
% 155.22/26.68 | | | | | | | | BETA: splitting (81) gives:
% 155.22/26.68 | | | | | | | |
% 155.22/26.68 | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | (82) all_58_2 = e1 & op(e2, e3) = e1
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | ALPHA: (82) implies:
% 155.22/26.68 | | | | | | | | | (83) op(e2, e3) = e1
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | BETA: splitting (11) gives:
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | (84) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1
% 155.22/26.68 | | | | | | | | | | & op(e0, e2) = e1)
% 155.22/26.68 | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | REF_CLOSE: (36), (43), (52), (55), (67), (76), (84) are
% 155.22/26.68 | | | | | | | | | | inconsistent by sub-proof #336.
% 155.22/26.68 | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | (85) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1
% 155.22/26.68 | | | | | | | | | | & op(e0, e0) = e1)
% 155.22/26.68 | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | BETA: splitting (85) gives:
% 155.22/26.68 | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | (86) all_58_14 = e1 & op(e0, e1) = e1
% 155.22/26.68 | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | ALPHA: (86) implies:
% 155.22/26.68 | | | | | | | | | | | (87) op(e0, e1) = e1
% 155.22/26.68 | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | BETA: splitting (27) gives:
% 155.22/26.68 | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | (88) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.22/26.68 | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.22/26.68 | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | BETA: splitting (88) gives:
% 155.22/26.68 | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | (89) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.22/26.68 | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 155.22/26.68 | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.22/26.68 | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | BETA: splitting (89) gives:
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | (90) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.22/26.68 | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | ALPHA: (90) implies:
% 155.22/26.68 | | | | | | | | | | | | | | (91) op(e2, e3) = e3
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | REF_CLOSE: (55), (67), (83), (91) are inconsistent by
% 155.22/26.68 | | | | | | | | | | | | | | sub-proof #1494.
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | (92) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.22/26.68 | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | REF_CLOSE: (18), (35), (45), (50), (55), (66), (92) are
% 155.22/26.68 | | | | | | | | | | | | | | inconsistent by sub-proof #146.
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | (93) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 155.22/26.68 | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.22/26.68 | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | BETA: splitting (93) gives:
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | (94) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | ALPHA: (94) implies:
% 155.22/26.68 | | | | | | | | | | | | | | (95) op(e3, e1) = e1
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | REF_CLOSE: (34), (40), (55), (95) are inconsistent by
% 155.22/26.68 | | | | | | | | | | | | | | sub-proof #1281.
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | (96) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.22/26.68 | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | (97) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 155.22/26.68 | | | | | | | | | | | | | | | (98) op(e3, e0) = e3
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (14), (39), (47), (48), (55), (56), (98)
% 155.22/26.68 | | | | | | | | | | | | | | | are inconsistent by sub-proof #121.
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | (99) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.22/26.68 | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 155.22/26.68 | | | | | | | | | | | | | | | (100) op(e3, e0) = e0
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | REF_CLOSE: (1), (40), (55), (100) are inconsistent by
% 155.22/26.68 | | | | | | | | | | | | | | | sub-proof #140.
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | (101) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.68 | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.22/26.68 | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.22/26.68 | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.22/26.68 | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | BETA: splitting (101) gives:
% 155.22/26.68 | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | (102) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 155.22/26.68 | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.68 | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 155.22/26.68 | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | REF_CLOSE: (26), (32), (36), (55), (67), (80), (102) are
% 155.22/26.68 | | | | | | | | | | | | | inconsistent by sub-proof #100.
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | (103) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.22/26.68 | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 155.22/26.68 | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.22/26.68 | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | BETA: splitting (103) gives:
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | (104) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.22/26.68 | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | ALPHA: (104) implies:
% 155.22/26.68 | | | | | | | | | | | | | | (105) op(e0, e2) = e0
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | REF_CLOSE: (22), (43), (52), (55), (105) are inconsistent by
% 155.22/26.68 | | | | | | | | | | | | | | sub-proof #1040.
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | (106) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.22/26.68 | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | (107) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.22/26.68 | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 155.22/26.68 | | | | | | | | | | | | | | | (108) op(e1, e0) = e1
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (39), (47), (53), (55), (56), (108) are
% 155.22/26.68 | | | | | | | | | | | | | | | inconsistent by sub-proof #1171.
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | (109) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.22/26.68 | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 155.22/26.68 | | | | | | | | | | | | | | | (110) op(e0, e1) = e0
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (87), (110) are inconsistent by
% 155.22/26.68 | | | | | | | | | | | | | | | sub-proof #129.
% 155.22/26.68 | | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | (111) all_58_15 = e1 & op(e0, e0) = e1
% 155.22/26.68 | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | | REF_CLOSE: (28), (33), (55), (111) are inconsistent by
% 155.22/26.68 | | | | | | | | | | | sub-proof #1418.
% 155.22/26.68 | | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | | |
% 155.22/26.68 | | | | | | | | | End of split
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | (112) all_58_3 = e1 & op(e2, e2) = e1
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | REF_CLOSE: (41), (54), (55), (112) are inconsistent by
% 155.22/26.68 | | | | | | | | | sub-proof #1423.
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | End of split
% 155.22/26.68 | | | | | | | |
% 155.22/26.68 | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | |
% 155.22/26.68 | | | | | | | | (113) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 155.22/26.68 | | | | | | | | op(e2, e0) = e1)
% 155.22/26.68 | | | | | | | |
% 155.22/26.68 | | | | | | | | BETA: splitting (113) gives:
% 155.22/26.68 | | | | | | | |
% 155.22/26.68 | | | | | | | | Case 1:
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | (114) all_58_5 = e1 & op(e2, e1) = e1
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | ALPHA: (114) implies:
% 155.22/26.68 | | | | | | | | | (115) op(e2, e1) = e1
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | REF_CLOSE: (55), (67), (80), (115) are inconsistent by
% 155.22/26.68 | | | | | | | | | sub-proof #352.
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | Case 2:
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | (116) all_58_10 = e1 & op(e2, e0) = e1
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | | REF_CLOSE: (21), (36), (116) are inconsistent by sub-proof
% 155.22/26.68 | | | | | | | | | #1199.
% 155.22/26.68 | | | | | | | | |
% 155.22/26.68 | | | | | | | | End of split
% 155.22/26.68 | | | | | | | |
% 155.22/26.68 | | | | | | | End of split
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | End of split
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | Case 2:
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | (117) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 155.22/26.68 | | | | | | op(e0, e1) = e3)
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | BETA: splitting (117) gives:
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | Case 1:
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | (118) all_58_8 = e3 & op(e1, e1) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | ALPHA: (118) implies:
% 155.22/26.68 | | | | | | | (119) all_58_8 = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | COMBINE_EQS: (38), (119) imply:
% 155.22/26.68 | | | | | | | (120) e3 = e2
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | SIMP: (120) implies:
% 155.22/26.68 | | | | | | | (121) e3 = e2
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | COMBINE_EQS: (59), (121) imply:
% 155.22/26.68 | | | | | | | (122) all_58_11 = e2
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | REF_CLOSE: (2), (12), (21), (22), (35), (36), (40), (44), (49),
% 155.22/26.68 | | | | | | | (55), (57), (58), (66), (67), (68), (122) are
% 155.22/26.68 | | | | | | | inconsistent by sub-proof #1027.
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | Case 2:
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | (123) all_58_14 = e3 & op(e0, e1) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | ALPHA: (123) implies:
% 155.22/26.68 | | | | | | | (124) all_58_14 = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | REF_CLOSE: (11), (22), (36), (40), (43), (52), (55), (58), (67),
% 155.22/26.68 | | | | | | | (68), (76), (124) are inconsistent by sub-proof #778.
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | End of split
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | End of split
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | Case 2:
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | (125) all_58_13 = e3 & op(e0, e2) = e3
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | REF_CLOSE: (10), (52), (55), (125) are inconsistent by sub-proof
% 155.22/26.68 | | | | | #1449.
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | End of split
% 155.22/26.68 | | | |
% 155.22/26.68 | | | Case 2:
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | (126) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 155.22/26.68 | | | | e0) = e3)
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | BETA: splitting (126) gives:
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | Case 1:
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | (127) all_58_14 = e3 & op(e0, e1) = e3
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | ALPHA: (127) implies:
% 155.22/26.68 | | | | | (128) all_58_14 = e3
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | BETA: splitting (15) gives:
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | Case 1:
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | (129) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2,
% 155.22/26.68 | | | | | | e3) = e3)
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | BETA: splitting (129) gives:
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | Case 1:
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | (130) all_58_0 = e3 & op(e3, e3) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | ALPHA: (130) implies:
% 155.22/26.68 | | | | | | | (131) all_58_0 = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | COMBINE_EQS: (2), (131) imply:
% 155.22/26.68 | | | | | | | (132) e3 = e2
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | SIMP: (132) implies:
% 155.22/26.68 | | | | | | | (133) e3 = e2
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | COMBINE_EQS: (59), (133) imply:
% 155.22/26.68 | | | | | | | (134) all_58_11 = e2
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | REF_CLOSE: (2), (12), (21), (22), (35), (36), (40), (44), (49),
% 155.22/26.68 | | | | | | | (55), (57), (58), (66), (67), (68), (134) are
% 155.22/26.68 | | | | | | | inconsistent by sub-proof #1027.
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | Case 2:
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | (135) all_58_2 = e3 & op(e2, e3) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | ALPHA: (135) implies:
% 155.22/26.68 | | | | | | | (136) op(e2, e3) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | REF_CLOSE: (9), (20), (29), (42), (55), (65), (73), (136) are
% 155.22/26.68 | | | | | | | inconsistent by sub-proof #1235.
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | End of split
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | Case 2:
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | (137) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 155.22/26.68 | | | | | | op(e0, e3) = e3)
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | BETA: splitting (137) gives:
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | | Case 1:
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | (138) all_58_6 = e3 & op(e1, e3) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | REF_CLOSE: (4), (22), (23), (35), (36), (38), (40), (41), (43),
% 155.22/26.68 | | | | | | | (51), (52), (54), (55), (67), (68), (138) are
% 155.22/26.68 | | | | | | | inconsistent by sub-proof #92.
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | Case 2:
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | (139) all_58_12 = e3 & op(e0, e3) = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | ALPHA: (139) implies:
% 155.22/26.68 | | | | | | | (140) all_58_12 = e3
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | | REF_CLOSE: (11), (22), (36), (40), (43), (52), (55), (58), (67),
% 155.22/26.68 | | | | | | | (68), (128), (140) are inconsistent by sub-proof #778.
% 155.22/26.68 | | | | | | |
% 155.22/26.68 | | | | | | End of split
% 155.22/26.68 | | | | | |
% 155.22/26.68 | | | | | End of split
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | Case 2:
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | (141) all_58_15 = e3 & op(e0, e0) = e3
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | ALPHA: (141) implies:
% 155.22/26.68 | | | | | (142) all_58_15 = e3
% 155.22/26.68 | | | | | (143) op(e0, e0) = e3
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | | REF_CLOSE: (4), (6), (7), (14), (16), (19), (22), (23), (25), (28),
% 155.22/26.68 | | | | | (30), (33), (35), (36), (38), (39), (40), (41), (43), (47),
% 155.22/26.68 | | | | | (52), (53), (54), (55), (56), (58), (142), (143) are
% 155.22/26.68 | | | | | inconsistent by sub-proof #91.
% 155.22/26.68 | | | | |
% 155.22/26.68 | | | | End of split
% 155.22/26.68 | | | |
% 155.22/26.68 | | | End of split
% 155.22/26.68 | | |
% 155.22/26.68 | | End of split
% 155.22/26.68 | |
% 155.22/26.68 | Case 2:
% 155.22/26.68 | |
% 155.22/26.68 | | (144) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 155.22/26.68 | |
% 155.22/26.68 | | BETA: splitting (144) gives:
% 155.22/26.68 | |
% 155.22/26.68 | | Case 1:
% 155.22/26.68 | | |
% 155.22/26.68 | | | (145) all_54_12 = e2
% 155.22/26.68 | | |
% 155.22/26.68 | | | COMBINE_EQS: (61), (145) imply:
% 155.22/26.68 | | | (146) all_16_0 = e2
% 155.22/26.68 | | |
% 155.22/26.68 | | | SIMP: (146) implies:
% 155.22/26.68 | | | (147) all_16_0 = e2
% 155.22/26.68 | | |
% 155.22/26.68 | | | REDUCE: (31), (147) imply:
% 155.22/26.68 | | | (148) $false
% 155.22/26.68 | | |
% 155.22/26.68 | | | CLOSE: (148) is inconsistent.
% 155.22/26.68 | | |
% 155.22/26.68 | | Case 2:
% 155.22/26.68 | | |
% 155.22/26.68 | | | (149) all_54_12 = e1 | all_54_12 = e0
% 155.22/26.68 | | |
% 155.22/26.68 | | | BETA: splitting (149) gives:
% 155.22/26.68 | | |
% 155.22/26.68 | | | Case 1:
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | (150) all_54_12 = e1
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | COMBINE_EQS: (61), (150) imply:
% 155.22/26.68 | | | | (151) all_16_0 = e1
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | SIMP: (151) implies:
% 155.22/26.68 | | | | (152) all_16_0 = e1
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | REDUCE: (24), (152) imply:
% 155.22/26.68 | | | | (153) $false
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | CLOSE: (153) is inconsistent.
% 155.22/26.68 | | | |
% 155.22/26.68 | | | Case 2:
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | (154) all_54_12 = e0
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | COMBINE_EQS: (61), (154) imply:
% 155.22/26.68 | | | | (155) all_16_0 = e0
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | SIMP: (155) implies:
% 155.22/26.68 | | | | (156) all_16_0 = e0
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | REDUCE: (37), (156) imply:
% 155.22/26.68 | | | | (157) $false
% 155.22/26.68 | | | |
% 155.22/26.68 | | | | CLOSE: (157) is inconsistent.
% 155.22/26.68 | | | |
% 155.22/26.68 | | | End of split
% 155.22/26.68 | | |
% 155.22/26.68 | | End of split
% 155.22/26.68 | |
% 155.22/26.68 | End of split
% 155.22/26.68 |
% 155.22/26.68 End of proof
% 155.22/26.68
% 155.22/26.68 Sub-proof #91 shows that the following formulas are inconsistent:
% 155.22/26.68 ----------------------------------------------------------------
% 155.22/26.68 (1) all_58_15 = e3
% 155.22/26.68 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.68 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 155.22/26.68 (3) ~ (all_52_14 = e2)
% 155.22/26.68 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 155.22/26.68 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.22/26.68 (5) ~ (all_52_14 = e0)
% 155.22/26.68 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 155.22/26.68 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 155.22/26.68 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.22/26.68 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.22/26.68 (8) ~ (e2 = e0)
% 155.22/26.68 (9) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 155.22/26.68 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.22/26.68 (10) op(e2, e0) = all_52_13
% 155.22/26.68 (11) ~ (all_4_2 = e1)
% 155.22/26.68 (12) all_58_7 = e1
% 155.22/26.68 (13) op(e0, e0) = all_4_2
% 155.22/26.68 (14) op(e3, e2) = e3
% 155.22/26.68 (15) ~ (e2 = e1)
% 155.22/26.68 (16) all_58_8 = e2
% 155.22/26.68 (17) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.22/26.68 (18) ~ (e1 = e0)
% 155.22/26.68 (19) ~ (all_8_2 = e1)
% 155.22/26.68 (20) op(e0, e2) = e2
% 155.22/26.68 (21) ~ (all_52_14 = e1)
% 155.22/26.68 (22) op(e0, e2) = all_52_7
% 155.22/26.68 (23) op(e1, e0) = all_52_14
% 155.22/26.68 (24) op(e2, e2) = all_8_2
% 155.22/26.68 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.68 (26) all_54_11 = all_52_14
% 155.22/26.68 (27) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 155.22/26.68 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 155.22/26.68 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 155.22/26.68 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 155.22/26.68 (28) op(e0, e0) = e3
% 155.22/26.68
% 155.22/26.68 Begin of proof
% 155.22/26.68 |
% 155.22/26.68 | BETA: splitting (17) gives:
% 155.22/26.68 |
% 155.22/26.68 | Case 1:
% 155.22/26.68 | |
% 155.22/26.68 | | (29) all_54_11 = e3
% 155.22/26.68 | |
% 155.22/26.68 | | COMBINE_EQS: (26), (29) imply:
% 155.22/26.68 | | (30) all_52_14 = e3
% 155.22/26.68 | |
% 155.22/26.68 | | SIMP: (30) implies:
% 155.22/26.68 | | (31) all_52_14 = e3
% 155.22/26.68 | |
% 155.22/26.68 | | REDUCE: (3), (31) imply:
% 155.22/26.68 | | (32) ~ (e3 = e2)
% 155.22/26.68 | |
% 155.22/26.68 | | REDUCE: (21), (31) imply:
% 155.22/26.68 | | (33) ~ (e3 = e1)
% 155.22/26.68 | |
% 155.22/26.68 | | REDUCE: (5), (31) imply:
% 155.22/26.68 | | (34) ~ (e3 = e0)
% 155.22/26.68 | |
% 155.22/26.68 | | REDUCE: (23), (31) imply:
% 155.22/26.68 | | (35) op(e1, e0) = e3
% 155.22/26.68 | |
% 155.22/26.68 | | BETA: splitting (27) gives:
% 155.22/26.68 | |
% 155.22/26.68 | | Case 1:
% 155.22/26.68 | | |
% 155.22/26.68 | | | (36) all_58_15 = e0 & op(e0, e0) = e0
% 155.22/26.68 | | |
% 155.22/26.68 | | | REF_CLOSE: (1), (34), (36) are inconsistent by sub-proof #1013.
% 155.22/26.68 | | |
% 155.22/26.68 | | Case 2:
% 155.22/26.68 | | |
% 155.22/26.68 | | | (37) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 155.22/26.68 | | | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0
% 155.22/26.68 | | | & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 155.22/26.68 | | | (all_58_14 = e0 & op(e0, e1) = e0))
% 155.22/26.68 | | |
% 155.22/26.68 | | | ALPHA: (37) implies:
% 155.22/26.69 | | | (38) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 155.22/26.69 | | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.22/26.69 | | |
% 155.22/26.69 | | | BETA: splitting (7) gives:
% 155.22/26.69 | | |
% 155.22/26.69 | | | Case 1:
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | (39) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 155.22/26.69 | | | | = e3)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | BETA: splitting (39) gives:
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | Case 1:
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | (40) all_58_6 = e3 & op(e1, e3) = e3
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | REF_CLOSE: (2), (8), (9), (14), (15), (16), (18), (19), (20), (22),
% 155.22/26.69 | | | | | (24), (25), (33), (34), (35), (40) are inconsistent by
% 155.22/26.69 | | | | | sub-proof #92.
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | Case 2:
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | (41) all_58_7 = e3 & op(e1, e2) = e3
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | ALPHA: (41) implies:
% 155.22/26.69 | | | | | (42) all_58_7 = e3
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | REF_CLOSE: (12), (33), (42) are inconsistent by sub-proof #1330.
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | End of split
% 155.22/26.69 | | | |
% 155.22/26.69 | | | Case 2:
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | (43) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 155.22/26.69 | | | | = e3)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | BETA: splitting (43) gives:
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | Case 1:
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | (44) all_58_8 = e3 & op(e1, e1) = e3
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | REF_CLOSE: (16), (32), (44) are inconsistent by sub-proof #1069.
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | Case 2:
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | (45) all_58_11 = e3 & op(e1, e0) = e3
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | ALPHA: (45) implies:
% 155.22/26.69 | | | | | (46) all_58_11 = e3
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | REF_CLOSE: (4), (6), (8), (10), (11), (13), (15), (18), (25), (28),
% 155.22/26.69 | | | | | (32), (33), (34), (35), (38), (46) are inconsistent by
% 155.22/26.69 | | | | | sub-proof #263.
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | End of split
% 155.22/26.69 | | | |
% 155.22/26.69 | | | End of split
% 155.22/26.69 | | |
% 155.22/26.69 | | End of split
% 155.22/26.69 | |
% 155.22/26.69 | Case 2:
% 155.22/26.69 | |
% 155.22/26.69 | | (47) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.22/26.69 | |
% 155.22/26.69 | | REF_CLOSE: (3), (5), (21), (26), (47) are inconsistent by sub-proof #1226.
% 155.22/26.69 | |
% 155.22/26.69 | End of split
% 155.22/26.69 |
% 155.22/26.69 End of proof
% 155.22/26.69
% 155.22/26.69 Sub-proof #92 shows that the following formulas are inconsistent:
% 155.22/26.69 ----------------------------------------------------------------
% 155.22/26.69 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.69 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 155.22/26.69 (2) all_58_6 = e3 & op(e1, e3) = e3
% 155.22/26.69 (3) ~ (e3 = e0)
% 155.22/26.69 (4) ~ (e2 = e0)
% 155.22/26.69 (5) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 155.22/26.69 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.22/26.69 (6) ~ (e3 = e1)
% 155.22/26.69 (7) op(e3, e2) = e3
% 155.22/26.69 (8) ~ (e2 = e1)
% 155.22/26.69 (9) all_58_8 = e2
% 155.22/26.69 (10) ~ (e1 = e0)
% 155.22/26.69 (11) ~ (all_8_2 = e1)
% 155.22/26.69 (12) op(e0, e2) = e2
% 155.22/26.69 (13) op(e1, e0) = e3
% 155.22/26.69 (14) op(e0, e2) = all_52_7
% 155.22/26.69 (15) op(e2, e2) = all_8_2
% 155.22/26.69 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.69
% 155.22/26.69 Begin of proof
% 155.22/26.69 |
% 155.22/26.69 | ALPHA: (2) implies:
% 155.22/26.69 | (17) all_58_6 = e3
% 155.22/26.69 |
% 155.22/26.69 | BETA: splitting (5) gives:
% 155.22/26.69 |
% 155.22/26.69 | Case 1:
% 155.22/26.69 | |
% 155.22/26.69 | | (18) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 155.22/26.69 | | e0)
% 155.22/26.69 | |
% 155.22/26.69 | | BETA: splitting (18) gives:
% 155.22/26.69 | |
% 155.22/26.69 | | Case 1:
% 155.22/26.69 | | |
% 155.22/26.69 | | | (19) all_58_6 = e0 & op(e1, e3) = e0
% 155.22/26.69 | | |
% 155.22/26.69 | | | REF_CLOSE: (3), (17), (19) are inconsistent by sub-proof #1350.
% 155.22/26.69 | | |
% 155.22/26.69 | | Case 2:
% 155.22/26.69 | | |
% 155.22/26.69 | | | (20) all_58_7 = e0 & op(e1, e2) = e0
% 155.22/26.69 | | |
% 155.22/26.69 | | | ALPHA: (20) implies:
% 155.22/26.69 | | | (21) all_58_7 = e0
% 155.22/26.69 | | |
% 155.22/26.69 | | | REF_CLOSE: (1), (6), (7), (8), (10), (11), (12), (14), (15), (16), (21)
% 155.22/26.69 | | | are inconsistent by sub-proof #1076.
% 155.22/26.69 | | |
% 155.22/26.69 | | End of split
% 155.22/26.69 | |
% 155.22/26.69 | Case 2:
% 155.22/26.69 | |
% 155.22/26.69 | | (22) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 155.22/26.69 | | e0)
% 155.22/26.69 | |
% 155.22/26.69 | | BETA: splitting (22) gives:
% 155.22/26.69 | |
% 155.22/26.69 | | Case 1:
% 155.22/26.69 | | |
% 155.22/26.69 | | | (23) all_58_8 = e0 & op(e1, e1) = e0
% 155.22/26.69 | | |
% 155.22/26.69 | | | REF_CLOSE: (4), (9), (23) are inconsistent by sub-proof #1342.
% 155.22/26.69 | | |
% 155.22/26.69 | | Case 2:
% 155.22/26.69 | | |
% 155.22/26.69 | | | (24) all_58_11 = e0 & op(e1, e0) = e0
% 155.22/26.69 | | |
% 155.22/26.69 | | | ALPHA: (24) implies:
% 155.22/26.69 | | | (25) op(e1, e0) = e0
% 155.22/26.69 | | |
% 155.22/26.69 | | | REF_CLOSE: (3), (13), (16), (25) are inconsistent by sub-proof #118.
% 155.22/26.69 | | |
% 155.22/26.69 | | End of split
% 155.22/26.69 | |
% 155.22/26.69 | End of split
% 155.22/26.69 |
% 155.22/26.69 End of proof
% 155.22/26.69
% 155.22/26.69 Sub-proof #93 shows that the following formulas are inconsistent:
% 155.22/26.69 ----------------------------------------------------------------
% 155.22/26.69 (1) all_56_14 = e2
% 155.22/26.69 (2) all_56_14 = e1
% 155.22/26.69 (3) ~ (e2 = e1)
% 155.22/26.69
% 155.22/26.69 Begin of proof
% 155.22/26.69 |
% 155.22/26.69 | COMBINE_EQS: (1), (2) imply:
% 155.22/26.69 | (4) e2 = e1
% 155.22/26.69 |
% 155.22/26.69 | SIMP: (4) implies:
% 155.22/26.69 | (5) e2 = e1
% 155.22/26.69 |
% 155.22/26.69 | REDUCE: (3), (5) imply:
% 155.22/26.69 | (6) $false
% 155.22/26.69 |
% 155.22/26.69 | CLOSE: (6) is inconsistent.
% 155.22/26.69 |
% 155.22/26.69 End of proof
% 155.22/26.69
% 155.22/26.69 Sub-proof #94 shows that the following formulas are inconsistent:
% 155.22/26.69 ----------------------------------------------------------------
% 155.22/26.69 (1) op(e3, e0) = all_52_12
% 155.22/26.69 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 155.22/26.69 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.22/26.69 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.69 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 155.22/26.69 (4) op(e3, e3) = all_10_2
% 155.22/26.69 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 155.22/26.69 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.22/26.69 (6) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 155.22/26.69 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 155.22/26.69 (7) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 155.22/26.69 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 155.22/26.69 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 155.22/26.69 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 155.22/26.69 (9) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 155.22/26.69 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 155.22/26.69 (10) op(e3, e2) = all_52_4
% 155.22/26.69 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.22/26.69 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.22/26.69 (12) ~ (all_52_12 = all_52_13)
% 155.22/26.69 (13) op(e2, e1) = all_52_9
% 155.22/26.69 (14) op(e2, e3) = all_52_1
% 155.22/26.69 (15) ~ (all_10_2 = e0)
% 155.22/26.69 (16) ~ (e3 = e0)
% 155.22/26.69 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.22/26.69 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.22/26.69 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 155.22/26.69 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 155.22/26.69 (19) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 155.22/26.69 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 155.22/26.69 e2)
% 155.22/26.69 (20) ~ (all_8_2 = e3)
% 155.22/26.69 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 155.22/26.69 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.22/26.69 (22) op(e1, e3) = all_52_2
% 155.22/26.69 (23) op(e2, e0) = all_52_13
% 155.22/26.69 (24) ~ (e3 = e1)
% 155.22/26.69 (25) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 155.22/26.69 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 155.22/26.69 (26) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 155.22/26.69 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.69 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 155.22/26.69 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.22/26.69 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 155.22/26.69 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.69 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 155.22/26.69 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 155.22/26.69 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.22/26.69 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.69 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 155.22/26.69 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 155.22/26.69 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 155.22/26.69 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 155.22/26.69 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 155.22/26.69 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 155.22/26.69 = e0)
% 155.22/26.69 (27) ~ (all_4_2 = e1)
% 155.22/26.69 (28) ~ (all_52_8 = e2)
% 155.22/26.69 (29) all_58_7 = e1
% 155.22/26.69 (30) all_56_13 = e0
% 155.22/26.69 (31) op(e1, e2) = e1
% 155.22/26.69 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 155.22/26.69 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 155.22/26.69 (33) ~ (all_52_7 = e0)
% 155.22/26.69 (34) op(e0, e0) = all_4_2
% 155.22/26.69 (35) all_56_15 = all_4_2
% 155.22/26.69 (36) op(e0, e1) = all_52_11
% 155.22/26.69 (37) ~ (all_52_13 = all_4_2)
% 155.22/26.69 (38) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 155.22/26.69 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 155.22/26.69 (39) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 155.22/26.69 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 155.22/26.69 (40) ~ (all_10_2 = e2)
% 155.22/26.69 (41) ~ (e2 = e1)
% 155.22/26.69 (42) all_58_8 = e2
% 155.22/26.69 (43) ~ (all_52_9 = e0)
% 155.22/26.69 (44) ~ (all_52_13 = e0)
% 155.22/26.69 (45) ~ (e1 = e0)
% 155.22/26.69 (46) ~ (all_8_2 = e1)
% 155.22/26.69 (47) ~ (all_52_1 = e0)
% 155.22/26.69 (48) ~ (all_56_13 = e0) | (all_56_5 = e2 & op(e2, e0) = e2)
% 155.22/26.69 (49) op(e3, e1) = all_52_8
% 155.22/26.69 (50) ( ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 & op(e2, e2) = all_6_1 &
% 155.22/26.69 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e3) & op(e2, e2) = all_6_1
% 155.22/26.69 & $i(all_6_1))
% 155.22/26.69 (51) ~ (all_52_7 = e1)
% 155.22/26.69 (52) op(e2, e2) = e0
% 155.22/26.69 (53) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 155.22/26.69 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 155.22/26.69 (54) op(e0, e2) = all_52_7
% 155.22/26.69 (55) op(e1, e0) = all_52_14
% 155.22/26.69 (56) op(e2, e2) = all_8_2
% 155.22/26.69 (57) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.22/26.69 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.22/26.69 (58) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.69 (59) ( ~ (all_18_0 = e3) & op(all_18_1, e1) = all_18_0 & op(e2, e2) =
% 155.22/26.69 all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e0) & op(e2,
% 155.22/26.69 e2) = all_18_1 & $i(all_18_1))
% 155.22/26.69 (60) ~ (all_52_13 = all_52_14)
% 155.22/26.69 (61) ~ (e3 = e2)
% 155.22/26.69 (62) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 155.22/26.69 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 155.22/26.69 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 155.22/26.69 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 155.22/26.69 (63) op(e0, e0) = all_30_1
% 155.22/26.69 (64) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 155.22/26.69 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 155.22/26.69
% 155.22/26.69 Begin of proof
% 155.22/26.69 |
% 155.22/26.69 | BETA: splitting (50) gives:
% 155.22/26.69 |
% 155.22/26.69 | Case 1:
% 155.22/26.69 | |
% 155.22/26.69 | | (65) ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 & op(e2, e2) = all_6_1
% 155.22/26.69 | | & $i(all_6_0) & $i(all_6_1)
% 155.22/26.69 | |
% 155.22/26.69 | | ALPHA: (65) implies:
% 155.22/26.69 | | (66) op(e2, e2) = all_6_1
% 155.22/26.69 | |
% 155.22/26.69 | | BETA: splitting (48) gives:
% 155.22/26.69 | |
% 155.22/26.69 | | Case 1:
% 155.22/26.69 | | |
% 155.22/26.69 | | | (67) ~ (all_56_13 = e0)
% 155.22/26.69 | | |
% 155.22/26.69 | | | REDUCE: (30), (67) imply:
% 155.22/26.69 | | | (68) $false
% 155.22/26.69 | | |
% 155.22/26.69 | | | CLOSE: (68) is inconsistent.
% 155.22/26.69 | | |
% 155.22/26.69 | | Case 2:
% 155.22/26.69 | | |
% 155.22/26.69 | | | (69) all_56_5 = e2 & op(e2, e0) = e2
% 155.22/26.69 | | |
% 155.22/26.69 | | | ALPHA: (69) implies:
% 155.22/26.69 | | | (70) op(e2, e0) = e2
% 155.22/26.69 | | |
% 155.22/26.69 | | | BETA: splitting (59) gives:
% 155.22/26.69 | | |
% 155.22/26.69 | | | Case 1:
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | (71) ~ (all_18_0 = e3) & op(all_18_1, e1) = all_18_0 & op(e2, e2) =
% 155.22/26.69 | | | | all_18_1 & $i(all_18_0) & $i(all_18_1)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | ALPHA: (71) implies:
% 155.22/26.69 | | | | (72) ~ (all_18_0 = e3)
% 155.22/26.69 | | | | (73) op(e2, e2) = all_18_1
% 155.22/26.69 | | | | (74) op(all_18_1, e1) = all_18_0
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | GROUND_INST: instantiating (58) with all_4_2, all_30_1, e0, e0,
% 155.22/26.69 | | | | simplifying with (34), (63) gives:
% 155.22/26.69 | | | | (75) all_30_1 = all_4_2
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | GROUND_INST: instantiating (58) with all_52_13, e2, e0, e2, simplifying
% 155.22/26.69 | | | | with (23), (70) gives:
% 155.22/26.69 | | | | (76) all_52_13 = e2
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | GROUND_INST: instantiating (58) with all_6_1, all_18_1, e2, e2,
% 155.22/26.69 | | | | simplifying with (66), (73) gives:
% 155.22/26.69 | | | | (77) all_18_1 = all_6_1
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | GROUND_INST: instantiating (58) with e0, all_18_1, e2, e2, simplifying
% 155.22/26.69 | | | | with (52), (73) gives:
% 155.22/26.69 | | | | (78) all_18_1 = e0
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | COMBINE_EQS: (77), (78) imply:
% 155.22/26.69 | | | | (79) all_6_1 = e0
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | REDUCE: (12), (76) imply:
% 155.22/26.69 | | | | (80) ~ (all_52_12 = e2)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | REDUCE: (60), (76) imply:
% 155.22/26.69 | | | | (81) ~ (all_52_14 = e2)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | SIMP: (81) implies:
% 155.22/26.69 | | | | (82) ~ (all_52_14 = e2)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | REDUCE: (37), (76) imply:
% 155.22/26.69 | | | | (83) ~ (all_4_2 = e2)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | SIMP: (83) implies:
% 155.22/26.69 | | | | (84) ~ (all_4_2 = e2)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | REDUCE: (44), (76) imply:
% 155.22/26.69 | | | | (85) ~ (e2 = e0)
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | REDUCE: (74), (78) imply:
% 155.22/26.69 | | | | (86) op(e0, e1) = all_18_0
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | BETA: splitting (9) gives:
% 155.22/26.69 | | | |
% 155.22/26.69 | | | | Case 1:
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | (87) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 155.22/26.69 | | | | | e0) = e2)
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | BETA: splitting (87) gives:
% 155.22/26.69 | | | | |
% 155.22/26.69 | | | | | Case 1:
% 155.22/26.69 | | | | | |
% 155.22/26.69 | | | | | | (88) all_58_9 = e2 & op(e3, e0) = e2
% 155.22/26.69 | | | | | |
% 155.22/26.69 | | | | | | REF_CLOSE: (1), (58), (80), (88) are inconsistent by sub-proof
% 155.22/26.69 | | | | | | #1238.
% 155.22/26.69 | | | | | |
% 155.22/26.69 | | | | | Case 2:
% 155.22/26.69 | | | | | |
% 155.22/26.69 | | | | | | (89) all_58_10 = e2 & op(e2, e0) = e2
% 155.22/26.69 | | | | | |
% 155.22/26.69 | | | | | | ALPHA: (89) implies:
% 155.22/26.69 | | | | | | (90) all_58_10 = e2
% 155.22/26.69 | | | | | |
% 155.22/26.69 | | | | | | BETA: splitting (38) gives:
% 155.22/26.69 | | | | | |
% 155.22/26.69 | | | | | | Case 1:
% 155.22/26.69 | | | | | | |
% 155.22/26.69 | | | | | | | (91) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 &
% 155.22/26.69 | | | | | | | op(e2, e3) = e2)
% 155.22/26.69 | | | | | | |
% 155.22/26.69 | | | | | | | REF_CLOSE: (3), (4), (14), (16), (24), (32), (39), (40), (41),
% 155.22/26.69 | | | | | | | (45), (46), (56), (58), (61), (85), (90), (91) are
% 155.22/26.69 | | | | | | | inconsistent by sub-proof #103.
% 155.22/26.69 | | | | | | |
% 155.22/26.69 | | | | | | Case 2:
% 155.22/26.69 | | | | | | |
% 155.22/26.69 | | | | | | | (92) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 155.22/26.69 | | | | | | | op(e0, e3) = e2)
% 155.22/26.69 | | | | | | |
% 155.22/26.69 | | | | | | | BETA: splitting (92) gives:
% 155.22/26.69 | | | | | | |
% 155.22/26.69 | | | | | | | Case 1:
% 155.22/26.69 | | | | | | | |
% 155.22/26.69 | | | | | | | | (93) all_58_6 = e2 & op(e1, e3) = e2
% 155.22/26.69 | | | | | | | |
% 155.22/26.69 | | | | | | | | ALPHA: (93) implies:
% 155.22/26.69 | | | | | | | | (94) all_58_6 = e2
% 155.22/26.69 | | | | | | | |
% 155.22/26.69 | | | | | | | | REF_CLOSE: (11), (16), (21), (24), (29), (42), (45), (58), (61),
% 155.22/26.69 | | | | | | | | (85), (94) are inconsistent by sub-proof #116.
% 155.22/26.69 | | | | | | | |
% 155.22/26.69 | | | | | | | Case 2:
% 155.22/26.69 | | | | | | | |
% 155.22/26.69 | | | | | | | | (95) all_58_12 = e2 & op(e0, e3) = e2
% 155.22/26.69 | | | | | | | |
% 155.22/26.69 | | | | | | | | ALPHA: (95) implies:
% 155.22/26.69 | | | | | | | | (96) all_58_12 = e2
% 155.22/26.69 | | | | | | | |
% 155.22/26.69 | | | | | | | | BETA: splitting (2) gives:
% 155.22/26.69 | | | | | | | |
% 155.22/26.69 | | | | | | | | Case 1:
% 155.22/26.69 | | | | | | | | |
% 155.22/26.69 | | | | | | | | | (97) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 155.22/26.69 | | | | | | | | | op(e2, e0) = e1)
% 155.22/26.69 | | | | | | | | |
% 155.22/26.69 | | | | | | | | | BETA: splitting (97) gives:
% 155.22/26.69 | | | | | | | | |
% 155.22/26.69 | | | | | | | | | Case 1:
% 155.22/26.69 | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | (98) all_58_9 = e1 & op(e3, e0) = e1
% 155.22/26.69 | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | ALPHA: (98) implies:
% 155.22/26.69 | | | | | | | | | | (99) all_58_9 = e1
% 155.22/26.69 | | | | | | | | | | (100) op(e3, e0) = e1
% 155.22/26.69 | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | BETA: splitting (5) gives:
% 155.22/26.69 | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | Case 1:
% 155.22/26.69 | | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | | (101) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 155.22/26.69 | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 155.22/26.69 | | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | | REF_CLOSE: (41), (51), (54), (58), (96), (101) are
% 155.22/26.69 | | | | | | | | | | | inconsistent by sub-proof #102.
% 155.22/26.69 | | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | Case 2:
% 155.22/26.69 | | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | | (102) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 155.22/26.69 | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 155.22/26.69 | | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | | BETA: splitting (102) gives:
% 155.22/26.69 | | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | | Case 1:
% 155.22/26.69 | | | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | | | (103) all_58_14 = e1 & op(e0, e1) = e1
% 155.22/26.69 | | | | | | | | | | | |
% 155.22/26.69 | | | | | | | | | | | | ALPHA: (103) implies:
% 155.22/26.70 | | | | | | | | | | | | (104) op(e0, e1) = e1
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | BETA: splitting (62) gives:
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | (105) all_58_15 = e0 & op(e0, e0) = e0
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | ALPHA: (105) implies:
% 155.22/26.70 | | | | | | | | | | | | | (106) all_58_15 = e0
% 155.22/26.70 | | | | | | | | | | | | | (107) op(e0, e0) = e0
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | BETA: splitting (25) gives:
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | (108) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 155.22/26.70 | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | (109) all_58_4 = e0 & op(e3, e1) = e0
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 155.22/26.70 | | | | | | | | | | | | | | | (110) all_58_4 = e0
% 155.22/26.70 | | | | | | | | | | | | | | | (111) op(e3, e1) = e0
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | (112) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | (113) all_58_1 = e3 & op(e3, e2) = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 155.22/26.70 | | | | | | | | | | | | | | | | | (114) op(e3, e2) = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (8), (10), (16), (17), (18), (24), (28),
% 155.22/26.70 | | | | | | | | | | | | | | | | | (41), (45), (49), (57), (58), (61), (80), (85),
% 155.22/26.70 | | | | | | | | | | | | | | | | | (96), (114) are inconsistent by sub-proof #101.
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | (115) all_58_3 = e3 & op(e2, e2) = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (56), (58), (115) are inconsistent by
% 155.22/26.70 | | | | | | | | | | | | | | | | | sub-proof #1437.
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | (116) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 155.22/26.70 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10),
% 155.22/26.70 | | | | | | | | | | | | | | | | (13), (14), (15), (16), (17), (18), (19), (22),
% 155.22/26.70 | | | | | | | | | | | | | | | | (24), (26), (27), (28), (29), (31), (32), (33),
% 155.22/26.70 | | | | | | | | | | | | | | | | (34), (35), (36), (38), (39), (40), (41), (42),
% 155.22/26.70 | | | | | | | | | | | | | | | | (45), (46), (47), (49), (53), (54), (55), (56),
% 155.22/26.70 | | | | | | | | | | | | | | | | (57), (58), (61), (72), (80), (84), (85), (86),
% 155.22/26.70 | | | | | | | | | | | | | | | | (90), (96), (99), (100), (104), (106), (107),
% 155.22/26.70 | | | | | | | | | | | | | | | | (110), (111), (116) are inconsistent by sub-proof
% 155.22/26.70 | | | | | | | | | | | | | | | | #99.
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | (117) all_58_5 = e0 & op(e2, e1) = e0
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 155.22/26.70 | | | | | | | | | | | | | | | (118) op(e2, e1) = e0
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | REF_CLOSE: (13), (43), (58), (118) are inconsistent by
% 155.22/26.70 | | | | | | | | | | | | | | | sub-proof #1300.
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | (119) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 155.22/26.70 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | REF_CLOSE: (42), (45), (58), (85), (104), (119) are
% 155.22/26.70 | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | (120) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 155.22/26.70 | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 155.22/26.70 | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 155.22/26.70 | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 155.22/26.70 | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | ALPHA: (120) implies:
% 155.22/26.70 | | | | | | | | | | | | | (121) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 155.22/26.70 | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 155.22/26.70 | | | | | | | | | | | | | e1) = e0)
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | REF_CLOSE: (33), (45), (54), (58), (85), (96), (104), (121)
% 155.22/26.70 | | | | | | | | | | | | | are inconsistent by sub-proof #97.
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | (122) all_58_15 = e1 & op(e0, e0) = e1
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | REF_CLOSE: (27), (34), (58), (122) are inconsistent by
% 155.22/26.70 | | | | | | | | | | | | sub-proof #1418.
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | (123) all_58_10 = e1 & op(e2, e0) = e1
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | REF_CLOSE: (41), (90), (123) are inconsistent by sub-proof
% 155.22/26.70 | | | | | | | | | | #1199.
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | | (124) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1
% 155.22/26.70 | | | | | | | | | & op(e0, e0) = e1)
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | | REF_CLOSE: (11), (16), (21), (24), (27), (29), (34), (42),
% 155.22/26.70 | | | | | | | | | (45), (58), (61), (85), (124) are inconsistent by
% 155.22/26.70 | | | | | | | | | sub-proof #104.
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | End of split
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | End of split
% 155.22/26.70 | | | | | | |
% 155.22/26.70 | | | | | | End of split
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | End of split
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | Case 2:
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | | (125) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 155.22/26.70 | | | | | e0) = e2)
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | | REF_CLOSE: (34), (55), (58), (82), (84), (125) are inconsistent by
% 155.22/26.70 | | | | | sub-proof #1185.
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | End of split
% 155.22/26.70 | | | |
% 155.22/26.70 | | | Case 2:
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | (126) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | ALPHA: (126) implies:
% 155.22/26.70 | | | | (127) ~ (all_18_1 = e0)
% 155.22/26.70 | | | | (128) op(e2, e2) = all_18_1
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | REF_CLOSE: (52), (58), (66), (127), (128) are inconsistent by sub-proof
% 155.22/26.70 | | | | #96.
% 155.22/26.70 | | | |
% 155.22/26.70 | | | End of split
% 155.22/26.70 | | |
% 155.22/26.70 | | End of split
% 155.22/26.70 | |
% 155.22/26.70 | Case 2:
% 155.22/26.70 | |
% 155.22/26.70 | | (129) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1)
% 155.22/26.70 | |
% 155.22/26.70 | | ALPHA: (129) implies:
% 155.22/26.70 | | (130) ~ (all_6_1 = e3)
% 155.22/26.70 | | (131) op(e2, e2) = all_6_1
% 155.22/26.70 | |
% 155.22/26.70 | | BETA: splitting (48) gives:
% 155.22/26.70 | |
% 155.22/26.70 | | Case 1:
% 155.22/26.70 | | |
% 155.22/26.70 | | | (132) ~ (all_56_13 = e0)
% 155.22/26.70 | | |
% 155.22/26.70 | | | REDUCE: (30), (132) imply:
% 155.22/26.70 | | | (133) $false
% 155.22/26.70 | | |
% 155.22/26.70 | | | CLOSE: (133) is inconsistent.
% 155.22/26.70 | | |
% 155.22/26.70 | | Case 2:
% 155.22/26.70 | | |
% 155.22/26.70 | | | (134) all_56_5 = e2 & op(e2, e0) = e2
% 155.22/26.70 | | |
% 155.22/26.70 | | | ALPHA: (134) implies:
% 155.22/26.70 | | | (135) op(e2, e0) = e2
% 155.22/26.70 | | |
% 155.22/26.70 | | | BETA: splitting (59) gives:
% 155.22/26.70 | | |
% 155.22/26.70 | | | Case 1:
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | (136) ~ (all_18_0 = e3) & op(all_18_1, e1) = all_18_0 & op(e2, e2) =
% 155.22/26.70 | | | | all_18_1 & $i(all_18_0) & $i(all_18_1)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | ALPHA: (136) implies:
% 155.22/26.70 | | | | (137) ~ (all_18_0 = e3)
% 155.22/26.70 | | | | (138) op(e2, e2) = all_18_1
% 155.22/26.70 | | | | (139) op(all_18_1, e1) = all_18_0
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | GROUND_INST: instantiating (58) with all_4_2, all_30_1, e0, e0,
% 155.22/26.70 | | | | simplifying with (34), (63) gives:
% 155.22/26.70 | | | | (140) all_30_1 = all_4_2
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | GROUND_INST: instantiating (58) with all_52_13, e2, e0, e2, simplifying
% 155.22/26.70 | | | | with (23), (135) gives:
% 155.22/26.70 | | | | (141) all_52_13 = e2
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | GROUND_INST: instantiating (58) with all_6_1, all_18_1, e2, e2,
% 155.22/26.70 | | | | simplifying with (131), (138) gives:
% 155.22/26.70 | | | | (142) all_18_1 = all_6_1
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | GROUND_INST: instantiating (58) with e0, all_18_1, e2, e2, simplifying
% 155.22/26.70 | | | | with (52), (138) gives:
% 155.22/26.70 | | | | (143) all_18_1 = e0
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | COMBINE_EQS: (142), (143) imply:
% 155.22/26.70 | | | | (144) all_6_1 = e0
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | REDUCE: (12), (141) imply:
% 155.22/26.70 | | | | (145) ~ (all_52_12 = e2)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | REDUCE: (60), (141) imply:
% 155.22/26.70 | | | | (146) ~ (all_52_14 = e2)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | SIMP: (146) implies:
% 155.22/26.70 | | | | (147) ~ (all_52_14 = e2)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | REDUCE: (37), (141) imply:
% 155.22/26.70 | | | | (148) ~ (all_4_2 = e2)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | SIMP: (148) implies:
% 155.22/26.70 | | | | (149) ~ (all_4_2 = e2)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | REDUCE: (44), (141) imply:
% 155.22/26.70 | | | | (150) ~ (e2 = e0)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | REDUCE: (130), (144) imply:
% 155.22/26.70 | | | | (151) ~ (e3 = e0)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | REDUCE: (139), (143) imply:
% 155.22/26.70 | | | | (152) op(e0, e1) = all_18_0
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | BETA: splitting (9) gives:
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | Case 1:
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | | (153) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 155.22/26.70 | | | | | e0) = e2)
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | | BETA: splitting (153) gives:
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | | Case 1:
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | | (154) all_58_9 = e2 & op(e3, e0) = e2
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | | REF_CLOSE: (1), (58), (145), (154) are inconsistent by sub-proof
% 155.22/26.70 | | | | | | #1238.
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | Case 2:
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | | (155) all_58_10 = e2 & op(e2, e0) = e2
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | | ALPHA: (155) implies:
% 155.22/26.70 | | | | | | (156) all_58_10 = e2
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | | BETA: splitting (38) gives:
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | | Case 1:
% 155.22/26.70 | | | | | | |
% 155.22/26.70 | | | | | | | (157) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 &
% 155.22/26.70 | | | | | | | op(e2, e3) = e2)
% 155.22/26.70 | | | | | | |
% 155.22/26.70 | | | | | | | REF_CLOSE: (3), (4), (14), (16), (24), (32), (39), (40), (41),
% 155.22/26.70 | | | | | | | (45), (46), (56), (58), (61), (150), (156), (157) are
% 155.22/26.70 | | | | | | | inconsistent by sub-proof #103.
% 155.22/26.70 | | | | | | |
% 155.22/26.70 | | | | | | Case 2:
% 155.22/26.70 | | | | | | |
% 155.22/26.70 | | | | | | | (158) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 155.22/26.70 | | | | | | | op(e0, e3) = e2)
% 155.22/26.70 | | | | | | |
% 155.22/26.70 | | | | | | | BETA: splitting (158) gives:
% 155.22/26.70 | | | | | | |
% 155.22/26.70 | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | | (159) all_58_6 = e2 & op(e1, e3) = e2
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | | ALPHA: (159) implies:
% 155.22/26.70 | | | | | | | | (160) all_58_6 = e2
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | | REF_CLOSE: (11), (16), (21), (24), (29), (42), (45), (58), (61),
% 155.22/26.70 | | | | | | | | (150), (160) are inconsistent by sub-proof #116.
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | | (161) all_58_12 = e2 & op(e0, e3) = e2
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | | ALPHA: (161) implies:
% 155.22/26.70 | | | | | | | | (162) all_58_12 = e2
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | | BETA: splitting (2) gives:
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | | (163) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 155.22/26.70 | | | | | | | | | op(e2, e0) = e1)
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | | BETA: splitting (163) gives:
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | (164) all_58_9 = e1 & op(e3, e0) = e1
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | ALPHA: (164) implies:
% 155.22/26.70 | | | | | | | | | | (165) all_58_9 = e1
% 155.22/26.70 | | | | | | | | | | (166) op(e3, e0) = e1
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | BETA: splitting (5) gives:
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | (167) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 155.22/26.70 | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 155.22/26.70 | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | REF_CLOSE: (41), (51), (54), (58), (162), (167) are
% 155.22/26.70 | | | | | | | | | | | inconsistent by sub-proof #102.
% 155.22/26.70 | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | (168) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 155.22/26.70 | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 155.22/26.70 | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | BETA: splitting (168) gives:
% 155.22/26.70 | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | (169) all_58_14 = e1 & op(e0, e1) = e1
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | ALPHA: (169) implies:
% 155.22/26.70 | | | | | | | | | | | | (170) op(e0, e1) = e1
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | BETA: splitting (62) gives:
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | (171) all_58_15 = e0 & op(e0, e0) = e0
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | ALPHA: (171) implies:
% 155.22/26.70 | | | | | | | | | | | | | (172) all_58_15 = e0
% 155.22/26.70 | | | | | | | | | | | | | (173) op(e0, e0) = e0
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | BETA: splitting (25) gives:
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | (174) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 155.22/26.70 | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | (175) all_58_4 = e0 & op(e3, e1) = e0
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 155.22/26.70 | | | | | | | | | | | | | | | (176) all_58_4 = e0
% 155.22/26.70 | | | | | | | | | | | | | | | (177) op(e3, e1) = e0
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | (178) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | Case 1:
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | (179) all_58_1 = e3 & op(e3, e2) = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 155.22/26.70 | | | | | | | | | | | | | | | | | (180) op(e3, e2) = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (8), (10), (16), (17), (18), (24), (28),
% 155.22/26.70 | | | | | | | | | | | | | | | | | (41), (45), (49), (57), (58), (61), (145), (150),
% 155.22/26.70 | | | | | | | | | | | | | | | | | (162), (180) are inconsistent by sub-proof #101.
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | (181) all_58_3 = e3 & op(e2, e2) = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 155.22/26.70 | | | | | | | | | | | | | | | | | (182) op(e2, e2) = e3
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (130), (131), (138), (182) are inconsistent
% 155.22/26.70 | | | | | | | | | | | | | | | | | by sub-proof #95.
% 155.22/26.70 | | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | (183) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 155.22/26.70 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10),
% 155.22/26.70 | | | | | | | | | | | | | | | | (13), (14), (15), (16), (17), (18), (19), (22),
% 155.22/26.70 | | | | | | | | | | | | | | | | (24), (26), (27), (28), (29), (31), (32), (33),
% 155.22/26.70 | | | | | | | | | | | | | | | | (34), (35), (36), (38), (39), (40), (41), (42),
% 155.22/26.70 | | | | | | | | | | | | | | | | (45), (46), (47), (49), (53), (54), (55), (56),
% 155.22/26.70 | | | | | | | | | | | | | | | | (57), (58), (61), (137), (145), (149), (150),
% 155.22/26.70 | | | | | | | | | | | | | | | | (152), (156), (162), (165), (166), (170), (172),
% 155.22/26.70 | | | | | | | | | | | | | | | | (173), (176), (177), (183) are inconsistent by
% 155.22/26.70 | | | | | | | | | | | | | | | | sub-proof #99.
% 155.22/26.70 | | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | (184) all_58_5 = e0 & op(e2, e1) = e0
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 155.22/26.70 | | | | | | | | | | | | | | | (185) op(e2, e1) = e0
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | | REF_CLOSE: (13), (43), (58), (185) are inconsistent by
% 155.22/26.70 | | | | | | | | | | | | | | | sub-proof #1300.
% 155.22/26.70 | | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | (186) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 155.22/26.70 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | | REF_CLOSE: (42), (45), (58), (150), (170), (186) are
% 155.22/26.70 | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 155.22/26.70 | | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | (187) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 155.22/26.70 | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 155.22/26.70 | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 155.22/26.70 | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 155.22/26.70 | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | ALPHA: (187) implies:
% 155.22/26.70 | | | | | | | | | | | | | (188) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 155.22/26.70 | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 155.22/26.70 | | | | | | | | | | | | | e1) = e0)
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | | REF_CLOSE: (33), (45), (54), (58), (150), (162), (170), (188)
% 155.22/26.70 | | | | | | | | | | | | | are inconsistent by sub-proof #97.
% 155.22/26.70 | | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | (189) all_58_15 = e1 & op(e0, e0) = e1
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | | REF_CLOSE: (27), (34), (58), (189) are inconsistent by
% 155.22/26.70 | | | | | | | | | | | | sub-proof #1418.
% 155.22/26.70 | | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | (190) all_58_10 = e1 & op(e2, e0) = e1
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | | REF_CLOSE: (41), (156), (190) are inconsistent by sub-proof
% 155.22/26.70 | | | | | | | | | | #1199.
% 155.22/26.70 | | | | | | | | | |
% 155.22/26.70 | | | | | | | | | End of split
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | Case 2:
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | | (191) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1
% 155.22/26.70 | | | | | | | | | & op(e0, e0) = e1)
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | | REF_CLOSE: (11), (16), (21), (24), (27), (29), (34), (42),
% 155.22/26.70 | | | | | | | | | (45), (58), (61), (150), (191) are inconsistent by
% 155.22/26.70 | | | | | | | | | sub-proof #104.
% 155.22/26.70 | | | | | | | | |
% 155.22/26.70 | | | | | | | | End of split
% 155.22/26.70 | | | | | | | |
% 155.22/26.70 | | | | | | | End of split
% 155.22/26.70 | | | | | | |
% 155.22/26.70 | | | | | | End of split
% 155.22/26.70 | | | | | |
% 155.22/26.70 | | | | | End of split
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | Case 2:
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | | (192) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 155.22/26.70 | | | | | e0) = e2)
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | | REF_CLOSE: (34), (55), (58), (147), (149), (192) are inconsistent by
% 155.22/26.70 | | | | | sub-proof #1185.
% 155.22/26.70 | | | | |
% 155.22/26.70 | | | | End of split
% 155.22/26.70 | | | |
% 155.22/26.70 | | | Case 2:
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | (193) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1)
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | ALPHA: (193) implies:
% 155.22/26.70 | | | | (194) ~ (all_18_1 = e0)
% 155.22/26.70 | | | | (195) op(e2, e2) = all_18_1
% 155.22/26.70 | | | |
% 155.22/26.70 | | | | REF_CLOSE: (52), (58), (131), (194), (195) are inconsistent by sub-proof
% 155.22/26.70 | | | | #96.
% 155.22/26.70 | | | |
% 155.22/26.70 | | | End of split
% 155.22/26.70 | | |
% 155.22/26.70 | | End of split
% 155.22/26.70 | |
% 155.22/26.70 | End of split
% 155.22/26.70 |
% 155.22/26.70 End of proof
% 155.22/26.70
% 155.22/26.70 Sub-proof #95 shows that the following formulas are inconsistent:
% 155.22/26.70 ----------------------------------------------------------------
% 155.22/26.70 (1) op(e2, e2) = e3
% 155.22/26.70 (2) ~ (all_6_1 = e3)
% 155.22/26.70 (3) op(e2, e2) = all_18_1
% 155.22/26.70 (4) op(e2, e2) = all_6_1
% 155.22/26.70 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.70
% 155.22/26.70 Begin of proof
% 155.22/26.70 |
% 155.22/26.70 | GROUND_INST: instantiating (5) with all_6_1, all_18_1, e2, e2, simplifying
% 155.22/26.70 | with (3), (4) gives:
% 155.22/26.70 | (6) all_18_1 = all_6_1
% 155.22/26.70 |
% 155.22/26.70 | GROUND_INST: instantiating (5) with e3, all_18_1, e2, e2, simplifying with
% 155.22/26.70 | (1), (3) gives:
% 155.22/26.70 | (7) all_18_1 = e3
% 155.22/26.70 |
% 155.22/26.70 | COMBINE_EQS: (6), (7) imply:
% 155.22/26.70 | (8) all_6_1 = e3
% 155.22/26.70 |
% 155.22/26.70 | REDUCE: (2), (8) imply:
% 155.22/26.70 | (9) $false
% 155.22/26.70 |
% 155.22/26.70 | CLOSE: (9) is inconsistent.
% 155.22/26.70 |
% 155.22/26.70 End of proof
% 155.22/26.70
% 155.22/26.70 Sub-proof #96 shows that the following formulas are inconsistent:
% 155.22/26.70 ----------------------------------------------------------------
% 155.22/26.70 (1) op(e2, e2) = all_18_1
% 155.22/26.70 (2) op(e2, e2) = all_6_1
% 155.22/26.70 (3) ~ (all_18_1 = e0)
% 155.22/26.70 (4) op(e2, e2) = e0
% 155.22/26.70 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.70
% 155.22/26.70 Begin of proof
% 155.22/26.71 |
% 155.22/26.71 | GROUND_INST: instantiating (5) with all_6_1, all_18_1, e2, e2, simplifying
% 155.22/26.71 | with (1), (2) gives:
% 155.22/26.71 | (6) all_18_1 = all_6_1
% 155.22/26.71 |
% 155.22/26.71 | GROUND_INST: instantiating (5) with e0, all_18_1, e2, e2, simplifying with
% 155.22/26.71 | (1), (4) gives:
% 155.22/26.71 | (7) all_18_1 = e0
% 155.22/26.71 |
% 155.22/26.71 | COMBINE_EQS: (6), (7) imply:
% 155.22/26.71 | (8) all_6_1 = e0
% 155.22/26.71 |
% 155.22/26.71 | REDUCE: (3), (7) imply:
% 155.22/26.71 | (9) $false
% 155.22/26.71 |
% 155.22/26.71 | CLOSE: (9) is inconsistent.
% 155.22/26.71 |
% 155.22/26.71 End of proof
% 155.22/26.71
% 155.22/26.71 Sub-proof #97 shows that the following formulas are inconsistent:
% 155.22/26.71 ----------------------------------------------------------------
% 155.22/26.71 (1) all_58_12 = e2
% 155.22/26.71 (2) ~ (e2 = e0)
% 155.22/26.71 (3) op(e0, e1) = e1
% 155.22/26.71 (4) ~ (all_52_7 = e0)
% 155.22/26.71 (5) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 155.22/26.71 (all_58_14 = e0 & op(e0, e1) = e0)
% 155.22/26.71 (6) ~ (e1 = e0)
% 155.22/26.71 (7) op(e0, e2) = all_52_7
% 155.22/26.71 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.71
% 155.22/26.71 Begin of proof
% 155.22/26.71 |
% 155.22/26.71 | BETA: splitting (5) gives:
% 155.22/26.71 |
% 155.22/26.71 | Case 1:
% 155.22/26.71 | |
% 155.22/26.71 | | (9) all_58_12 = e0 & op(e0, e3) = e0
% 155.22/26.71 | |
% 155.22/26.71 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1369.
% 155.22/26.71 | |
% 155.22/26.71 | Case 2:
% 155.22/26.71 | |
% 155.22/26.71 | | (10) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 155.22/26.71 | | e0)
% 155.22/26.71 | |
% 155.22/26.71 | | BETA: splitting (10) gives:
% 155.22/26.71 | |
% 155.22/26.71 | | Case 1:
% 155.22/26.71 | | |
% 155.22/26.71 | | | (11) all_58_13 = e0 & op(e0, e2) = e0
% 155.22/26.71 | | |
% 155.22/26.71 | | | ALPHA: (11) implies:
% 155.22/26.71 | | | (12) op(e0, e2) = e0
% 155.22/26.71 | | |
% 155.22/26.71 | | | REF_CLOSE: (4), (7), (8), (12) are inconsistent by sub-proof #1532.
% 155.22/26.71 | | |
% 155.22/26.71 | | Case 2:
% 155.22/26.71 | | |
% 155.22/26.71 | | | (13) all_58_14 = e0 & op(e0, e1) = e0
% 155.22/26.71 | | |
% 155.22/26.71 | | | ALPHA: (13) implies:
% 155.22/26.71 | | | (14) op(e0, e1) = e0
% 155.22/26.71 | | |
% 155.22/26.71 | | | REF_CLOSE: (3), (6), (8), (14) are inconsistent by sub-proof #129.
% 155.22/26.71 | | |
% 155.22/26.71 | | End of split
% 155.22/26.71 | |
% 155.22/26.71 | End of split
% 155.22/26.71 |
% 155.22/26.71 End of proof
% 155.22/26.71
% 155.22/26.71 Sub-proof #98 shows that the following formulas are inconsistent:
% 155.22/26.71 ----------------------------------------------------------------
% 155.22/26.71 (1) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 155.22/26.71 (2) ~ (e2 = e0)
% 155.22/26.71 (3) op(e0, e1) = e1
% 155.22/26.71 (4) all_58_8 = e2
% 155.22/26.71 (5) ~ (e1 = e0)
% 155.22/26.71 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.22/26.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.22/26.71
% 155.22/26.71 Begin of proof
% 155.22/26.71 |
% 155.22/26.71 | BETA: splitting (1) gives:
% 155.22/26.71 |
% 155.22/26.71 | Case 1:
% 155.22/26.71 | |
% 155.22/26.71 | | (7) all_58_8 = e0 & op(e1, e1) = e0
% 155.22/26.71 | |
% 155.22/26.71 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #1071.
% 155.22/26.71 | |
% 155.22/26.71 | Case 2:
% 155.22/26.71 | |
% 155.22/26.71 | | (8) all_58_14 = e0 & op(e0, e1) = e0
% 155.22/26.71 | |
% 155.22/26.71 | | ALPHA: (8) implies:
% 155.22/26.71 | | (9) op(e0, e1) = e0
% 155.22/26.71 | |
% 155.22/26.71 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #129.
% 155.22/26.71 | |
% 155.22/26.71 | End of split
% 155.22/26.71 |
% 155.22/26.71 End of proof
% 155.22/26.71
% 155.22/26.71 Sub-proof #99 shows that the following formulas are inconsistent:
% 155.22/26.71 ----------------------------------------------------------------
% 155.22/26.71 (1) all_58_15 = e0
% 155.22/26.71 (2) all_58_12 = e2
% 155.22/26.71 (3) op(e3, e0) = e1
% 155.22/26.71 (4) op(e3, e0) = all_52_12
% 155.22/26.71 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 155.22/26.71 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.22/26.71 (6) ~ (all_52_12 = e2)
% 155.22/26.71 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.22/26.71 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 155.22/26.71 (8) op(e3, e3) = all_10_2
% 155.22/26.71 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 155.22/26.71 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.22/26.71 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 155.22/26.71 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 155.22/26.71 (11) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 155.22/26.71 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 155.22/26.71 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 155.22/26.71 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 155.22/26.71 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 155.22/26.71 (14) op(e3, e2) = all_52_4
% 155.22/26.71 (15) ~ (all_4_2 = e2)
% 155.22/26.71 (16) op(e2, e1) = all_52_9
% 155.22/26.71 (17) op(e2, e3) = all_52_1
% 155.22/26.71 (18) all_58_10 = e2
% 155.22/26.71 (19) ~ (all_10_2 = e0)
% 155.22/26.71 (20) ~ (e3 = e0)
% 155.22/26.71 (21) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.22/26.71 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.22/26.71 (22) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 155.22/26.71 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 155.22/26.71 (23) op(e0, e0) = e0
% 155.22/26.71 (24) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 155.22/26.71 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 155.22/26.71 e2)
% 155.22/26.71 (25) ~ (e2 = e0)
% 155.22/26.71 (26) op(e1, e3) = all_52_2
% 155.22/26.71 (27) op(e0, e1) = all_18_0
% 155.22/26.71 (28) ~ (e3 = e1)
% 155.22/26.71 (29) op(e0, e1) = e1
% 155.22/26.71 (30) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 155.22/26.71 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.22/26.71 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 155.22/26.71 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.22/26.71 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 155.22/26.71 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.22/26.71 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 155.22/26.71 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 155.22/26.71 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.22/26.71 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.22/26.71 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 155.22/26.71 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 155.22/26.71 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 155.22/26.71 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 155.22/26.71 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 155.22/26.71 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 155.22/26.71 = e0)
% 155.22/26.71 (31) ~ (all_4_2 = e1)
% 155.22/26.71 (32) ~ (all_52_8 = e2)
% 155.22/26.71 (33) all_58_7 = e1
% 155.22/26.71 (34) op(e1, e2) = e1
% 155.22/26.71 (35) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 155.22/26.71 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 155.22/26.71 (36) ~ (all_52_7 = e0)
% 155.22/26.71 (37) op(e0, e0) = all_4_2
% 155.22/26.71 (38) op(e3, e1) = e0
% 155.22/26.71 (39) all_56_15 = all_4_2
% 155.22/26.71 (40) op(e0, e1) = all_52_11
% 155.22/26.71 (41) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 155.22/26.71 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 155.22/26.71 (42) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 155.22/26.71 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 155.22/26.71 (43) ~ (all_10_2 = e2)
% 155.22/26.71 (44) ~ (e2 = e1)
% 155.22/26.71 (45) all_58_8 = e2
% 155.22/26.71 (46) ~ (e1 = e0)
% 155.22/26.71 (47) ~ (all_8_2 = e1)
% 155.88/26.71 (48) ~ (all_52_1 = e0)
% 155.88/26.71 (49) all_58_4 = e0
% 155.88/26.71 (50) all_58_9 = e1
% 155.88/26.71 (51) op(e3, e1) = all_52_8
% 155.88/26.71 (52) ~ (all_18_0 = e3)
% 155.88/26.71 (53) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 155.88/26.71 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 155.88/26.71 (54) op(e0, e2) = all_52_7
% 155.88/26.71 (55) op(e1, e0) = all_52_14
% 155.88/26.71 (56) op(e2, e2) = all_8_2
% 155.88/26.71 (57) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.88/26.71 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.88/26.71 (58) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.71 (59) ~ (e3 = e2)
% 155.88/26.71
% 155.88/26.71 Begin of proof
% 155.88/26.71 |
% 155.88/26.71 | BETA: splitting (11) gives:
% 155.88/26.71 |
% 155.88/26.71 | Case 1:
% 155.88/26.71 | |
% 155.88/26.71 | | (60) all_58_7 = e3 & op(e1, e2) = e3
% 155.88/26.71 | |
% 155.88/26.71 | | ALPHA: (60) implies:
% 155.88/26.71 | | (61) all_58_7 = e3
% 155.88/26.71 | |
% 155.88/26.71 | | REF_CLOSE: (28), (33), (61) are inconsistent by sub-proof #1330.
% 155.88/26.71 | |
% 155.88/26.71 | Case 2:
% 155.88/26.71 | |
% 155.88/26.71 | | (62) all_58_13 = e3 & op(e0, e2) = e3
% 155.88/26.71 | |
% 155.88/26.71 | | ALPHA: (62) implies:
% 155.88/26.71 | | (63) all_58_13 = e3
% 155.88/26.71 | |
% 155.88/26.71 | | BETA: splitting (57) gives:
% 155.88/26.71 | |
% 155.88/26.71 | | Case 1:
% 155.88/26.71 | | |
% 155.88/26.71 | | | (64) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 155.88/26.71 | | | e0)
% 155.88/26.71 | | |
% 155.88/26.71 | | | BETA: splitting (64) gives:
% 155.88/26.71 | | |
% 155.88/26.71 | | | Case 1:
% 155.88/26.71 | | | |
% 155.88/26.71 | | | | (65) all_58_0 = e0 & op(e3, e3) = e0
% 155.88/26.71 | | | |
% 155.88/26.71 | | | | REF_CLOSE: (8), (19), (58), (65) are inconsistent by sub-proof #165.
% 155.88/26.71 | | | |
% 155.88/26.71 | | | Case 2:
% 155.88/26.71 | | | |
% 155.88/26.71 | | | | (66) all_58_2 = e0 & op(e2, e3) = e0
% 155.88/26.71 | | | |
% 155.88/26.71 | | | | REF_CLOSE: (17), (48), (58), (66) are inconsistent by sub-proof #1433.
% 155.88/26.71 | | | |
% 155.88/26.71 | | | End of split
% 155.88/26.71 | | |
% 155.88/26.71 | | Case 2:
% 155.88/26.71 | | |
% 155.88/26.71 | | | (67) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 155.88/26.71 | | | e0)
% 155.88/26.71 | | |
% 155.88/26.71 | | | BETA: splitting (67) gives:
% 155.88/26.71 | | |
% 155.88/26.71 | | | Case 1:
% 155.88/26.71 | | | |
% 155.88/26.71 | | | | (68) all_58_6 = e0 & op(e1, e3) = e0
% 155.88/26.71 | | | |
% 155.88/26.71 | | | | ALPHA: (68) implies:
% 155.88/26.71 | | | | (69) all_58_6 = e0
% 155.88/26.71 | | | | (70) op(e1, e3) = e0
% 155.88/26.71 | | | |
% 155.88/26.71 | | | | BETA: splitting (12) gives:
% 155.88/26.71 | | | |
% 155.88/26.71 | | | | Case 1:
% 155.88/26.71 | | | | |
% 155.88/26.71 | | | | | (71) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 155.88/26.71 | | | | | e1) = e3)
% 155.88/26.71 | | | | |
% 155.88/26.71 | | | | | BETA: splitting (71) gives:
% 155.88/26.71 | | | | |
% 155.88/26.71 | | | | | Case 1:
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | (72) all_58_4 = e3 & op(e3, e1) = e3
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | ALPHA: (72) implies:
% 155.88/26.71 | | | | | | (73) all_58_4 = e3
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | COMBINE_EQS: (49), (73) imply:
% 155.88/26.71 | | | | | | (74) e3 = e0
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | REDUCE: (20), (74) imply:
% 155.88/26.71 | | | | | | (75) $false
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | CLOSE: (75) is inconsistent.
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | Case 2:
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | (76) all_58_5 = e3 & op(e2, e1) = e3
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | ALPHA: (76) implies:
% 155.88/26.71 | | | | | | (77) op(e2, e1) = e3
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | BETA: splitting (10) gives:
% 155.88/26.71 | | | | | |
% 155.88/26.71 | | | | | | Case 1:
% 155.88/26.71 | | | | | | |
% 155.88/26.71 | | | | | | | (78) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 155.88/26.71 | | | | | | | op(e2, e0) = e3)
% 155.88/26.71 | | | | | | |
% 155.88/26.71 | | | | | | | BETA: splitting (78) gives:
% 155.88/26.71 | | | | | | |
% 155.88/26.71 | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | (79) all_58_9 = e3 & op(e3, e0) = e3
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | ALPHA: (79) implies:
% 155.88/26.71 | | | | | | | | (80) all_58_9 = e3
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | REF_CLOSE: (28), (50), (80) are inconsistent by sub-proof #1461.
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | Case 2:
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | (81) all_58_10 = e3 & op(e2, e0) = e3
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | REF_CLOSE: (18), (59), (81) are inconsistent by sub-proof #1218.
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | End of split
% 155.88/26.71 | | | | | | |
% 155.88/26.71 | | | | | | Case 2:
% 155.88/26.71 | | | | | | |
% 155.88/26.71 | | | | | | | (82) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 155.88/26.71 | | | | | | | op(e0, e0) = e3)
% 155.88/26.71 | | | | | | |
% 155.88/26.71 | | | | | | | BETA: splitting (82) gives:
% 155.88/26.71 | | | | | | |
% 155.88/26.71 | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | (83) all_58_11 = e3 & op(e1, e0) = e3
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | ALPHA: (83) implies:
% 155.88/26.71 | | | | | | | | (84) op(e1, e0) = e3
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | BETA: splitting (7) gives:
% 155.88/26.71 | | | | | | | |
% 155.88/26.71 | | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | | |
% 155.88/26.71 | | | | | | | | | (85) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 155.88/26.71 | | | | | | | | | op(e2, e2) = e1)
% 155.88/26.71 | | | | | | | | |
% 155.88/26.71 | | | | | | | | | BETA: splitting (85) gives:
% 155.88/26.71 | | | | | | | | |
% 155.88/26.71 | | | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | (86) all_58_2 = e1 & op(e2, e3) = e1
% 155.88/26.71 | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | ALPHA: (86) implies:
% 155.88/26.71 | | | | | | | | | | (87) op(e2, e3) = e1
% 155.88/26.71 | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | BETA: splitting (53) gives:
% 155.88/26.71 | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | (88) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 155.88/26.71 | | | | | | | | | | | & op(e3, e2) = e3)
% 155.88/26.71 | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | BETA: splitting (88) gives:
% 155.88/26.71 | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | (89) all_58_0 = e3 & op(e3, e3) = e3
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | ALPHA: (89) implies:
% 155.88/26.71 | | | | | | | | | | | | (90) op(e3, e3) = e3
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_4_2, e0, e0, e0,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (23), (37) gives:
% 155.88/26.71 | | | | | | | | | | | | (91) all_4_2 = e0
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_52_11, e1, e1, e0,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (29), (40) gives:
% 155.88/26.71 | | | | | | | | | | | | (92) all_52_11 = e1
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_52_11, all_18_0, e1,
% 155.88/26.71 | | | | | | | | | | | | e0, simplifying with (27), (40) gives:
% 155.88/26.71 | | | | | | | | | | | | (93) all_52_11 = all_18_0
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_52_14, e3, e0, e1,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (55), (84) gives:
% 155.88/26.71 | | | | | | | | | | | | (94) all_52_14 = e3
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_52_2, e0, e3, e1,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (26), (70) gives:
% 155.88/26.71 | | | | | | | | | | | | (95) all_52_2 = e0
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_52_9, e3, e1, e2,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (16), (77) gives:
% 155.88/26.71 | | | | | | | | | | | | (96) all_52_9 = e3
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_52_1, e1, e3, e2,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (17), (87) gives:
% 155.88/26.71 | | | | | | | | | | | | (97) all_52_1 = e1
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_52_12, e1, e0, e3,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (3), (4) gives:
% 155.88/26.71 | | | | | | | | | | | | (98) all_52_12 = e1
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_52_8, e0, e1, e3,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (38), (51) gives:
% 155.88/26.71 | | | | | | | | | | | | (99) all_52_8 = e0
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | GROUND_INST: instantiating (58) with all_10_2, e3, e3, e3,
% 155.88/26.71 | | | | | | | | | | | | simplifying with (8), (90) gives:
% 155.88/26.71 | | | | | | | | | | | | (100) all_10_2 = e3
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | COMBINE_EQS: (92), (93) imply:
% 155.88/26.71 | | | | | | | | | | | | (101) all_18_0 = e1
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | SIMP: (101) implies:
% 155.88/26.71 | | | | | | | | | | | | (102) all_18_0 = e1
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | COMBINE_EQS: (39), (91) imply:
% 155.88/26.71 | | | | | | | | | | | | (103) all_56_15 = e0
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | REDUCE: (6), (98) imply:
% 155.88/26.71 | | | | | | | | | | | | (104) ~ (e2 = e1)
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | REDUCE: (52), (102) imply:
% 155.88/26.71 | | | | | | | | | | | | (105) ~ (e3 = e1)
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | REDUCE: (31), (91) imply:
% 155.88/26.71 | | | | | | | | | | | | (106) ~ (e1 = e0)
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | BETA: splitting (30) gives:
% 155.88/26.71 | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | (107) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.88/26.71 | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 155.88/26.71 | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.88/26.71 | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.88/26.71 | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.88/26.71 | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 155.88/26.71 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.88/26.71 | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 155.88/26.71 | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.88/26.71 | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.88/26.71 | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.88/26.71 | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.88/26.71 | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | BETA: splitting (107) gives:
% 155.88/26.71 | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | (108) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.88/26.71 | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 155.88/26.71 | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.88/26.71 | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.88/26.71 | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.88/26.71 | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 155.88/26.71 | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 155.88/26.71 | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | (109) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 155.88/26.71 | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 155.88/26.71 | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 155.88/26.71 | | | | | | | | | | | | | | | (110) op(e2, e3) = e3
% 155.88/26.71 | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | REF_CLOSE: (28), (58), (87), (110) are inconsistent by
% 155.88/26.71 | | | | | | | | | | | | | | | sub-proof #1494.
% 155.88/26.71 | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | Case 2:
% 155.88/26.71 | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | (111) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.88/26.71 | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 155.88/26.71 | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.88/26.71 | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 155.88/26.71 | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 155.88/26.71 | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | Case 1:
% 155.88/26.71 | | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | | (112) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 155.88/26.71 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 155.88/26.71 | | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 155.88/26.71 | | | | | | | | | | | | | | | | (113) op(e2, e3) = e2
% 155.88/26.71 | | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | | REF_CLOSE: (44), (58), (87), (113) are inconsistent by
% 155.88/26.71 | | | | | | | | | | | | | | | | sub-proof #1430.
% 155.88/26.71 | | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | Case 2:
% 155.88/26.71 | | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | | (114) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 155.88/26.71 | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 155.88/26.71 | | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 155.88/26.71 | | | | | | | | | | | | | | | | (115) op(e1, e3) = e3
% 155.88/26.71 | | | | | | | | | | | | | | | |
% 155.88/26.71 | | | | | | | | | | | | | | | | REF_CLOSE: (20), (58), (70), (115) are inconsistent by
% 155.88/26.71 | | | | | | | | | | | | | | | | sub-proof #114.
% 155.88/26.71 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | (116) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.88/26.72 | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 155.88/26.72 | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.88/26.72 | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.88/26.72 | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | (117) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 155.88/26.72 | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 155.88/26.72 | | | | | | | | | | | | | | | (118) op(e3, e1) = e1
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | REF_CLOSE: (38), (46), (58), (118) are inconsistent by
% 155.88/26.72 | | | | | | | | | | | | | | | sub-proof #1281.
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | (119) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 155.88/26.72 | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.88/26.72 | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | (120) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 155.88/26.72 | | | | | | | | | | | | | | | | (121) ~ (all_56_15 = e0)
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | REDUCE: (103), (121) imply:
% 155.88/26.72 | | | | | | | | | | | | | | | | (122) $false
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | (123) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 155.88/26.72 | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 155.88/26.72 | | | | | | | | | | | | | | | | (124) op(e3, e0) = e0
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (46), (58), (124) are inconsistent by
% 155.88/26.72 | | | | | | | | | | | | | | | | sub-proof #140.
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | (125) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 155.88/26.72 | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 155.88/26.72 | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.88/26.72 | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 155.88/26.72 | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 155.88/26.72 | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.88/26.72 | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 155.88/26.72 | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.88/26.72 | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.88/26.72 | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.88/26.72 | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | BETA: splitting (125) gives:
% 155.88/26.72 | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | (126) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 155.88/26.72 | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 155.88/26.72 | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 155.88/26.72 | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 155.88/26.72 | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | REF_CLOSE: (28), (34), (44), (58), (77), (103), (126) are
% 155.88/26.72 | | | | | | | | | | | | | | inconsistent by sub-proof #100.
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | (127) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.88/26.72 | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 155.88/26.72 | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.88/26.72 | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.88/26.72 | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | (128) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 155.88/26.72 | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 155.88/26.72 | | | | | | | | | | | | | | | (129) op(e0, e2) = e0
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | REF_CLOSE: (36), (54), (58), (129) are inconsistent by
% 155.88/26.72 | | | | | | | | | | | | | | | sub-proof #1532.
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | (130) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 155.88/26.72 | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.88/26.72 | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | (131) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 155.88/26.72 | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 155.88/26.72 | | | | | | | | | | | | | | | | (132) op(e1, e0) = e1
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | REF_CLOSE: (28), (58), (84), (132) are inconsistent by
% 155.88/26.72 | | | | | | | | | | | | | | | | sub-proof #1275.
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | (133) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 155.88/26.72 | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 155.88/26.72 | | | | | | | | | | | | | | | | (134) op(e0, e1) = e0
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | | REF_CLOSE: (29), (46), (58), (134) are inconsistent by
% 155.88/26.72 | | | | | | | | | | | | | | | | sub-proof #129.
% 155.88/26.72 | | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | (135) all_58_1 = e3 & op(e3, e2) = e3
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | ALPHA: (135) implies:
% 155.88/26.72 | | | | | | | | | | | | (136) op(e3, e2) = e3
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (13), (14), (20), (21), (22), (25),
% 155.88/26.72 | | | | | | | | | | | | (28), (32), (44), (46), (51), (57), (58), (59),
% 155.88/26.72 | | | | | | | | | | | | (136) are inconsistent by sub-proof #101.
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | (137) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 155.88/26.72 | | | | | | | | | | | & op(e3, e0) = e3)
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | BETA: splitting (137) gives:
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | (138) all_58_4 = e3 & op(e3, e1) = e3
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | ALPHA: (138) implies:
% 155.88/26.72 | | | | | | | | | | | | (139) all_58_4 = e3
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | REF_CLOSE: (20), (49), (139) are inconsistent by sub-proof
% 155.88/26.72 | | | | | | | | | | | | #1501.
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | (140) all_58_9 = e3 & op(e3, e0) = e3
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | ALPHA: (140) implies:
% 155.88/26.72 | | | | | | | | | | | | (141) all_58_9 = e3
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | REF_CLOSE: (5), (18), (28), (31), (37), (44), (58), (84),
% 155.88/26.72 | | | | | | | | | | | | (141) are inconsistent by sub-proof #246.
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | (142) all_58_3 = e1 & op(e2, e2) = e1
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | REF_CLOSE: (47), (56), (58), (142) are inconsistent by
% 155.88/26.72 | | | | | | | | | | sub-proof #1423.
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | |
% 155.88/26.72 | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | |
% 155.88/26.72 | | | | | | | | | (143) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 155.88/26.72 | | | | | | | | | op(e2, e0) = e1)
% 155.88/26.72 | | | | | | | | |
% 155.88/26.72 | | | | | | | | | BETA: splitting (143) gives:
% 155.88/26.72 | | | | | | | | |
% 155.88/26.72 | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | (144) all_58_5 = e1 & op(e2, e1) = e1
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | ALPHA: (144) implies:
% 155.88/26.72 | | | | | | | | | | (145) op(e2, e1) = e1
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | REF_CLOSE: (28), (58), (77), (145) are inconsistent by
% 155.88/26.72 | | | | | | | | | | sub-proof #352.
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | (146) all_58_10 = e1 & op(e2, e0) = e1
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | ALPHA: (146) implies:
% 155.88/26.72 | | | | | | | | | | (147) all_58_10 = e1
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | COMBINE_EQS: (18), (147) imply:
% 155.88/26.72 | | | | | | | | | | (148) e2 = e1
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | COMBINE_EQS: (2), (148) imply:
% 155.88/26.72 | | | | | | | | | | (149) all_58_12 = e1
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | BETA: splitting (41) gives:
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | (150) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 155.88/26.72 | | | | | | | | | | | & op(e2, e3) = e2)
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | REF_CLOSE: (7), (8), (17), (18), (20), (25), (28), (35),
% 155.88/26.72 | | | | | | | | | | | (42), (43), (44), (46), (47), (56), (58), (59),
% 155.88/26.72 | | | | | | | | | | | (150) are inconsistent by sub-proof #103.
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | (151) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 155.88/26.72 | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | BETA: splitting (151) gives:
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | Case 1:
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | (152) all_58_6 = e2 & op(e1, e3) = e2
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | ALPHA: (152) implies:
% 155.88/26.72 | | | | | | | | | | | | (153) all_58_6 = e2
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | REF_CLOSE: (25), (69), (153) are inconsistent by sub-proof
% 155.88/26.72 | | | | | | | | | | | | #1514.
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | (154) all_58_12 = e2 & op(e0, e3) = e2
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | | REF_CLOSE: (2), (44), (149) are inconsistent by sub-proof
% 155.88/26.72 | | | | | | | | | | | | #1486.
% 155.88/26.72 | | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | | |
% 155.88/26.72 | | | | | | | | | End of split
% 155.88/26.72 | | | | | | | | |
% 155.88/26.72 | | | | | | | | End of split
% 155.88/26.72 | | | | | | | |
% 155.88/26.72 | | | | | | | Case 2:
% 155.88/26.72 | | | | | | | |
% 155.88/26.72 | | | | | | | | (155) all_58_15 = e3 & op(e0, e0) = e3
% 155.88/26.72 | | | | | | | |
% 155.88/26.72 | | | | | | | | REF_CLOSE: (1), (20), (155) are inconsistent by sub-proof #1357.
% 155.88/26.72 | | | | | | | |
% 155.88/26.72 | | | | | | | End of split
% 155.88/26.72 | | | | | | |
% 155.88/26.72 | | | | | | End of split
% 155.88/26.72 | | | | | |
% 155.88/26.72 | | | | | End of split
% 155.88/26.72 | | | | |
% 155.88/26.72 | | | | Case 2:
% 155.88/26.72 | | | | |
% 155.88/26.72 | | | | | (156) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 155.88/26.72 | | | | | e1) = e3)
% 155.88/26.72 | | | | |
% 155.88/26.72 | | | | | BETA: splitting (156) gives:
% 155.88/26.72 | | | | |
% 155.88/26.72 | | | | | Case 1:
% 155.88/26.72 | | | | | |
% 155.88/26.72 | | | | | | (157) all_58_8 = e3 & op(e1, e1) = e3
% 155.88/26.72 | | | | | |
% 155.88/26.72 | | | | | | REF_CLOSE: (45), (59), (157) are inconsistent by sub-proof #1069.
% 155.88/26.72 | | | | | |
% 155.88/26.72 | | | | | Case 2:
% 155.88/26.72 | | | | | |
% 155.88/26.72 | | | | | | (158) all_58_14 = e3 & op(e0, e1) = e3
% 155.88/26.72 | | | | | |
% 155.88/26.72 | | | | | | ALPHA: (158) implies:
% 155.88/26.72 | | | | | | (159) all_58_14 = e3
% 155.88/26.72 | | | | | |
% 155.88/26.72 | | | | | | REF_CLOSE: (9), (15), (24), (28), (31), (37), (44), (58), (59),
% 155.88/26.72 | | | | | | (63), (159) are inconsistent by sub-proof #202.
% 155.88/26.72 | | | | | |
% 155.88/26.72 | | | | | End of split
% 155.88/26.72 | | | | |
% 155.88/26.72 | | | | End of split
% 155.88/26.72 | | | |
% 155.88/26.72 | | | Case 2:
% 155.88/26.72 | | | |
% 155.88/26.72 | | | | (160) all_58_12 = e0 & op(e0, e3) = e0
% 155.88/26.72 | | | |
% 155.88/26.72 | | | | REF_CLOSE: (2), (25), (160) are inconsistent by sub-proof #1369.
% 155.88/26.72 | | | |
% 155.88/26.72 | | | End of split
% 155.88/26.72 | | |
% 155.88/26.72 | | End of split
% 155.88/26.72 | |
% 155.88/26.72 | End of split
% 155.88/26.72 |
% 155.88/26.72 End of proof
% 155.88/26.72
% 155.88/26.72 Sub-proof #100 shows that the following formulas are inconsistent:
% 155.88/26.72 ----------------------------------------------------------------
% 155.88/26.72 (1) op(e2, e1) = e3
% 155.88/26.72 (2) all_56_15 = e0
% 155.88/26.72 (3) ~ (e3 = e1)
% 155.88/26.72 (4) op(e1, e2) = e1
% 155.88/26.72 (5) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.88/26.72 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2)
% 155.88/26.72 & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2
% 155.88/26.72 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.88/26.72 (6) ~ (e2 = e1)
% 155.88/26.72 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.72
% 155.88/26.72 Begin of proof
% 155.88/26.72 |
% 155.88/26.72 | BETA: splitting (5) gives:
% 155.88/26.72 |
% 155.88/26.72 | Case 1:
% 155.88/26.72 | |
% 155.88/26.72 | | (8) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2
% 155.88/26.72 | | & op(e1, e2) = e2
% 155.88/26.72 | |
% 155.88/26.72 | | ALPHA: (8) implies:
% 155.88/26.72 | | (9) op(e1, e2) = e2
% 155.88/26.72 | |
% 155.88/26.72 | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #1088.
% 155.88/26.72 | |
% 155.88/26.72 | Case 2:
% 155.88/26.72 | |
% 155.88/26.72 | | (10) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) =
% 155.88/26.72 | | e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 155.88/26.72 | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.88/26.72 | |
% 155.88/26.72 | | REF_CLOSE: (1), (2), (3), (7), (10) are inconsistent by sub-proof #340.
% 155.88/26.72 | |
% 155.88/26.72 | End of split
% 155.88/26.72 |
% 155.88/26.72 End of proof
% 155.88/26.72
% 155.88/26.72 Sub-proof #101 shows that the following formulas are inconsistent:
% 155.88/26.72 ----------------------------------------------------------------
% 155.88/26.72 (1) all_58_12 = e2
% 155.88/26.72 (2) op(e3, e0) = all_52_12
% 155.88/26.72 (3) ~ (all_52_12 = e2)
% 155.88/26.72 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 155.88/26.72 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 155.88/26.72 (5) op(e3, e2) = all_52_4
% 155.88/26.72 (6) ~ (e3 = e0)
% 155.88/26.72 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.88/26.72 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.88/26.72 (8) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 155.88/26.72 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 155.88/26.72 (9) ~ (e2 = e0)
% 155.88/26.72 (10) ~ (e3 = e1)
% 155.88/26.72 (11) ~ (all_52_8 = e2)
% 155.88/26.72 (12) op(e3, e2) = e3
% 155.88/26.72 (13) ~ (e2 = e1)
% 155.88/26.72 (14) ~ (e1 = e0)
% 155.88/26.72 (15) op(e3, e1) = all_52_8
% 155.88/26.72 (16) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.88/26.72 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.88/26.72 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.72 (18) ~ (e3 = e2)
% 155.88/26.72
% 155.88/26.72 Begin of proof
% 155.88/26.72 |
% 155.88/26.72 | BETA: splitting (8) gives:
% 155.88/26.72 |
% 155.88/26.72 | Case 1:
% 155.88/26.72 | |
% 155.88/26.72 | | (19) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 155.88/26.72 | | e2)
% 155.88/26.72 | |
% 155.88/26.72 | | BETA: splitting (19) gives:
% 155.88/26.72 | |
% 155.88/26.72 | | Case 1:
% 155.88/26.72 | | |
% 155.88/26.72 | | | (20) all_58_0 = e2 & op(e3, e3) = e2
% 155.88/26.72 | | |
% 155.88/26.72 | | | ALPHA: (20) implies:
% 155.88/26.72 | | | (21) all_58_0 = e2
% 155.88/26.72 | | |
% 155.88/26.72 | | | REF_CLOSE: (1), (4), (6), (7), (9), (10), (13), (14), (16), (18), (21) are
% 155.88/26.72 | | | inconsistent by sub-proof #999.
% 155.88/26.72 | | |
% 155.88/26.72 | | Case 2:
% 155.88/26.72 | | |
% 155.88/26.72 | | | (22) all_58_1 = e2 & op(e3, e2) = e2
% 155.88/26.72 | | |
% 155.88/26.72 | | | ALPHA: (22) implies:
% 155.88/26.72 | | | (23) op(e3, e2) = e2
% 155.88/26.72 | | |
% 155.88/26.72 | | | REF_CLOSE: (5), (12), (17), (18), (23) are inconsistent by sub-proof
% 155.88/26.72 | | | #1094.
% 155.88/26.72 | | |
% 155.88/26.72 | | End of split
% 155.88/26.72 | |
% 155.88/26.72 | Case 2:
% 155.88/26.72 | |
% 155.88/26.72 | | (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 155.88/26.72 | | e2)
% 155.88/26.72 | |
% 155.88/26.72 | | REF_CLOSE: (2), (3), (11), (15), (17), (24) are inconsistent by sub-proof
% 155.88/26.72 | | #868.
% 155.88/26.72 | |
% 155.88/26.72 | End of split
% 155.88/26.72 |
% 155.88/26.72 End of proof
% 155.88/26.72
% 155.88/26.72 Sub-proof #102 shows that the following formulas are inconsistent:
% 155.88/26.72 ----------------------------------------------------------------
% 155.88/26.72 (1) all_58_12 = e2
% 155.88/26.72 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 155.88/26.72 (3) ~ (e2 = e1)
% 155.88/26.72 (4) ~ (all_52_7 = e1)
% 155.88/26.72 (5) op(e0, e2) = all_52_7
% 155.88/26.72 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.72
% 155.88/26.72 Begin of proof
% 155.88/26.72 |
% 155.88/26.72 | BETA: splitting (2) gives:
% 155.88/26.72 |
% 155.88/26.72 | Case 1:
% 155.88/26.72 | |
% 155.88/26.72 | | (7) all_58_12 = e1 & op(e0, e3) = e1
% 155.88/26.72 | |
% 155.88/26.72 | | ALPHA: (7) implies:
% 155.88/26.72 | | (8) all_58_12 = e1
% 155.88/26.72 | |
% 155.88/26.72 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1486.
% 155.88/26.72 | |
% 155.88/26.72 | Case 2:
% 155.88/26.72 | |
% 155.88/26.72 | | (9) all_58_13 = e1 & op(e0, e2) = e1
% 155.88/26.72 | |
% 155.88/26.72 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #192.
% 155.88/26.72 | |
% 155.88/26.72 | End of split
% 155.88/26.72 |
% 155.88/26.72 End of proof
% 155.88/26.72
% 155.88/26.72 Sub-proof #103 shows that the following formulas are inconsistent:
% 155.88/26.72 ----------------------------------------------------------------
% 155.88/26.72 (1) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 155.88/26.72 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 155.88/26.72 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 155.88/26.72 (3) op(e3, e3) = all_10_2
% 155.88/26.72 (4) op(e2, e3) = all_52_1
% 155.88/26.72 (5) all_58_10 = e2
% 155.88/26.72 (6) ~ (e3 = e0)
% 155.88/26.72 (7) ~ (e2 = e0)
% 155.88/26.72 (8) ~ (e3 = e1)
% 155.88/26.72 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 155.88/26.72 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 155.88/26.72 (10) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 155.88/26.72 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 155.88/26.72 (11) ~ (all_10_2 = e2)
% 155.88/26.72 (12) ~ (e2 = e1)
% 155.88/26.72 (13) ~ (e1 = e0)
% 155.88/26.72 (14) ~ (all_8_2 = e1)
% 155.88/26.72 (15) op(e2, e2) = all_8_2
% 155.88/26.72 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.72 (17) ~ (e3 = e2)
% 155.88/26.72
% 155.88/26.72 Begin of proof
% 155.88/26.72 |
% 155.88/26.72 | BETA: splitting (1) gives:
% 155.88/26.72 |
% 155.88/26.72 | Case 1:
% 155.88/26.72 | |
% 155.88/26.72 | | (18) all_58_0 = e2 & op(e3, e3) = e2
% 155.88/26.72 | |
% 155.88/26.72 | | REF_CLOSE: (3), (11), (16), (18) are inconsistent by sub-proof #1523.
% 155.88/26.72 | |
% 155.88/26.72 | Case 2:
% 155.88/26.72 | |
% 155.88/26.72 | | (19) all_58_2 = e2 & op(e2, e3) = e2
% 155.88/26.72 | |
% 155.88/26.72 | | ALPHA: (19) implies:
% 155.88/26.72 | | (20) op(e2, e3) = e2
% 155.88/26.72 | |
% 155.88/26.72 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 155.88/26.72 | | (16), (17), (20) are inconsistent by sub-proof #905.
% 155.88/26.72 | |
% 155.88/26.72 | End of split
% 155.88/26.72 |
% 155.88/26.72 End of proof
% 155.88/26.72
% 155.88/26.72 Sub-proof #104 shows that the following formulas are inconsistent:
% 155.88/26.72 ----------------------------------------------------------------
% 155.88/26.72 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.88/26.72 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.88/26.72 (2) ~ (e3 = e0)
% 155.88/26.72 (3) ~ (e2 = e0)
% 155.88/26.72 (4) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 155.88/26.72 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.88/26.72 (5) ~ (e3 = e1)
% 155.88/26.72 (6) ~ (all_4_2 = e1)
% 155.88/26.72 (7) all_58_7 = e1
% 155.88/26.72 (8) op(e0, e0) = all_4_2
% 155.88/26.72 (9) all_58_8 = e2
% 155.88/26.72 (10) ~ (e1 = e0)
% 155.88/26.72 (11) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.88/26.72 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.72 (13) ~ (e3 = e2)
% 155.88/26.72
% 155.88/26.72 Begin of proof
% 155.88/26.72 |
% 155.88/26.72 | BETA: splitting (11) gives:
% 155.88/26.72 |
% 155.88/26.72 | Case 1:
% 155.88/26.72 | |
% 155.88/26.72 | | (14) all_58_11 = e1 & op(e1, e0) = e1
% 155.88/26.72 | |
% 155.88/26.72 | | ALPHA: (14) implies:
% 155.88/26.72 | | (15) all_58_11 = e1
% 155.88/26.72 | | (16) op(e1, e0) = e1
% 155.88/26.72 | |
% 155.88/26.73 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (12), (13), (15), (16)
% 155.88/26.73 | | are inconsistent by sub-proof #105.
% 155.88/26.73 | |
% 155.88/26.73 | Case 2:
% 155.88/26.73 | |
% 155.88/26.73 | | (17) all_58_15 = e1 & op(e0, e0) = e1
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (6), (8), (12), (17) are inconsistent by sub-proof #1418.
% 155.88/26.73 | |
% 155.88/26.73 | End of split
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #105 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) all_58_11 = e1
% 155.88/26.73 (2) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.88/26.73 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.88/26.73 (3) ~ (e3 = e0)
% 155.88/26.73 (4) ~ (e2 = e0)
% 155.88/26.73 (5) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 155.88/26.73 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.88/26.73 (6) ~ (e3 = e1)
% 155.88/26.73 (7) all_58_7 = e1
% 155.88/26.73 (8) op(e1, e0) = e1
% 155.88/26.73 (9) all_58_8 = e2
% 155.88/26.73 (10) ~ (e1 = e0)
% 155.88/26.73 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (12) ~ (e3 = e2)
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | BETA: splitting (5) gives:
% 155.88/26.73 |
% 155.88/26.73 | Case 1:
% 155.88/26.73 | |
% 155.88/26.73 | | (13) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 155.88/26.73 | | e0)
% 155.88/26.73 | |
% 155.88/26.73 | | BETA: splitting (13) gives:
% 155.88/26.73 | |
% 155.88/26.73 | | Case 1:
% 155.88/26.73 | | |
% 155.88/26.73 | | | (14) all_58_6 = e0 & op(e1, e3) = e0
% 155.88/26.73 | | |
% 155.88/26.73 | | | ALPHA: (14) implies:
% 155.88/26.73 | | | (15) all_58_6 = e0
% 155.88/26.73 | | |
% 155.88/26.73 | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (11), (12), (15) are inconsistent
% 155.88/26.73 | | | by sub-proof #106.
% 155.88/26.73 | | |
% 155.88/26.73 | | Case 2:
% 155.88/26.73 | | |
% 155.88/26.73 | | | (16) all_58_7 = e0 & op(e1, e2) = e0
% 155.88/26.73 | | |
% 155.88/26.73 | | | REF_CLOSE: (7), (10), (16) are inconsistent by sub-proof #992.
% 155.88/26.73 | | |
% 155.88/26.73 | | End of split
% 155.88/26.73 | |
% 155.88/26.73 | Case 2:
% 155.88/26.73 | |
% 155.88/26.73 | | (17) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 155.88/26.73 | | e0)
% 155.88/26.73 | |
% 155.88/26.73 | | BETA: splitting (17) gives:
% 155.88/26.73 | |
% 155.88/26.73 | | Case 1:
% 155.88/26.73 | | |
% 155.88/26.73 | | | (18) all_58_8 = e0 & op(e1, e1) = e0
% 155.88/26.73 | | |
% 155.88/26.73 | | | REF_CLOSE: (4), (9), (18) are inconsistent by sub-proof #1071.
% 155.88/26.73 | | |
% 155.88/26.73 | | Case 2:
% 155.88/26.73 | | |
% 155.88/26.73 | | | (19) all_58_11 = e0 & op(e1, e0) = e0
% 155.88/26.73 | | |
% 155.88/26.73 | | | ALPHA: (19) implies:
% 155.88/26.73 | | | (20) all_58_11 = e0
% 155.88/26.73 | | |
% 155.88/26.73 | | | REF_CLOSE: (1), (10), (20) are inconsistent by sub-proof #1297.
% 155.88/26.73 | | |
% 155.88/26.73 | | End of split
% 155.88/26.73 | |
% 155.88/26.73 | End of split
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #106 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.88/26.73 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.88/26.73 (2) ~ (e3 = e0)
% 155.88/26.73 (3) all_58_6 = e0
% 155.88/26.73 (4) ~ (e3 = e1)
% 155.88/26.73 (5) all_58_7 = e1
% 155.88/26.73 (6) op(e1, e0) = e1
% 155.88/26.73 (7) all_58_8 = e2
% 155.88/26.73 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (9) ~ (e3 = e2)
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | BETA: splitting (1) gives:
% 155.88/26.73 |
% 155.88/26.73 | Case 1:
% 155.88/26.73 | |
% 155.88/26.73 | | (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 155.88/26.73 | | e3)
% 155.88/26.73 | |
% 155.88/26.73 | | BETA: splitting (10) gives:
% 155.88/26.73 | |
% 155.88/26.73 | | Case 1:
% 155.88/26.73 | | |
% 155.88/26.73 | | | (11) all_58_6 = e3 & op(e1, e3) = e3
% 155.88/26.73 | | |
% 155.88/26.73 | | | ALPHA: (11) implies:
% 155.88/26.73 | | | (12) all_58_6 = e3
% 155.88/26.73 | | |
% 155.88/26.73 | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #1321.
% 155.88/26.73 | | |
% 155.88/26.73 | | Case 2:
% 155.88/26.73 | | |
% 155.88/26.73 | | | (13) all_58_7 = e3 & op(e1, e2) = e3
% 155.88/26.73 | | |
% 155.88/26.73 | | | ALPHA: (13) implies:
% 155.88/26.73 | | | (14) all_58_7 = e3
% 155.88/26.73 | | |
% 155.88/26.73 | | | REF_CLOSE: (4), (5), (14) are inconsistent by sub-proof #1330.
% 155.88/26.73 | | |
% 155.88/26.73 | | End of split
% 155.88/26.73 | |
% 155.88/26.73 | Case 2:
% 155.88/26.73 | |
% 155.88/26.73 | | (15) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 155.88/26.73 | | e3)
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (4), (6), (7), (8), (9), (15) are inconsistent by sub-proof #107.
% 155.88/26.73 | |
% 155.88/26.73 | End of split
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #107 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.88/26.73 (2) ~ (e3 = e1)
% 155.88/26.73 (3) op(e1, e0) = e1
% 155.88/26.73 (4) all_58_8 = e2
% 155.88/26.73 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (6) ~ (e3 = e2)
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | BETA: splitting (1) gives:
% 155.88/26.73 |
% 155.88/26.73 | Case 1:
% 155.88/26.73 | |
% 155.88/26.73 | | (7) all_58_8 = e3 & op(e1, e1) = e3
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #1069.
% 155.88/26.73 | |
% 155.88/26.73 | Case 2:
% 155.88/26.73 | |
% 155.88/26.73 | | (8) all_58_11 = e3 & op(e1, e0) = e3
% 155.88/26.73 | |
% 155.88/26.73 | | ALPHA: (8) implies:
% 155.88/26.73 | | (9) op(e1, e0) = e3
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1275.
% 155.88/26.73 | |
% 155.88/26.73 | End of split
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #108 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (2) op(e1, e0) = all_52_14
% 155.88/26.73 (3) op(e1, e0) = e1
% 155.88/26.73 (4) ~ (all_52_14 = e1)
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | GROUND_INST: instantiating (1) with all_52_14, e1, e0, e1, simplifying with
% 155.88/26.73 | (2), (3) gives:
% 155.88/26.73 | (5) all_52_14 = e1
% 155.88/26.73 |
% 155.88/26.73 | REDUCE: (4), (5) imply:
% 155.88/26.73 | (6) $false
% 155.88/26.73 |
% 155.88/26.73 | CLOSE: (6) is inconsistent.
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #109 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) ~ (all_8_2 = e0)
% 155.88/26.73 (2) op(e2, e0) = all_52_13
% 155.88/26.73 (3) ~ (all_52_6 = all_8_2)
% 155.88/26.73 (4) all_56_13 = e2
% 155.88/26.73 (5) op(e1, e2) = all_52_6
% 155.88/26.73 (6) ~ (all_52_13 = e2)
% 155.88/26.73 (7) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.88/26.73 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2)
% 155.88/26.73 & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2
% 155.88/26.73 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.88/26.73 (8) ~ (all_8_2 = e1)
% 155.88/26.73 (9) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.88/26.73 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (11) all_54_5 = all_8_2
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | BETA: splitting (7) gives:
% 155.88/26.73 |
% 155.88/26.73 | Case 1:
% 155.88/26.73 | |
% 155.88/26.73 | | (12) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) =
% 155.88/26.73 | | e2 & op(e1, e2) = e2
% 155.88/26.73 | |
% 155.88/26.73 | | ALPHA: (12) implies:
% 155.88/26.73 | | (13) op(e1, e2) = e2
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (11), (13) are inconsistent by
% 155.88/26.73 | | sub-proof #1173.
% 155.88/26.73 | |
% 155.88/26.73 | Case 2:
% 155.88/26.73 | |
% 155.88/26.73 | | (14) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) =
% 155.88/26.73 | | e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 155.88/26.73 | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (2), (4), (6), (10), (14) are inconsistent by sub-proof #1534.
% 155.88/26.73 | |
% 155.88/26.73 | End of split
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #110 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 155.88/26.73 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0)
% 155.88/26.73 & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 &
% 155.88/26.73 ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.88/26.73 (2) ~ (all_4_2 = e2)
% 155.88/26.73 (3) ~ (e2 = e0)
% 155.88/26.73 (4) op(e1, e3) = all_52_2
% 155.88/26.73 (5) ~ (all_4_2 = e1)
% 155.88/26.73 (6) all_56_15 = all_4_2
% 155.88/26.73 (7) op(e3, e0) = e2
% 155.88/26.73 (8) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 155.88/26.73 (9) ~ (all_52_2 = e1)
% 155.88/26.73 (10) all_54_15 = all_4_2
% 155.88/26.73 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (12) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | BETA: splitting (1) gives:
% 155.88/26.73 |
% 155.88/26.73 | Case 1:
% 155.88/26.73 | |
% 155.88/26.73 | | (13) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) =
% 155.88/26.73 | | e1 & op(e1, e3) = e1
% 155.88/26.73 | |
% 155.88/26.73 | | ALPHA: (13) implies:
% 155.88/26.73 | | (14) op(e1, e3) = e1
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (4), (9), (11), (14) are inconsistent by sub-proof #1412.
% 155.88/26.73 | |
% 155.88/26.73 | Case 2:
% 155.88/26.73 | |
% 155.88/26.73 | | (15) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 155.88/26.73 | | e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 155.88/26.73 | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 155.88/26.73 | |
% 155.88/26.73 | | BETA: splitting (15) gives:
% 155.88/26.73 | |
% 155.88/26.73 | | Case 1:
% 155.88/26.73 | | |
% 155.88/26.73 | | | (16) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 155.88/26.73 | | | e3 & op(e0, e3) = e3
% 155.88/26.73 | | |
% 155.88/26.73 | | | REF_CLOSE: (2), (5), (6), (8), (10), (12), (16) are inconsistent by
% 155.88/26.73 | | | sub-proof #1294.
% 155.88/26.73 | | |
% 155.88/26.73 | | Case 2:
% 155.88/26.73 | | |
% 155.88/26.73 | | | (17) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 155.88/26.73 | | | e0 & op(e0, e3) = e0
% 155.88/26.73 | | |
% 155.88/26.73 | | | ALPHA: (17) implies:
% 155.88/26.73 | | | (18) op(e3, e0) = e0
% 155.88/26.73 | | |
% 155.88/26.73 | | | REF_CLOSE: (3), (7), (11), (18) are inconsistent by sub-proof #1500.
% 155.88/26.73 | | |
% 155.88/26.73 | | End of split
% 155.88/26.73 | |
% 155.88/26.73 | End of split
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #111 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) ~ (all_52_14 = e2)
% 155.88/26.73 (2) ~ (all_52_14 = e0)
% 155.88/26.73 (3) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.88/26.73 (4) op(e1, e0) = e0
% 155.88/26.73 (5) ~ (all_52_14 = e1)
% 155.88/26.73 (6) op(e1, e0) = all_52_14
% 155.88/26.73 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (8) all_54_11 = all_52_14
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | BETA: splitting (3) gives:
% 155.88/26.73 |
% 155.88/26.73 | Case 1:
% 155.88/26.73 | |
% 155.88/26.73 | | (9) all_54_11 = e3
% 155.88/26.73 | |
% 155.88/26.73 | | COMBINE_EQS: (8), (9) imply:
% 155.88/26.73 | | (10) all_52_14 = e3
% 155.88/26.73 | |
% 155.88/26.73 | | SIMP: (10) implies:
% 155.88/26.73 | | (11) all_52_14 = e3
% 155.88/26.73 | |
% 155.88/26.73 | | REDUCE: (2), (11) imply:
% 155.88/26.73 | | (12) ~ (e3 = e0)
% 155.88/26.73 | |
% 155.88/26.73 | | REDUCE: (6), (11) imply:
% 155.88/26.73 | | (13) op(e1, e0) = e3
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (4), (7), (12), (13) are inconsistent by sub-proof #118.
% 155.88/26.73 | |
% 155.88/26.73 | Case 2:
% 155.88/26.73 | |
% 155.88/26.73 | | (14) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (1), (2), (5), (8), (14) are inconsistent by sub-proof #1226.
% 155.88/26.73 | |
% 155.88/26.73 | End of split
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #112 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) all_58_8 = e3 & op(e1, e1) = e3
% 155.88/26.73 (2) all_58_8 = e2
% 155.88/26.73 (3) ~ (e3 = e2)
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | ALPHA: (1) implies:
% 155.88/26.73 | (4) all_58_8 = e3
% 155.88/26.73 |
% 155.88/26.73 | COMBINE_EQS: (2), (4) imply:
% 155.88/26.73 | (5) e3 = e2
% 155.88/26.73 |
% 155.88/26.73 | SIMP: (5) implies:
% 155.88/26.73 | (6) e3 = e2
% 155.88/26.73 |
% 155.88/26.73 | REDUCE: (3), (6) imply:
% 155.88/26.73 | (7) $false
% 155.88/26.73 |
% 155.88/26.73 | CLOSE: (7) is inconsistent.
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #113 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) ~ (all_52_1 = all_8_2)
% 155.88/26.73 (2) op(e2, e1) = all_52_9
% 155.88/26.73 (3) op(e2, e3) = all_52_1
% 155.88/26.73 (4) ~ (all_8_2 = e0)
% 155.88/26.73 (5) all_58_8 = e0 & op(e1, e1) = e0
% 155.88/26.73 (6) op(e2, e0) = all_52_13
% 155.88/26.73 (7) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 155.88/26.73 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 155.88/26.73 (8) all_58_8 = e2
% 155.88/26.73 (9) ~ (all_8_2 = e1)
% 155.88/26.73 (10) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 155.88/26.73 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (12) all_54_5 = all_8_2
% 155.88/26.73 (13) ~ (all_52_9 = all_8_2)
% 155.88/26.73 (14) ~ (all_52_13 = all_8_2)
% 155.88/26.73 (15) all_58_3 = e2
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | ALPHA: (5) implies:
% 155.88/26.73 | (16) all_58_8 = e0
% 155.88/26.73 |
% 155.88/26.73 | COMBINE_EQS: (8), (16) imply:
% 155.88/26.73 | (17) e2 = e0
% 155.88/26.73 |
% 155.88/26.73 | SIMP: (17) implies:
% 155.88/26.73 | (18) e2 = e0
% 155.88/26.73 |
% 155.88/26.73 | COMBINE_EQS: (15), (18) imply:
% 155.88/26.73 | (19) all_58_3 = e0
% 155.88/26.73 |
% 155.88/26.73 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 155.88/26.73 | (19) are inconsistent by sub-proof #324.
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #114 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (2) op(e1, e3) = e3
% 155.88/26.73 (3) op(e1, e3) = e0
% 155.88/26.73 (4) ~ (e3 = e0)
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | GROUND_INST: instantiating (1) with e0, e3, e3, e1, simplifying with (2), (3)
% 155.88/26.73 | gives:
% 155.88/26.73 | (5) e3 = e0
% 155.88/26.73 |
% 155.88/26.73 | REDUCE: (4), (5) imply:
% 155.88/26.73 | (6) $false
% 155.88/26.73 |
% 155.88/26.73 | CLOSE: (6) is inconsistent.
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #115 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.73 (1) all_58_12 = e2
% 155.88/26.73 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 155.88/26.73 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 155.88/26.73 (3) op(e3, e2) = all_52_4
% 155.88/26.73 (4) ~ (all_52_4 = e2)
% 155.88/26.73 (5) ~ (e3 = e0)
% 155.88/26.73 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.88/26.73 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.88/26.73 (7) ~ (e2 = e0)
% 155.88/26.73 (8) ~ (e3 = e1)
% 155.88/26.73 (9) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 155.88/26.73 (10) ~ (e2 = e1)
% 155.88/26.73 (11) ~ (e1 = e0)
% 155.88/26.73 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 155.88/26.73 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 155.88/26.73 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.73 (14) ~ (e3 = e2)
% 155.88/26.73
% 155.88/26.73 Begin of proof
% 155.88/26.73 |
% 155.88/26.73 | BETA: splitting (9) gives:
% 155.88/26.73 |
% 155.88/26.73 | Case 1:
% 155.88/26.73 | |
% 155.88/26.73 | | (15) all_58_0 = e2 & op(e3, e3) = e2
% 155.88/26.73 | |
% 155.88/26.73 | | ALPHA: (15) implies:
% 155.88/26.73 | | (16) all_58_0 = e2
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (14), (16) are
% 155.88/26.73 | | inconsistent by sub-proof #999.
% 155.88/26.73 | |
% 155.88/26.73 | Case 2:
% 155.88/26.73 | |
% 155.88/26.73 | | (17) all_58_1 = e2 & op(e3, e2) = e2
% 155.88/26.73 | |
% 155.88/26.73 | | ALPHA: (17) implies:
% 155.88/26.73 | | (18) op(e3, e2) = e2
% 155.88/26.73 | |
% 155.88/26.73 | | REF_CLOSE: (3), (4), (13), (18) are inconsistent by sub-proof #1539.
% 155.88/26.73 | |
% 155.88/26.73 | End of split
% 155.88/26.73 |
% 155.88/26.73 End of proof
% 155.88/26.73
% 155.88/26.73 Sub-proof #116 shows that the following formulas are inconsistent:
% 155.88/26.73 ----------------------------------------------------------------
% 155.88/26.74 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 155.88/26.74 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 155.88/26.74 (2) all_58_6 = e2
% 155.88/26.74 (3) ~ (e3 = e0)
% 155.88/26.74 (4) ~ (e2 = e0)
% 155.88/26.74 (5) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 155.88/26.74 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.88/26.74 (6) ~ (e3 = e1)
% 155.88/26.74 (7) all_58_7 = e1
% 155.88/26.74 (8) all_58_8 = e2
% 155.88/26.74 (9) ~ (e1 = e0)
% 155.88/26.74 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74 (11) ~ (e3 = e2)
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | BETA: splitting (1) gives:
% 155.88/26.74 |
% 155.88/26.74 | Case 1:
% 155.88/26.74 | |
% 155.88/26.74 | | (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 155.88/26.74 | | e3)
% 155.88/26.74 | |
% 155.88/26.74 | | BETA: splitting (12) gives:
% 155.88/26.74 | |
% 155.88/26.74 | | Case 1:
% 155.88/26.74 | | |
% 155.88/26.74 | | | (13) all_58_6 = e3 & op(e1, e3) = e3
% 155.88/26.74 | | |
% 155.88/26.74 | | | ALPHA: (13) implies:
% 155.88/26.74 | | | (14) all_58_6 = e3
% 155.88/26.74 | | |
% 155.88/26.74 | | | REF_CLOSE: (2), (11), (14) are inconsistent by sub-proof #1376.
% 155.88/26.74 | | |
% 155.88/26.74 | | Case 2:
% 155.88/26.74 | | |
% 155.88/26.74 | | | (15) all_58_7 = e3 & op(e1, e2) = e3
% 155.88/26.74 | | |
% 155.88/26.74 | | | ALPHA: (15) implies:
% 155.88/26.74 | | | (16) all_58_7 = e3
% 155.88/26.74 | | |
% 155.88/26.74 | | | REF_CLOSE: (6), (7), (16) are inconsistent by sub-proof #1330.
% 155.88/26.74 | | |
% 155.88/26.74 | | End of split
% 155.88/26.74 | |
% 155.88/26.74 | Case 2:
% 155.88/26.74 | |
% 155.88/26.74 | | (17) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 155.88/26.74 | | e3)
% 155.88/26.74 | |
% 155.88/26.74 | | BETA: splitting (17) gives:
% 155.88/26.74 | |
% 155.88/26.74 | | Case 1:
% 155.88/26.74 | | |
% 155.88/26.74 | | | (18) all_58_8 = e3 & op(e1, e1) = e3
% 155.88/26.74 | | |
% 155.88/26.74 | | | REF_CLOSE: (8), (11), (18) are inconsistent by sub-proof #1069.
% 155.88/26.74 | | |
% 155.88/26.74 | | Case 2:
% 155.88/26.74 | | |
% 155.88/26.74 | | | (19) all_58_11 = e3 & op(e1, e0) = e3
% 155.88/26.74 | | |
% 155.88/26.74 | | | ALPHA: (19) implies:
% 155.88/26.74 | | | (20) op(e1, e0) = e3
% 155.88/26.74 | | |
% 155.88/26.74 | | | BETA: splitting (5) gives:
% 155.88/26.74 | | |
% 155.88/26.74 | | | Case 1:
% 155.88/26.74 | | | |
% 155.88/26.74 | | | | (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 155.88/26.74 | | | | = e0)
% 155.88/26.74 | | | |
% 155.88/26.74 | | | | BETA: splitting (21) gives:
% 155.88/26.74 | | | |
% 155.88/26.74 | | | | Case 1:
% 155.88/26.74 | | | | |
% 155.88/26.74 | | | | | (22) all_58_6 = e0 & op(e1, e3) = e0
% 155.88/26.74 | | | | |
% 155.88/26.74 | | | | | REF_CLOSE: (2), (4), (22) are inconsistent by sub-proof #1483.
% 155.88/26.74 | | | | |
% 155.88/26.74 | | | | Case 2:
% 155.88/26.74 | | | | |
% 155.88/26.74 | | | | | (23) all_58_7 = e0 & op(e1, e2) = e0
% 155.88/26.74 | | | | |
% 155.88/26.74 | | | | | ALPHA: (23) implies:
% 155.88/26.74 | | | | | (24) all_58_7 = e0
% 155.88/26.74 | | | | |
% 155.88/26.74 | | | | | REF_CLOSE: (7), (9), (24) are inconsistent by sub-proof #1072.
% 155.88/26.74 | | | | |
% 155.88/26.74 | | | | End of split
% 155.88/26.74 | | | |
% 155.88/26.74 | | | Case 2:
% 155.88/26.74 | | | |
% 155.88/26.74 | | | | (25) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 155.88/26.74 | | | | = e0)
% 155.88/26.74 | | | |
% 155.88/26.74 | | | | REF_CLOSE: (3), (4), (8), (10), (20), (25) are inconsistent by sub-proof
% 155.88/26.74 | | | | #117.
% 155.88/26.74 | | | |
% 155.88/26.74 | | | End of split
% 155.88/26.74 | | |
% 155.88/26.74 | | End of split
% 155.88/26.74 | |
% 155.88/26.74 | End of split
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #117 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) ~ (e3 = e0)
% 155.88/26.74 (2) ~ (e2 = e0)
% 155.88/26.74 (3) all_58_8 = e2
% 155.88/26.74 (4) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 155.88/26.74 (5) op(e1, e0) = e3
% 155.88/26.74 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | BETA: splitting (4) gives:
% 155.88/26.74 |
% 155.88/26.74 | Case 1:
% 155.88/26.74 | |
% 155.88/26.74 | | (7) all_58_8 = e0 & op(e1, e1) = e0
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #1071.
% 155.88/26.74 | |
% 155.88/26.74 | Case 2:
% 155.88/26.74 | |
% 155.88/26.74 | | (8) all_58_11 = e0 & op(e1, e0) = e0
% 155.88/26.74 | |
% 155.88/26.74 | | ALPHA: (8) implies:
% 155.88/26.74 | | (9) op(e1, e0) = e0
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #118.
% 155.88/26.74 | |
% 155.88/26.74 | End of split
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #118 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74 (2) op(e1, e0) = e3
% 155.88/26.74 (3) op(e1, e0) = e0
% 155.88/26.74 (4) ~ (e3 = e0)
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | GROUND_INST: instantiating (1) with e0, e3, e0, e1, simplifying with (2), (3)
% 155.88/26.74 | gives:
% 155.88/26.74 | (5) e3 = e0
% 155.88/26.74 |
% 155.88/26.74 | REDUCE: (4), (5) imply:
% 155.88/26.74 | (6) $false
% 155.88/26.74 |
% 155.88/26.74 | CLOSE: (6) is inconsistent.
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #119 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) op(e2, e1) = all_52_9
% 155.88/26.74 (2) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 155.88/26.74 (3) ~ (all_52_8 = e2)
% 155.88/26.74 (4) op(e3, e1) = all_52_8
% 155.88/26.74 (5) ~ (all_52_9 = e2)
% 155.88/26.74 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | BETA: splitting (2) gives:
% 155.88/26.74 |
% 155.88/26.74 | Case 1:
% 155.88/26.74 | |
% 155.88/26.74 | | (7) all_58_4 = e2 & op(e3, e1) = e2
% 155.88/26.74 | |
% 155.88/26.74 | | ALPHA: (7) implies:
% 155.88/26.74 | | (8) op(e3, e1) = e2
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1212.
% 155.88/26.74 | |
% 155.88/26.74 | Case 2:
% 155.88/26.74 | |
% 155.88/26.74 | | (9) all_58_5 = e2 & op(e2, e1) = e2
% 155.88/26.74 | |
% 155.88/26.74 | | ALPHA: (9) implies:
% 155.88/26.74 | | (10) op(e2, e1) = e2
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #1441.
% 155.88/26.74 | |
% 155.88/26.74 | End of split
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #120 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 155.88/26.74 (2) op(e1, e2) = all_52_6
% 155.88/26.74 (3) ~ (all_52_6 = e1)
% 155.88/26.74 (4) ~ (all_52_7 = e1)
% 155.88/26.74 (5) op(e0, e2) = all_52_7
% 155.88/26.74 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | BETA: splitting (1) gives:
% 155.88/26.74 |
% 155.88/26.74 | Case 1:
% 155.88/26.74 | |
% 155.88/26.74 | | (7) all_58_7 = e1 & op(e1, e2) = e1
% 155.88/26.74 | |
% 155.88/26.74 | | ALPHA: (7) implies:
% 155.88/26.74 | | (8) op(e1, e2) = e1
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1166.
% 155.88/26.74 | |
% 155.88/26.74 | Case 2:
% 155.88/26.74 | |
% 155.88/26.74 | | (9) all_58_13 = e1 & op(e0, e2) = e1
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #192.
% 155.88/26.74 | |
% 155.88/26.74 | End of split
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #121 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) op(e3, e0) = all_52_12
% 155.88/26.74 (2) ~ (all_52_14 = e2)
% 155.88/26.74 (3) ~ (all_52_14 = e0)
% 155.88/26.74 (4) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.88/26.74 (5) op(e3, e0) = e3
% 155.88/26.74 (6) ~ (all_52_14 = e1)
% 155.88/26.74 (7) ~ (all_52_12 = all_52_14)
% 155.88/26.74 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74 (9) all_54_11 = all_52_14
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | BETA: splitting (4) gives:
% 155.88/26.74 |
% 155.88/26.74 | Case 1:
% 155.88/26.74 | |
% 155.88/26.74 | | (10) all_54_11 = e3
% 155.88/26.74 | |
% 155.88/26.74 | | COMBINE_EQS: (9), (10) imply:
% 155.88/26.74 | | (11) all_52_14 = e3
% 155.88/26.74 | |
% 155.88/26.74 | | REDUCE: (7), (11) imply:
% 155.88/26.74 | | (12) ~ (all_52_12 = e3)
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (1), (5), (8), (12) are inconsistent by sub-proof #210.
% 155.88/26.74 | |
% 155.88/26.74 | Case 2:
% 155.88/26.74 | |
% 155.88/26.74 | | (13) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (2), (3), (6), (9), (13) are inconsistent by sub-proof #1226.
% 155.88/26.74 | |
% 155.88/26.74 | End of split
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #122 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) all_58_5 = e2
% 155.88/26.74 (2) ~ (all_38_0 = e2)
% 155.88/26.74 (3) all_58_0 = e2
% 155.88/26.74 (4) all_58_14 = e3
% 155.88/26.74 (5) ~ (all_52_7 = e3)
% 155.88/26.74 (6) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 155.88/26.74 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 155.88/26.74 (7) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.88/26.74 (8) op(e1, e3) = all_38_0
% 155.88/26.74 (9) all_54_2 = all_52_8
% 155.88/26.74 (10) ~ (e3 = e0)
% 155.88/26.74 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.88/26.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.88/26.74 (12) all_56_14 = e1 | all_56_15 = e0
% 155.88/26.74 (13) ~ (e2 = e0)
% 155.88/26.74 (14) ~ (all_38_0 = e1)
% 155.88/26.74 (15) op(e1, e3) = all_52_2
% 155.88/26.74 (16) ~ (e3 = e1)
% 155.88/26.74 (17) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 155.88/26.74 (18) ~ (all_52_8 = e2)
% 155.88/26.74 (19) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 155.88/26.74 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 155.88/26.74 (20) op(e0, e0) = e2
% 155.88/26.74 (21) op(e3, e2) = e3
% 155.88/26.74 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 155.88/26.74 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 155.88/26.74 (23) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 155.88/26.74 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 155.88/26.74 (24) ~ (all_52_8 = all_6_2)
% 155.88/26.74 (25) ~ (e2 = e1)
% 155.88/26.74 (26) ~ (e1 = e0)
% 155.88/26.74 (27) op(e3, e1) = all_52_8
% 155.88/26.74 (28) ~ (all_38_0 = e0)
% 155.88/26.74 (29) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 155.88/26.74 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 155.88/26.74 e3)
% 155.88/26.74 (30) all_56_14 = all_6_2
% 155.88/26.74 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 155.88/26.74 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 155.88/26.74 (32) ~ (all_52_8 = e3)
% 155.88/26.74 (33) op(e0, e2) = all_52_7
% 155.88/26.74 (34) all_58_12 = e3 & op(e0, e3) = e3
% 155.88/26.74 (35) all_56_15 = e2
% 155.88/26.74 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74 (37) op(e2, e1) = e2
% 155.88/26.74 (38) ~ (e3 = e2)
% 155.88/26.74 (39) all_58_12 = e1
% 155.88/26.74 (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 155.88/26.74 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 155.88/26.74 (41) all_54_8 = all_38_0
% 155.88/26.74 (42) all_58_3 = e1
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | ALPHA: (34) implies:
% 155.88/26.74 | (43) all_58_12 = e3
% 155.88/26.74 |
% 155.88/26.74 | COMBINE_EQS: (39), (43) imply:
% 155.88/26.74 | (44) e3 = e1
% 155.88/26.74 |
% 155.88/26.74 | SIMP: (44) implies:
% 155.88/26.74 | (45) e3 = e1
% 155.88/26.74 |
% 155.88/26.74 | COMBINE_EQS: (4), (45) imply:
% 155.88/26.74 | (46) all_58_14 = e1
% 155.88/26.74 |
% 155.88/26.74 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 155.88/26.74 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 155.88/26.74 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36),
% 155.88/26.74 | (37), (38), (40), (41), (42), (46) are inconsistent by sub-proof
% 155.88/26.74 | #126.
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #123 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) all_58_0 = e2
% 155.88/26.74 (2) all_58_14 = e3
% 155.88/26.74 (3) ~ (all_52_7 = e3)
% 155.88/26.74 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 155.88/26.74 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 155.88/26.74 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 155.88/26.74 (6) op(e2, e3) = all_52_1
% 155.88/26.74 (7) ~ (e3 = e0)
% 155.88/26.74 (8) ~ (e2 = e0)
% 155.88/26.74 (9) ~ (e3 = e1)
% 155.88/26.74 (10) op(e0, e0) = e2
% 155.88/26.74 (11) all_58_15 = e2
% 155.88/26.74 (12) ~ (e2 = e1)
% 155.88/26.74 (13) ~ (e1 = e0)
% 155.88/26.74 (14) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 155.88/26.74 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 155.88/26.74 e3)
% 155.88/26.74 (15) op(e0, e2) = all_52_7
% 155.88/26.74 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74 (17) ~ (e3 = e2)
% 155.88/26.74 (18) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 155.88/26.74 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 155.88/26.74 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 155.88/26.74 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 155.88/26.74 (19) ~ (all_52_1 = e3)
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | BETA: splitting (5) gives:
% 155.88/26.74 |
% 155.88/26.74 | Case 1:
% 155.88/26.74 | |
% 155.88/26.74 | | (20) all_58_0 = e3 & op(e3, e3) = e3
% 155.88/26.74 | |
% 155.88/26.74 | | ALPHA: (20) implies:
% 155.88/26.74 | | (21) all_58_0 = e3
% 155.88/26.74 | |
% 155.88/26.74 | | COMBINE_EQS: (1), (21) imply:
% 155.88/26.74 | | (22) e3 = e2
% 155.88/26.74 | |
% 155.88/26.74 | | SIMP: (22) implies:
% 155.88/26.74 | | (23) e3 = e2
% 155.88/26.74 | |
% 155.88/26.74 | | COMBINE_EQS: (2), (23) imply:
% 155.88/26.74 | | (24) all_58_14 = e2
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 155.88/26.74 | | (16), (17), (18), (24) are inconsistent by sub-proof #1380.
% 155.88/26.74 | |
% 155.88/26.74 | Case 2:
% 155.88/26.74 | |
% 155.88/26.74 | | (25) all_58_2 = e3 & op(e2, e3) = e3
% 155.88/26.74 | |
% 155.88/26.74 | | ALPHA: (25) implies:
% 155.88/26.74 | | (26) op(e2, e3) = e3
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (6), (16), (19), (26) are inconsistent by sub-proof #1183.
% 155.88/26.74 | |
% 155.88/26.74 | End of split
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #124 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) all_56_14 = e1
% 155.88/26.74 (2) op(e2, e0) = all_52_13
% 155.88/26.74 (3) op(e1, e2) = all_52_6
% 155.88/26.74 (4) ~ (all_52_13 = e2)
% 155.88/26.74 (5) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 155.88/26.74 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2)
% 155.88/26.74 & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2
% 155.88/26.74 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.88/26.74 (6) ~ (all_52_6 = e1)
% 155.88/26.74 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | BETA: splitting (5) gives:
% 155.88/26.74 |
% 155.88/26.74 | Case 1:
% 155.88/26.74 | |
% 155.88/26.74 | | (8) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2
% 155.88/26.74 | | & op(e1, e2) = e2
% 155.88/26.74 | |
% 155.88/26.74 | | ALPHA: (8) implies:
% 155.88/26.74 | | (9) ~ (all_56_14 = e1)
% 155.88/26.74 | |
% 155.88/26.74 | | REDUCE: (1), (9) imply:
% 155.88/26.74 | | (10) $false
% 155.88/26.74 | |
% 155.88/26.74 | | CLOSE: (10) is inconsistent.
% 155.88/26.74 | |
% 155.88/26.74 | Case 2:
% 155.88/26.74 | |
% 155.88/26.74 | | (11) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) =
% 155.88/26.74 | | e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 155.88/26.74 | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (2), (3), (4), (6), (7), (11) are inconsistent by sub-proof
% 155.88/26.74 | | #1129.
% 155.88/26.74 | |
% 155.88/26.74 | End of split
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #125 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) all_58_0 = e2
% 155.88/26.74 (2) all_56_14 = e1
% 155.88/26.74 (3) all_56_14 = e1 | all_56_15 = e0
% 155.88/26.74 (4) ~ (e2 = e0)
% 155.88/26.74 (5) ~ (e3 = e1)
% 155.88/26.74 (6) all_58_9 = e0
% 155.88/26.74 (7) op(e3, e1) = e0
% 155.88/26.74 (8) op(e3, e2) = e3
% 155.88/26.74 (9) ~ (e2 = e1)
% 155.88/26.74 (10) ~ (e1 = e0)
% 155.88/26.74 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 155.88/26.74 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 155.88/26.74 (12) all_56_15 = e2
% 155.88/26.74 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.74
% 155.88/26.74 Begin of proof
% 155.88/26.74 |
% 155.88/26.74 | BETA: splitting (11) gives:
% 155.88/26.74 |
% 155.88/26.74 | Case 1:
% 155.88/26.74 | |
% 155.88/26.74 | | (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 155.88/26.74 | | e1)
% 155.88/26.74 | |
% 155.88/26.74 | | REF_CLOSE: (1), (5), (8), (9), (13), (14) are inconsistent by sub-proof
% 155.88/26.74 | | #1255.
% 155.88/26.74 | |
% 155.88/26.74 | Case 2:
% 155.88/26.74 | |
% 155.88/26.74 | | (15) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 155.88/26.74 | | e1)
% 155.88/26.74 | |
% 155.88/26.74 | | BETA: splitting (15) gives:
% 155.88/26.74 | |
% 155.88/26.74 | | Case 1:
% 155.88/26.74 | | |
% 155.88/26.74 | | | (16) all_58_4 = e1 & op(e3, e1) = e1
% 155.88/26.74 | | |
% 155.88/26.74 | | | ALPHA: (16) implies:
% 155.88/26.74 | | | (17) op(e3, e1) = e1
% 155.88/26.74 | | |
% 155.88/26.74 | | | REF_CLOSE: (7), (10), (13), (17) are inconsistent by sub-proof #1281.
% 155.88/26.74 | | |
% 155.88/26.74 | | Case 2:
% 155.88/26.74 | | |
% 155.88/26.74 | | | (18) all_58_9 = e1 & op(e3, e0) = e1
% 155.88/26.74 | | |
% 155.88/26.74 | | | ALPHA: (18) implies:
% 155.88/26.74 | | | (19) all_58_9 = e1
% 155.88/26.74 | | |
% 155.88/26.74 | | | COMBINE_EQS: (6), (19) imply:
% 155.88/26.74 | | | (20) e1 = e0
% 155.88/26.74 | | |
% 155.88/26.74 | | | SIMP: (20) implies:
% 155.88/26.74 | | | (21) e1 = e0
% 155.88/26.74 | | |
% 155.88/26.74 | | | COMBINE_EQS: (2), (21) imply:
% 155.88/26.74 | | | (22) all_56_14 = e0
% 155.88/26.74 | | |
% 155.88/26.74 | | | REF_CLOSE: (3), (4), (10), (12), (22) are inconsistent by sub-proof #149.
% 155.88/26.74 | | |
% 155.88/26.74 | | End of split
% 155.88/26.74 | |
% 155.88/26.74 | End of split
% 155.88/26.74 |
% 155.88/26.74 End of proof
% 155.88/26.74
% 155.88/26.74 Sub-proof #126 shows that the following formulas are inconsistent:
% 155.88/26.74 ----------------------------------------------------------------
% 155.88/26.74 (1) all_58_5 = e2
% 155.88/26.74 (2) ~ (all_38_0 = e2)
% 155.88/26.74 (3) all_58_0 = e2
% 155.88/26.74 (4) ~ (all_52_7 = e3)
% 155.88/26.75 (5) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 155.88/26.75 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 155.88/26.75 (6) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.88/26.75 (7) op(e1, e3) = all_38_0
% 155.88/26.75 (8) all_58_14 = e1
% 155.88/26.75 (9) all_54_2 = all_52_8
% 155.88/26.75 (10) ~ (e3 = e0)
% 155.88/26.75 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 155.88/26.75 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 155.88/26.75 (12) all_56_14 = e1 | all_56_15 = e0
% 155.88/26.75 (13) ~ (e2 = e0)
% 155.88/26.75 (14) ~ (all_38_0 = e1)
% 155.88/26.75 (15) op(e1, e3) = all_52_2
% 155.88/26.75 (16) ~ (e3 = e1)
% 155.88/26.75 (17) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 155.88/26.75 (18) ~ (all_52_8 = e2)
% 155.88/26.75 (19) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 155.88/26.75 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 155.88/26.75 (20) op(e0, e0) = e2
% 155.88/26.75 (21) op(e3, e2) = e3
% 155.88/26.75 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 155.88/26.75 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 155.88/26.75 (23) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 155.88/26.75 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 155.88/26.75 (24) ~ (all_52_8 = all_6_2)
% 155.88/26.75 (25) ~ (e2 = e1)
% 155.88/26.75 (26) ~ (e1 = e0)
% 155.88/26.75 (27) op(e3, e1) = all_52_8
% 155.88/26.75 (28) ~ (all_38_0 = e0)
% 155.88/26.75 (29) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 155.88/26.75 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 155.88/26.75 e3)
% 155.88/26.75 (30) all_56_14 = all_6_2
% 155.88/26.75 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 155.88/26.75 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 155.88/26.75 (32) ~ (all_52_8 = e3)
% 155.88/26.75 (33) op(e0, e2) = all_52_7
% 155.88/26.75 (34) all_56_15 = e2
% 155.88/26.75 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.75 (36) op(e2, e1) = e2
% 155.88/26.75 (37) ~ (e3 = e2)
% 155.88/26.75 (38) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 155.88/26.75 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 155.88/26.75 (39) all_54_8 = all_38_0
% 155.88/26.75 (40) all_58_3 = e1
% 155.88/26.75
% 155.88/26.75 Begin of proof
% 155.88/26.75 |
% 155.88/26.75 | BETA: splitting (5) gives:
% 155.88/26.75 |
% 155.88/26.75 | Case 1:
% 155.88/26.75 | |
% 155.88/26.75 | | (41) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 155.88/26.75 | | e3)
% 155.88/26.75 | |
% 155.88/26.75 | | REF_CLOSE: (1), (3), (10), (13), (16), (21), (25), (26), (31), (35), (37),
% 155.88/26.75 | | (38), (41) are inconsistent by sub-proof #147.
% 155.88/26.75 | |
% 155.88/26.75 | Case 2:
% 155.88/26.75 | |
% 155.88/26.75 | | (42) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 155.88/26.75 | | e3)
% 155.88/26.75 | |
% 155.88/26.75 | | BETA: splitting (42) gives:
% 155.88/26.75 | |
% 155.88/26.75 | | Case 1:
% 155.88/26.75 | | |
% 155.88/26.75 | | | (43) all_58_8 = e3 & op(e1, e1) = e3
% 155.88/26.75 | | |
% 155.88/26.75 | | | ALPHA: (43) implies:
% 155.88/26.75 | | | (44) all_58_8 = e3
% 155.88/26.75 | | |
% 155.88/26.75 | | | BETA: splitting (11) gives:
% 155.88/26.75 | | |
% 155.88/26.75 | | | Case 1:
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | (45) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 155.88/26.75 | | | | = e1)
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | REF_CLOSE: (1), (3), (10), (13), (16), (19), (22), (25), (26), (35),
% 155.88/26.75 | | | | (37), (40), (45) are inconsistent by sub-proof #130.
% 155.88/26.75 | | | |
% 155.88/26.75 | | | Case 2:
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | (46) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 155.88/26.75 | | | | = e1)
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | BETA: splitting (46) gives:
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | Case 1:
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | (47) all_58_6 = e1 & op(e1, e3) = e1
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | ALPHA: (47) implies:
% 155.88/26.75 | | | | | (48) op(e1, e3) = e1
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | BETA: splitting (6) gives:
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | Case 1:
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | | (49) all_54_8 = e3
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | | COMBINE_EQS: (39), (49) imply:
% 155.88/26.75 | | | | | | (50) all_38_0 = e3
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | | SIMP: (50) implies:
% 155.88/26.75 | | | | | | (51) all_38_0 = e3
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | | REDUCE: (7), (51) imply:
% 155.88/26.75 | | | | | | (52) op(e1, e3) = e3
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | | REF_CLOSE: (15), (16), (35), (48), (52) are inconsistent by
% 155.88/26.75 | | | | | | sub-proof #1164.
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | Case 2:
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | | (53) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | | REF_CLOSE: (2), (14), (28), (39), (53) are inconsistent by sub-proof
% 155.88/26.75 | | | | | | #127.
% 155.88/26.75 | | | | | |
% 155.88/26.75 | | | | | End of split
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | Case 2:
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | (54) all_58_12 = e1 & op(e0, e3) = e1
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | ALPHA: (54) implies:
% 155.88/26.75 | | | | | (55) all_58_12 = e1
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | REF_CLOSE: (3), (4), (9), (10), (12), (13), (16), (17), (18), (20),
% 155.88/26.75 | | | | | (21), (23), (24), (25), (26), (27), (29), (30), (31), (32),
% 155.88/26.75 | | | | | (33), (34), (35), (36), (37), (38), (44), (55) are
% 155.88/26.75 | | | | | inconsistent by sub-proof #128.
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | End of split
% 155.88/26.75 | | | |
% 155.88/26.75 | | | End of split
% 155.88/26.75 | | |
% 155.88/26.75 | | Case 2:
% 155.88/26.75 | | |
% 155.88/26.75 | | | (56) all_58_14 = e3 & op(e0, e1) = e3
% 155.88/26.75 | | |
% 155.88/26.75 | | | REF_CLOSE: (8), (16), (56) are inconsistent by sub-proof #872.
% 155.88/26.75 | | |
% 155.88/26.75 | | End of split
% 155.88/26.75 | |
% 155.88/26.75 | End of split
% 155.88/26.75 |
% 155.88/26.75 End of proof
% 155.88/26.75
% 155.88/26.75 Sub-proof #127 shows that the following formulas are inconsistent:
% 155.88/26.75 ----------------------------------------------------------------
% 155.88/26.75 (1) ~ (all_38_0 = e2)
% 155.88/26.75 (2) ~ (all_38_0 = e1)
% 155.88/26.75 (3) ~ (all_38_0 = e0)
% 155.88/26.75 (4) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 155.88/26.75 (5) all_54_8 = all_38_0
% 155.88/26.75
% 155.88/26.75 Begin of proof
% 155.88/26.75 |
% 155.88/26.75 | BETA: splitting (4) gives:
% 155.88/26.75 |
% 155.88/26.75 | Case 1:
% 155.88/26.75 | |
% 155.88/26.75 | | (6) all_54_8 = e2
% 155.88/26.75 | |
% 155.88/26.75 | | COMBINE_EQS: (5), (6) imply:
% 155.88/26.75 | | (7) all_38_0 = e2
% 155.88/26.75 | |
% 155.88/26.75 | | SIMP: (7) implies:
% 155.88/26.75 | | (8) all_38_0 = e2
% 155.88/26.75 | |
% 155.88/26.75 | | REDUCE: (1), (8) imply:
% 155.88/26.75 | | (9) $false
% 155.88/26.75 | |
% 155.88/26.75 | | CLOSE: (9) is inconsistent.
% 155.88/26.75 | |
% 155.88/26.75 | Case 2:
% 155.88/26.75 | |
% 155.88/26.75 | | (10) all_54_8 = e1 | all_54_8 = e0
% 155.88/26.75 | |
% 155.88/26.75 | | BETA: splitting (10) gives:
% 155.88/26.75 | |
% 155.88/26.75 | | Case 1:
% 155.88/26.75 | | |
% 155.88/26.75 | | | (11) all_54_8 = e1
% 155.88/26.75 | | |
% 155.88/26.75 | | | COMBINE_EQS: (5), (11) imply:
% 155.88/26.75 | | | (12) all_38_0 = e1
% 155.88/26.75 | | |
% 155.88/26.75 | | | SIMP: (12) implies:
% 155.88/26.75 | | | (13) all_38_0 = e1
% 155.88/26.75 | | |
% 155.88/26.75 | | | REDUCE: (2), (13) imply:
% 155.88/26.75 | | | (14) $false
% 155.88/26.75 | | |
% 155.88/26.75 | | | CLOSE: (14) is inconsistent.
% 155.88/26.75 | | |
% 155.88/26.75 | | Case 2:
% 155.88/26.75 | | |
% 155.88/26.75 | | | (15) all_54_8 = e0
% 155.88/26.75 | | |
% 155.88/26.75 | | | REF_CLOSE: (3), (5), (15) are inconsistent by sub-proof #134.
% 155.88/26.75 | | |
% 155.88/26.75 | | End of split
% 155.88/26.75 | |
% 155.88/26.75 | End of split
% 155.88/26.75 |
% 155.88/26.75 End of proof
% 155.88/26.75
% 155.88/26.75 Sub-proof #128 shows that the following formulas are inconsistent:
% 155.88/26.75 ----------------------------------------------------------------
% 155.88/26.75 (1) all_58_0 = e2
% 155.88/26.75 (2) ~ (all_52_7 = e3)
% 155.88/26.75 (3) all_58_8 = e3
% 155.88/26.75 (4) all_54_2 = all_52_8
% 155.88/26.75 (5) ~ (e3 = e0)
% 155.88/26.75 (6) all_56_14 = e1 | all_56_15 = e0
% 155.88/26.75 (7) ~ (e2 = e0)
% 155.88/26.75 (8) ~ (e3 = e1)
% 155.88/26.75 (9) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 155.88/26.75 (10) ~ (all_52_8 = e2)
% 155.88/26.75 (11) op(e0, e0) = e2
% 155.88/26.75 (12) op(e3, e2) = e3
% 155.88/26.75 (13) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 155.88/26.75 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 155.88/26.75 (14) ~ (all_52_8 = all_6_2)
% 155.88/26.75 (15) ~ (e2 = e1)
% 155.88/26.75 (16) ~ (e1 = e0)
% 155.88/26.75 (17) op(e3, e1) = all_52_8
% 155.88/26.75 (18) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 155.88/26.75 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 155.88/26.75 e3)
% 155.88/26.75 (19) all_56_14 = all_6_2
% 155.88/26.75 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 155.88/26.75 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 155.88/26.75 (21) ~ (all_52_8 = e3)
% 155.88/26.75 (22) op(e0, e2) = all_52_7
% 155.88/26.75 (23) all_56_15 = e2
% 155.88/26.75 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.75 (25) op(e2, e1) = e2
% 155.88/26.75 (26) ~ (e3 = e2)
% 155.88/26.75 (27) all_58_12 = e1
% 155.88/26.75 (28) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 155.88/26.75 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 155.88/26.75
% 155.88/26.75 Begin of proof
% 155.88/26.75 |
% 155.88/26.75 | BETA: splitting (20) gives:
% 155.88/26.75 |
% 155.88/26.75 | Case 1:
% 155.88/26.75 | |
% 155.88/26.75 | | (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 155.88/26.75 | | e1)
% 155.88/26.75 | |
% 155.88/26.75 | | REF_CLOSE: (1), (8), (12), (15), (24), (29) are inconsistent by sub-proof
% 155.88/26.75 | | #1255.
% 155.88/26.75 | |
% 155.88/26.75 | Case 2:
% 155.88/26.75 | |
% 155.88/26.75 | | (30) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 155.88/26.75 | | e1)
% 155.88/26.75 | |
% 155.88/26.75 | | BETA: splitting (30) gives:
% 155.88/26.75 | |
% 155.88/26.75 | | Case 1:
% 155.88/26.75 | | |
% 155.88/26.75 | | | (31) all_58_4 = e1 & op(e3, e1) = e1
% 155.88/26.75 | | |
% 155.88/26.75 | | | ALPHA: (31) implies:
% 155.88/26.75 | | | (32) op(e3, e1) = e1
% 155.88/26.75 | | |
% 155.88/26.75 | | | REF_CLOSE: (4), (6), (7), (9), (10), (14), (17), (19), (21), (23), (24),
% 155.88/26.75 | | | (32) are inconsistent by sub-proof #888.
% 155.88/26.75 | | |
% 155.88/26.75 | | Case 2:
% 155.88/26.75 | | |
% 155.88/26.75 | | | (33) all_58_9 = e1 & op(e3, e0) = e1
% 155.88/26.75 | | |
% 155.88/26.75 | | | ALPHA: (33) implies:
% 155.88/26.75 | | | (34) all_58_9 = e1
% 155.88/26.75 | | |
% 155.88/26.75 | | | BETA: splitting (18) gives:
% 155.88/26.75 | | |
% 155.88/26.75 | | | Case 1:
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | (35) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 155.88/26.75 | | | | e2) = e3)
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | REF_CLOSE: (2), (8), (22), (24), (27), (35) are inconsistent by
% 155.88/26.75 | | | | sub-proof #996.
% 155.88/26.75 | | | |
% 155.88/26.75 | | | Case 2:
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | (36) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 155.88/26.75 | | | | e0) = e3)
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | BETA: splitting (36) gives:
% 155.88/26.75 | | | |
% 155.88/26.75 | | | | Case 1:
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | (37) all_58_14 = e3 & op(e0, e1) = e3
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | ALPHA: (37) implies:
% 155.88/26.75 | | | | | (38) all_58_14 = e3
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (12), (13), (15), (16), (24),
% 155.88/26.75 | | | | | (25), (28), (34), (38) are inconsistent by sub-proof #921.
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | Case 2:
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | (39) all_58_15 = e3 & op(e0, e0) = e3
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | ALPHA: (39) implies:
% 155.88/26.75 | | | | | (40) op(e0, e0) = e3
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | | REF_CLOSE: (11), (24), (26), (40) are inconsistent by sub-proof #1382.
% 155.88/26.75 | | | | |
% 155.88/26.75 | | | | End of split
% 155.88/26.75 | | | |
% 155.88/26.75 | | | End of split
% 155.88/26.75 | | |
% 155.88/26.75 | | End of split
% 155.88/26.75 | |
% 155.88/26.75 | End of split
% 155.88/26.75 |
% 155.88/26.75 End of proof
% 155.88/26.75
% 155.88/26.75 Sub-proof #129 shows that the following formulas are inconsistent:
% 155.88/26.75 ----------------------------------------------------------------
% 155.88/26.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 155.88/26.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 155.88/26.75 (2) op(e0, e1) = e1
% 155.88/26.75 (3) op(e0, e1) = e0
% 155.88/26.75 (4) ~ (e1 = e0)
% 155.88/26.75
% 155.88/26.75 Begin of proof
% 155.88/26.75 |
% 155.88/26.75 | GROUND_INST: instantiating (1) with e0, e1, e1, e0, simplifying with (2), (3)
% 155.88/26.75 | gives:
% 155.88/26.75 | (5) e1 = e0
% 155.88/26.75 |
% 155.88/26.75 | REDUCE: (4), (5) imply:
% 155.88/26.75 | (6) $false
% 155.88/26.75 |
% 155.88/26.75 | CLOSE: (6) is inconsistent.
% 156.04/26.75 |
% 156.04/26.75 End of proof
% 156.04/26.75
% 156.04/26.75 Sub-proof #130 shows that the following formulas are inconsistent:
% 156.04/26.75 ----------------------------------------------------------------
% 156.04/26.75 (1) all_58_5 = e2
% 156.04/26.75 (2) all_58_0 = e2
% 156.04/26.75 (3) ~ (e3 = e0)
% 156.04/26.75 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 156.04/26.75 (5) ~ (e2 = e0)
% 156.04/26.75 (6) ~ (e3 = e1)
% 156.04/26.75 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.75 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 156.04/26.75 (8) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.04/26.75 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.04/26.75 (9) ~ (e2 = e1)
% 156.04/26.75 (10) ~ (e1 = e0)
% 156.04/26.75 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.75 (12) ~ (e3 = e2)
% 156.04/26.75 (13) all_58_3 = e1
% 156.04/26.75
% 156.04/26.75 Begin of proof
% 156.04/26.75 |
% 156.04/26.75 | BETA: splitting (4) gives:
% 156.04/26.75 |
% 156.04/26.75 | Case 1:
% 156.04/26.75 | |
% 156.04/26.75 | | (14) all_58_0 = e1 & op(e3, e3) = e1
% 156.04/26.75 | |
% 156.04/26.75 | | REF_CLOSE: (2), (9), (14) are inconsistent by sub-proof #1337.
% 156.04/26.75 | |
% 156.04/26.75 | Case 2:
% 156.04/26.75 | |
% 156.04/26.75 | | (15) all_58_2 = e1 & op(e2, e3) = e1
% 156.04/26.75 | |
% 156.04/26.75 | | ALPHA: (15) implies:
% 156.04/26.75 | | (16) all_58_2 = e1
% 156.04/26.75 | | (17) op(e2, e3) = e1
% 156.04/26.75 | |
% 156.04/26.75 | | BETA: splitting (8) gives:
% 156.04/26.75 | |
% 156.04/26.75 | | Case 1:
% 156.04/26.75 | | |
% 156.04/26.75 | | | (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 156.04/26.75 | | | e3)
% 156.04/26.75 | | |
% 156.04/26.75 | | | BETA: splitting (18) gives:
% 156.04/26.75 | | |
% 156.04/26.75 | | | Case 1:
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | (19) all_58_2 = e3 & op(e2, e3) = e3
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | ALPHA: (19) implies:
% 156.04/26.75 | | | | (20) op(e2, e3) = e3
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | REF_CLOSE: (6), (11), (17), (20) are inconsistent by sub-proof #1494.
% 156.04/26.75 | | | |
% 156.04/26.75 | | | Case 2:
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | (21) all_58_3 = e3 & op(e2, e2) = e3
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | REF_CLOSE: (6), (13), (21) are inconsistent by sub-proof #164.
% 156.04/26.75 | | | |
% 156.04/26.75 | | | End of split
% 156.04/26.75 | | |
% 156.04/26.75 | | Case 2:
% 156.04/26.75 | | |
% 156.04/26.75 | | | (22) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 156.04/26.75 | | | e3)
% 156.04/26.75 | | |
% 156.04/26.75 | | | BETA: splitting (22) gives:
% 156.04/26.75 | | |
% 156.04/26.75 | | | Case 1:
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | (23) all_58_5 = e3 & op(e2, e1) = e3
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | ALPHA: (23) implies:
% 156.04/26.75 | | | | (24) all_58_5 = e3
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | REF_CLOSE: (1), (12), (24) are inconsistent by sub-proof #897.
% 156.04/26.75 | | | |
% 156.04/26.75 | | | Case 2:
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | (25) all_58_10 = e3 & op(e2, e0) = e3
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | ALPHA: (25) implies:
% 156.04/26.75 | | | | (26) all_58_10 = e3
% 156.04/26.75 | | | |
% 156.04/26.75 | | | | REF_CLOSE: (1), (3), (5), (7), (10), (13), (16), (26) are inconsistent
% 156.04/26.75 | | | | by sub-proof #160.
% 156.04/26.75 | | | |
% 156.04/26.75 | | | End of split
% 156.04/26.75 | | |
% 156.04/26.75 | | End of split
% 156.04/26.75 | |
% 156.04/26.75 | End of split
% 156.04/26.75 |
% 156.04/26.75 End of proof
% 156.04/26.75
% 156.04/26.75 Sub-proof #131 shows that the following formulas are inconsistent:
% 156.04/26.75 ----------------------------------------------------------------
% 156.04/26.75 (1) all_58_15 = e0
% 156.04/26.75 (2) all_58_0 = e2
% 156.04/26.75 (3) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.04/26.75 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.04/26.75 (4) ~ (all_52_13 = e3)
% 156.04/26.75 (5) ~ (e3 = e0)
% 156.04/26.75 (6) ~ (e2 = e0)
% 156.04/26.75 (7) op(e2, e0) = all_52_13
% 156.04/26.75 (8) ~ (e3 = e1)
% 156.04/26.75 (9) op(e1, e0) = e1
% 156.04/26.75 (10) op(e3, e2) = e3
% 156.04/26.75 (11) ~ (e2 = e1)
% 156.04/26.75 (12) ~ (e1 = e0)
% 156.04/26.75 (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.04/26.75 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.04/26.75 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.75 (15) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.04/26.75 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.04/26.75
% 156.04/26.75 Begin of proof
% 156.04/26.75 |
% 156.04/26.75 | BETA: splitting (3) gives:
% 156.04/26.75 |
% 156.04/26.75 | Case 1:
% 156.04/26.75 | |
% 156.04/26.75 | | (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 156.04/26.75 | | e3)
% 156.04/26.75 | |
% 156.04/26.75 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 156.04/26.75 | | (16) are inconsistent by sub-proof #1025.
% 156.04/26.75 | |
% 156.04/26.75 | Case 2:
% 156.04/26.75 | |
% 156.04/26.75 | | (17) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 156.04/26.75 | | e3)
% 156.04/26.75 | |
% 156.04/26.75 | | BETA: splitting (17) gives:
% 156.04/26.75 | |
% 156.04/26.75 | | Case 1:
% 156.04/26.75 | | |
% 156.04/26.75 | | | (18) all_58_11 = e3 & op(e1, e0) = e3
% 156.04/26.75 | | |
% 156.04/26.75 | | | ALPHA: (18) implies:
% 156.04/26.75 | | | (19) op(e1, e0) = e3
% 156.04/26.75 | | |
% 156.04/26.75 | | | REF_CLOSE: (8), (9), (14), (19) are inconsistent by sub-proof #1275.
% 156.04/26.75 | | |
% 156.04/26.75 | | Case 2:
% 156.04/26.75 | | |
% 156.04/26.75 | | | (20) all_58_15 = e3 & op(e0, e0) = e3
% 156.04/26.75 | | |
% 156.04/26.75 | | | REF_CLOSE: (1), (5), (20) are inconsistent by sub-proof #1357.
% 156.04/26.75 | | |
% 156.04/26.75 | | End of split
% 156.04/26.75 | |
% 156.04/26.75 | End of split
% 156.04/26.75 |
% 156.04/26.75 End of proof
% 156.04/26.75
% 156.04/26.75 Sub-proof #132 shows that the following formulas are inconsistent:
% 156.04/26.75 ----------------------------------------------------------------
% 156.04/26.75 (1) op(e1, e2) = e0
% 156.04/26.75 (2) ~ (e2 = e0)
% 156.04/26.75 (3) op(e2, e0) = all_52_13
% 156.04/26.75 (4) op(e1, e2) = all_52_6
% 156.04/26.75 (5) ~ (all_52_13 = e2)
% 156.04/26.75 (6) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.04/26.75 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2)
% 156.04/26.75 & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2
% 156.04/26.75 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.04/26.75 (7) ~ (all_52_6 = e1)
% 156.04/26.75 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.75
% 156.04/26.75 Begin of proof
% 156.04/26.75 |
% 156.04/26.75 | BETA: splitting (6) gives:
% 156.04/26.75 |
% 156.04/26.75 | Case 1:
% 156.04/26.75 | |
% 156.04/26.75 | | (9) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2
% 156.04/26.75 | | & op(e1, e2) = e2
% 156.04/26.75 | |
% 156.04/26.75 | | ALPHA: (9) implies:
% 156.04/26.75 | | (10) op(e1, e2) = e2
% 156.04/26.75 | |
% 156.04/26.75 | | REF_CLOSE: (1), (2), (8), (10) are inconsistent by sub-proof #139.
% 156.04/26.75 | |
% 156.04/26.75 | Case 2:
% 156.04/26.75 | |
% 156.04/26.75 | | (11) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) =
% 156.04/26.75 | | e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 156.04/26.75 | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.04/26.75 | |
% 156.04/26.75 | | REF_CLOSE: (3), (4), (5), (7), (8), (11) are inconsistent by sub-proof
% 156.04/26.75 | | #1129.
% 156.04/26.75 | |
% 156.04/26.75 | End of split
% 156.04/26.75 |
% 156.04/26.75 End of proof
% 156.04/26.75
% 156.04/26.75 Sub-proof #133 shows that the following formulas are inconsistent:
% 156.04/26.75 ----------------------------------------------------------------
% 156.04/26.75 (1) ~ (all_38_0 = e2)
% 156.04/26.76 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.04/26.76 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.04/26.76 (3) ~ (all_38_0 = all_6_2)
% 156.04/26.76 (4) all_54_10 = all_6_2
% 156.04/26.76 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.04/26.76 (6) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 156.04/26.76 (7) ~ (all_4_2 = e2)
% 156.04/26.76 (8) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.04/26.76 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.04/26.76 (9) op(e1, e3) = all_38_0
% 156.04/26.76 (10) ~ (all_52_13 = e3)
% 156.04/26.76 (11) ~ (e2 = e0)
% 156.04/26.76 (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.04/26.76 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.04/26.76 (13) all_56_13 = e1
% 156.04/26.76 (14) op(e1, e3) = all_52_2
% 156.04/26.76 (15) op(e1, e2) = all_52_6
% 156.04/26.76 (16) ~ (all_4_2 = e1)
% 156.04/26.76 (17) all_54_7 = all_52_13
% 156.04/26.76 (18) ~ (all_6_2 = e0)
% 156.04/26.76 (19) ~ (all_52_13 = e2)
% 156.04/26.76 (20) all_56_15 = all_4_2
% 156.04/26.76 (21) all_58_11 = e2
% 156.04/26.76 (22) ~ (all_52_13 = all_4_2)
% 156.04/26.76 (23) all_56_12 = e2
% 156.04/26.76 (24) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.04/26.76 (25) ~ (all_6_2 = e2)
% 156.04/26.76 (26) ~ (all_38_0 = e0)
% 156.04/26.76 (27) ~ (all_52_13 = e1)
% 156.04/26.76 (28) all_56_14 = all_6_2
% 156.04/26.76 (29) all_54_15 = all_4_2
% 156.04/26.76 (30) ~ (all_38_0 = e3)
% 156.04/26.76 (31) ~ (all_52_6 = e3)
% 156.04/26.76 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.76 (33) ~ (e3 = e2)
% 156.04/26.76 (34) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.04/26.76 (35) all_54_8 = all_38_0
% 156.04/26.76 (36) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.04/26.76
% 156.04/26.76 Begin of proof
% 156.04/26.76 |
% 156.04/26.76 | BETA: splitting (6) gives:
% 156.04/26.76 |
% 156.04/26.76 | Case 1:
% 156.04/26.76 | |
% 156.04/26.76 | | (37) all_54_8 = e3
% 156.04/26.76 | |
% 156.04/26.76 | | COMBINE_EQS: (35), (37) imply:
% 156.04/26.76 | | (38) all_38_0 = e3
% 156.04/26.76 | |
% 156.04/26.76 | | REDUCE: (30), (38) imply:
% 156.04/26.76 | | (39) $false
% 156.04/26.76 | |
% 156.04/26.76 | | CLOSE: (39) is inconsistent.
% 156.04/26.76 | |
% 156.04/26.76 | Case 2:
% 156.04/26.76 | |
% 156.04/26.76 | | (40) ~ (all_54_8 = e3)
% 156.04/26.76 | | (41) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 156.04/26.76 | |
% 156.04/26.76 | | BETA: splitting (41) gives:
% 156.04/26.76 | |
% 156.04/26.76 | | Case 1:
% 156.04/26.76 | | |
% 156.04/26.76 | | | (42) all_54_8 = e2
% 156.04/26.76 | | |
% 156.04/26.76 | | | COMBINE_EQS: (35), (42) imply:
% 156.04/26.76 | | | (43) all_38_0 = e2
% 156.04/26.76 | | |
% 156.04/26.76 | | | REDUCE: (1), (43) imply:
% 156.04/26.76 | | | (44) $false
% 156.04/26.76 | | |
% 156.04/26.76 | | | CLOSE: (44) is inconsistent.
% 156.04/26.76 | | |
% 156.04/26.76 | | Case 2:
% 156.04/26.76 | | |
% 156.04/26.76 | | | (45) ~ (all_54_8 = e2)
% 156.04/26.76 | | | (46) all_54_8 = e1 | all_54_8 = e0
% 156.04/26.76 | | |
% 156.04/26.76 | | | BETA: splitting (8) gives:
% 156.04/26.76 | | |
% 156.04/26.76 | | | Case 1:
% 156.04/26.76 | | | |
% 156.04/26.76 | | | | (47) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 156.04/26.76 | | | | = e3)
% 156.04/26.76 | | | |
% 156.04/26.76 | | | | BETA: splitting (47) gives:
% 156.04/26.76 | | | |
% 156.04/26.76 | | | | Case 1:
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | (48) all_58_6 = e3 & op(e1, e3) = e3
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | ALPHA: (48) implies:
% 156.04/26.76 | | | | | (49) op(e1, e3) = e3
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | BETA: splitting (46) gives:
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | Case 1:
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | (50) all_54_8 = e1
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | COMBINE_EQS: (35), (50) imply:
% 156.04/26.76 | | | | | | (51) all_38_0 = e1
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | SIMP: (51) implies:
% 156.04/26.76 | | | | | | (52) all_38_0 = e1
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | REDUCE: (30), (52) imply:
% 156.04/26.76 | | | | | | (53) ~ (e3 = e1)
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | SIMP: (53) implies:
% 156.04/26.76 | | | | | | (54) ~ (e3 = e1)
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | REDUCE: (9), (52) imply:
% 156.04/26.76 | | | | | | (55) op(e1, e3) = e1
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | REF_CLOSE: (14), (32), (49), (54), (55) are inconsistent by
% 156.04/26.76 | | | | | | sub-proof #1164.
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | Case 2:
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | (56) all_54_8 = e0
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | REF_CLOSE: (26), (35), (56) are inconsistent by sub-proof #134.
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | End of split
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | Case 2:
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | (57) all_58_7 = e3 & op(e1, e2) = e3
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | REF_CLOSE: (15), (31), (32), (57) are inconsistent by sub-proof #1184.
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | End of split
% 156.04/26.76 | | | |
% 156.04/26.76 | | | Case 2:
% 156.04/26.76 | | | |
% 156.04/26.76 | | | | (58) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 156.04/26.76 | | | | = e3)
% 156.04/26.76 | | | |
% 156.04/26.76 | | | | BETA: splitting (58) gives:
% 156.04/26.76 | | | |
% 156.04/26.76 | | | | Case 1:
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | (59) all_58_8 = e3 & op(e1, e1) = e3
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | ALPHA: (59) implies:
% 156.04/26.76 | | | | | (60) all_58_8 = e3
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | BETA: splitting (46) gives:
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | Case 1:
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | (61) all_54_8 = e1
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | COMBINE_EQS: (35), (61) imply:
% 156.04/26.76 | | | | | | (62) all_38_0 = e1
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | SIMP: (62) implies:
% 156.04/26.76 | | | | | | (63) all_38_0 = e1
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | REDUCE: (3), (63) imply:
% 156.04/26.76 | | | | | | (64) ~ (all_6_2 = e1)
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | SIMP: (64) implies:
% 156.04/26.76 | | | | | | (65) ~ (all_6_2 = e1)
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | REDUCE: (1), (63) imply:
% 156.04/26.76 | | | | | | (66) ~ (e2 = e1)
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | SIMP: (66) implies:
% 156.04/26.76 | | | | | | (67) ~ (e2 = e1)
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | REDUCE: (26), (63) imply:
% 156.04/26.76 | | | | | | (68) ~ (e1 = e0)
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | BETA: splitting (24) gives:
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | Case 1:
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | (69) all_54_10 = e3
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | COMBINE_EQS: (4), (69) imply:
% 156.04/26.76 | | | | | | | (70) all_6_2 = e3
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | SIMP: (70) implies:
% 156.04/26.76 | | | | | | | (71) all_6_2 = e3
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | COMBINE_EQS: (28), (71) imply:
% 156.04/26.76 | | | | | | | (72) all_56_14 = e3
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | REDUCE: (65), (71) imply:
% 156.04/26.76 | | | | | | | (73) ~ (e3 = e1)
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | REDUCE: (18), (71) imply:
% 156.04/26.76 | | | | | | | (74) ~ (e3 = e0)
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | BETA: splitting (5) gives:
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | Case 1:
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | | (75) all_54_7 = e3
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | | COMBINE_EQS: (17), (75) imply:
% 156.04/26.76 | | | | | | | | (76) all_52_13 = e3
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | | REDUCE: (10), (76) imply:
% 156.04/26.76 | | | | | | | | (77) $false
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | | CLOSE: (77) is inconsistent.
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | Case 2:
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | | (78) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | | BETA: splitting (36) gives:
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | | Case 1:
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | | (79) all_56_12 = e3
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | | COMBINE_EQS: (23), (79) imply:
% 156.04/26.76 | | | | | | | | | (80) e3 = e2
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | | COMBINE_EQS: (60), (80) imply:
% 156.04/26.76 | | | | | | | | | (81) all_58_8 = e2
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | | REF_CLOSE: (2), (8), (11), (12), (15), (21), (31), (32), (33),
% 156.04/26.76 | | | | | | | | | (67), (68), (73), (74), (81) are inconsistent by
% 156.04/26.76 | | | | | | | | | sub-proof #1068.
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | Case 2:
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | | (82) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | | BETA: splitting (82) gives:
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | | Case 1:
% 156.04/26.76 | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | (83) all_56_13 = e2
% 156.04/26.76 | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | REF_CLOSE: (13), (67), (83) are inconsistent by sub-proof
% 156.04/26.76 | | | | | | | | | | #150.
% 156.04/26.76 | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | Case 2:
% 156.04/26.76 | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | (84) all_56_14 = e1 | all_56_15 = e0
% 156.04/26.76 | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | BETA: splitting (78) gives:
% 156.04/26.76 | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | Case 1:
% 156.04/26.76 | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | (85) all_54_7 = e2
% 156.04/26.76 | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | REF_CLOSE: (17), (19), (85) are inconsistent by sub-proof
% 156.04/26.76 | | | | | | | | | | | #1427.
% 156.04/26.76 | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | Case 2:
% 156.04/26.76 | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | (86) all_54_7 = e1 | all_54_7 = e0
% 156.04/26.76 | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | BETA: splitting (86) gives:
% 156.04/26.76 | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | Case 1:
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | (87) all_54_7 = e1
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | REF_CLOSE: (17), (27), (87) are inconsistent by sub-proof
% 156.04/26.76 | | | | | | | | | | | | #1426.
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | Case 2:
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | (88) all_54_7 = e0
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | COMBINE_EQS: (17), (88) imply:
% 156.04/26.76 | | | | | | | | | | | | (89) all_52_13 = e0
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | SIMP: (89) implies:
% 156.04/26.76 | | | | | | | | | | | | (90) all_52_13 = e0
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | REDUCE: (22), (90) imply:
% 156.04/26.76 | | | | | | | | | | | | (91) ~ (all_4_2 = e0)
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | SIMP: (91) implies:
% 156.04/26.76 | | | | | | | | | | | | (92) ~ (all_4_2 = e0)
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | BETA: splitting (34) gives:
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | Case 1:
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | (93) all_54_15 = e3
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | COMBINE_EQS: (29), (93) imply:
% 156.04/26.76 | | | | | | | | | | | | | (94) all_4_2 = e3
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | SIMP: (94) implies:
% 156.04/26.76 | | | | | | | | | | | | | (95) all_4_2 = e3
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | COMBINE_EQS: (20), (95) imply:
% 156.04/26.76 | | | | | | | | | | | | | (96) all_56_15 = e3
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | BETA: splitting (84) gives:
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | Case 1:
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | | (97) all_56_14 = e1
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | | COMBINE_EQS: (72), (97) imply:
% 156.04/26.76 | | | | | | | | | | | | | | (98) e3 = e1
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | | REDUCE: (73), (98) imply:
% 156.04/26.76 | | | | | | | | | | | | | | (99) $false
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | | CLOSE: (99) is inconsistent.
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | Case 2:
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | | (100) all_56_15 = e0
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | | COMBINE_EQS: (96), (100) imply:
% 156.04/26.76 | | | | | | | | | | | | | | (101) e3 = e0
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | | REDUCE: (74), (101) imply:
% 156.04/26.76 | | | | | | | | | | | | | | (102) $false
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | | CLOSE: (102) is inconsistent.
% 156.04/26.76 | | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | End of split
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | Case 2:
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | (103) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | | REF_CLOSE: (7), (16), (29), (92), (103) are inconsistent by
% 156.04/26.76 | | | | | | | | | | | | | sub-proof #1014.
% 156.04/26.76 | | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | | End of split
% 156.04/26.76 | | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | | End of split
% 156.04/26.76 | | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | | End of split
% 156.04/26.76 | | | | | | | | | |
% 156.04/26.76 | | | | | | | | | End of split
% 156.04/26.76 | | | | | | | | |
% 156.04/26.76 | | | | | | | | End of split
% 156.04/26.76 | | | | | | | |
% 156.04/26.76 | | | | | | | End of split
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | Case 2:
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | (104) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | | REF_CLOSE: (4), (18), (25), (65), (104) are inconsistent by
% 156.04/26.76 | | | | | | | sub-proof #1527.
% 156.04/26.76 | | | | | | |
% 156.04/26.76 | | | | | | End of split
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | Case 2:
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | (105) all_54_8 = e0
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | | REF_CLOSE: (26), (35), (105) are inconsistent by sub-proof #134.
% 156.04/26.76 | | | | | |
% 156.04/26.76 | | | | | End of split
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | Case 2:
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | (106) all_58_11 = e3 & op(e1, e0) = e3
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | ALPHA: (106) implies:
% 156.04/26.76 | | | | | (107) all_58_11 = e3
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | | REF_CLOSE: (21), (33), (107) are inconsistent by sub-proof #1049.
% 156.04/26.76 | | | | |
% 156.04/26.76 | | | | End of split
% 156.04/26.76 | | | |
% 156.04/26.76 | | | End of split
% 156.04/26.76 | | |
% 156.04/26.76 | | End of split
% 156.04/26.76 | |
% 156.04/26.76 | End of split
% 156.04/26.76 |
% 156.04/26.76 End of proof
% 156.04/26.76
% 156.04/26.76 Sub-proof #134 shows that the following formulas are inconsistent:
% 156.04/26.76 ----------------------------------------------------------------
% 156.04/26.76 (1) all_54_8 = all_38_0
% 156.04/26.76 (2) all_54_8 = e0
% 156.04/26.76 (3) ~ (all_38_0 = e0)
% 156.04/26.76
% 156.04/26.76 Begin of proof
% 156.04/26.76 |
% 156.04/26.76 | COMBINE_EQS: (1), (2) imply:
% 156.04/26.76 | (4) all_38_0 = e0
% 156.04/26.76 |
% 156.04/26.76 | SIMP: (4) implies:
% 156.04/26.76 | (5) all_38_0 = e0
% 156.04/26.76 |
% 156.04/26.76 | REDUCE: (3), (5) imply:
% 156.04/26.76 | (6) $false
% 156.04/26.76 |
% 156.04/26.76 | CLOSE: (6) is inconsistent.
% 156.04/26.76 |
% 156.04/26.76 End of proof
% 156.04/26.76
% 156.04/26.76 Sub-proof #135 shows that the following formulas are inconsistent:
% 156.04/26.76 ----------------------------------------------------------------
% 156.04/26.76 (1) op(e3, e3) = all_10_2
% 156.04/26.76 (2) ~ (all_10_2 = e0)
% 156.04/26.76 (3) ~ (e3 = e0)
% 156.04/26.76 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 156.04/26.76 (5) op(e3, e2) = e3
% 156.04/26.76 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.76
% 156.04/26.76 Begin of proof
% 156.04/26.76 |
% 156.04/26.76 | BETA: splitting (4) gives:
% 156.04/26.76 |
% 156.04/26.76 | Case 1:
% 156.04/26.76 | |
% 156.04/26.76 | | (7) all_58_0 = e0 & op(e3, e3) = e0
% 156.04/26.76 | |
% 156.04/26.76 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #165.
% 156.04/26.76 | |
% 156.04/26.76 | Case 2:
% 156.04/26.76 | |
% 156.04/26.76 | | (8) all_58_1 = e0 & op(e3, e2) = e0
% 156.04/26.76 | |
% 156.04/26.76 | | ALPHA: (8) implies:
% 156.04/26.76 | | (9) op(e3, e2) = e0
% 156.04/26.76 | |
% 156.04/26.76 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #1303.
% 156.04/26.76 | |
% 156.04/26.76 | End of split
% 156.04/26.76 |
% 156.04/26.76 End of proof
% 156.04/26.76
% 156.04/26.76 Sub-proof #136 shows that the following formulas are inconsistent:
% 156.04/26.76 ----------------------------------------------------------------
% 156.04/26.76 (1) all_56_14 = e3
% 156.04/26.76 (2) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.04/26.76 (3) all_56_13 = e1
% 156.04/26.76 (4) ~ (e3 = e1)
% 156.04/26.76 (5) all_54_7 = all_52_13
% 156.04/26.76 (6) ~ (all_52_13 = e2)
% 156.04/26.76 (7) all_56_15 = all_4_2
% 156.04/26.76 (8) ~ (all_52_13 = all_4_2)
% 156.04/26.76 (9) ~ (e2 = e1)
% 156.04/26.76 (10) ~ (all_52_13 = e1)
% 156.04/26.76 (11) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.04/26.76
% 156.04/26.76 Begin of proof
% 156.04/26.76 |
% 156.04/26.76 | BETA: splitting (2) gives:
% 156.04/26.76 |
% 156.04/26.76 | Case 1:
% 156.04/26.76 | |
% 156.04/26.76 | | (12) all_56_13 = e2
% 156.04/26.76 | |
% 156.04/26.76 | | COMBINE_EQS: (3), (12) imply:
% 156.04/26.76 | | (13) e2 = e1
% 156.04/26.76 | |
% 156.04/26.76 | | REDUCE: (9), (13) imply:
% 156.04/26.76 | | (14) $false
% 156.04/26.76 | |
% 156.04/26.76 | | CLOSE: (14) is inconsistent.
% 156.04/26.76 | |
% 156.04/26.76 | Case 2:
% 156.04/26.76 | |
% 156.04/26.76 | | (15) all_56_14 = e1 | all_56_15 = e0
% 156.04/26.76 | |
% 156.04/26.76 | | BETA: splitting (15) gives:
% 156.04/26.76 | |
% 156.04/26.76 | | Case 1:
% 156.04/26.76 | | |
% 156.04/26.76 | | | (16) all_56_14 = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | REF_CLOSE: (1), (4), (16) are inconsistent by sub-proof #585.
% 156.04/26.76 | | |
% 156.04/26.76 | | Case 2:
% 156.04/26.76 | | |
% 156.04/26.76 | | | (17) all_56_15 = e0
% 156.04/26.76 | | |
% 156.04/26.76 | | | COMBINE_EQS: (7), (17) imply:
% 156.04/26.76 | | | (18) all_4_2 = e0
% 156.04/26.76 | | |
% 156.04/26.76 | | | SIMP: (18) implies:
% 156.04/26.76 | | | (19) all_4_2 = e0
% 156.04/26.76 | | |
% 156.04/26.76 | | | REDUCE: (8), (19) imply:
% 156.04/26.76 | | | (20) ~ (all_52_13 = e0)
% 156.04/26.76 | | |
% 156.04/26.76 | | | REF_CLOSE: (5), (6), (10), (11), (20) are inconsistent by sub-proof #179.
% 156.04/26.76 | | |
% 156.04/26.76 | | End of split
% 156.04/26.76 | |
% 156.04/26.76 | End of split
% 156.04/26.76 |
% 156.04/26.76 End of proof
% 156.04/26.76
% 156.04/26.76 Sub-proof #137 shows that the following formulas are inconsistent:
% 156.04/26.76 ----------------------------------------------------------------
% 156.04/26.76 (1) all_58_0 = e2
% 156.04/26.76 (2) ~ (e3 = e0)
% 156.04/26.76 (3) ~ (e2 = e0)
% 156.04/26.76 (4) op(e2, e0) = all_52_13
% 156.04/26.76 (5) ~ (e3 = e1)
% 156.04/26.76 (6) ~ (all_52_13 = e2)
% 156.04/26.76 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.04/26.76 (8) op(e3, e2) = e3
% 156.04/26.76 (9) ~ (e2 = e1)
% 156.04/26.76 (10) ~ (e1 = e0)
% 156.04/26.76 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.04/26.76 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.04/26.76 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.76 (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.04/26.76 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.04/26.76
% 156.04/26.76 Begin of proof
% 156.04/26.76 |
% 156.04/26.76 | BETA: splitting (7) gives:
% 156.04/26.76 |
% 156.04/26.76 | Case 1:
% 156.04/26.76 | |
% 156.04/26.76 | | (14) all_58_9 = e2 & op(e3, e0) = e2
% 156.04/26.76 | |
% 156.04/26.76 | | ALPHA: (14) implies:
% 156.04/26.76 | | (15) all_58_9 = e2
% 156.04/26.76 | |
% 156.04/26.76 | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (11), (12), (13), (15) are
% 156.04/26.76 | | inconsistent by sub-proof #1251.
% 156.04/26.76 | |
% 156.04/26.76 | Case 2:
% 156.04/26.76 | |
% 156.04/26.76 | | (16) all_58_10 = e2 & op(e2, e0) = e2
% 156.04/26.76 | |
% 156.04/26.76 | | ALPHA: (16) implies:
% 156.04/26.76 | | (17) op(e2, e0) = e2
% 156.04/26.76 | |
% 156.04/26.76 | | REF_CLOSE: (4), (6), (12), (17) are inconsistent by sub-proof #1535.
% 156.04/26.76 | |
% 156.04/26.76 | End of split
% 156.04/26.76 |
% 156.04/26.76 End of proof
% 156.04/26.76
% 156.04/26.76 Sub-proof #138 shows that the following formulas are inconsistent:
% 156.04/26.76 ----------------------------------------------------------------
% 156.04/26.76 (1) all_58_14 = e3
% 156.04/26.76 (2) all_54_2 = all_52_8
% 156.04/26.76 (3) ~ (e3 = e1)
% 156.04/26.76 (4) ~ (all_52_8 = e2)
% 156.04/26.76 (5) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.04/26.76 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.04/26.76 (6) ~ (e2 = e1)
% 156.04/26.76 (7) ~ (e1 = e0)
% 156.04/26.76 (8) op(e3, e1) = all_52_8
% 156.04/26.76 (9) ~ (all_52_8 = e1)
% 156.04/26.76 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.76 (11) op(e2, e1) = e2
% 156.04/26.76 (12) all_58_8 = e0
% 156.04/26.76 (13) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.04/26.76
% 156.04/26.76 Begin of proof
% 156.04/26.76 |
% 156.04/26.76 | BETA: splitting (5) gives:
% 156.04/26.76 |
% 156.04/26.76 | Case 1:
% 156.04/26.76 | |
% 156.04/26.76 | | (14) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 156.04/26.76 | | e1)
% 156.04/26.76 | |
% 156.04/26.76 | | BETA: splitting (14) gives:
% 156.04/26.76 | |
% 156.04/26.76 | | Case 1:
% 156.04/26.76 | | |
% 156.04/26.76 | | | (15) all_58_4 = e1 & op(e3, e1) = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | ALPHA: (15) implies:
% 156.04/26.76 | | | (16) op(e3, e1) = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | REF_CLOSE: (2), (4), (8), (9), (10), (13), (16) are inconsistent by
% 156.04/26.76 | | | sub-proof #1023.
% 156.04/26.76 | | |
% 156.04/26.76 | | Case 2:
% 156.04/26.76 | | |
% 156.04/26.76 | | | (17) all_58_5 = e1 & op(e2, e1) = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | ALPHA: (17) implies:
% 156.04/26.76 | | | (18) op(e2, e1) = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | REF_CLOSE: (6), (10), (11), (18) are inconsistent by sub-proof #956.
% 156.04/26.76 | | |
% 156.04/26.76 | | End of split
% 156.04/26.76 | |
% 156.04/26.76 | Case 2:
% 156.04/26.76 | |
% 156.04/26.76 | | (19) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 156.04/26.76 | | e1)
% 156.04/26.76 | |
% 156.04/26.76 | | BETA: splitting (19) gives:
% 156.04/26.76 | |
% 156.04/26.76 | | Case 1:
% 156.04/26.76 | | |
% 156.04/26.76 | | | (20) all_58_8 = e1 & op(e1, e1) = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | ALPHA: (20) implies:
% 156.04/26.76 | | | (21) all_58_8 = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | REF_CLOSE: (7), (12), (21) are inconsistent by sub-proof #1445.
% 156.04/26.76 | | |
% 156.04/26.76 | | Case 2:
% 156.04/26.76 | | |
% 156.04/26.76 | | | (22) all_58_14 = e1 & op(e0, e1) = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | ALPHA: (22) implies:
% 156.04/26.76 | | | (23) all_58_14 = e1
% 156.04/26.76 | | |
% 156.04/26.76 | | | REF_CLOSE: (1), (3), (23) are inconsistent by sub-proof #1147.
% 156.04/26.76 | | |
% 156.04/26.76 | | End of split
% 156.04/26.76 | |
% 156.04/26.76 | End of split
% 156.04/26.76 |
% 156.04/26.76 End of proof
% 156.04/26.76
% 156.04/26.76 Sub-proof #139 shows that the following formulas are inconsistent:
% 156.04/26.76 ----------------------------------------------------------------
% 156.04/26.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.76 (2) op(e1, e2) = e2
% 156.04/26.76 (3) op(e1, e2) = e0
% 156.04/26.76 (4) ~ (e2 = e0)
% 156.04/26.76
% 156.04/26.76 Begin of proof
% 156.04/26.76 |
% 156.04/26.76 | GROUND_INST: instantiating (1) with e0, e2, e2, e1, simplifying with (2), (3)
% 156.04/26.76 | gives:
% 156.04/26.76 | (5) e2 = e0
% 156.04/26.76 |
% 156.04/26.76 | REDUCE: (4), (5) imply:
% 156.04/26.76 | (6) $false
% 156.04/26.76 |
% 156.04/26.76 | CLOSE: (6) is inconsistent.
% 156.04/26.76 |
% 156.04/26.76 End of proof
% 156.04/26.76
% 156.04/26.76 Sub-proof #140 shows that the following formulas are inconsistent:
% 156.04/26.76 ----------------------------------------------------------------
% 156.04/26.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.76 (2) op(e3, e0) = e1
% 156.04/26.76 (3) op(e3, e0) = e0
% 156.04/26.76 (4) ~ (e1 = e0)
% 156.04/26.76
% 156.04/26.76 Begin of proof
% 156.04/26.76 |
% 156.04/26.76 | GROUND_INST: instantiating (1) with e1, e0, e0, e3, simplifying with (2), (3)
% 156.04/26.76 | gives:
% 156.04/26.76 | (5) e1 = e0
% 156.04/26.76 |
% 156.04/26.76 | REDUCE: (4), (5) imply:
% 156.04/26.76 | (6) $false
% 156.04/26.76 |
% 156.04/26.76 | CLOSE: (6) is inconsistent.
% 156.04/26.76 |
% 156.04/26.76 End of proof
% 156.04/26.76
% 156.04/26.76 Sub-proof #141 shows that the following formulas are inconsistent:
% 156.04/26.76 ----------------------------------------------------------------
% 156.04/26.77 (1) all_58_14 = e3
% 156.04/26.77 (2) ~ (all_52_7 = e3)
% 156.04/26.77 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.04/26.77 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.04/26.77 (4) ~ (e3 = e0)
% 156.04/26.77 (5) ~ (e2 = e0)
% 156.04/26.77 (6) ~ (e3 = e1)
% 156.04/26.77 (7) all_56_12 = e3
% 156.04/26.77 (8) op(e0, e0) = e2
% 156.04/26.77 (9) all_56_12 = e2
% 156.04/26.77 (10) all_58_15 = e2
% 156.04/26.77 (11) ~ (e2 = e1)
% 156.04/26.77 (12) ~ (e1 = e0)
% 156.04/26.77 (13) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.04/26.77 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 156.04/26.77 e3)
% 156.04/26.77 (14) op(e0, e2) = all_52_7
% 156.04/26.77 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77 (16) ~ (e3 = e2)
% 156.04/26.77 (17) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.04/26.77 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.04/26.77 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.04/26.77 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | COMBINE_EQS: (7), (9) imply:
% 156.04/26.77 | (18) e3 = e2
% 156.04/26.77 |
% 156.04/26.77 | SIMP: (18) implies:
% 156.04/26.77 | (19) e3 = e2
% 156.04/26.77 |
% 156.04/26.77 | COMBINE_EQS: (1), (19) imply:
% 156.04/26.77 | (20) all_58_14 = e2
% 156.04/26.77 |
% 156.04/26.77 | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14), (15),
% 156.04/26.77 | (16), (17), (20) are inconsistent by sub-proof #1380.
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #142 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) all_58_0 = e2
% 156.04/26.77 (2) all_58_14 = e3
% 156.04/26.77 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.04/26.77 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.04/26.77 (4) all_58_6 = e3
% 156.04/26.77 (5) ~ (e3 = e0)
% 156.04/26.77 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.04/26.77 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.04/26.77 (7) ~ (e2 = e0)
% 156.04/26.77 (8) ~ (e3 = e1)
% 156.04/26.77 (9) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 156.04/26.77 (all_58_14 = e0 & op(e0, e1) = e0)
% 156.04/26.77 (10) ~ (e2 = e1)
% 156.04/26.77 (11) ~ (e1 = e0)
% 156.04/26.77 (12) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.04/26.77 (13) op(e0, e2) = all_52_7
% 156.04/26.77 (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.04/26.77 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.04/26.77 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77 (16) ~ (e3 = e2)
% 156.04/26.77 (17) all_58_12 = e1
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | BETA: splitting (12) gives:
% 156.04/26.77 |
% 156.04/26.77 | Case 1:
% 156.04/26.77 | |
% 156.04/26.77 | | (18) all_58_12 = e2 & op(e0, e3) = e2
% 156.04/26.77 | |
% 156.04/26.77 | | ALPHA: (18) implies:
% 156.04/26.77 | | (19) all_58_12 = e2
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (14), (16), (19)
% 156.04/26.77 | | are inconsistent by sub-proof #1331.
% 156.04/26.77 | |
% 156.04/26.77 | Case 2:
% 156.04/26.77 | |
% 156.04/26.77 | | (20) all_58_13 = e2 & op(e0, e2) = e2
% 156.04/26.77 | |
% 156.04/26.77 | | ALPHA: (20) implies:
% 156.04/26.77 | | (21) op(e0, e2) = e2
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (2), (5), (7), (9), (11), (13), (15), (17), (21) are inconsistent
% 156.04/26.77 | | by sub-proof #845.
% 156.04/26.77 | |
% 156.04/26.77 | End of split
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #143 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77 (2) op(e2, e0) = e3
% 156.04/26.77 (3) op(e2, e0) = e0
% 156.04/26.77 (4) ~ (e3 = e0)
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | GROUND_INST: instantiating (1) with e3, e0, e0, e2, simplifying with (2), (3)
% 156.04/26.77 | gives:
% 156.04/26.77 | (5) e3 = e0
% 156.04/26.77 |
% 156.04/26.77 | REDUCE: (4), (5) imply:
% 156.04/26.77 | (6) $false
% 156.04/26.77 |
% 156.04/26.77 | CLOSE: (6) is inconsistent.
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #144 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) op(e1, e3) = e3
% 156.04/26.77 (2) all_56_14 = e3
% 156.04/26.77 (3) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 156.04/26.77 (4) op(e1, e3) = all_52_2
% 156.04/26.77 (5) ~ (e3 = e1)
% 156.04/26.77 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | BETA: splitting (3) gives:
% 156.04/26.77 |
% 156.04/26.77 | Case 1:
% 156.04/26.77 | |
% 156.04/26.77 | | (7) ~ (all_56_14 = e3)
% 156.04/26.77 | |
% 156.04/26.77 | | REDUCE: (2), (7) imply:
% 156.04/26.77 | | (8) $false
% 156.04/26.77 | |
% 156.04/26.77 | | CLOSE: (8) is inconsistent.
% 156.04/26.77 | |
% 156.04/26.77 | Case 2:
% 156.04/26.77 | |
% 156.04/26.77 | | (9) all_56_6 = e1 & op(e1, e3) = e1
% 156.04/26.77 | |
% 156.04/26.77 | | ALPHA: (9) implies:
% 156.04/26.77 | | (10) op(e1, e3) = e1
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (1), (4), (5), (6), (10) are inconsistent by sub-proof #1164.
% 156.04/26.77 | |
% 156.04/26.77 | End of split
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #145 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) op(e3, e2) = all_52_4
% 156.04/26.77 (2) op(e2, e3) = all_52_1
% 156.04/26.77 (3) op(e3, e2) = e3
% 156.04/26.77 (4) op(e3, e1) = all_52_8
% 156.04/26.77 (5) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.04/26.77 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3)
% 156.04/26.77 & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 &
% 156.04/26.77 ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.04/26.77 (6) ~ (all_52_8 = e3)
% 156.04/26.77 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77 (8) ~ (e3 = e2)
% 156.04/26.77 (9) ~ (all_52_1 = e3)
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | BETA: splitting (5) gives:
% 156.04/26.77 |
% 156.04/26.77 | Case 1:
% 156.04/26.77 | |
% 156.04/26.77 | | (10) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) =
% 156.04/26.77 | | e3 & op(e2, e3) = e3
% 156.04/26.77 | |
% 156.04/26.77 | | ALPHA: (10) implies:
% 156.04/26.77 | | (11) op(e2, e3) = e3
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (2), (7), (9), (11) are inconsistent by sub-proof #1183.
% 156.04/26.77 | |
% 156.04/26.77 | Case 2:
% 156.04/26.77 | |
% 156.04/26.77 | | (12) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) =
% 156.04/26.77 | | e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~
% 156.04/26.77 | | (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (12) are inconsistent by sub-proof
% 156.04/26.77 | | #146.
% 156.04/26.77 | |
% 156.04/26.77 | End of split
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #146 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) op(e3, e2) = all_52_4
% 156.04/26.77 (2) op(e3, e2) = e3
% 156.04/26.77 (3) op(e3, e1) = all_52_8
% 156.04/26.77 (4) ~ (all_52_8 = e3)
% 156.04/26.77 (5) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 &
% 156.04/26.77 op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1)
% 156.04/26.77 & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.04/26.77 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77 (7) ~ (e3 = e2)
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | BETA: splitting (5) gives:
% 156.04/26.77 |
% 156.04/26.77 | Case 1:
% 156.04/26.77 | |
% 156.04/26.77 | | (8) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2
% 156.04/26.77 | | & op(e2, e3) = e2
% 156.04/26.77 | |
% 156.04/26.77 | | ALPHA: (8) implies:
% 156.04/26.77 | | (9) op(e3, e2) = e2
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (1), (2), (6), (7), (9) are inconsistent by sub-proof #1094.
% 156.04/26.77 | |
% 156.04/26.77 | Case 2:
% 156.04/26.77 | |
% 156.04/26.77 | | (10) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) =
% 156.04/26.77 | | e3 & op(e1, e3) = e3
% 156.04/26.77 | |
% 156.04/26.77 | | ALPHA: (10) implies:
% 156.04/26.77 | | (11) op(e3, e1) = e3
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (3), (4), (6), (11) are inconsistent by sub-proof #1538.
% 156.04/26.77 | |
% 156.04/26.77 | End of split
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #147 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) all_58_5 = e2
% 156.04/26.77 (2) all_58_0 = e2
% 156.04/26.77 (3) ~ (e3 = e0)
% 156.04/26.77 (4) ~ (e2 = e0)
% 156.04/26.77 (5) ~ (e3 = e1)
% 156.04/26.77 (6) op(e3, e2) = e3
% 156.04/26.77 (7) ~ (e2 = e1)
% 156.04/26.77 (8) ~ (e1 = e0)
% 156.04/26.77 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 156.04/26.77 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.04/26.77 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.04/26.77 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77 (12) ~ (e3 = e2)
% 156.04/26.77 (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.04/26.77 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | BETA: splitting (9) gives:
% 156.04/26.77 |
% 156.04/26.77 | Case 1:
% 156.04/26.77 | |
% 156.04/26.77 | | (14) all_58_4 = e3 & op(e3, e1) = e3
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14) are
% 156.04/26.77 | | inconsistent by sub-proof #1093.
% 156.04/26.77 | |
% 156.04/26.77 | Case 2:
% 156.04/26.77 | |
% 156.04/26.77 | | (15) all_58_5 = e3 & op(e2, e1) = e3
% 156.04/26.77 | |
% 156.04/26.77 | | ALPHA: (15) implies:
% 156.04/26.77 | | (16) all_58_5 = e3
% 156.04/26.77 | |
% 156.04/26.77 | | REF_CLOSE: (1), (12), (16) are inconsistent by sub-proof #897.
% 156.04/26.77 | |
% 156.04/26.77 | End of split
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #148 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 156.04/26.77 (2) all_56_12 = all_10_2
% 156.04/26.77 (3) all_54_0 = all_10_2
% 156.04/26.77 (4) ~ (all_10_2 = e0)
% 156.04/26.77 (5) ~ (e2 = e0)
% 156.04/26.77 (6) ~ (all_52_11 = all_6_2)
% 156.04/26.77 (7) all_56_13 = e1
% 156.04/26.77 (8) ~ (all_10_2 = e3)
% 156.04/26.77 (9) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.04/26.77 (10) ~ (all_52_11 = e2)
% 156.04/26.77 (11) ~ (all_10_2 = e2)
% 156.04/26.77 (12) ~ (e2 = e1)
% 156.04/26.77 (13) ~ (all_52_8 = all_52_11)
% 156.04/26.77 (14) op(e3, e1) = all_52_8
% 156.04/26.77 (15) all_56_14 = all_6_2
% 156.04/26.77 (16) all_54_14 = all_52_11
% 156.04/26.77 (17) all_56_15 = e2
% 156.04/26.77 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77 (19) ~ (all_52_11 = e0)
% 156.04/26.77 (20) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.04/26.77 (21) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | BETA: splitting (9) gives:
% 156.04/26.77 |
% 156.04/26.77 | Case 1:
% 156.04/26.77 | |
% 156.04/26.77 | | (22) all_54_0 = e3
% 156.04/26.77 | |
% 156.04/26.77 | | COMBINE_EQS: (3), (22) imply:
% 156.04/26.77 | | (23) all_10_2 = e3
% 156.04/26.77 | |
% 156.04/26.77 | | REDUCE: (8), (23) imply:
% 156.04/26.77 | | (24) $false
% 156.04/26.77 | |
% 156.04/26.77 | | CLOSE: (24) is inconsistent.
% 156.04/26.77 | |
% 156.04/26.77 | Case 2:
% 156.04/26.77 | |
% 156.04/26.77 | | (25) ~ (all_54_0 = e3)
% 156.04/26.77 | | (26) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.04/26.77 | |
% 156.04/26.77 | | BETA: splitting (26) gives:
% 156.04/26.77 | |
% 156.04/26.77 | | Case 1:
% 156.04/26.77 | | |
% 156.04/26.77 | | | (27) all_54_0 = e2
% 156.04/26.77 | | |
% 156.04/26.77 | | | COMBINE_EQS: (3), (27) imply:
% 156.04/26.77 | | | (28) all_10_2 = e2
% 156.04/26.77 | | |
% 156.04/26.77 | | | REDUCE: (11), (28) imply:
% 156.04/26.77 | | | (29) $false
% 156.04/26.77 | | |
% 156.04/26.77 | | | CLOSE: (29) is inconsistent.
% 156.04/26.77 | | |
% 156.04/26.77 | | Case 2:
% 156.04/26.77 | | |
% 156.04/26.77 | | | (30) all_54_0 = e1 | all_54_0 = e0
% 156.04/26.77 | | |
% 156.04/26.77 | | | BETA: splitting (21) gives:
% 156.04/26.77 | | |
% 156.04/26.77 | | | Case 1:
% 156.04/26.77 | | | |
% 156.04/26.77 | | | | (31) all_56_12 = e3
% 156.04/26.77 | | | |
% 156.04/26.77 | | | | COMBINE_EQS: (2), (31) imply:
% 156.04/26.77 | | | | (32) all_10_2 = e3
% 156.04/26.77 | | | |
% 156.04/26.77 | | | | SIMP: (32) implies:
% 156.04/26.77 | | | | (33) all_10_2 = e3
% 156.04/26.77 | | | |
% 156.04/26.77 | | | | REDUCE: (8), (33) imply:
% 156.04/26.77 | | | | (34) $false
% 156.04/26.77 | | | |
% 156.04/26.77 | | | | CLOSE: (34) is inconsistent.
% 156.04/26.77 | | | |
% 156.04/26.77 | | | Case 2:
% 156.04/26.77 | | | |
% 156.04/26.77 | | | | (35) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.04/26.77 | | | |
% 156.04/26.77 | | | | BETA: splitting (35) gives:
% 156.04/26.77 | | | |
% 156.04/26.77 | | | | Case 1:
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | | (36) all_56_13 = e2
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | | COMBINE_EQS: (7), (36) imply:
% 156.04/26.77 | | | | | (37) e2 = e1
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | | REDUCE: (12), (37) imply:
% 156.04/26.77 | | | | | (38) $false
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | | CLOSE: (38) is inconsistent.
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | Case 2:
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | | (39) all_56_14 = e1 | all_56_15 = e0
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | | BETA: splitting (39) gives:
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | | Case 1:
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | (40) all_56_14 = e1
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | COMBINE_EQS: (15), (40) imply:
% 156.04/26.77 | | | | | | (41) all_6_2 = e1
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | REDUCE: (6), (41) imply:
% 156.04/26.77 | | | | | | (42) ~ (all_52_11 = e1)
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | BETA: splitting (20) gives:
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | Case 1:
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | | (43) all_54_14 = e3
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | | COMBINE_EQS: (16), (43) imply:
% 156.04/26.77 | | | | | | | (44) all_52_11 = e3
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | | SIMP: (44) implies:
% 156.04/26.77 | | | | | | | (45) all_52_11 = e3
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | | REDUCE: (13), (45) imply:
% 156.04/26.77 | | | | | | | (46) ~ (all_52_8 = e3)
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | | BETA: splitting (1) gives:
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | | Case 1:
% 156.04/26.77 | | | | | | | |
% 156.04/26.77 | | | | | | | | (47) ~ (all_56_12 = e1)
% 156.04/26.77 | | | | | | | |
% 156.04/26.77 | | | | | | | | REDUCE: (2), (47) imply:
% 156.04/26.77 | | | | | | | | (48) ~ (all_10_2 = e1)
% 156.04/26.77 | | | | | | | |
% 156.04/26.77 | | | | | | | | REF_CLOSE: (3), (4), (30), (48) are inconsistent by sub-proof
% 156.04/26.77 | | | | | | | | #1308.
% 156.04/26.77 | | | | | | | |
% 156.04/26.77 | | | | | | | Case 2:
% 156.04/26.77 | | | | | | | |
% 156.04/26.77 | | | | | | | | (49) all_56_1 = e3 & op(e3, e1) = e3
% 156.04/26.77 | | | | | | | |
% 156.04/26.77 | | | | | | | | ALPHA: (49) implies:
% 156.04/26.77 | | | | | | | | (50) op(e3, e1) = e3
% 156.04/26.77 | | | | | | | |
% 156.04/26.77 | | | | | | | | REF_CLOSE: (14), (18), (46), (50) are inconsistent by sub-proof
% 156.04/26.77 | | | | | | | | #1538.
% 156.04/26.77 | | | | | | | |
% 156.04/26.77 | | | | | | | End of split
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | Case 2:
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | | (51) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | | REF_CLOSE: (10), (16), (19), (42), (51) are inconsistent by
% 156.04/26.77 | | | | | | | sub-proof #1149.
% 156.04/26.77 | | | | | | |
% 156.04/26.77 | | | | | | End of split
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | Case 2:
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | (52) all_56_15 = e0
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | COMBINE_EQS: (17), (52) imply:
% 156.04/26.77 | | | | | | (53) e2 = e0
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | REDUCE: (5), (53) imply:
% 156.04/26.77 | | | | | | (54) $false
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | | CLOSE: (54) is inconsistent.
% 156.04/26.77 | | | | | |
% 156.04/26.77 | | | | | End of split
% 156.04/26.77 | | | | |
% 156.04/26.77 | | | | End of split
% 156.04/26.77 | | | |
% 156.04/26.77 | | | End of split
% 156.04/26.77 | | |
% 156.04/26.77 | | End of split
% 156.04/26.77 | |
% 156.04/26.77 | End of split
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #149 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) all_56_14 = e1 | all_56_15 = e0
% 156.04/26.77 (2) ~ (e2 = e0)
% 156.04/26.77 (3) all_56_14 = e0
% 156.04/26.77 (4) ~ (e1 = e0)
% 156.04/26.77 (5) all_56_15 = e2
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | BETA: splitting (1) gives:
% 156.04/26.77 |
% 156.04/26.77 | Case 1:
% 156.04/26.77 | |
% 156.04/26.77 | | (6) all_56_14 = e1
% 156.04/26.77 | |
% 156.04/26.77 | | COMBINE_EQS: (3), (6) imply:
% 156.04/26.77 | | (7) e1 = e0
% 156.04/26.77 | |
% 156.04/26.77 | | SIMP: (7) implies:
% 156.04/26.77 | | (8) e1 = e0
% 156.04/26.77 | |
% 156.04/26.77 | | REDUCE: (4), (8) imply:
% 156.04/26.77 | | (9) $false
% 156.04/26.77 | |
% 156.04/26.77 | | CLOSE: (9) is inconsistent.
% 156.04/26.77 | |
% 156.04/26.77 | Case 2:
% 156.04/26.77 | |
% 156.04/26.77 | | (10) all_56_15 = e0
% 156.04/26.77 | |
% 156.04/26.77 | | COMBINE_EQS: (5), (10) imply:
% 156.04/26.77 | | (11) e2 = e0
% 156.04/26.77 | |
% 156.04/26.77 | | REDUCE: (2), (11) imply:
% 156.04/26.77 | | (12) $false
% 156.04/26.77 | |
% 156.04/26.77 | | CLOSE: (12) is inconsistent.
% 156.04/26.77 | |
% 156.04/26.77 | End of split
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #150 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) all_56_13 = e2
% 156.04/26.77 (2) all_56_13 = e1
% 156.04/26.77 (3) ~ (e2 = e1)
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | COMBINE_EQS: (1), (2) imply:
% 156.04/26.77 | (4) e2 = e1
% 156.04/26.77 |
% 156.04/26.77 | SIMP: (4) implies:
% 156.04/26.77 | (5) e2 = e1
% 156.04/26.77 |
% 156.04/26.77 | REDUCE: (3), (5) imply:
% 156.04/26.77 | (6) $false
% 156.04/26.77 |
% 156.04/26.77 | CLOSE: (6) is inconsistent.
% 156.04/26.77 |
% 156.04/26.77 End of proof
% 156.04/26.77
% 156.04/26.77 Sub-proof #151 shows that the following formulas are inconsistent:
% 156.04/26.77 ----------------------------------------------------------------
% 156.04/26.77 (1) all_58_12 = e2
% 156.04/26.77 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.04/26.77 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.04/26.77 (3) ~ (e3 = e0)
% 156.04/26.77 (4) ~ (e2 = e0)
% 156.04/26.77 (5) ~ (e3 = e1)
% 156.04/26.77 (6) op(e0, e0) = e2
% 156.04/26.77 (7) op(e0, e2) = e0
% 156.04/26.77 (8) all_58_15 = e2
% 156.04/26.77 (9) ~ (e2 = e1)
% 156.04/26.77 (10) ~ (e1 = e0)
% 156.04/26.77 (11) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.04/26.77 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 156.04/26.77 e3)
% 156.04/26.77 (12) op(e0, e2) = all_52_7
% 156.04/26.77 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.77 (14) ~ (e3 = e2)
% 156.04/26.77 (15) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.04/26.77 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.04/26.77 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.04/26.77 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.04/26.77
% 156.04/26.77 Begin of proof
% 156.04/26.77 |
% 156.04/26.77 | BETA: splitting (2) gives:
% 156.04/26.77 |
% 156.04/26.77 | Case 1:
% 156.04/26.77 | |
% 156.04/26.77 | | (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 156.04/26.77 | | e1)
% 156.04/26.77 | |
% 156.04/26.77 | | BETA: splitting (16) gives:
% 156.04/26.77 | |
% 156.04/26.77 | | Case 1:
% 156.04/26.77 | | |
% 156.04/26.77 | | | (17) all_58_12 = e1 & op(e0, e3) = e1
% 156.04/26.77 | | |
% 156.04/26.77 | | | REF_CLOSE: (1), (9), (17) are inconsistent by sub-proof #1492.
% 156.04/26.77 | | |
% 156.04/26.77 | | Case 2:
% 156.04/26.77 | | |
% 156.04/26.77 | | | (18) all_58_13 = e1 & op(e0, e2) = e1
% 156.04/26.77 | | |
% 156.04/26.77 | | | ALPHA: (18) implies:
% 156.04/26.77 | | | (19) op(e0, e2) = e1
% 156.04/26.77 | | |
% 156.04/26.77 | | | REF_CLOSE: (7), (10), (12), (13), (19) are inconsistent by sub-proof
% 156.04/26.77 | | | #1396.
% 156.04/26.77 | | |
% 156.04/26.77 | | End of split
% 156.04/26.78 | |
% 156.04/26.78 | Case 2:
% 156.04/26.78 | |
% 156.04/26.78 | | (20) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 156.04/26.78 | | e1)
% 156.04/26.78 | |
% 156.04/26.78 | | BETA: splitting (20) gives:
% 156.04/26.78 | |
% 156.04/26.78 | | Case 1:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (21) all_58_14 = e1 & op(e0, e1) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | ALPHA: (21) implies:
% 156.04/26.78 | | | (22) all_58_14 = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | BETA: splitting (15) gives:
% 156.04/26.78 | | |
% 156.04/26.78 | | | Case 1:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | (23) all_58_15 = e0 & op(e0, e0) = e0
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | ALPHA: (23) implies:
% 156.04/26.78 | | | | (24) all_58_15 = e0
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | REF_CLOSE: (4), (8), (24) are inconsistent by sub-proof #1462.
% 156.04/26.78 | | | |
% 156.04/26.78 | | | Case 2:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | (25) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 156.04/26.78 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 156.04/26.78 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 156.04/26.78 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | ALPHA: (25) implies:
% 156.04/26.78 | | | | (26) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 156.04/26.78 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | BETA: splitting (11) gives:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | Case 1:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | (27) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 156.04/26.78 | | | | | e2) = e3)
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | BETA: splitting (27) gives:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | Case 1:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (28) all_58_12 = e3 & op(e0, e3) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | ALPHA: (28) implies:
% 156.04/26.78 | | | | | | (29) all_58_12 = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (1), (14), (29) are inconsistent by sub-proof #1490.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | Case 2:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (30) all_58_13 = e3 & op(e0, e2) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | ALPHA: (30) implies:
% 156.04/26.78 | | | | | | (31) all_58_13 = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | BETA: splitting (26) gives:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | Case 1:
% 156.04/26.78 | | | | | | |
% 156.04/26.78 | | | | | | | (32) all_58_12 = e0 & op(e0, e3) = e0
% 156.04/26.78 | | | | | | |
% 156.04/26.78 | | | | | | | REF_CLOSE: (1), (4), (32) are inconsistent by sub-proof #1369.
% 156.04/26.78 | | | | | | |
% 156.04/26.78 | | | | | | Case 2:
% 156.04/26.78 | | | | | | |
% 156.04/26.78 | | | | | | | (33) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 156.04/26.78 | | | | | | | op(e0, e1) = e0)
% 156.04/26.78 | | | | | | |
% 156.04/26.78 | | | | | | | BETA: splitting (33) gives:
% 156.04/26.78 | | | | | | |
% 156.04/26.78 | | | | | | | Case 1:
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | (34) all_58_13 = e0 & op(e0, e2) = e0
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | ALPHA: (34) implies:
% 156.04/26.78 | | | | | | | | (35) all_58_13 = e0
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | COMBINE_EQS: (31), (35) imply:
% 156.04/26.78 | | | | | | | | (36) e3 = e0
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | SIMP: (36) implies:
% 156.04/26.78 | | | | | | | | (37) e3 = e0
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | REDUCE: (3), (37) imply:
% 156.04/26.78 | | | | | | | | (38) $false
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | CLOSE: (38) is inconsistent.
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | Case 2:
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | (39) all_58_14 = e0 & op(e0, e1) = e0
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | ALPHA: (39) implies:
% 156.04/26.78 | | | | | | | | (40) all_58_14 = e0
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | | REF_CLOSE: (10), (22), (40) are inconsistent by sub-proof #614.
% 156.04/26.78 | | | | | | | |
% 156.04/26.78 | | | | | | | End of split
% 156.04/26.78 | | | | | | |
% 156.04/26.78 | | | | | | End of split
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | End of split
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | Case 2:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | (41) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 156.04/26.78 | | | | | e0) = e3)
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | BETA: splitting (41) gives:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | Case 1:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (42) all_58_14 = e3 & op(e0, e1) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (5), (22), (42) are inconsistent by sub-proof #872.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | Case 2:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (43) all_58_15 = e3 & op(e0, e0) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | ALPHA: (43) implies:
% 156.04/26.78 | | | | | | (44) op(e0, e0) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (6), (13), (14), (44) are inconsistent by sub-proof
% 156.04/26.78 | | | | | | #1382.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | End of split
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | End of split
% 156.04/26.78 | | | |
% 156.04/26.78 | | | End of split
% 156.04/26.78 | | |
% 156.04/26.78 | | Case 2:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (45) all_58_15 = e1 & op(e0, e0) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | ALPHA: (45) implies:
% 156.04/26.78 | | | (46) op(e0, e0) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | REF_CLOSE: (6), (9), (13), (46) are inconsistent by sub-proof #1386.
% 156.04/26.78 | | |
% 156.04/26.78 | | End of split
% 156.04/26.78 | |
% 156.04/26.78 | End of split
% 156.04/26.78 |
% 156.04/26.78 End of proof
% 156.04/26.78
% 156.04/26.78 Sub-proof #152 shows that the following formulas are inconsistent:
% 156.04/26.78 ----------------------------------------------------------------
% 156.04/26.78 (1) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1)
% 156.04/26.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.78 (3) op(e2, e2) = e1
% 156.04/26.78
% 156.04/26.78 Begin of proof
% 156.04/26.78 |
% 156.04/26.78 | ALPHA: (1) implies:
% 156.04/26.78 | (4) ~ (all_20_1 = e1)
% 156.04/26.78 | (5) op(e2, e2) = all_20_1
% 156.04/26.78 |
% 156.04/26.78 | GROUND_INST: instantiating (2) with e1, all_20_1, e2, e2, simplifying with
% 156.04/26.78 | (3), (5) gives:
% 156.04/26.78 | (6) all_20_1 = e1
% 156.04/26.78 |
% 156.04/26.78 | REDUCE: (4), (6) imply:
% 156.04/26.78 | (7) $false
% 156.04/26.78 |
% 156.04/26.78 | CLOSE: (7) is inconsistent.
% 156.04/26.78 |
% 156.04/26.78 End of proof
% 156.04/26.78
% 156.04/26.78 Sub-proof #153 shows that the following formulas are inconsistent:
% 156.04/26.78 ----------------------------------------------------------------
% 156.04/26.78 (1) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.04/26.78 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.04/26.78 (2) all_58_6 = e2
% 156.04/26.78 (3) ~ (e3 = e0)
% 156.04/26.78 (4) ~ (e2 = e0)
% 156.04/26.78 (5) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.78 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.04/26.78 (6) ~ (e3 = e1)
% 156.04/26.78 (7) op(e1, e2) = all_52_6
% 156.04/26.78 (8) op(e0, e0) = e2
% 156.04/26.78 (9) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.04/26.78 (10) ~ (all_52_6 = e0)
% 156.04/26.78 (11) op(e0, e2) = e0
% 156.04/26.78 (12) ~ (e2 = e1)
% 156.04/26.78 (13) ~ (e1 = e0)
% 156.04/26.78 (14) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.04/26.78 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 156.04/26.78 e3)
% 156.04/26.78 (15) op(e0, e2) = all_52_7
% 156.04/26.78 (16) all_58_1 = e2
% 156.04/26.78 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.78 (18) ~ (e3 = e2)
% 156.04/26.78 (19) all_58_3 = e1
% 156.04/26.78
% 156.04/26.78 Begin of proof
% 156.04/26.78 |
% 156.04/26.78 | BETA: splitting (9) gives:
% 156.04/26.78 |
% 156.04/26.78 | Case 1:
% 156.04/26.78 | |
% 156.04/26.78 | | (20) all_58_6 = e0 & op(e1, e3) = e0
% 156.04/26.78 | |
% 156.04/26.78 | | REF_CLOSE: (2), (4), (20) are inconsistent by sub-proof #1483.
% 156.04/26.78 | |
% 156.04/26.78 | Case 2:
% 156.04/26.78 | |
% 156.04/26.78 | | (21) all_58_12 = e0 & op(e0, e3) = e0
% 156.04/26.78 | |
% 156.04/26.78 | | ALPHA: (21) implies:
% 156.04/26.78 | | (22) all_58_12 = e0
% 156.04/26.78 | |
% 156.04/26.78 | | BETA: splitting (1) gives:
% 156.04/26.78 | |
% 156.04/26.78 | | Case 1:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (23) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2)
% 156.04/26.78 | | | = e1)
% 156.04/26.78 | | |
% 156.04/26.78 | | | BETA: splitting (23) gives:
% 156.04/26.78 | | |
% 156.04/26.78 | | | Case 1:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | (24) all_58_12 = e1 & op(e0, e3) = e1
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | REF_CLOSE: (13), (22), (24) are inconsistent by sub-proof #1422.
% 156.04/26.78 | | | |
% 156.04/26.78 | | | Case 2:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | (25) all_58_13 = e1 & op(e0, e2) = e1
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | ALPHA: (25) implies:
% 156.04/26.78 | | | | (26) op(e0, e2) = e1
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | REF_CLOSE: (11), (13), (15), (17), (26) are inconsistent by sub-proof
% 156.04/26.78 | | | | #1396.
% 156.04/26.78 | | | |
% 156.04/26.78 | | | End of split
% 156.04/26.78 | | |
% 156.04/26.78 | | Case 2:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (27) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0)
% 156.04/26.78 | | | = e1)
% 156.04/26.78 | | |
% 156.04/26.78 | | | BETA: splitting (27) gives:
% 156.04/26.78 | | |
% 156.04/26.78 | | | Case 1:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | (28) all_58_14 = e1 & op(e0, e1) = e1
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | ALPHA: (28) implies:
% 156.04/26.78 | | | | (29) all_58_14 = e1
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | BETA: splitting (14) gives:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | Case 1:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | (30) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 156.04/26.78 | | | | | e2) = e3)
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | BETA: splitting (30) gives:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | Case 1:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (31) all_58_12 = e3 & op(e0, e3) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | ALPHA: (31) implies:
% 156.04/26.78 | | | | | | (32) all_58_12 = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (3), (22), (32) are inconsistent by sub-proof #1463.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | Case 2:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (33) all_58_13 = e3 & op(e0, e2) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (3), (4), (5), (7), (10), (13), (16), (17), (19), (33)
% 156.04/26.78 | | | | | | are inconsistent by sub-proof #155.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | End of split
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | Case 2:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | (34) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 156.04/26.78 | | | | | e0) = e3)
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | BETA: splitting (34) gives:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | Case 1:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (35) all_58_14 = e3 & op(e0, e1) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | ALPHA: (35) implies:
% 156.04/26.78 | | | | | | (36) all_58_14 = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (6), (29), (36) are inconsistent by sub-proof #1147.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | Case 2:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (37) all_58_15 = e3 & op(e0, e0) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | ALPHA: (37) implies:
% 156.04/26.78 | | | | | | (38) op(e0, e0) = e3
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (8), (17), (18), (38) are inconsistent by sub-proof
% 156.04/26.78 | | | | | | #1382.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | End of split
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | End of split
% 156.04/26.78 | | | |
% 156.04/26.78 | | | Case 2:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | (39) all_58_15 = e1 & op(e0, e0) = e1
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | ALPHA: (39) implies:
% 156.04/26.78 | | | | (40) op(e0, e0) = e1
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | REF_CLOSE: (8), (12), (17), (40) are inconsistent by sub-proof #1386.
% 156.04/26.78 | | | |
% 156.04/26.78 | | | End of split
% 156.04/26.78 | | |
% 156.04/26.78 | | End of split
% 156.04/26.78 | |
% 156.04/26.78 | End of split
% 156.04/26.78 |
% 156.04/26.78 End of proof
% 156.04/26.78
% 156.04/26.78 Sub-proof #154 shows that the following formulas are inconsistent:
% 156.04/26.78 ----------------------------------------------------------------
% 156.04/26.78 (1) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.04/26.78 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.04/26.78 (2) ~ (all_52_7 = e2)
% 156.04/26.78 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.04/26.78 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.04/26.78 (4) all_58_6 = e2
% 156.04/26.78 (5) ~ (e3 = e0)
% 156.04/26.78 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.04/26.78 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.04/26.78 (7) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 156.04/26.78 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.04/26.78 (8) ~ (e2 = e0)
% 156.04/26.78 (9) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.78 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.04/26.78 (10) ~ (e3 = e1)
% 156.04/26.78 (11) op(e1, e2) = all_52_6
% 156.04/26.78 (12) op(e0, e0) = e2
% 156.04/26.78 (13) op(e0, e1) = all_52_11
% 156.04/26.78 (14) ~ (all_52_6 = e0)
% 156.04/26.78 (15) op(e0, e2) = e0
% 156.04/26.78 (16) ~ (e2 = e1)
% 156.04/26.78 (17) ~ (e1 = e0)
% 156.04/26.78 (18) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.04/26.78 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 156.04/26.78 e3)
% 156.04/26.78 (19) op(e0, e2) = all_52_7
% 156.04/26.78 (20) all_58_1 = e2
% 156.04/26.78 (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.04/26.78 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.04/26.78 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.78 (23) ~ (e3 = e2)
% 156.04/26.78 (24) all_58_3 = e1
% 156.04/26.78 (25) all_58_14 = e0 & op(e0, e1) = e0
% 156.04/26.78
% 156.04/26.78 Begin of proof
% 156.04/26.78 |
% 156.04/26.78 | ALPHA: (25) implies:
% 156.04/26.78 | (26) all_58_14 = e0
% 156.04/26.78 | (27) op(e0, e1) = e0
% 156.04/26.78 |
% 156.04/26.78 | BETA: splitting (1) gives:
% 156.04/26.78 |
% 156.04/26.78 | Case 1:
% 156.04/26.78 | |
% 156.04/26.78 | | (28) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 156.04/26.78 | | e1)
% 156.04/26.78 | |
% 156.04/26.78 | | BETA: splitting (28) gives:
% 156.04/26.78 | |
% 156.04/26.78 | | Case 1:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (29) all_58_12 = e1 & op(e0, e3) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | ALPHA: (29) implies:
% 156.04/26.78 | | | (30) all_58_12 = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | BETA: splitting (18) gives:
% 156.04/26.78 | | |
% 156.04/26.78 | | | Case 1:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | (31) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 156.04/26.78 | | | | e2) = e3)
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | BETA: splitting (31) gives:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | Case 1:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | (32) all_58_12 = e3 & op(e0, e3) = e3
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | REF_CLOSE: (10), (30), (32) are inconsistent by sub-proof #1278.
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | Case 2:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | (33) all_58_13 = e3 & op(e0, e2) = e3
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | REF_CLOSE: (5), (8), (9), (11), (14), (17), (20), (22), (24), (33) are
% 156.04/26.78 | | | | | inconsistent by sub-proof #155.
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | End of split
% 156.04/26.78 | | | |
% 156.04/26.78 | | | Case 2:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | (34) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 156.04/26.78 | | | | e0) = e3)
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | BETA: splitting (34) gives:
% 156.04/26.78 | | | |
% 156.04/26.78 | | | | Case 1:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | (35) all_58_14 = e3 & op(e0, e1) = e3
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | ALPHA: (35) implies:
% 156.04/26.78 | | | | | (36) all_58_14 = e3
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | REF_CLOSE: (5), (26), (36) are inconsistent by sub-proof #1444.
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | Case 2:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | (37) all_58_15 = e3 & op(e0, e0) = e3
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | ALPHA: (37) implies:
% 156.04/26.78 | | | | | (38) op(e0, e0) = e3
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | BETA: splitting (7) gives:
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | | Case 1:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (39) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 156.04/26.78 | | | | | | op(e0, e2) = e2)
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (16), (17), (19),
% 156.04/26.78 | | | | | | (21), (22), (23), (39) are inconsistent by sub-proof
% 156.04/26.78 | | | | | | #1478.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | Case 2:
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | (40) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 156.04/26.78 | | | | | | op(e0, e0) = e2)
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | | REF_CLOSE: (8), (13), (22), (23), (27), (38), (40) are inconsistent
% 156.04/26.78 | | | | | | by sub-proof #1371.
% 156.04/26.78 | | | | | |
% 156.04/26.78 | | | | | End of split
% 156.04/26.78 | | | | |
% 156.04/26.78 | | | | End of split
% 156.04/26.78 | | | |
% 156.04/26.78 | | | End of split
% 156.04/26.78 | | |
% 156.04/26.78 | | Case 2:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (41) all_58_13 = e1 & op(e0, e2) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | ALPHA: (41) implies:
% 156.04/26.78 | | | (42) op(e0, e2) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | REF_CLOSE: (15), (17), (19), (22), (42) are inconsistent by sub-proof
% 156.04/26.78 | | | #1396.
% 156.04/26.78 | | |
% 156.04/26.78 | | End of split
% 156.04/26.78 | |
% 156.04/26.78 | Case 2:
% 156.04/26.78 | |
% 156.04/26.78 | | (43) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 156.04/26.78 | | e1)
% 156.04/26.78 | |
% 156.04/26.78 | | BETA: splitting (43) gives:
% 156.04/26.78 | |
% 156.04/26.78 | | Case 1:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (44) all_58_14 = e1 & op(e0, e1) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | REF_CLOSE: (17), (26), (44) are inconsistent by sub-proof #482.
% 156.04/26.78 | | |
% 156.04/26.78 | | Case 2:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (45) all_58_15 = e1 & op(e0, e0) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | ALPHA: (45) implies:
% 156.04/26.78 | | | (46) op(e0, e0) = e1
% 156.04/26.78 | | |
% 156.04/26.78 | | | REF_CLOSE: (12), (16), (22), (46) are inconsistent by sub-proof #1386.
% 156.04/26.78 | | |
% 156.04/26.78 | | End of split
% 156.04/26.78 | |
% 156.04/26.78 | End of split
% 156.04/26.78 |
% 156.04/26.78 End of proof
% 156.04/26.78
% 156.04/26.78 Sub-proof #155 shows that the following formulas are inconsistent:
% 156.04/26.78 ----------------------------------------------------------------
% 156.04/26.78 (1) all_58_13 = e3 & op(e0, e2) = e3
% 156.04/26.78 (2) ~ (e3 = e0)
% 156.04/26.78 (3) ~ (e2 = e0)
% 156.04/26.78 (4) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.78 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.04/26.78 (5) op(e1, e2) = all_52_6
% 156.04/26.78 (6) ~ (all_52_6 = e0)
% 156.04/26.78 (7) ~ (e1 = e0)
% 156.04/26.78 (8) all_58_1 = e2
% 156.04/26.78 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.78 (10) all_58_3 = e1
% 156.04/26.78
% 156.04/26.78 Begin of proof
% 156.04/26.78 |
% 156.04/26.78 | ALPHA: (1) implies:
% 156.04/26.78 | (11) all_58_13 = e3
% 156.04/26.78 |
% 156.04/26.78 | BETA: splitting (4) gives:
% 156.04/26.78 |
% 156.04/26.78 | Case 1:
% 156.04/26.78 | |
% 156.04/26.78 | | (12) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 156.04/26.78 | | e0)
% 156.04/26.78 | |
% 156.04/26.78 | | BETA: splitting (12) gives:
% 156.04/26.78 | |
% 156.04/26.78 | | Case 1:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (13) all_58_1 = e0 & op(e3, e2) = e0
% 156.04/26.78 | | |
% 156.04/26.78 | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #796.
% 156.04/26.78 | | |
% 156.04/26.78 | | Case 2:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (14) all_58_3 = e0 & op(e2, e2) = e0
% 156.04/26.78 | | |
% 156.04/26.78 | | | REF_CLOSE: (7), (10), (14) are inconsistent by sub-proof #203.
% 156.04/26.78 | | |
% 156.04/26.78 | | End of split
% 156.04/26.78 | |
% 156.04/26.78 | Case 2:
% 156.04/26.78 | |
% 156.04/26.78 | | (15) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 156.04/26.78 | | e0)
% 156.04/26.78 | |
% 156.04/26.78 | | BETA: splitting (15) gives:
% 156.04/26.78 | |
% 156.04/26.78 | | Case 1:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (16) all_58_7 = e0 & op(e1, e2) = e0
% 156.04/26.78 | | |
% 156.04/26.78 | | | REF_CLOSE: (5), (6), (9), (16) are inconsistent by sub-proof #1301.
% 156.04/26.78 | | |
% 156.04/26.78 | | Case 2:
% 156.04/26.78 | | |
% 156.04/26.78 | | | (17) all_58_13 = e0 & op(e0, e2) = e0
% 156.04/26.78 | | |
% 156.04/26.78 | | | REF_CLOSE: (2), (11), (17) are inconsistent by sub-proof #1139.
% 156.04/26.78 | | |
% 156.04/26.78 | | End of split
% 156.04/26.78 | |
% 156.04/26.78 | End of split
% 156.04/26.78 |
% 156.04/26.78 End of proof
% 156.04/26.78
% 156.04/26.78 Sub-proof #156 shows that the following formulas are inconsistent:
% 156.04/26.78 ----------------------------------------------------------------
% 156.04/26.78 (1) all_58_5 = e2
% 156.04/26.78 (2) ~ (all_52_12 = e3)
% 156.04/26.78 (3) op(e3, e2) = e2
% 156.04/26.78 (4) op(e3, e0) = all_52_12
% 156.04/26.78 (5) all_54_10 = all_6_2
% 156.04/26.78 (6) all_56_12 = all_10_2
% 156.04/26.78 (7) ~ (all_26_0 = e2)
% 156.04/26.78 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.04/26.78 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.04/26.78 (9) op(e3, e2) = all_52_4
% 156.04/26.78 (10) ~ (all_52_3 = e0)
% 156.04/26.78 (11) all_54_0 = all_10_2
% 156.04/26.78 (12) op(e2, e3) = all_52_1
% 156.04/26.78 (13) all_58_6 = e2
% 156.04/26.78 (14) all_54_2 = all_52_8
% 156.04/26.78 (15) op(e1, e0) = all_26_0
% 156.04/26.78 (16) ~ (all_10_2 = e0)
% 156.04/26.78 (17) ~ (e3 = e0)
% 156.04/26.78 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.04/26.78 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.04/26.78 (19) ~ (e2 = e0)
% 156.04/26.78 (20) ~ (all_52_11 = all_6_2)
% 156.04/26.78 (21) ~ (all_52_6 = e2)
% 156.04/26.78 (22) ~ (all_52_3 = e2)
% 156.04/26.78 (23) op(e1, e0) = all_20_0
% 156.04/26.78 (24) op(e2, e0) = all_52_13
% 156.04/26.78 (25) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.04/26.78 (26) ~ (e3 = e1)
% 156.04/26.78 (27) op(e1, e2) = all_52_6
% 156.04/26.79 (28) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.04/26.79 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.79 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.04/26.79 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.04/26.79 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.04/26.79 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.04/26.79 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.04/26.79 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.04/26.79 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.04/26.79 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.04/26.79 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.04/26.79 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.04/26.79 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.04/26.79 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.04/26.79 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.04/26.79 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.04/26.79 = e0)
% 156.04/26.79 (29) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.04/26.79 (30) ~ (all_52_8 = e2)
% 156.04/26.79 (31) ~ (all_52_11 = e2)
% 156.04/26.79 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.79 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 156.04/26.79 (33) ~ (all_52_3 = all_10_2)
% 156.04/26.79 (34) ~ (all_6_2 = e3)
% 156.04/26.79 (35) ~ (all_52_8 = all_10_2)
% 156.04/26.79 (36) ~ (all_6_2 = e0)
% 156.04/26.79 (37) ~ (all_52_13 = e2)
% 156.04/26.79 (38) ~ (all_26_0 = all_6_2)
% 156.04/26.79 (39) op(e0, e1) = all_52_11
% 156.04/26.79 (40) ~ (all_52_6 = e1)
% 156.04/26.79 (41) ~ (all_52_8 = all_6_2)
% 156.04/26.79 (42) ~ (all_10_2 = e2)
% 156.04/26.79 (43) all_58_10 = e3
% 156.04/26.79 (44) ~ (e2 = e1)
% 156.04/26.79 (45) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.04/26.79 (46) ~ (all_52_12 = all_10_2)
% 156.04/26.79 (47) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 156.04/26.79 (48) ~ (e1 = e0)
% 156.04/26.79 (49) all_58_4 = e0
% 156.04/26.79 (50) op(e3, e1) = all_52_8
% 156.04/26.79 (51) ~ (all_6_2 = e2)
% 156.04/26.79 (52) all_56_14 = all_6_2
% 156.04/26.79 (53) all_54_14 = all_52_11
% 156.04/26.79 (54) all_54_11 = all_26_0
% 156.04/26.79 (55) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 156.04/26.79 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 156.04/26.79 (56) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.04/26.79 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.04/26.79 (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.79 (58) ~ (all_52_3 = all_52_11)
% 156.04/26.79 (59) ~ (e3 = e2)
% 156.04/26.79 (60) ~ (all_52_11 = e0)
% 156.04/26.79 (61) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.04/26.79 (62) all_54_12 = all_52_3
% 156.04/26.79 (63) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.04/26.79 (64) all_58_2 = e0
% 156.04/26.79 (65) op(e2, e0) = e3
% 156.04/26.79 (66) all_58_3 = e1
% 156.04/26.79 (67) ~ (all_26_0 = e3)
% 156.04/26.79
% 156.04/26.79 Begin of proof
% 156.04/26.79 |
% 156.04/26.79 | BETA: splitting (55) gives:
% 156.04/26.79 |
% 156.04/26.79 | Case 1:
% 156.04/26.79 | |
% 156.04/26.79 | | (68) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 156.04/26.79 | | e3)
% 156.04/26.79 | |
% 156.04/26.79 | | BETA: splitting (68) gives:
% 156.04/26.79 | |
% 156.04/26.79 | | Case 1:
% 156.04/26.79 | | |
% 156.04/26.79 | | | (69) all_58_0 = e3 & op(e3, e3) = e3
% 156.04/26.79 | | |
% 156.04/26.79 | | | ALPHA: (69) implies:
% 156.04/26.79 | | | (70) all_58_0 = e3
% 156.04/26.79 | | |
% 156.04/26.79 | | | BETA: splitting (47) gives:
% 156.04/26.79 | | |
% 156.04/26.79 | | | Case 1:
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | (71) all_54_11 = e3
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | REF_CLOSE: (54), (67), (71) are inconsistent by sub-proof #162.
% 156.04/26.79 | | | |
% 156.04/26.79 | | | Case 2:
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | (72) ~ (all_54_11 = e3)
% 156.04/26.79 | | | | (73) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | BETA: splitting (45) gives:
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | Case 1:
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | (74) all_54_10 = e3
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | REF_CLOSE: (5), (34), (74) are inconsistent by sub-proof #1531.
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | Case 2:
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | (75) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | BETA: splitting (75) gives:
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | Case 1:
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | (76) all_54_10 = e2
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | REF_CLOSE: (5), (51), (76) are inconsistent by sub-proof #1530.
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | Case 2:
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | (77) all_54_10 = e1 | all_54_10 = e0
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.04/26.79 | | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 156.04/26.79 | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 156.04/26.79 | | | | | | (31), (32), (33), (35), (36), (37), (38), (39), (40),
% 156.04/26.79 | | | | | | (41), (42), (43), (44), (46), (48), (50), (52), (53),
% 156.04/26.79 | | | | | | (54), (56), (57), (58), (60), (61), (62), (63), (64),
% 156.04/26.79 | | | | | | (65), (66), (67), (70), (73), (77) are inconsistent by
% 156.04/26.79 | | | | | | sub-proof #157.
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | End of split
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | End of split
% 156.04/26.79 | | | |
% 156.04/26.79 | | | End of split
% 156.04/26.79 | | |
% 156.04/26.79 | | Case 2:
% 156.04/26.79 | | |
% 156.04/26.79 | | | (78) all_58_1 = e3 & op(e3, e2) = e3
% 156.04/26.79 | | |
% 156.04/26.79 | | | ALPHA: (78) implies:
% 156.04/26.79 | | | (79) op(e3, e2) = e3
% 156.04/26.79 | | |
% 156.04/26.79 | | | REF_CLOSE: (3), (9), (57), (59), (79) are inconsistent by sub-proof #1094.
% 156.04/26.79 | | |
% 156.04/26.79 | | End of split
% 156.04/26.79 | |
% 156.04/26.79 | Case 2:
% 156.04/26.79 | |
% 156.04/26.79 | | (80) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 156.04/26.79 | | e3)
% 156.04/26.79 | |
% 156.04/26.79 | | BETA: splitting (80) gives:
% 156.04/26.79 | |
% 156.04/26.79 | | Case 1:
% 156.04/26.79 | | |
% 156.04/26.79 | | | (81) all_58_4 = e3 & op(e3, e1) = e3
% 156.04/26.79 | | |
% 156.04/26.79 | | | ALPHA: (81) implies:
% 156.04/26.79 | | | (82) all_58_4 = e3
% 156.04/26.79 | | |
% 156.04/26.79 | | | REF_CLOSE: (17), (49), (82) are inconsistent by sub-proof #1501.
% 156.04/26.79 | | |
% 156.04/26.79 | | Case 2:
% 156.04/26.79 | | |
% 156.04/26.79 | | | (83) all_58_9 = e3 & op(e3, e0) = e3
% 156.04/26.79 | | |
% 156.04/26.79 | | | ALPHA: (83) implies:
% 156.04/26.79 | | | (84) op(e3, e0) = e3
% 156.04/26.79 | | |
% 156.04/26.79 | | | REF_CLOSE: (2), (4), (57), (84) are inconsistent by sub-proof #210.
% 156.04/26.79 | | |
% 156.04/26.79 | | End of split
% 156.04/26.79 | |
% 156.04/26.79 | End of split
% 156.04/26.79 |
% 156.04/26.79 End of proof
% 156.04/26.79
% 156.04/26.79 Sub-proof #157 shows that the following formulas are inconsistent:
% 156.04/26.79 ----------------------------------------------------------------
% 156.04/26.79 (1) all_58_5 = e2
% 156.04/26.79 (2) op(e3, e2) = e2
% 156.04/26.79 (3) op(e3, e0) = all_52_12
% 156.04/26.79 (4) all_54_10 = all_6_2
% 156.04/26.79 (5) all_56_12 = all_10_2
% 156.04/26.79 (6) ~ (all_26_0 = e2)
% 156.04/26.79 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.04/26.79 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.04/26.79 (8) op(e3, e2) = all_52_4
% 156.04/26.79 (9) ~ (all_52_3 = e0)
% 156.04/26.79 (10) all_54_0 = all_10_2
% 156.04/26.79 (11) op(e2, e3) = all_52_1
% 156.04/26.79 (12) all_58_6 = e2
% 156.04/26.79 (13) all_54_2 = all_52_8
% 156.04/26.79 (14) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 156.04/26.79 (15) op(e1, e0) = all_26_0
% 156.04/26.79 (16) ~ (all_10_2 = e0)
% 156.04/26.79 (17) ~ (e3 = e0)
% 156.04/26.79 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.04/26.79 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.04/26.79 (19) ~ (e2 = e0)
% 156.04/26.79 (20) ~ (all_52_11 = all_6_2)
% 156.04/26.79 (21) ~ (all_52_6 = e2)
% 156.04/26.79 (22) ~ (all_52_3 = e2)
% 156.04/26.79 (23) op(e1, e0) = all_20_0
% 156.04/26.79 (24) op(e2, e0) = all_52_13
% 156.04/26.79 (25) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.04/26.79 (26) ~ (e3 = e1)
% 156.04/26.79 (27) op(e1, e2) = all_52_6
% 156.04/26.79 (28) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.04/26.79 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.79 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.04/26.79 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.04/26.79 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.04/26.79 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.04/26.79 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.04/26.79 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.04/26.79 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.04/26.79 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.04/26.79 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.04/26.79 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.04/26.79 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.04/26.79 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.04/26.79 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.04/26.79 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.04/26.79 = e0)
% 156.04/26.79 (29) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.04/26.79 (30) ~ (all_52_8 = e2)
% 156.04/26.79 (31) ~ (all_52_11 = e2)
% 156.04/26.79 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.79 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 156.04/26.79 (33) ~ (all_52_3 = all_10_2)
% 156.04/26.79 (34) ~ (all_52_8 = all_10_2)
% 156.04/26.79 (35) ~ (all_6_2 = e0)
% 156.04/26.79 (36) ~ (all_52_13 = e2)
% 156.04/26.79 (37) all_54_10 = e1 | all_54_10 = e0
% 156.04/26.79 (38) ~ (all_26_0 = all_6_2)
% 156.04/26.79 (39) op(e0, e1) = all_52_11
% 156.04/26.79 (40) all_58_0 = e3
% 156.04/26.79 (41) ~ (all_52_6 = e1)
% 156.04/26.79 (42) ~ (all_52_8 = all_6_2)
% 156.04/26.79 (43) ~ (all_10_2 = e2)
% 156.04/26.79 (44) all_58_10 = e3
% 156.04/26.79 (45) ~ (e2 = e1)
% 156.04/26.79 (46) ~ (all_52_12 = all_10_2)
% 156.04/26.79 (47) ~ (e1 = e0)
% 156.04/26.79 (48) op(e3, e1) = all_52_8
% 156.04/26.79 (49) all_56_14 = all_6_2
% 156.04/26.79 (50) all_54_14 = all_52_11
% 156.04/26.79 (51) all_54_11 = all_26_0
% 156.04/26.79 (52) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.04/26.79 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.04/26.79 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.79 (54) ~ (all_52_3 = all_52_11)
% 156.04/26.79 (55) ~ (all_52_11 = e0)
% 156.04/26.79 (56) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.04/26.79 (57) all_54_12 = all_52_3
% 156.04/26.79 (58) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.04/26.79 (59) all_58_2 = e0
% 156.04/26.79 (60) op(e2, e0) = e3
% 156.04/26.79 (61) all_58_3 = e1
% 156.04/26.79 (62) ~ (all_26_0 = e3)
% 156.04/26.79
% 156.04/26.79 Begin of proof
% 156.04/26.79 |
% 156.04/26.79 | BETA: splitting (18) gives:
% 156.04/26.79 |
% 156.04/26.79 | Case 1:
% 156.04/26.79 | |
% 156.04/26.79 | | (63) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 156.04/26.79 | | e1)
% 156.04/26.79 | |
% 156.04/26.79 | | BETA: splitting (63) gives:
% 156.04/26.79 | |
% 156.04/26.79 | | Case 1:
% 156.04/26.79 | | |
% 156.04/26.79 | | | (64) all_58_0 = e1 & op(e3, e3) = e1
% 156.04/26.79 | | |
% 156.04/26.79 | | | REF_CLOSE: (26), (40), (64) are inconsistent by sub-proof #1487.
% 156.04/26.79 | | |
% 156.04/26.79 | | Case 2:
% 156.04/26.79 | | |
% 156.04/26.79 | | | (65) all_58_2 = e1 & op(e2, e3) = e1
% 156.04/26.79 | | |
% 156.04/26.79 | | | ALPHA: (65) implies:
% 156.04/26.79 | | | (66) all_58_2 = e1
% 156.04/26.79 | | |
% 156.04/26.79 | | | REF_CLOSE: (1), (17), (19), (32), (44), (47), (61), (66) are inconsistent
% 156.04/26.79 | | | by sub-proof #160.
% 156.04/26.79 | | |
% 156.04/26.79 | | End of split
% 156.04/26.79 | |
% 156.04/26.79 | Case 2:
% 156.04/26.79 | |
% 156.04/26.79 | | (67) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 156.04/26.79 | | e1)
% 156.04/26.79 | |
% 156.04/26.79 | | BETA: splitting (67) gives:
% 156.04/26.79 | |
% 156.04/26.79 | | Case 1:
% 156.04/26.79 | | |
% 156.04/26.79 | | | (68) all_58_6 = e1 & op(e1, e3) = e1
% 156.04/26.79 | | |
% 156.04/26.79 | | | REF_CLOSE: (12), (45), (68) are inconsistent by sub-proof #1498.
% 156.04/26.79 | | |
% 156.04/26.79 | | Case 2:
% 156.04/26.79 | | |
% 156.04/26.79 | | | (69) all_58_12 = e1 & op(e0, e3) = e1
% 156.04/26.79 | | |
% 156.04/26.79 | | | ALPHA: (69) implies:
% 156.04/26.79 | | | (70) all_58_12 = e1
% 156.04/26.79 | | |
% 156.04/26.79 | | | BETA: splitting (37) gives:
% 156.04/26.79 | | |
% 156.04/26.79 | | | Case 1:
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | (71) all_54_10 = e1
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | COMBINE_EQS: (4), (71) imply:
% 156.04/26.79 | | | | (72) all_6_2 = e1
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | SIMP: (72) implies:
% 156.04/26.79 | | | | (73) all_6_2 = e1
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | COMBINE_EQS: (49), (73) imply:
% 156.04/26.79 | | | | (74) all_56_14 = e1
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | REDUCE: (42), (73) imply:
% 156.04/26.79 | | | | (75) ~ (all_52_8 = e1)
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | REDUCE: (20), (73) imply:
% 156.04/26.79 | | | | (76) ~ (all_52_11 = e1)
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | REDUCE: (38), (73) imply:
% 156.04/26.79 | | | | (77) ~ (all_26_0 = e1)
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | BETA: splitting (14) gives:
% 156.04/26.79 | | | |
% 156.04/26.79 | | | | Case 1:
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | (78) all_54_11 = e2
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | REF_CLOSE: (6), (51), (78) are inconsistent by sub-proof #159.
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | Case 2:
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | (79) all_54_11 = e1 | all_54_11 = e0
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | BETA: splitting (58) gives:
% 156.04/26.79 | | | | |
% 156.04/26.79 | | | | | Case 1:
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | (80) all_54_14 = e3
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | COMBINE_EQS: (50), (80) imply:
% 156.04/26.79 | | | | | | (81) all_52_11 = e3
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | SIMP: (81) implies:
% 156.04/26.79 | | | | | | (82) all_52_11 = e3
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | REDUCE: (54), (82) imply:
% 156.04/26.79 | | | | | | (83) ~ (all_52_3 = e3)
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | REDUCE: (39), (82) imply:
% 156.04/26.79 | | | | | | (84) op(e0, e1) = e3
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | BETA: splitting (56) gives:
% 156.04/26.79 | | | | | |
% 156.04/26.79 | | | | | | Case 1:
% 156.04/26.79 | | | | | | |
% 156.04/26.79 | | | | | | | (85) all_54_12 = e3
% 156.04/26.79 | | | | | | |
% 156.04/26.79 | | | | | | | REF_CLOSE: (57), (83), (85) are inconsistent by sub-proof #1234.
% 156.04/26.79 | | | | | | |
% 156.04/26.79 | | | | | | Case 2:
% 156.04/26.79 | | | | | | |
% 156.04/26.79 | | | | | | | (86) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.04/26.79 | | | | | | |
% 156.04/26.79 | | | | | | | BETA: splitting (86) gives:
% 156.04/26.79 | | | | | | |
% 156.04/26.79 | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | |
% 156.04/26.79 | | | | | | | | (87) all_54_12 = e2
% 156.04/26.79 | | | | | | | |
% 156.04/26.79 | | | | | | | | REF_CLOSE: (22), (57), (87) are inconsistent by sub-proof #1189.
% 156.04/26.79 | | | | | | | |
% 156.04/26.79 | | | | | | | Case 2:
% 156.04/26.79 | | | | | | | |
% 156.04/26.79 | | | | | | | | (88) ~ (all_54_12 = e2)
% 156.04/26.79 | | | | | | | | (89) all_54_12 = e1 | all_54_12 = e0
% 156.04/26.79 | | | | | | | |
% 156.04/26.79 | | | | | | | | BETA: splitting (89) gives:
% 156.04/26.79 | | | | | | | |
% 156.04/26.79 | | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | | |
% 156.04/26.79 | | | | | | | | | (90) all_54_12 = e1
% 156.04/26.79 | | | | | | | | |
% 156.04/26.79 | | | | | | | | | COMBINE_EQS: (57), (90) imply:
% 156.04/26.79 | | | | | | | | | (91) all_52_3 = e1
% 156.04/26.79 | | | | | | | | |
% 156.04/26.79 | | | | | | | | | SIMP: (91) implies:
% 156.04/26.79 | | | | | | | | | (92) all_52_3 = e1
% 156.04/26.79 | | | | | | | | |
% 156.04/26.79 | | | | | | | | | REDUCE: (33), (92) imply:
% 156.04/26.79 | | | | | | | | | (93) ~ (all_10_2 = e1)
% 156.04/26.79 | | | | | | | | |
% 156.04/26.79 | | | | | | | | | SIMP: (93) implies:
% 156.04/26.79 | | | | | | | | | (94) ~ (all_10_2 = e1)
% 156.04/26.79 | | | | | | | | |
% 156.04/26.79 | | | | | | | | | REDUCE: (22), (92) imply:
% 156.04/26.79 | | | | | | | | | (95) ~ (e2 = e1)
% 156.04/26.79 | | | | | | | | |
% 156.04/26.79 | | | | | | | | | BETA: splitting (25) gives:
% 156.04/26.79 | | | | | | | | |
% 156.04/26.79 | | | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | (96) all_54_0 = e3
% 156.04/26.79 | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | COMBINE_EQS: (10), (96) imply:
% 156.04/26.79 | | | | | | | | | | (97) all_10_2 = e3
% 156.04/26.79 | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | COMBINE_EQS: (5), (97) imply:
% 156.04/26.79 | | | | | | | | | | (98) all_56_12 = e3
% 156.04/26.79 | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | REDUCE: (34), (97) imply:
% 156.04/26.79 | | | | | | | | | | (99) ~ (all_52_8 = e3)
% 156.04/26.79 | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | REDUCE: (46), (97) imply:
% 156.04/26.79 | | | | | | | | | | (100) ~ (all_52_12 = e3)
% 156.04/26.79 | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | REDUCE: (43), (97) imply:
% 156.04/26.79 | | | | | | | | | | (101) ~ (e3 = e2)
% 156.04/26.79 | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | BETA: splitting (29) gives:
% 156.04/26.79 | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | (102) all_54_2 = e3
% 156.04/26.79 | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | COMBINE_EQS: (13), (102) imply:
% 156.04/26.79 | | | | | | | | | | | (103) all_52_8 = e3
% 156.04/26.79 | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | REDUCE: (99), (103) imply:
% 156.04/26.79 | | | | | | | | | | | (104) $false
% 156.04/26.79 | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | CLOSE: (104) is inconsistent.
% 156.04/26.79 | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | Case 2:
% 156.04/26.79 | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | (105) ~ (all_54_2 = e3)
% 156.04/26.79 | | | | | | | | | | | (106) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.04/26.79 | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | BETA: splitting (106) gives:
% 156.04/26.79 | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | (107) all_54_2 = e2
% 156.04/26.79 | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | COMBINE_EQS: (13), (107) imply:
% 156.04/26.79 | | | | | | | | | | | | (108) all_52_8 = e2
% 156.04/26.79 | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | REDUCE: (30), (108) imply:
% 156.04/26.79 | | | | | | | | | | | | (109) $false
% 156.04/26.79 | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | CLOSE: (109) is inconsistent.
% 156.04/26.79 | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | Case 2:
% 156.04/26.79 | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | (110) all_54_2 = e1 | all_54_2 = e0
% 156.04/26.79 | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | BETA: splitting (28) gives:
% 156.04/26.79 | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | (111) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.04/26.79 | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.04/26.79 | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.04/26.79 | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.04/26.79 | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.04/26.79 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.04/26.79 | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.04/26.79 | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.04/26.79 | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.04/26.79 | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | BETA: splitting (111) gives:
% 156.04/26.79 | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | (112) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.04/26.79 | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.04/26.79 | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.04/26.79 | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.04/26.79 | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.04/26.79 | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 156.04/26.79 | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | (113) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.04/26.79 | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 156.04/26.79 | | | | | | | | | | | | | | | (114) op(e3, e2) = e3
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (53), (101), (114) are inconsistent by
% 156.04/26.79 | | | | | | | | | | | | | | | sub-proof #1094.
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | Case 2:
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | (115) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.04/26.79 | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.04/26.79 | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (12), (17), (18), (19), (26), (45),
% 156.04/26.79 | | | | | | | | | | | | | | | (47), (48), (52), (53), (99), (101), (115) are
% 156.04/26.79 | | | | | | | | | | | | | | | inconsistent by sub-proof #211.
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | End of split
% 156.04/26.79 | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | Case 2:
% 156.04/26.79 | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | (116) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.04/26.79 | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.04/26.79 | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.04/26.79 | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.04/26.79 | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 156.04/26.79 | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | Case 1:
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | (117) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 156.04/26.79 | | | | | | | | | | | | | | | (118) op(e3, e1) = e1
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | REF_CLOSE: (13), (48), (53), (75), (110), (118) are
% 156.04/26.79 | | | | | | | | | | | | | | | inconsistent by sub-proof #1024.
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | Case 2:
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.79 | | | | | | | | | | | | | | | (119) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.04/26.79 | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.04/26.79 | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.04/26.79 | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.04/26.79 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | REF_CLOSE: (3), (53), (98), (100), (119) are inconsistent by
% 156.04/26.80 | | | | | | | | | | | | | | | sub-proof #168.
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | Case 2:
% 156.04/26.80 | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | (120) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.04/26.80 | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.04/26.80 | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.04/26.80 | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.04/26.80 | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.04/26.80 | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 156.04/26.80 | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.04/26.80 | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.04/26.80 | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.04/26.80 | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.04/26.80 | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.04/26.80 | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.04/26.80 | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | BETA: splitting (120) gives:
% 156.04/26.80 | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | Case 1:
% 156.04/26.80 | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | (121) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.04/26.80 | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.04/26.80 | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.04/26.80 | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.04/26.80 | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.04/26.80 | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.04/26.80 | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (27), (36), (41), (53), (121) are
% 156.04/26.80 | | | | | | | | | | | | | | inconsistent by sub-proof #1128.
% 156.04/26.80 | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | Case 2:
% 156.04/26.80 | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | (122) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.04/26.80 | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.04/26.80 | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.04/26.80 | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.04/26.80 | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.04/26.80 | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.04/26.80 | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 156.04/26.80 | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | Case 1:
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | (123) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.04/26.80 | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 156.04/26.80 | | | | | | | | | | | | | | | (124) op(e2, e0) = e0
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | Case 1:
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | (125) all_54_11 = e1
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | REF_CLOSE: (51), (77), (125) are inconsistent by sub-proof
% 156.04/26.80 | | | | | | | | | | | | | | | | #158.
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | Case 2:
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | (126) all_54_11 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (126) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | (127) all_26_0 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | SIMP: (127) implies:
% 156.04/26.80 | | | | | | | | | | | | | | | | (128) all_26_0 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | REDUCE: (62), (128) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | (129) ~ (e3 = e0)
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with e3, e0, e0, e2,
% 156.04/26.80 | | | | | | | | | | | | | | | | simplifying with (60), (124) gives:
% 156.04/26.80 | | | | | | | | | | | | | | | | (130) e3 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (130) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | (131) all_58_0 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (17), (26), (59), (70), (101), (131)
% 156.04/26.80 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1248.
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | Case 2:
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | (132) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.04/26.80 | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.04/26.80 | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.04/26.80 | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | Case 1:
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | (133) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.04/26.80 | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 156.04/26.80 | | | | | | | | | | | | | | | | (134) op(e0, e1) = e1
% 156.04/26.80 | | | | | | | | | | | | | | | | (135) op(e1, e0) = e1
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | (136) all_54_11 = e1
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (77), (136) are inconsistent by sub-proof
% 156.04/26.80 | | | | | | | | | | | | | | | | | #158.
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | (137) all_54_11 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (137) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (138) all_26_0 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | SIMP: (138) implies:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (139) all_26_0 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | REDUCE: (62), (139) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (140) ~ (e3 = e0)
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | REDUCE: (15), (139) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (141) op(e1, e0) = e0
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with e1, e3, e1, e0,
% 156.04/26.80 | | | | | | | | | | | | | | | | | simplifying with (84), (134) gives:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (142) e3 = e1
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with e1, all_20_0, e0, e1,
% 156.04/26.80 | | | | | | | | | | | | | | | | | simplifying with (23), (135) gives:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (143) all_20_0 = e1
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with e0, all_20_0, e0, e1,
% 156.04/26.80 | | | | | | | | | | | | | | | | | simplifying with (23), (141) gives:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (144) all_20_0 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (144) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (145) e1 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (145) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (146) e3 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (146) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | | (147) all_58_0 = e0
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (17), (26), (59), (70), (101), (147)
% 156.04/26.80 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1248.
% 156.04/26.80 | | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | Case 2:
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | (148) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.04/26.80 | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 156.04/26.80 | | | | | | | | | | | | | | | | (149) ~ (all_56_14 = e1)
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | REDUCE: (74), (149) imply:
% 156.04/26.80 | | | | | | | | | | | | | | | | (150) $false
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 156.04/26.80 | | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | Case 2:
% 156.04/26.80 | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | (151) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.04/26.80 | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | | REF_CLOSE: (10), (16), (43), (94), (151) are inconsistent by
% 156.04/26.80 | | | | | | | | | | sub-proof #1307.
% 156.04/26.80 | | | | | | | | | |
% 156.04/26.80 | | | | | | | | | End of split
% 156.04/26.80 | | | | | | | | |
% 156.04/26.80 | | | | | | | | Case 2:
% 156.04/26.80 | | | | | | | | |
% 156.04/26.80 | | | | | | | | | (152) all_54_12 = e0
% 156.04/26.80 | | | | | | | | |
% 156.04/26.80 | | | | | | | | | REF_CLOSE: (9), (57), (152) are inconsistent by sub-proof
% 156.04/26.80 | | | | | | | | | #1223.
% 156.04/26.80 | | | | | | | | |
% 156.04/26.80 | | | | | | | | End of split
% 156.04/26.80 | | | | | | | |
% 156.04/26.80 | | | | | | | End of split
% 156.04/26.80 | | | | | | |
% 156.04/26.80 | | | | | | End of split
% 156.04/26.80 | | | | | |
% 156.04/26.80 | | | | | Case 2:
% 156.04/26.80 | | | | | |
% 156.04/26.80 | | | | | | (153) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.04/26.80 | | | | | |
% 156.04/26.80 | | | | | | REF_CLOSE: (31), (50), (55), (76), (153) are inconsistent by
% 156.04/26.80 | | | | | | sub-proof #1149.
% 156.04/26.80 | | | | | |
% 156.04/26.80 | | | | | End of split
% 156.04/26.80 | | | | |
% 156.04/26.80 | | | | End of split
% 156.04/26.80 | | | |
% 156.04/26.80 | | | Case 2:
% 156.04/26.80 | | | |
% 156.04/26.80 | | | | (154) all_54_10 = e0
% 156.04/26.80 | | | |
% 156.04/26.80 | | | | REF_CLOSE: (4), (35), (154) are inconsistent by sub-proof #1528.
% 156.04/26.80 | | | |
% 156.04/26.80 | | | End of split
% 156.04/26.80 | | |
% 156.04/26.80 | | End of split
% 156.04/26.80 | |
% 156.04/26.80 | End of split
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #158 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) all_54_11 = all_26_0
% 156.04/26.80 (2) all_54_11 = e1
% 156.04/26.80 (3) ~ (all_26_0 = e1)
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | COMBINE_EQS: (1), (2) imply:
% 156.04/26.80 | (4) all_26_0 = e1
% 156.04/26.80 |
% 156.04/26.80 | SIMP: (4) implies:
% 156.04/26.80 | (5) all_26_0 = e1
% 156.04/26.80 |
% 156.04/26.80 | REDUCE: (3), (5) imply:
% 156.04/26.80 | (6) $false
% 156.04/26.80 |
% 156.04/26.80 | CLOSE: (6) is inconsistent.
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #159 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) all_54_11 = all_26_0
% 156.04/26.80 (2) all_54_11 = e2
% 156.04/26.80 (3) ~ (all_26_0 = e2)
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | COMBINE_EQS: (1), (2) imply:
% 156.04/26.80 | (4) all_26_0 = e2
% 156.04/26.80 |
% 156.04/26.80 | SIMP: (4) implies:
% 156.04/26.80 | (5) all_26_0 = e2
% 156.04/26.80 |
% 156.04/26.80 | REDUCE: (3), (5) imply:
% 156.04/26.80 | (6) $false
% 156.04/26.80 |
% 156.04/26.80 | CLOSE: (6) is inconsistent.
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #160 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) all_58_5 = e2
% 156.04/26.80 (2) all_58_2 = e1
% 156.04/26.80 (3) ~ (e3 = e0)
% 156.04/26.80 (4) ~ (e2 = e0)
% 156.04/26.80 (5) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.80 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 156.04/26.80 (6) all_58_10 = e3
% 156.04/26.80 (7) ~ (e1 = e0)
% 156.04/26.80 (8) all_58_3 = e1
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | BETA: splitting (5) gives:
% 156.04/26.80 |
% 156.04/26.80 | Case 1:
% 156.04/26.80 | |
% 156.04/26.80 | | (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 156.04/26.80 | |
% 156.04/26.80 | | BETA: splitting (9) gives:
% 156.04/26.80 | |
% 156.04/26.80 | | Case 1:
% 156.04/26.80 | | |
% 156.04/26.80 | | | (10) all_58_2 = e0 & op(e2, e3) = e0
% 156.04/26.80 | | |
% 156.04/26.80 | | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #1351.
% 156.04/26.80 | | |
% 156.04/26.80 | | Case 2:
% 156.04/26.80 | | |
% 156.04/26.80 | | | (11) all_58_3 = e0 & op(e2, e2) = e0
% 156.04/26.80 | | |
% 156.04/26.80 | | | REF_CLOSE: (7), (8), (11) are inconsistent by sub-proof #161.
% 156.04/26.80 | | |
% 156.04/26.80 | | End of split
% 156.04/26.80 | |
% 156.04/26.80 | Case 2:
% 156.04/26.80 | |
% 156.04/26.80 | | (12) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 156.04/26.80 | | e0)
% 156.04/26.80 | |
% 156.04/26.80 | | BETA: splitting (12) gives:
% 156.04/26.80 | |
% 156.04/26.80 | | Case 1:
% 156.04/26.80 | | |
% 156.04/26.80 | | | (13) all_58_5 = e0 & op(e2, e1) = e0
% 156.04/26.80 | | |
% 156.04/26.80 | | | REF_CLOSE: (1), (4), (13) are inconsistent by sub-proof #180.
% 156.04/26.80 | | |
% 156.04/26.80 | | Case 2:
% 156.04/26.80 | | |
% 156.04/26.80 | | | (14) all_58_10 = e0 & op(e2, e0) = e0
% 156.04/26.80 | | |
% 156.04/26.80 | | | ALPHA: (14) implies:
% 156.04/26.80 | | | (15) all_58_10 = e0
% 156.04/26.80 | | |
% 156.04/26.80 | | | COMBINE_EQS: (6), (15) imply:
% 156.04/26.80 | | | (16) e3 = e0
% 156.04/26.80 | | |
% 156.04/26.80 | | | REDUCE: (3), (16) imply:
% 156.04/26.80 | | | (17) $false
% 156.04/26.80 | | |
% 156.04/26.80 | | | CLOSE: (17) is inconsistent.
% 156.04/26.80 | | |
% 156.04/26.80 | | End of split
% 156.04/26.80 | |
% 156.04/26.80 | End of split
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #161 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) all_58_3 = e0 & op(e2, e2) = e0
% 156.04/26.80 (2) all_58_3 = e1
% 156.04/26.80 (3) ~ (e1 = e0)
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | ALPHA: (1) implies:
% 156.04/26.80 | (4) all_58_3 = e0
% 156.04/26.80 |
% 156.04/26.80 | COMBINE_EQS: (2), (4) imply:
% 156.04/26.80 | (5) e1 = e0
% 156.04/26.80 |
% 156.04/26.80 | SIMP: (5) implies:
% 156.04/26.80 | (6) e1 = e0
% 156.04/26.80 |
% 156.04/26.80 | REDUCE: (3), (6) imply:
% 156.04/26.80 | (7) $false
% 156.04/26.80 |
% 156.04/26.80 | CLOSE: (7) is inconsistent.
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #162 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) all_54_11 = all_26_0
% 156.04/26.80 (2) all_54_11 = e3
% 156.04/26.80 (3) ~ (all_26_0 = e3)
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | COMBINE_EQS: (1), (2) imply:
% 156.04/26.80 | (4) all_26_0 = e3
% 156.04/26.80 |
% 156.04/26.80 | SIMP: (4) implies:
% 156.04/26.80 | (5) all_26_0 = e3
% 156.04/26.80 |
% 156.04/26.80 | REDUCE: (3), (5) imply:
% 156.04/26.80 | (6) $false
% 156.04/26.80 |
% 156.04/26.80 | CLOSE: (6) is inconsistent.
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #163 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 156.04/26.80 (2) ~ (e3 = e0)
% 156.04/26.80 (3) ~ (e3 = e1)
% 156.04/26.80 (4) all_58_2 = e0
% 156.04/26.80 (5) all_58_3 = e1
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | BETA: splitting (1) gives:
% 156.04/26.80 |
% 156.04/26.80 | Case 1:
% 156.04/26.80 | |
% 156.04/26.80 | | (6) all_58_2 = e3 & op(e2, e3) = e3
% 156.04/26.80 | |
% 156.04/26.80 | | ALPHA: (6) implies:
% 156.04/26.80 | | (7) all_58_2 = e3
% 156.04/26.80 | |
% 156.04/26.80 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #1485.
% 156.04/26.80 | |
% 156.04/26.80 | Case 2:
% 156.04/26.80 | |
% 156.04/26.80 | | (8) all_58_3 = e3 & op(e2, e2) = e3
% 156.04/26.80 | |
% 156.04/26.80 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #164.
% 156.04/26.80 | |
% 156.04/26.80 | End of split
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #164 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) all_58_3 = e3 & op(e2, e2) = e3
% 156.04/26.80 (2) all_58_3 = e1
% 156.04/26.80 (3) ~ (e3 = e1)
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | ALPHA: (1) implies:
% 156.04/26.80 | (4) all_58_3 = e3
% 156.04/26.80 |
% 156.04/26.80 | COMBINE_EQS: (2), (4) imply:
% 156.04/26.80 | (5) e3 = e1
% 156.04/26.80 |
% 156.04/26.80 | REDUCE: (3), (5) imply:
% 156.04/26.80 | (6) $false
% 156.04/26.80 |
% 156.04/26.80 | CLOSE: (6) is inconsistent.
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #165 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) all_58_0 = e0 & op(e3, e3) = e0
% 156.04/26.80 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.80 (3) op(e3, e3) = all_10_2
% 156.04/26.80 (4) ~ (all_10_2 = e0)
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | ALPHA: (1) implies:
% 156.04/26.80 | (5) op(e3, e3) = e0
% 156.04/26.80 |
% 156.04/26.80 | GROUND_INST: instantiating (2) with all_10_2, e0, e3, e3, simplifying with
% 156.04/26.80 | (3), (5) gives:
% 156.04/26.80 | (6) all_10_2 = e0
% 156.04/26.80 |
% 156.04/26.80 | REDUCE: (4), (6) imply:
% 156.04/26.80 | (7) $false
% 156.04/26.80 |
% 156.04/26.80 | CLOSE: (7) is inconsistent.
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #166 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) op(e3, e0) = all_52_12
% 156.04/26.80 (2) ~ (all_52_12 = e2)
% 156.04/26.80 (3) op(e2, e0) = all_52_13
% 156.04/26.80 (4) ~ (all_52_13 = e2)
% 156.04/26.80 (5) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.04/26.80 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | BETA: splitting (5) gives:
% 156.04/26.80 |
% 156.04/26.80 | Case 1:
% 156.04/26.80 | |
% 156.04/26.80 | | (7) all_58_9 = e2 & op(e3, e0) = e2
% 156.04/26.80 | |
% 156.04/26.80 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #1238.
% 156.04/26.80 | |
% 156.04/26.80 | Case 2:
% 156.04/26.80 | |
% 156.04/26.80 | | (8) all_58_10 = e2 & op(e2, e0) = e2
% 156.04/26.80 | |
% 156.04/26.80 | | ALPHA: (8) implies:
% 156.04/26.80 | | (9) op(e2, e0) = e2
% 156.04/26.80 | |
% 156.04/26.80 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1535.
% 156.04/26.80 | |
% 156.04/26.80 | End of split
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #167 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) ~ (all_52_4 = all_52_6)
% 156.04/26.80 (2) all_54_1 = all_52_4
% 156.04/26.80 (3) op(e1, e2) = e2
% 156.04/26.80 (4) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 156.04/26.80 (5) op(e1, e2) = all_52_6
% 156.04/26.80 (6) ~ (all_52_4 = e0)
% 156.04/26.80 (7) ~ (all_52_4 = e1)
% 156.04/26.80 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | BETA: splitting (4) gives:
% 156.04/26.80 |
% 156.04/26.80 | Case 1:
% 156.04/26.80 | |
% 156.04/26.80 | | (9) all_54_1 = e2
% 156.04/26.80 | |
% 156.04/26.80 | | COMBINE_EQS: (2), (9) imply:
% 156.04/26.80 | | (10) all_52_4 = e2
% 156.04/26.80 | |
% 156.04/26.80 | | REDUCE: (1), (10) imply:
% 156.04/26.80 | | (11) ~ (all_52_6 = e2)
% 156.04/26.80 | |
% 156.04/26.80 | | SIMP: (11) implies:
% 156.04/26.80 | | (12) ~ (all_52_6 = e2)
% 156.04/26.80 | |
% 156.04/26.80 | | REF_CLOSE: (3), (5), (8), (12) are inconsistent by sub-proof #1536.
% 156.04/26.80 | |
% 156.04/26.80 | Case 2:
% 156.04/26.80 | |
% 156.04/26.80 | | (13) all_54_1 = e1 | all_54_1 = e0
% 156.04/26.80 | |
% 156.04/26.80 | | REF_CLOSE: (2), (6), (7), (13) are inconsistent by sub-proof #1108.
% 156.04/26.80 | |
% 156.04/26.80 | End of split
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #168 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) ~ (all_52_12 = e3)
% 156.04/26.80 (2) op(e3, e0) = all_52_12
% 156.04/26.80 (3) all_56_12 = e3
% 156.04/26.80 (4) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 &
% 156.04/26.80 op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3)
% 156.04/26.80 & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.04/26.80 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.80
% 156.04/26.80 Begin of proof
% 156.04/26.80 |
% 156.04/26.80 | BETA: splitting (4) gives:
% 156.04/26.80 |
% 156.04/26.80 | Case 1:
% 156.04/26.80 | |
% 156.04/26.80 | | (6) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3
% 156.04/26.80 | | & op(e0, e3) = e3
% 156.04/26.80 | |
% 156.04/26.80 | | ALPHA: (6) implies:
% 156.04/26.80 | | (7) op(e3, e0) = e3
% 156.04/26.80 | |
% 156.04/26.80 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #210.
% 156.04/26.80 | |
% 156.04/26.80 | Case 2:
% 156.04/26.80 | |
% 156.04/26.80 | | (8) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0
% 156.04/26.80 | | & op(e0, e3) = e0
% 156.04/26.80 | |
% 156.04/26.80 | | ALPHA: (8) implies:
% 156.04/26.80 | | (9) ~ (all_56_12 = e3)
% 156.04/26.80 | |
% 156.04/26.80 | | REDUCE: (3), (9) imply:
% 156.04/26.80 | | (10) $false
% 156.04/26.80 | |
% 156.04/26.80 | | CLOSE: (10) is inconsistent.
% 156.04/26.80 | |
% 156.04/26.80 | End of split
% 156.04/26.80 |
% 156.04/26.80 End of proof
% 156.04/26.80
% 156.04/26.80 Sub-proof #169 shows that the following formulas are inconsistent:
% 156.04/26.80 ----------------------------------------------------------------
% 156.04/26.80 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 156.04/26.80 (2) op(e1, e1) = all_32_1
% 156.04/26.80 (3) all_58_5 = e2
% 156.04/26.80 (4) op(e0, e3) = all_52_3
% 156.04/26.80 (5) op(e3, e0) = all_52_12
% 156.04/26.80 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.04/26.80 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.04/26.80 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.04/26.80 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.04/26.80 (8) op(e3, e3) = all_10_2
% 156.04/26.80 (9) all_54_13 = all_52_7
% 156.04/26.80 (10) ~ (all_52_1 = e2)
% 156.04/26.80 (11) op(e1, e1) = all_6_2
% 156.04/26.80 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.04/26.80 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 156.04/26.80 e1)
% 156.04/26.80 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.04/26.80 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.04/26.80 (14) ~ (all_52_6 = all_52_14)
% 156.04/26.80 (15) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.04/26.80 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.04/26.80 (16) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.04/26.80 (17) ~ (all_52_7 = all_52_11)
% 156.04/26.80 (18) ~ (all_52_12 = all_4_2)
% 156.04/26.80 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.04/26.80 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.04/26.80 (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.04/26.80 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.04/26.80 (21) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.04/26.80 (22) op(e3, e2) = all_52_4
% 156.04/26.80 (23) ~ (all_4_2 = e2)
% 156.04/26.80 (24) ~ (all_52_1 = all_52_13)
% 156.04/26.80 (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.04/26.80 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.04/26.80 (26) ~ (all_52_12 = all_52_13)
% 156.04/26.80 (27) op(e2, e3) = all_52_1
% 156.04/26.80 (28) ~ (all_52_1 = all_52_3)
% 156.04/26.80 (29) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.04/26.80 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.04/26.80 (30) ~ (e3 = e0)
% 156.04/26.80 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.04/26.80 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.04/26.80 (32) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.04/26.80 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.04/26.80 (33) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.04/26.80 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.04/26.80 e2)
% 156.04/26.80 (34) ~ (e2 = e0)
% 156.04/26.80 (35) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 156.04/26.80 (36) all_56_13 = e1
% 156.04/26.80 (37) op(e1, e3) = all_52_2
% 156.04/26.80 (38) op(e2, e0) = all_52_13
% 156.04/26.80 (39) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.80 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.04/26.80 (40) ~ (e3 = e1)
% 156.04/26.80 (41) all_56_12 = e1
% 156.04/26.81 (42) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.04/26.81 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.04/26.81 (43) op(e1, e2) = all_52_6
% 156.04/26.81 (44) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.04/26.81 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.81 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.04/26.81 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.04/26.81 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.04/26.81 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.04/26.81 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.04/26.81 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.04/26.81 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.04/26.81 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.04/26.81 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.04/26.81 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.04/26.81 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.04/26.81 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.04/26.81 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.04/26.81 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.04/26.81 = e0)
% 156.04/26.81 (45) ~ (all_4_2 = e1)
% 156.04/26.81 (46) all_54_4 = all_52_1
% 156.04/26.81 (47) ~ (all_52_8 = e2)
% 156.04/26.81 (48) ~ (all_52_11 = e2)
% 156.04/26.81 (49) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e2) & op(all_50_1, e3) = all_50_0 &
% 156.04/26.81 op(e1, e1) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 156.04/26.81 e0) & op(e1, e1) = all_50_1 & $i(all_50_1))
% 156.04/26.81 (50) ~ (all_6_2 = e3)
% 156.04/26.81 (51) op(e0, e0) = all_4_2
% 156.04/26.81 (52) all_54_7 = all_52_13
% 156.04/26.81 (53) ~ (all_52_1 = e1)
% 156.04/26.81 (54) op(e3, e3) = e1
% 156.04/26.81 (55) ~ (all_52_13 = e2)
% 156.04/26.81 (56) all_50_2 = e1
% 156.04/26.81 (57) all_56_15 = all_4_2
% 156.04/26.81 (58) op(e0, e1) = all_52_11
% 156.04/26.81 (59) ~ (all_52_4 = e1)
% 156.04/26.81 (60) ~ (all_52_13 = all_4_2)
% 156.04/26.81 (61) ~ (all_52_2 = e1)
% 156.04/26.81 (62) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 156.04/26.81 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.04/26.81 (63) ~ (all_52_2 = all_52_14)
% 156.04/26.81 (64) ~ (all_52_6 = e1)
% 156.04/26.81 (65) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.04/26.81 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.04/26.81 (66) ~ (all_52_6 = all_52_7)
% 156.04/26.81 (67) ~ (all_10_2 = e2)
% 156.04/26.81 (68) ~ (e2 = e1)
% 156.04/26.81 (69) ~ (e1 = e0)
% 156.04/26.81 (70) op(e3, e1) = all_52_8
% 156.04/26.81 (71) ~ (all_6_2 = e2)
% 156.04/26.81 (72) ~ (all_52_13 = e1)
% 156.04/26.81 (73) all_56_14 = all_6_2
% 156.04/26.81 (74) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.04/26.81 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.04/26.81 (75) ~ (all_52_7 = all_4_2)
% 156.04/26.81 (76) ~ (all_52_7 = e1)
% 156.04/26.81 (77) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 156.04/26.81 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 156.04/26.81 (78) op(e0, e2) = all_52_7
% 156.04/26.81 (79) op(e1, e0) = all_52_14
% 156.04/26.81 (80) ~ (all_52_8 = e1)
% 156.04/26.81 (81) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.04/26.81 (82) ~ (all_52_14 = all_6_2)
% 156.04/26.81 (83) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.04/26.81 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.04/26.81 (84) ~ (all_52_12 = e1)
% 156.04/26.81 (85) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.81 (86) ~ (all_52_3 = all_52_11)
% 156.04/26.81 (87) ~ (all_52_13 = all_52_14)
% 156.04/26.81 (88) ~ (e3 = e2)
% 156.04/26.81 (89) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.04/26.81 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.04/26.81 (90) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.04/26.81 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.04/26.81 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.04/26.81 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.04/26.81 (91) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.04/26.81 (92) all_54_12 = all_52_3
% 156.04/26.81 (93) ~ (all_52_14 = all_4_2)
% 156.04/26.81 (94) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.04/26.81 (95) all_58_3 = e1
% 156.04/26.81 (96) ~ (all_52_3 = all_52_7)
% 156.04/26.81 (97) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.04/26.81 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.04/26.81
% 156.04/26.81 Begin of proof
% 156.04/26.81 |
% 156.04/26.81 | BETA: splitting (1) gives:
% 156.04/26.81 |
% 156.04/26.81 | Case 1:
% 156.04/26.81 | |
% 156.04/26.81 | | (98) ~ (all_56_12 = e1)
% 156.04/26.81 | |
% 156.04/26.81 | | REDUCE: (41), (98) imply:
% 156.04/26.81 | | (99) $false
% 156.04/26.81 | |
% 156.04/26.81 | | CLOSE: (99) is inconsistent.
% 156.04/26.81 | |
% 156.04/26.81 | Case 2:
% 156.04/26.81 | |
% 156.04/26.81 | | (100) all_56_1 = e3 & op(e3, e1) = e3
% 156.04/26.81 | |
% 156.04/26.81 | | ALPHA: (100) implies:
% 156.04/26.81 | | (101) op(e3, e1) = e3
% 156.04/26.81 | |
% 156.04/26.81 | | BETA: splitting (7) gives:
% 156.04/26.81 | |
% 156.04/26.81 | | Case 1:
% 156.04/26.81 | | |
% 156.04/26.81 | | | (102) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 156.04/26.81 | | | = e1)
% 156.04/26.81 | | |
% 156.04/26.81 | | | BETA: splitting (102) gives:
% 156.04/26.81 | | |
% 156.04/26.81 | | | Case 1:
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | (103) all_58_9 = e1 & op(e3, e0) = e1
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | ALPHA: (103) implies:
% 156.04/26.81 | | | | (104) all_58_9 = e1
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | BETA: splitting (12) gives:
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | Case 1:
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | (105) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 156.04/26.81 | | | | | e2) = e1)
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | BETA: splitting (105) gives:
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | Case 1:
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | (106) all_58_12 = e1 & op(e0, e3) = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | ALPHA: (106) implies:
% 156.04/26.81 | | | | | | (107) all_58_12 = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | REF_CLOSE: (3), (6), (8), (10), (11), (15), (19), (20), (22), (23),
% 156.04/26.81 | | | | | | (25), (27), (30), (31), (32), (33), (34), (37), (38),
% 156.04/26.81 | | | | | | (39), (40), (42), (43), (48), (50), (51), (54), (55),
% 156.04/26.81 | | | | | | (58), (59), (61), (62), (64), (67), (68), (69), (70),
% 156.04/26.81 | | | | | | (74), (77), (78), (83), (85), (88), (89), (95), (101),
% 156.04/26.81 | | | | | | (106), (107) are inconsistent by sub-proof #174.
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | Case 2:
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | (108) all_58_13 = e1 & op(e0, e2) = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | REF_CLOSE: (76), (78), (85), (108) are inconsistent by sub-proof
% 156.04/26.81 | | | | | | #192.
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | End of split
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | Case 2:
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | (109) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 156.04/26.81 | | | | | e0) = e1)
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | BETA: splitting (109) gives:
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | Case 1:
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | (110) all_58_14 = e1 & op(e0, e1) = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | ALPHA: (110) implies:
% 156.04/26.81 | | | | | | (111) all_58_14 = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | REF_CLOSE: (3), (6), (11), (15), (20), (23), (30), (34), (37), (38),
% 156.04/26.81 | | | | | | (40), (42), (43), (50), (51), (55), (61), (64), (68),
% 156.04/26.81 | | | | | | (69), (85), (88), (104), (111) are inconsistent by
% 156.04/26.81 | | | | | | sub-proof #171.
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | Case 2:
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | (112) all_58_15 = e1 & op(e0, e0) = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | REF_CLOSE: (45), (51), (85), (112) are inconsistent by sub-proof
% 156.04/26.81 | | | | | | #1418.
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | End of split
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | End of split
% 156.04/26.81 | | | |
% 156.04/26.81 | | | Case 2:
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | (113) all_58_10 = e1 & op(e2, e0) = e1
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | REF_CLOSE: (38), (72), (85), (113) are inconsistent by sub-proof #212.
% 156.04/26.81 | | | |
% 156.04/26.81 | | | End of split
% 156.04/26.81 | | |
% 156.04/26.81 | | Case 2:
% 156.04/26.81 | | |
% 156.04/26.81 | | | (114) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0)
% 156.04/26.81 | | | = e1)
% 156.04/26.81 | | |
% 156.04/26.81 | | | BETA: splitting (114) gives:
% 156.04/26.81 | | |
% 156.04/26.81 | | | Case 1:
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | (115) all_58_11 = e1 & op(e1, e0) = e1
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | BETA: splitting (12) gives:
% 156.04/26.81 | | | |
% 156.04/26.81 | | | | Case 1:
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | (116) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 156.04/26.81 | | | | | e2) = e1)
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | BETA: splitting (116) gives:
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | Case 1:
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | (117) all_58_12 = e1 & op(e0, e3) = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | ALPHA: (117) implies:
% 156.04/26.81 | | | | | | (118) all_58_12 = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | REF_CLOSE: (3), (6), (8), (10), (11), (15), (19), (20), (22), (23),
% 156.04/26.81 | | | | | | (25), (27), (30), (31), (32), (33), (34), (37), (38),
% 156.04/26.81 | | | | | | (39), (40), (42), (43), (48), (50), (51), (54), (55),
% 156.04/26.81 | | | | | | (58), (59), (61), (62), (64), (67), (68), (69), (70),
% 156.04/26.81 | | | | | | (74), (77), (78), (83), (85), (88), (89), (95), (101),
% 156.04/26.81 | | | | | | (117), (118) are inconsistent by sub-proof #174.
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | Case 2:
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | (119) all_58_13 = e1 & op(e0, e2) = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | REF_CLOSE: (76), (78), (85), (119) are inconsistent by sub-proof
% 156.04/26.81 | | | | | | #192.
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | End of split
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | Case 2:
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | (120) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 156.04/26.81 | | | | | e0) = e1)
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | BETA: splitting (120) gives:
% 156.04/26.81 | | | | |
% 156.04/26.81 | | | | | Case 1:
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | (121) all_58_14 = e1 & op(e0, e1) = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | ALPHA: (121) implies:
% 156.04/26.81 | | | | | | (122) all_58_14 = e1
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | BETA: splitting (20) gives:
% 156.04/26.81 | | | | | |
% 156.04/26.81 | | | | | | Case 1:
% 156.04/26.81 | | | | | | |
% 156.04/26.81 | | | | | | | (123) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 156.04/26.81 | | | | | | | op(e2, e0) = e2)
% 156.04/26.81 | | | | | | |
% 156.04/26.81 | | | | | | | BETA: splitting (123) gives:
% 156.04/26.81 | | | | | | |
% 156.04/26.81 | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | |
% 156.04/26.81 | | | | | | | | (124) all_58_9 = e2 & op(e3, e0) = e2
% 156.04/26.81 | | | | | | | |
% 156.04/26.81 | | | | | | | | ALPHA: (124) implies:
% 156.04/26.81 | | | | | | | | (125) op(e3, e0) = e2
% 156.04/26.81 | | | | | | | |
% 156.04/26.81 | | | | | | | | BETA: splitting (15) gives:
% 156.04/26.81 | | | | | | | |
% 156.04/26.81 | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | |
% 156.04/26.81 | | | | | | | | | (126) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 156.04/26.81 | | | | | | | | | op(e2, e1) = e3)
% 156.04/26.81 | | | | | | | | |
% 156.04/26.81 | | | | | | | | | BETA: splitting (126) gives:
% 156.04/26.81 | | | | | | | | |
% 156.04/26.81 | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | (127) all_58_4 = e3 & op(e3, e1) = e3
% 156.04/26.81 | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | ALPHA: (127) implies:
% 156.04/26.81 | | | | | | | | | | (128) all_58_4 = e3
% 156.04/26.81 | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | BETA: splitting (74) gives:
% 156.04/26.81 | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | (129) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 156.04/26.81 | | | | | | | | | | | & op(e3, e2) = e1)
% 156.04/26.81 | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | BETA: splitting (129) gives:
% 156.04/26.81 | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | (130) all_58_0 = e1 & op(e3, e3) = e1
% 156.04/26.81 | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | ALPHA: (130) implies:
% 156.04/26.81 | | | | | | | | | | | | (131) all_58_0 = e1
% 156.04/26.81 | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | BETA: splitting (42) gives:
% 156.04/26.81 | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | (132) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 156.04/26.81 | | | | | | | | | | | | | & op(e2, e1) = e0)
% 156.04/26.81 | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | REF_CLOSE: (3), (30), (34), (128), (132) are inconsistent by
% 156.04/26.81 | | | | | | | | | | | | | sub-proof #173.
% 156.04/26.81 | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | (133) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 156.04/26.81 | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 156.04/26.81 | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | BETA: splitting (133) gives:
% 156.04/26.81 | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | (134) all_58_8 = e0 & op(e1, e1) = e0
% 156.04/26.81 | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | ALPHA: (134) implies:
% 156.04/26.81 | | | | | | | | | | | | | | (135) op(e1, e1) = e0
% 156.04/26.81 | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 156.04/26.81 | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | (136) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 156.04/26.81 | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 156.04/26.81 | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | (137) all_58_0 = e0 & op(e3, e3) = e0
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | REF_CLOSE: (69), (131), (137) are inconsistent by sub-proof
% 156.04/26.81 | | | | | | | | | | | | | | | | #1520.
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | (138) all_58_1 = e0 & op(e3, e2) = e0
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | (139) op(e3, e2) = e0
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | (140) all_58_9 = e2
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | (141) op(e0, e1) = e1
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | (142) all_58_11 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | (143) op(e1, e0) = e1
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with all_52_11, e1, e1, e0,
% 156.04/26.81 | | | | | | | | | | | | | | | | simplifying with (58), (141) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | (144) all_52_11 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with all_52_14, e1, e0, e1,
% 156.04/26.81 | | | | | | | | | | | | | | | | simplifying with (79), (143) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | (145) all_52_14 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with all_6_2, all_32_1, e1, e1,
% 156.04/26.81 | | | | | | | | | | | | | | | | simplifying with (2), (11) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | (146) all_32_1 = all_6_2
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with e0, all_32_1, e1, e1,
% 156.04/26.81 | | | | | | | | | | | | | | | | simplifying with (2), (135) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | (147) all_32_1 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with all_52_12, e2, e0, e3,
% 156.04/26.81 | | | | | | | | | | | | | | | | simplifying with (5), (125) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | (148) all_52_12 = e2
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with all_52_8, e3, e1, e3,
% 156.04/26.81 | | | | | | | | | | | | | | | | simplifying with (70), (101) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | (149) all_52_8 = e3
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with all_52_4, e0, e2, e3,
% 156.04/26.81 | | | | | | | | | | | | | | | | simplifying with (22), (139) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | (150) all_52_4 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | COMBINE_EQS: (146), (147) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | (151) all_6_2 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | SIMP: (151) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | (152) all_6_2 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (152) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | (153) all_56_14 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | REDUCE: (86), (144) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | (154) ~ (all_52_3 = e1)
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | REDUCE: (26), (148) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | (155) ~ (all_52_13 = e2)
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | REDUCE: (18), (148) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | (156) ~ (all_4_2 = e2)
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | REDUCE: (93), (145) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | (157) ~ (all_4_2 = e1)
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | REDUCE: (50), (152) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | (158) ~ (e3 = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | REDUCE: (71), (152) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | (159) ~ (e2 = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | (160) ~ (all_50_2 = e1)
% 156.04/26.81 | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | REDUCE: (56), (160) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | (161) $false
% 156.04/26.81 | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 156.04/26.81 | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | (162) ( ~ (all_50_0 = e2) & op(all_50_1, e3) = all_50_0
% 156.04/26.81 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_50_1 & $i(all_50_0) &
% 156.04/26.81 | | | | | | | | | | | | | | | | | $i(all_50_1)) | ( ~ (all_50_1 = e0) & op(e1, e1)
% 156.04/26.81 | | | | | | | | | | | | | | | | | = all_50_1 & $i(all_50_1))
% 156.04/26.81 | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | (163) ~ (all_56_14 = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | REDUCE: (153), (163) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | (164) $false
% 156.04/26.81 | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 156.04/26.81 | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | (165) all_56_8 = e1 & op(e1, e0) = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | (166) all_56_8 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | (167) all_56_12 = e3
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (167) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | (168) e3 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | REDUCE: (40), (168) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | (169) $false
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | (170) ~ (all_56_12 = e3)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | (171) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | REDUCE: (41), (170) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | (172) ~ (e3 = e1)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | (173) ~ (all_50_0 = e2) & op(all_50_1, e3) = all_50_0 &
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_50_1 & $i(all_50_0) &
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | $i(all_50_1)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | (174) ~ (all_50_0 = e2)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | (175) op(e1, e1) = all_50_1
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | (176) op(all_50_1, e3) = all_50_0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | (177) all_56_13 = e2
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (177) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | (178) e2 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (178) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | (179) all_58_9 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (11), (15), (20), (23), (30), (34),
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | (37), (38), (40), (42), (43), (50), (51), (55),
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | (61), (64), (68), (69), (85), (88), (122), (179)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #171.
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | (180) ~ (all_56_13 = e2)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | (181) all_56_14 = e1 | all_56_15 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (180) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | (182) ~ (e2 = e1)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | (183) all_56_14 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (183) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | (184) e1 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (184) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | (185) $false
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | (186) all_56_15 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (186) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | (187) all_4_2 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (187) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | (188) ~ (all_52_7 = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (187) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | (189) ~ (all_52_13 = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (187) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | (190) ~ (e1 = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | (191) all_54_7 = e3
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (191) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | (192) all_52_13 = e3
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (192) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | (193) ~ (all_52_1 = e3)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | (194) all_58_15 = e0 & op(e0, e0) = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | (195) all_58_15 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | (196) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_58_9 = e3 & op(e3, e0) = e3
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (140), (197) are inconsistent by sub-proof
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | #194.
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_10 = e3 & op(e2, e0) = e3
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_58_10 = e3
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_54_4 = e3
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (200) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_52_1 = e3
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (201) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) $false
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent.
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) ~ (all_54_4 = e3)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_0 = e0 & op(e3, e3) = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (131), (206) are inconsistent by sub-proof
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1520.
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_58_2 = e0 & op(e2, e3) = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_58_2 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_4 = e2
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (209) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_52_1 = e2
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (210) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) $false
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) ~ (all_54_4 = e2)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_54_4 = e1 | all_54_4 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_54_4 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (214) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_52_1 = e1
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (215) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) $false
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (216) is inconsistent.
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_54_4 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (217) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_52_1 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (218) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) ~ (all_52_3 = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (219) implies:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_52_3 = e0)
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (218) imply:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) op(e2, e3) = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with e0, all_50_1, e1, e1,
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (135), (175) gives:
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_50_1 = e0
% 156.04/26.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (222) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) op(e0, e3) = all_50_0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with all_52_3, all_50_0, e3,
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (4), (223) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_52_3 = all_50_0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (224) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_54_12 = all_50_0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (224) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) ~ (all_52_7 = all_50_0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (226) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) ~ (all_52_7 = all_50_0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (224) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_50_0 = e1)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (224) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) ~ (all_50_0 = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (34), (67), (85), (221), (230) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #183.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_58_6 = e2 & op(e1, e3) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_6 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) op(e1, e3) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_54_12 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (225), (235) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_50_0 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (236) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_50_0 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (227), (237) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) ~ (all_52_7 = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_54_13 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (238), (239) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1435.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) ~ (all_54_13 = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) op(e2, e3) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (85), (193), (245) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1183.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) op(e2, e3) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (27), (30), (31), (34), (40), (68), (69),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (85), (88), (233), (248) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1152.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) ~ (all_56_14 = e1)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) op(e1, e3) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (40), (85), (131), (193), (252) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #191.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_58_6 = e3 & op(e1, e3) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_58_6 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (20), (23), (29), (43), (51), (66),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (71), (76), (85), (88), (140), (142), (188),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (241), (255) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #189.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_58_12 = e3 & op(e0, e3) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_58_12 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (30), (40), (85), (88), (95), (131), (139),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (233), (257), (258) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #188.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_58_7 = e3 & op(e1, e2) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_58_7 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with e2, e3, e3, e1,
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (234), (251) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) e3 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (262) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_12 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (19), (20), (23), (29), (30), (31), (34),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (40), (51), (68), (69), (71), (83), (85), (88),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (140), (142), (199), (261), (263) are inconsistent
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #200.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_58_13 = e3 & op(e0, e2) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_58_13 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (23), (30), (31), (33), (34), (40), (48),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (58), (68), (69), (83), (85), (88), (233),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) are inconsistent by sub-proof #1174.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (37), (61), (85), (125), (186), (266) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #187.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) op(e1, e2) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (43), (66), (76), (81), (85), (188), (238),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) are inconsistent by sub-proof #208.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (43), (55), (64), (85), (271) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1129.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) op(e0, e2) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (76), (78), (85), (188), (241), (274) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #874.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) ~ (all_56_15 = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (277) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) $false
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (278) is inconsistent.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_56_8 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (280) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) e1 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (281) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) $false
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (282) is inconsistent.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (154), (174), (220), (225), (283) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #186.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_58_12 = e2 & op(e0, e3) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_12 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_54_12 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (225), (286) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_50_0 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (287) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_50_0 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (227), (288) imply:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) ~ (all_52_7 = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_54_13 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (289), (290) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1435.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_58_6 = e2 & op(e1, e3) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_6 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (30), (31), (34), (40), (68), (69), (83),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (88), (285), (294) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1481.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_58_7 = e2 & op(e1, e2) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) op(e1, e2) = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (43), (66), (76), (85), (188), (291), (296)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #209.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (20), (23), (51), (68), (71), (85), (88),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (140), (142), (199), (297) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #204.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (154), (174), (220), (225), (298) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #186.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_6 = e0 & op(e1, e3) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (19), (20), (23), (27), (29), (30),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (34), (40), (45), (51), (58), (68), (71),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (88), (95), (97), (131), (139), (140),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (142), (193), (199), (300) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #170.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_12 = e0 & op(e0, e3) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_12 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (27), (67), (85), (303) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1522.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (27), (30), (34), (40), (85), (88), (131),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193), (302), (304) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #182.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | (305) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_58_11 = e3 & op(e1, e0) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (307) op(e1, e0) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (85), (143), (307) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1275.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_15 = e3 & op(e0, e0) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_58_15 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (195), (309) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | #1318.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | (310) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | (311) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | (312) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (40), (85), (95), (193), (312) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #213.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | (313) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_58_5 = e3 & op(e2, e1) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_5 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (88), (315) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | #897.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_58_10 = e3 & op(e2, e0) = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_10 = e3
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_58_0 = e0 & op(e3, e3) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (131), (319) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1520.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_2 = e0 & op(e2, e3) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) op(e2, e3) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (27), (30), (34), (40), (62), (67),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (78), (85), (88), (122), (131), (188),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193), (311), (321) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #181.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_58_6 = e0 & op(e1, e3) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (19), (20), (23), (27), (29), (30),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (34), (40), (45), (51), (58), (68), (71),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (88), (95), (97), (131), (139), (140),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (142), (193), (317), (323) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #170.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_58_12 = e0 & op(e0, e3) = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_12 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (27), (67), (85), (326) are
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1522.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (27), (30), (34), (40), (85), (88), (131),
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193), (325), (327) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #182.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | (328) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (55), (72), (189), (328) are inconsistent by
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #179.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | (329) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 &
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | $i(all_50_1)
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (135), (329) are inconsistent by sub-proof
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | | #185.
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | | End of split
% 156.04/26.82 | | | | | | | | | | | | | | |
% 156.04/26.82 | | | | | | | | | | | | | | Case 2:
% 156.04/26.82 | | | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | | | | (330) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 156.04/26.83 | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 156.04/26.83 | | | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | | | | REF_CLOSE: (30), (34), (85), (125), (128), (330) are
% 156.04/26.83 | | | | | | | | | | | | | | | inconsistent by sub-proof #1499.
% 156.04/26.83 | | | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | | | End of split
% 156.04/26.83 | | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | | | (331) all_58_14 = e0 & op(e0, e1) = e0
% 156.04/26.83 | | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | | | ALPHA: (331) implies:
% 156.04/26.83 | | | | | | | | | | | | | | (332) all_58_14 = e0
% 156.04/26.83 | | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | | | REF_CLOSE: (69), (122), (332) are inconsistent by sub-proof
% 156.04/26.83 | | | | | | | | | | | | | | #614.
% 156.04/26.83 | | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | | End of split
% 156.04/26.83 | | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | End of split
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | (333) all_58_1 = e1 & op(e3, e2) = e1
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | REF_CLOSE: (22), (59), (85), (333) are inconsistent by
% 156.04/26.83 | | | | | | | | | | | | sub-proof #1284.
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | End of split
% 156.04/26.83 | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | (334) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 156.04/26.83 | | | | | | | | | | | & op(e3, e0) = e1)
% 156.04/26.83 | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | BETA: splitting (334) gives:
% 156.04/26.83 | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | Case 1:
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | (335) all_58_4 = e1 & op(e3, e1) = e1
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | REF_CLOSE: (40), (128), (335) are inconsistent by sub-proof
% 156.04/26.83 | | | | | | | | | | | | #1345.
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | (336) all_58_9 = e1 & op(e3, e0) = e1
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | ALPHA: (336) implies:
% 156.04/26.83 | | | | | | | | | | | | (337) all_58_9 = e1
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | | REF_CLOSE: (3), (6), (11), (15), (20), (23), (30), (34),
% 156.04/26.83 | | | | | | | | | | | | (37), (38), (40), (42), (43), (50), (51), (55),
% 156.04/26.83 | | | | | | | | | | | | (61), (64), (68), (69), (85), (88), (122), (337)
% 156.04/26.83 | | | | | | | | | | | | are inconsistent by sub-proof #171.
% 156.04/26.83 | | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | | End of split
% 156.04/26.83 | | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | End of split
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | (338) all_58_5 = e3 & op(e2, e1) = e3
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | ALPHA: (338) implies:
% 156.04/26.83 | | | | | | | | | | (339) all_58_5 = e3
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | REF_CLOSE: (3), (88), (339) are inconsistent by sub-proof
% 156.04/26.83 | | | | | | | | | | #897.
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | End of split
% 156.04/26.83 | | | | | | | | |
% 156.04/26.83 | | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | | |
% 156.04/26.83 | | | | | | | | | (340) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 156.04/26.83 | | | | | | | | | op(e0, e1) = e3)
% 156.04/26.83 | | | | | | | | |
% 156.04/26.83 | | | | | | | | | BETA: splitting (340) gives:
% 156.04/26.83 | | | | | | | | |
% 156.04/26.83 | | | | | | | | | Case 1:
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | (341) all_58_8 = e3 & op(e1, e1) = e3
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | REF_CLOSE: (11), (50), (85), (341) are inconsistent by
% 156.04/26.83 | | | | | | | | | | sub-proof #1469.
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | (342) all_58_14 = e3 & op(e0, e1) = e3
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | | REF_CLOSE: (40), (122), (342) are inconsistent by sub-proof
% 156.04/26.83 | | | | | | | | | | #872.
% 156.04/26.83 | | | | | | | | | |
% 156.04/26.83 | | | | | | | | | End of split
% 156.04/26.83 | | | | | | | | |
% 156.04/26.83 | | | | | | | | End of split
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | | (343) all_58_10 = e2 & op(e2, e0) = e2
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | | ALPHA: (343) implies:
% 156.04/26.83 | | | | | | | | (344) op(e2, e0) = e2
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | | REF_CLOSE: (38), (55), (85), (344) are inconsistent by sub-proof
% 156.04/26.83 | | | | | | | | #1535.
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | End of split
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | Case 2:
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | (345) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 156.04/26.83 | | | | | | | op(e0, e0) = e2)
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | BETA: splitting (345) gives:
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | Case 1:
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | | (346) all_58_11 = e2 & op(e1, e0) = e2
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | | ALPHA: (346) implies:
% 156.04/26.83 | | | | | | | | (347) all_58_11 = e2
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | | REF_CLOSE: (3), (6), (11), (15), (30), (34), (37), (40), (42),
% 156.04/26.83 | | | | | | | | (43), (50), (61), (64), (68), (69), (85), (88),
% 156.04/26.83 | | | | | | | | (122), (347) are inconsistent by sub-proof #172.
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | Case 2:
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | | (348) all_58_15 = e2 & op(e0, e0) = e2
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | | REF_CLOSE: (23), (51), (85), (348) are inconsistent by sub-proof
% 156.04/26.83 | | | | | | | | #1452.
% 156.04/26.83 | | | | | | | |
% 156.04/26.83 | | | | | | | End of split
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | End of split
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | Case 2:
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | (349) all_58_15 = e1 & op(e0, e0) = e1
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | REF_CLOSE: (45), (51), (85), (349) are inconsistent by sub-proof
% 156.04/26.83 | | | | | | #1418.
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | End of split
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | End of split
% 156.04/26.83 | | | |
% 156.04/26.83 | | | Case 2:
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | (350) all_58_15 = e1 & op(e0, e0) = e1
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | REF_CLOSE: (45), (51), (85), (350) are inconsistent by sub-proof #1418.
% 156.04/26.83 | | | |
% 156.04/26.83 | | | End of split
% 156.04/26.83 | | |
% 156.04/26.83 | | End of split
% 156.04/26.83 | |
% 156.04/26.83 | End of split
% 156.04/26.83 |
% 156.04/26.83 End of proof
% 156.04/26.83
% 156.04/26.83 Sub-proof #170 shows that the following formulas are inconsistent:
% 156.04/26.83 ----------------------------------------------------------------
% 156.04/26.83 (1) all_58_11 = e1
% 156.04/26.83 (2) op(e1, e1) = all_6_2
% 156.04/26.83 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.04/26.83 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.04/26.83 (4) all_58_0 = e1
% 156.04/26.83 (5) all_58_6 = e0 & op(e1, e3) = e0
% 156.04/26.83 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.04/26.83 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.04/26.83 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.04/26.83 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.04/26.83 (8) ~ (all_4_2 = e2)
% 156.04/26.83 (9) op(e2, e3) = all_52_1
% 156.04/26.83 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.04/26.83 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.04/26.83 (11) ~ (e3 = e0)
% 156.04/26.83 (12) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.04/26.83 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.04/26.83 e2)
% 156.04/26.83 (13) ~ (e2 = e0)
% 156.04/26.83 (14) ~ (e3 = e1)
% 156.04/26.83 (15) ~ (all_4_2 = e1)
% 156.04/26.83 (16) op(e0, e0) = all_4_2
% 156.04/26.83 (17) op(e3, e2) = e0
% 156.04/26.83 (18) op(e0, e1) = all_52_11
% 156.04/26.83 (19) all_58_10 = e3
% 156.04/26.83 (20) ~ (e2 = e1)
% 156.04/26.83 (21) ~ (all_6_2 = e2)
% 156.04/26.83 (22) all_58_9 = e2
% 156.04/26.83 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.83 (24) ~ (e3 = e2)
% 156.04/26.83 (25) all_58_3 = e1
% 156.04/26.83 (26) ~ (all_52_1 = e3)
% 156.04/26.83 (27) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.04/26.83 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.04/26.83
% 156.04/26.83 Begin of proof
% 156.04/26.83 |
% 156.04/26.83 | ALPHA: (5) implies:
% 156.04/26.83 | (28) all_58_6 = e0
% 156.04/26.83 |
% 156.04/26.83 | BETA: splitting (10) gives:
% 156.04/26.83 |
% 156.04/26.83 | Case 1:
% 156.04/26.83 | |
% 156.04/26.83 | | (29) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 156.04/26.83 | | e2)
% 156.04/26.83 | |
% 156.04/26.83 | | BETA: splitting (29) gives:
% 156.04/26.83 | |
% 156.04/26.83 | | Case 1:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (30) all_58_6 = e2 & op(e1, e3) = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | REF_CLOSE: (13), (28), (30) are inconsistent by sub-proof #345.
% 156.04/26.83 | | |
% 156.04/26.83 | | Case 2:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (31) all_58_7 = e2 & op(e1, e2) = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | ALPHA: (31) implies:
% 156.04/26.83 | | | (32) all_58_7 = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | BETA: splitting (27) gives:
% 156.04/26.83 | | |
% 156.04/26.83 | | | Case 1:
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | (33) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2)
% 156.04/26.83 | | | | = e3)
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | BETA: splitting (33) gives:
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | Case 1:
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | (34) all_58_1 = e3 & op(e3, e2) = e3
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | ALPHA: (34) implies:
% 156.04/26.83 | | | | | (35) op(e3, e2) = e3
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | REF_CLOSE: (11), (17), (23), (35) are inconsistent by sub-proof #1303.
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | Case 2:
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | (36) all_58_3 = e3 & op(e2, e2) = e3
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | ALPHA: (36) implies:
% 156.04/26.83 | | | | | (37) all_58_3 = e3
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | REF_CLOSE: (14), (25), (37) are inconsistent by sub-proof #841.
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | End of split
% 156.04/26.83 | | | |
% 156.04/26.83 | | | Case 2:
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | (38) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2)
% 156.04/26.83 | | | | = e3)
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | BETA: splitting (38) gives:
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | Case 1:
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | (39) all_58_7 = e3 & op(e1, e2) = e3
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | ALPHA: (39) implies:
% 156.04/26.83 | | | | | (40) all_58_7 = e3
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | REF_CLOSE: (24), (32), (40) are inconsistent by sub-proof #1215.
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | Case 2:
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | (41) all_58_13 = e3 & op(e0, e2) = e3
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | ALPHA: (41) implies:
% 156.04/26.83 | | | | | (42) all_58_13 = e3
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | BETA: splitting (6) gives:
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | Case 1:
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | (43) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2,
% 156.04/26.83 | | | | | | e3) = e3)
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | REF_CLOSE: (4), (9), (14), (23), (26), (43) are inconsistent by
% 156.04/26.83 | | | | | | sub-proof #191.
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | Case 2:
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | (44) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0,
% 156.04/26.83 | | | | | | e3) = e3)
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | BETA: splitting (44) gives:
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | Case 1:
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | (45) all_58_6 = e3 & op(e1, e3) = e3
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | REF_CLOSE: (11), (28), (45) are inconsistent by sub-proof #749.
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | Case 2:
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | (46) all_58_12 = e3 & op(e0, e3) = e3
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | REF_CLOSE: (3), (8), (12), (14), (15), (16), (18), (20), (23),
% 156.04/26.83 | | | | | | | (24), (42), (46) are inconsistent by sub-proof #1163.
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | End of split
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | End of split
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | End of split
% 156.04/26.83 | | | |
% 156.04/26.83 | | | End of split
% 156.04/26.83 | | |
% 156.04/26.83 | | End of split
% 156.04/26.83 | |
% 156.04/26.83 | Case 2:
% 156.04/26.83 | |
% 156.04/26.83 | | (47) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 156.04/26.83 | | e2)
% 156.04/26.83 | |
% 156.04/26.83 | | REF_CLOSE: (1), (2), (7), (8), (16), (19), (20), (21), (22), (23), (24),
% 156.04/26.83 | | (47) are inconsistent by sub-proof #204.
% 156.04/26.83 | |
% 156.04/26.83 | End of split
% 156.04/26.83 |
% 156.04/26.83 End of proof
% 156.04/26.83
% 156.04/26.83 Sub-proof #171 shows that the following formulas are inconsistent:
% 156.04/26.83 ----------------------------------------------------------------
% 156.04/26.83 (1) all_58_5 = e2
% 156.04/26.83 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.04/26.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.04/26.83 (3) op(e1, e1) = all_6_2
% 156.04/26.83 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.04/26.83 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.04/26.83 (5) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.04/26.83 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.04/26.83 (6) ~ (all_4_2 = e2)
% 156.04/26.83 (7) all_58_14 = e1
% 156.04/26.83 (8) ~ (e3 = e0)
% 156.04/26.83 (9) ~ (e2 = e0)
% 156.04/26.83 (10) op(e1, e3) = all_52_2
% 156.04/26.83 (11) op(e2, e0) = all_52_13
% 156.04/26.83 (12) ~ (e3 = e1)
% 156.04/26.83 (13) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.04/26.83 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.04/26.83 (14) op(e1, e2) = all_52_6
% 156.04/26.83 (15) ~ (all_6_2 = e3)
% 156.04/26.83 (16) op(e0, e0) = all_4_2
% 156.04/26.83 (17) ~ (all_52_13 = e2)
% 156.04/26.83 (18) ~ (all_52_2 = e1)
% 156.04/26.83 (19) ~ (all_52_6 = e1)
% 156.04/26.83 (20) ~ (e2 = e1)
% 156.04/26.83 (21) ~ (e1 = e0)
% 156.04/26.83 (22) all_58_9 = e1
% 156.04/26.83 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.83 (24) ~ (e3 = e2)
% 156.04/26.83
% 156.04/26.83 Begin of proof
% 156.04/26.83 |
% 156.04/26.83 | BETA: splitting (5) gives:
% 156.04/26.83 |
% 156.04/26.83 | Case 1:
% 156.04/26.83 | |
% 156.04/26.83 | | (25) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 156.04/26.83 | | e2)
% 156.04/26.83 | |
% 156.04/26.83 | | REF_CLOSE: (11), (17), (20), (22), (23), (25) are inconsistent by sub-proof
% 156.04/26.83 | | #198.
% 156.04/26.83 | |
% 156.04/26.83 | Case 2:
% 156.04/26.83 | |
% 156.04/26.83 | | (26) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.04/26.83 | | e2)
% 156.04/26.83 | |
% 156.04/26.83 | | BETA: splitting (26) gives:
% 156.04/26.83 | |
% 156.04/26.83 | | Case 1:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (27) all_58_11 = e2 & op(e1, e0) = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | ALPHA: (27) implies:
% 156.04/26.83 | | | (28) all_58_11 = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (13), (14),
% 156.04/26.83 | | | (15), (18), (19), (20), (21), (23), (24), (28) are inconsistent
% 156.04/26.83 | | | by sub-proof #172.
% 156.04/26.83 | | |
% 156.04/26.83 | | Case 2:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (29) all_58_15 = e2 & op(e0, e0) = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | REF_CLOSE: (6), (16), (23), (29) are inconsistent by sub-proof #1452.
% 156.04/26.83 | | |
% 156.04/26.83 | | End of split
% 156.04/26.83 | |
% 156.04/26.83 | End of split
% 156.04/26.83 |
% 156.04/26.83 End of proof
% 156.04/26.83
% 156.04/26.83 Sub-proof #172 shows that the following formulas are inconsistent:
% 156.04/26.83 ----------------------------------------------------------------
% 156.04/26.83 (1) all_58_5 = e2
% 156.04/26.83 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.04/26.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.04/26.83 (3) op(e1, e1) = all_6_2
% 156.04/26.83 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.04/26.83 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.04/26.83 (5) all_58_14 = e1
% 156.04/26.83 (6) ~ (e3 = e0)
% 156.04/26.83 (7) ~ (e2 = e0)
% 156.04/26.83 (8) op(e1, e3) = all_52_2
% 156.04/26.83 (9) ~ (e3 = e1)
% 156.04/26.83 (10) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.04/26.83 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.04/26.83 (11) op(e1, e2) = all_52_6
% 156.04/26.83 (12) ~ (all_6_2 = e3)
% 156.04/26.83 (13) all_58_11 = e2
% 156.04/26.83 (14) ~ (all_52_2 = e1)
% 156.04/26.83 (15) ~ (all_52_6 = e1)
% 156.04/26.83 (16) ~ (e2 = e1)
% 156.04/26.83 (17) ~ (e1 = e0)
% 156.04/26.83 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.83 (19) ~ (e3 = e2)
% 156.04/26.83
% 156.04/26.83 Begin of proof
% 156.04/26.83 |
% 156.04/26.83 | BETA: splitting (4) gives:
% 156.04/26.83 |
% 156.04/26.83 | Case 1:
% 156.04/26.83 | |
% 156.04/26.83 | | (20) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 156.04/26.83 | | e3)
% 156.04/26.83 | |
% 156.04/26.83 | | BETA: splitting (20) gives:
% 156.04/26.83 | |
% 156.04/26.83 | | Case 1:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (21) all_58_4 = e3 & op(e3, e1) = e3
% 156.04/26.83 | | |
% 156.04/26.83 | | | ALPHA: (21) implies:
% 156.04/26.83 | | | (22) all_58_4 = e3
% 156.04/26.83 | | |
% 156.04/26.83 | | | BETA: splitting (10) gives:
% 156.04/26.83 | | |
% 156.04/26.83 | | | Case 1:
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | (23) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 156.04/26.83 | | | | = e0)
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | REF_CLOSE: (1), (6), (7), (22), (23) are inconsistent by sub-proof #173.
% 156.04/26.83 | | | |
% 156.04/26.83 | | | Case 2:
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | (24) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1)
% 156.04/26.83 | | | | = e0)
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | BETA: splitting (24) gives:
% 156.04/26.83 | | | |
% 156.04/26.83 | | | | Case 1:
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | (25) all_58_8 = e0 & op(e1, e1) = e0
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | ALPHA: (25) implies:
% 156.04/26.83 | | | | | (26) all_58_8 = e0
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | BETA: splitting (2) gives:
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | Case 1:
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | (27) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 156.04/26.83 | | | | | | e2) = e1)
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | REF_CLOSE: (8), (11), (14), (15), (18), (27) are inconsistent by
% 156.04/26.83 | | | | | | sub-proof #196.
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | Case 2:
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | (28) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 156.04/26.83 | | | | | | e0) = e1)
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | BETA: splitting (28) gives:
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | | Case 1:
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | (29) all_58_8 = e1 & op(e1, e1) = e1
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | REF_CLOSE: (17), (26), (29) are inconsistent by sub-proof #1474.
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | Case 2:
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | (30) all_58_11 = e1 & op(e1, e0) = e1
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | | REF_CLOSE: (13), (16), (30) are inconsistent by sub-proof #1455.
% 156.04/26.83 | | | | | | |
% 156.04/26.83 | | | | | | End of split
% 156.04/26.83 | | | | | |
% 156.04/26.83 | | | | | End of split
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | Case 2:
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | (31) all_58_14 = e0 & op(e0, e1) = e0
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | ALPHA: (31) implies:
% 156.04/26.83 | | | | | (32) all_58_14 = e0
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | | REF_CLOSE: (5), (17), (32) are inconsistent by sub-proof #614.
% 156.04/26.83 | | | | |
% 156.04/26.83 | | | | End of split
% 156.04/26.83 | | | |
% 156.04/26.83 | | | End of split
% 156.04/26.83 | | |
% 156.04/26.83 | | Case 2:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (33) all_58_5 = e3 & op(e2, e1) = e3
% 156.04/26.83 | | |
% 156.04/26.83 | | | ALPHA: (33) implies:
% 156.04/26.83 | | | (34) all_58_5 = e3
% 156.04/26.83 | | |
% 156.04/26.83 | | | REF_CLOSE: (1), (19), (34) are inconsistent by sub-proof #897.
% 156.04/26.83 | | |
% 156.04/26.83 | | End of split
% 156.04/26.83 | |
% 156.04/26.83 | Case 2:
% 156.04/26.83 | |
% 156.04/26.83 | | (35) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 156.04/26.83 | | e3)
% 156.04/26.83 | |
% 156.04/26.83 | | BETA: splitting (35) gives:
% 156.04/26.83 | |
% 156.04/26.83 | | Case 1:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (36) all_58_8 = e3 & op(e1, e1) = e3
% 156.04/26.83 | | |
% 156.04/26.83 | | | REF_CLOSE: (3), (12), (18), (36) are inconsistent by sub-proof #1469.
% 156.04/26.83 | | |
% 156.04/26.83 | | Case 2:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (37) all_58_14 = e3 & op(e0, e1) = e3
% 156.04/26.83 | | |
% 156.04/26.83 | | | REF_CLOSE: (5), (9), (37) are inconsistent by sub-proof #872.
% 156.04/26.83 | | |
% 156.04/26.83 | | End of split
% 156.04/26.83 | |
% 156.04/26.83 | End of split
% 156.04/26.83 |
% 156.04/26.83 End of proof
% 156.04/26.83
% 156.04/26.83 Sub-proof #173 shows that the following formulas are inconsistent:
% 156.04/26.83 ----------------------------------------------------------------
% 156.04/26.83 (1) all_58_5 = e2
% 156.04/26.83 (2) ~ (e3 = e0)
% 156.04/26.83 (3) ~ (e2 = e0)
% 156.04/26.83 (4) all_58_4 = e3
% 156.04/26.83 (5) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 156.04/26.83
% 156.04/26.83 Begin of proof
% 156.04/26.83 |
% 156.04/26.83 | BETA: splitting (5) gives:
% 156.04/26.83 |
% 156.04/26.83 | Case 1:
% 156.04/26.83 | |
% 156.04/26.83 | | (6) all_58_4 = e0 & op(e3, e1) = e0
% 156.04/26.83 | |
% 156.04/26.83 | | ALPHA: (6) implies:
% 156.04/26.83 | | (7) all_58_4 = e0
% 156.04/26.83 | |
% 156.04/26.83 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #1501.
% 156.04/26.83 | |
% 156.04/26.83 | Case 2:
% 156.04/26.83 | |
% 156.04/26.83 | | (8) all_58_5 = e0 & op(e2, e1) = e0
% 156.04/26.83 | |
% 156.04/26.83 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #180.
% 156.04/26.83 | |
% 156.04/26.83 | End of split
% 156.04/26.83 |
% 156.04/26.83 End of proof
% 156.04/26.83
% 156.04/26.83 Sub-proof #174 shows that the following formulas are inconsistent:
% 156.04/26.83 ----------------------------------------------------------------
% 156.04/26.83 (1) all_58_5 = e2
% 156.04/26.83 (2) op(e3, e1) = e3
% 156.04/26.83 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.04/26.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.04/26.83 (4) op(e3, e3) = all_10_2
% 156.04/26.83 (5) ~ (all_52_1 = e2)
% 156.04/26.83 (6) op(e1, e1) = all_6_2
% 156.04/26.83 (7) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.04/26.83 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.04/26.83 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.04/26.83 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.04/26.83 (9) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.04/26.83 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.04/26.83 (10) op(e3, e2) = all_52_4
% 156.04/26.83 (11) ~ (all_4_2 = e2)
% 156.04/26.83 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.04/26.83 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.04/26.83 (13) op(e2, e3) = all_52_1
% 156.04/26.83 (14) ~ (e3 = e0)
% 156.04/26.83 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.04/26.83 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.04/26.83 (16) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.04/26.83 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.04/26.83 (17) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.04/26.83 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.04/26.83 e2)
% 156.04/26.83 (18) ~ (e2 = e0)
% 156.04/26.83 (19) op(e1, e3) = all_52_2
% 156.04/26.83 (20) op(e2, e0) = all_52_13
% 156.04/26.83 (21) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.04/26.83 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.04/26.83 (22) ~ (e3 = e1)
% 156.04/26.83 (23) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.04/26.83 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.04/26.83 (24) op(e1, e2) = all_52_6
% 156.04/26.83 (25) ~ (all_52_11 = e2)
% 156.04/26.83 (26) ~ (all_6_2 = e3)
% 156.04/26.83 (27) op(e0, e0) = all_4_2
% 156.04/26.83 (28) op(e3, e3) = e1
% 156.04/26.83 (29) ~ (all_52_13 = e2)
% 156.04/26.83 (30) op(e0, e1) = all_52_11
% 156.04/26.83 (31) ~ (all_52_4 = e1)
% 156.04/26.83 (32) ~ (all_52_2 = e1)
% 156.04/26.83 (33) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 156.04/26.83 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.04/26.83 (34) ~ (all_52_6 = e1)
% 156.04/26.83 (35) ~ (all_10_2 = e2)
% 156.04/26.83 (36) ~ (e2 = e1)
% 156.04/26.83 (37) ~ (e1 = e0)
% 156.04/26.83 (38) op(e3, e1) = all_52_8
% 156.04/26.83 (39) all_58_12 = e1 & op(e0, e3) = e1
% 156.04/26.83 (40) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.04/26.83 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.04/26.83 (41) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 156.04/26.83 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 156.04/26.83 (42) op(e0, e2) = all_52_7
% 156.04/26.83 (43) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.04/26.83 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.04/26.83 (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.04/26.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.04/26.83 (45) ~ (e3 = e2)
% 156.04/26.83 (46) all_58_12 = e1
% 156.04/26.83 (47) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.04/26.83 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.04/26.83 (48) all_58_3 = e1
% 156.04/26.83
% 156.04/26.83 Begin of proof
% 156.04/26.83 |
% 156.04/26.83 | BETA: splitting (9) gives:
% 156.04/26.83 |
% 156.04/26.83 | Case 1:
% 156.04/26.83 | |
% 156.04/26.83 | | (49) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 156.04/26.83 | | e2)
% 156.04/26.83 | |
% 156.04/26.83 | | BETA: splitting (49) gives:
% 156.04/26.83 | |
% 156.04/26.83 | | Case 1:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (50) all_58_9 = e2 & op(e3, e0) = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | ALPHA: (50) implies:
% 156.04/26.83 | | | (51) all_58_9 = e2
% 156.04/26.83 | | | (52) op(e3, e0) = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (13), (14), (15),
% 156.04/26.83 | | | (18), (19), (22), (23), (24), (26), (28), (31), (32), (33),
% 156.04/26.83 | | | (34), (35), (36), (37), (38), (39), (40), (41), (43), (44),
% 156.04/26.83 | | | (45), (46), (47), (51), (52) are inconsistent by sub-proof
% 156.04/26.83 | | | #193.
% 156.04/26.83 | | |
% 156.04/26.83 | | Case 2:
% 156.04/26.83 | | |
% 156.04/26.83 | | | (53) all_58_10 = e2 & op(e2, e0) = e2
% 156.04/26.83 | | |
% 156.04/26.83 | | | ALPHA: (53) implies:
% 156.04/26.84 | | | (54) op(e2, e0) = e2
% 156.04/26.84 | | |
% 156.04/26.84 | | | REF_CLOSE: (20), (29), (44), (54) are inconsistent by sub-proof #1535.
% 156.04/26.84 | | |
% 156.04/26.84 | | End of split
% 156.04/26.84 | |
% 156.04/26.84 | Case 2:
% 156.04/26.84 | |
% 156.04/26.84 | | (55) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.04/26.84 | | e2)
% 156.04/26.84 | |
% 156.04/26.84 | | BETA: splitting (55) gives:
% 156.04/26.84 | |
% 156.04/26.84 | | Case 1:
% 156.04/26.84 | | |
% 156.04/26.84 | | | (56) all_58_11 = e2 & op(e1, e0) = e2
% 156.04/26.84 | | |
% 156.04/26.84 | | | ALPHA: (56) implies:
% 156.04/26.84 | | | (57) all_58_11 = e2
% 156.04/26.84 | | |
% 156.04/26.84 | | | BETA: splitting (17) gives:
% 156.04/26.84 | | |
% 156.04/26.84 | | | Case 1:
% 156.04/26.84 | | | |
% 156.04/26.84 | | | | (58) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 156.04/26.84 | | | | e2) = e2)
% 156.04/26.84 | | | |
% 156.04/26.84 | | | | BETA: splitting (58) gives:
% 156.04/26.84 | | | |
% 156.04/26.84 | | | | Case 1:
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | (59) all_58_12 = e2 & op(e0, e3) = e2
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | REF_CLOSE: (36), (46), (59) are inconsistent by sub-proof #1511.
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | Case 2:
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | (60) all_58_13 = e2 & op(e0, e2) = e2
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | ALPHA: (60) implies:
% 156.04/26.84 | | | | | (61) op(e0, e2) = e2
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | BETA: splitting (16) gives:
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | Case 1:
% 156.04/26.84 | | | | | |
% 156.04/26.84 | | | | | | (62) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 156.04/26.84 | | | | | | e2) = e2)
% 156.04/26.84 | | | | | |
% 156.04/26.84 | | | | | | BETA: splitting (62) gives:
% 156.04/26.84 | | | | | |
% 156.04/26.84 | | | | | | Case 1:
% 156.04/26.84 | | | | | | |
% 156.04/26.84 | | | | | | | (63) all_58_0 = e2 & op(e3, e3) = e2
% 156.04/26.84 | | | | | | |
% 156.04/26.84 | | | | | | | REF_CLOSE: (4), (35), (44), (63) are inconsistent by sub-proof
% 156.04/26.84 | | | | | | | #1523.
% 156.04/26.84 | | | | | | |
% 156.04/26.84 | | | | | | Case 2:
% 156.04/26.84 | | | | | | |
% 156.04/26.84 | | | | | | | (64) all_58_1 = e2 & op(e3, e2) = e2
% 156.04/26.84 | | | | | | |
% 156.04/26.84 | | | | | | | ALPHA: (64) implies:
% 156.04/26.84 | | | | | | | (65) all_58_1 = e2
% 156.04/26.84 | | | | | | |
% 156.04/26.84 | | | | | | | BETA: splitting (21) gives:
% 156.04/26.84 | | | | | | |
% 156.04/26.84 | | | | | | | Case 1:
% 156.04/26.84 | | | | | | | |
% 156.04/26.84 | | | | | | | | (66) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 156.04/26.84 | | | | | | | | op(e2, e2) = e0)
% 156.04/26.84 | | | | | | | |
% 156.04/26.84 | | | | | | | | BETA: splitting (66) gives:
% 156.04/26.84 | | | | | | | |
% 156.04/26.84 | | | | | | | | Case 1:
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | (67) all_58_1 = e0 & op(e3, e2) = e0
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | REF_CLOSE: (18), (65), (67) are inconsistent by sub-proof
% 156.04/26.84 | | | | | | | | | #796.
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | Case 2:
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | (68) all_58_3 = e0 & op(e2, e2) = e0
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | REF_CLOSE: (37), (48), (68) are inconsistent by sub-proof
% 156.04/26.84 | | | | | | | | | #203.
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | End of split
% 156.04/26.84 | | | | | | | |
% 156.04/26.84 | | | | | | | Case 2:
% 156.04/26.84 | | | | | | | |
% 156.04/26.84 | | | | | | | | (69) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 156.04/26.84 | | | | | | | | op(e0, e2) = e0)
% 156.04/26.84 | | | | | | | |
% 156.04/26.84 | | | | | | | | BETA: splitting (69) gives:
% 156.04/26.84 | | | | | | | |
% 156.04/26.84 | | | | | | | | Case 1:
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | (70) all_58_7 = e0 & op(e1, e2) = e0
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | ALPHA: (70) implies:
% 156.04/26.84 | | | | | | | | | (71) all_58_7 = e0
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | BETA: splitting (12) gives:
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | Case 1:
% 156.04/26.84 | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | (72) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 156.04/26.84 | | | | | | | | | | op(e1, e2) = e3)
% 156.04/26.84 | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | BETA: splitting (72) gives:
% 156.04/26.84 | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | Case 1:
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | (73) all_58_6 = e3 & op(e1, e3) = e3
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | ALPHA: (73) implies:
% 156.04/26.84 | | | | | | | | | | | (74) all_58_6 = e3
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | BETA: splitting (33) gives:
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | Case 1:
% 156.04/26.84 | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | (75) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 156.04/26.84 | | | | | | | | | | | | & op(e2, e3) = e2)
% 156.04/26.84 | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | REF_CLOSE: (4), (5), (13), (35), (44), (75) are inconsistent
% 156.04/26.84 | | | | | | | | | | | | by sub-proof #1522.
% 156.04/26.84 | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | Case 2:
% 156.04/26.84 | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | (76) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 156.04/26.84 | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 156.04/26.84 | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | BETA: splitting (76) gives:
% 156.04/26.84 | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | Case 1:
% 156.04/26.84 | | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | | (77) all_58_6 = e2 & op(e1, e3) = e2
% 156.04/26.84 | | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | | REF_CLOSE: (45), (74), (77) are inconsistent by sub-proof
% 156.04/26.84 | | | | | | | | | | | | | #1352.
% 156.04/26.84 | | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | Case 2:
% 156.04/26.84 | | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | | (78) all_58_12 = e2 & op(e0, e3) = e2
% 156.04/26.84 | | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | | ALPHA: (78) implies:
% 156.04/26.84 | | | | | | | | | | | | | (79) all_58_12 = e2
% 156.04/26.84 | | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | | REF_CLOSE: (36), (46), (79) are inconsistent by sub-proof
% 156.04/26.84 | | | | | | | | | | | | | #1486.
% 156.04/26.84 | | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | | End of split
% 156.04/26.84 | | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | End of split
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | Case 2:
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | (80) all_58_7 = e3 & op(e1, e2) = e3
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | ALPHA: (80) implies:
% 156.04/26.84 | | | | | | | | | | | (81) all_58_7 = e3
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | COMBINE_EQS: (71), (81) imply:
% 156.04/26.84 | | | | | | | | | | | (82) e3 = e0
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | REDUCE: (14), (82) imply:
% 156.04/26.84 | | | | | | | | | | | (83) $false
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | CLOSE: (83) is inconsistent.
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | End of split
% 156.04/26.84 | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | Case 2:
% 156.04/26.84 | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | (84) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3
% 156.04/26.84 | | | | | | | | | | & op(e1, e0) = e3)
% 156.04/26.84 | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | BETA: splitting (84) gives:
% 156.04/26.84 | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | Case 1:
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | (85) all_58_8 = e3 & op(e1, e1) = e3
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | REF_CLOSE: (6), (26), (44), (85) are inconsistent by
% 156.04/26.84 | | | | | | | | | | | sub-proof #1469.
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | Case 2:
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | (86) all_58_11 = e3 & op(e1, e0) = e3
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | ALPHA: (86) implies:
% 156.04/26.84 | | | | | | | | | | | (87) all_58_11 = e3
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | | REF_CLOSE: (45), (57), (87) are inconsistent by sub-proof
% 156.04/26.84 | | | | | | | | | | | #1049.
% 156.04/26.84 | | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | | End of split
% 156.04/26.84 | | | | | | | | | |
% 156.04/26.84 | | | | | | | | | End of split
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | Case 2:
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | (88) all_58_13 = e0 & op(e0, e2) = e0
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | ALPHA: (88) implies:
% 156.04/26.84 | | | | | | | | | (89) op(e0, e2) = e0
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | | REF_CLOSE: (18), (42), (44), (61), (89) are inconsistent by
% 156.04/26.84 | | | | | | | | | sub-proof #1040.
% 156.04/26.84 | | | | | | | | |
% 156.04/26.84 | | | | | | | | End of split
% 156.04/26.84 | | | | | | | |
% 156.04/26.84 | | | | | | | End of split
% 156.04/26.84 | | | | | | |
% 156.04/26.84 | | | | | | End of split
% 156.04/26.84 | | | | | |
% 156.04/26.84 | | | | | Case 2:
% 156.04/26.84 | | | | | |
% 156.04/26.84 | | | | | | (90) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 156.04/26.84 | | | | | | e0) = e2)
% 156.04/26.84 | | | | | |
% 156.04/26.84 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (13), (14),
% 156.04/26.84 | | | | | | (15), (18), (19), (22), (23), (24), (26), (28), (31),
% 156.04/26.84 | | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 156.04/26.84 | | | | | | (41), (43), (44), (45), (46), (47), (90) are inconsistent
% 156.04/26.84 | | | | | | by sub-proof #175.
% 156.04/26.84 | | | | | |
% 156.04/26.84 | | | | | End of split
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | End of split
% 156.04/26.84 | | | |
% 156.04/26.84 | | | Case 2:
% 156.04/26.84 | | | |
% 156.04/26.84 | | | | (91) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 156.04/26.84 | | | | e0) = e2)
% 156.04/26.84 | | | |
% 156.04/26.84 | | | | BETA: splitting (91) gives:
% 156.04/26.84 | | | |
% 156.04/26.84 | | | | Case 1:
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | (92) all_58_14 = e2 & op(e0, e1) = e2
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | REF_CLOSE: (25), (30), (44), (92) are inconsistent by sub-proof #1175.
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | Case 2:
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | (93) all_58_15 = e2 & op(e0, e0) = e2
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | | REF_CLOSE: (11), (27), (44), (93) are inconsistent by sub-proof #1452.
% 156.04/26.84 | | | | |
% 156.04/26.84 | | | | End of split
% 156.04/26.84 | | | |
% 156.04/26.84 | | | End of split
% 156.04/26.84 | | |
% 156.04/26.84 | | Case 2:
% 156.04/26.84 | | |
% 156.04/26.84 | | | (94) all_58_15 = e2 & op(e0, e0) = e2
% 156.04/26.84 | | |
% 156.04/26.84 | | | REF_CLOSE: (11), (27), (44), (94) are inconsistent by sub-proof #1452.
% 156.04/26.84 | | |
% 156.04/26.84 | | End of split
% 156.04/26.84 | |
% 156.04/26.84 | End of split
% 156.04/26.84 |
% 156.04/26.84 End of proof
% 156.04/26.84
% 156.04/26.84 Sub-proof #175 shows that the following formulas are inconsistent:
% 156.04/26.84 ----------------------------------------------------------------
% 156.04/26.84 (1) all_58_5 = e2
% 156.04/26.84 (2) op(e3, e1) = e3
% 156.04/26.84 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.04/26.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.04/26.84 (4) op(e3, e3) = all_10_2
% 156.04/26.84 (5) ~ (all_52_1 = e2)
% 156.04/26.84 (6) op(e1, e1) = all_6_2
% 156.04/26.84 (7) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.04/26.84 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.04/26.84 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.04/26.84 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.04/26.84 (9) op(e3, e2) = all_52_4
% 156.04/26.84 (10) op(e2, e3) = all_52_1
% 156.04/26.84 (11) ~ (e3 = e0)
% 156.04/26.84 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.04/26.84 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.04/26.84 (13) ~ (e2 = e0)
% 156.04/26.84 (14) op(e1, e3) = all_52_2
% 156.04/26.84 (15) ~ (e3 = e1)
% 156.04/26.84 (16) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.04/26.84 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.04/26.84 (17) op(e1, e2) = all_52_6
% 156.39/26.84 (18) ~ (all_6_2 = e3)
% 156.39/26.84 (19) op(e3, e3) = e1
% 156.39/26.84 (20) ~ (all_52_4 = e1)
% 156.39/26.84 (21) ~ (all_52_2 = e1)
% 156.39/26.84 (22) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 156.39/26.84 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.39/26.84 (23) ~ (all_52_6 = e1)
% 156.39/26.84 (24) ~ (all_10_2 = e2)
% 156.39/26.84 (25) ~ (e2 = e1)
% 156.39/26.84 (26) ~ (e1 = e0)
% 156.39/26.84 (27) op(e3, e1) = all_52_8
% 156.39/26.84 (28) all_58_12 = e1 & op(e0, e3) = e1
% 156.39/26.84 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.39/26.84 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.39/26.84 (30) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 156.39/26.84 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 156.39/26.84 (31) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.39/26.84 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.39/26.84 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.84 (33) ~ (e3 = e2)
% 156.39/26.84 (34) all_58_12 = e1
% 156.39/26.84 (35) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.39/26.84 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.39/26.84 (36) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.39/26.84
% 156.39/26.84 Begin of proof
% 156.39/26.84 |
% 156.39/26.84 | BETA: splitting (36) gives:
% 156.39/26.84 |
% 156.39/26.84 | Case 1:
% 156.39/26.84 | |
% 156.39/26.84 | | (37) all_58_4 = e2 & op(e3, e1) = e2
% 156.39/26.84 | |
% 156.39/26.84 | | ALPHA: (37) implies:
% 156.39/26.84 | | (38) op(e3, e1) = e2
% 156.39/26.84 | |
% 156.39/26.84 | | REF_CLOSE: (2), (32), (33), (38) are inconsistent by sub-proof #1502.
% 156.39/26.84 | |
% 156.39/26.84 | Case 2:
% 156.39/26.84 | |
% 156.39/26.84 | | (39) all_58_9 = e2 & op(e3, e0) = e2
% 156.39/26.84 | |
% 156.39/26.84 | | ALPHA: (39) implies:
% 156.39/26.84 | | (40) all_58_9 = e2
% 156.39/26.84 | | (41) op(e3, e0) = e2
% 156.39/26.84 | |
% 156.39/26.84 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.39/26.84 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 156.39/26.84 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 156.39/26.84 | | (35), (40), (41) are inconsistent by sub-proof #193.
% 156.39/26.84 | |
% 156.39/26.84 | End of split
% 156.39/26.84 |
% 156.39/26.84 End of proof
% 156.39/26.84
% 156.39/26.84 Sub-proof #176 shows that the following formulas are inconsistent:
% 156.39/26.84 ----------------------------------------------------------------
% 156.39/26.84 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 156.39/26.84 (2) all_58_5 = e2
% 156.39/26.84 (3) op(e0, e3) = all_52_3
% 156.39/26.84 (4) op(e3, e0) = all_52_12
% 156.39/26.84 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.39/26.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.39/26.84 (6) op(e3, e3) = all_10_2
% 156.39/26.84 (7) all_54_13 = all_52_7
% 156.39/26.84 (8) ~ (all_52_1 = e2)
% 156.39/26.84 (9) op(e1, e1) = all_6_2
% 156.39/26.84 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.39/26.84 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 156.39/26.84 e1)
% 156.39/26.84 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.39/26.84 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.39/26.84 (12) ~ (all_52_6 = all_52_14)
% 156.39/26.84 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.39/26.84 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.39/26.84 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.39/26.84 (15) ~ (all_52_7 = all_52_11)
% 156.39/26.84 (16) ~ (all_52_12 = all_4_2)
% 156.39/26.84 (17) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.39/26.84 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.39/26.84 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.39/26.84 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.39/26.84 (19) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.39/26.84 (20) op(e3, e2) = all_52_4
% 156.39/26.84 (21) ~ (all_4_2 = e2)
% 156.39/26.84 (22) ~ (all_52_1 = all_52_13)
% 156.39/26.84 (23) ~ (all_52_12 = all_52_13)
% 156.39/26.84 (24) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 & op(e1, e1) =
% 156.39/26.84 all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e2) & op(e1,
% 156.39/26.84 e1) = all_32_1 & $i(all_32_1))
% 156.39/26.84 (25) op(all_6_2, e2) = all_8_0
% 156.39/26.84 (26) op(e2, e3) = all_52_1
% 156.39/26.84 (27) ~ (all_52_1 = all_52_3)
% 156.39/26.84 (28) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.39/26.84 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.39/26.84 (29) ~ (e3 = e0)
% 156.39/26.84 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.39/26.84 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.39/26.84 (31) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.39/26.84 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.39/26.84 e2)
% 156.39/26.84 (32) ~ (e2 = e0)
% 156.39/26.84 (33) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 156.39/26.84 (34) all_56_13 = e1
% 156.39/26.84 (35) op(e1, e3) = all_52_2
% 156.39/26.84 (36) op(e2, e0) = all_52_13
% 156.39/26.84 (37) ~ (e3 = e1)
% 156.39/26.84 (38) all_56_12 = e1
% 156.39/26.84 (39) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.39/26.84 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.39/26.84 (40) op(e1, e2) = all_52_6
% 156.39/26.84 (41) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.39/26.84 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.39/26.84 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.39/26.84 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.39/26.84 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.39/26.84 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.39/26.84 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.39/26.84 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.39/26.84 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.39/26.84 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.39/26.84 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.39/26.84 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.39/26.84 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.39/26.84 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.39/26.84 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.39/26.84 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.39/26.84 = e0)
% 156.39/26.84 (42) ~ (all_4_2 = e1)
% 156.39/26.84 (43) all_54_4 = all_52_1
% 156.39/26.84 (44) ~ (all_52_11 = e2)
% 156.39/26.84 (45) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e2) & op(all_50_1, e3) = all_50_0 &
% 156.39/26.84 op(e1, e1) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 156.39/26.84 e0) & op(e1, e1) = all_50_1 & $i(all_50_1))
% 156.39/26.84 (46) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.39/26.84 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 156.39/26.84 (47) ~ (all_6_2 = e3)
% 156.39/26.84 (48) op(e0, e0) = all_4_2
% 156.39/26.84 (49) all_54_7 = all_52_13
% 156.39/26.84 (50) ~ (all_52_1 = e1)
% 156.39/26.84 (51) op(e3, e3) = e1
% 156.39/26.84 (52) ~ (all_52_13 = e2)
% 156.39/26.84 (53) all_50_2 = e1
% 156.39/26.84 (54) all_56_15 = all_4_2
% 156.39/26.84 (55) op(e0, e1) = all_52_11
% 156.39/26.84 (56) ~ (all_52_4 = e1)
% 156.39/26.84 (57) ~ (all_52_13 = all_4_2)
% 156.39/26.84 (58) ~ (all_52_2 = e1)
% 156.39/26.84 (59) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 156.39/26.84 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.39/26.84 (60) ~ (all_52_2 = all_52_14)
% 156.39/26.84 (61) ~ (all_52_6 = e1)
% 156.39/26.84 (62) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.39/26.84 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.39/26.84 (63) ~ (all_52_6 = all_52_7)
% 156.39/26.84 (64) ~ (all_10_2 = e2)
% 156.39/26.84 (65) ~ (e2 = e1)
% 156.39/26.84 (66) ~ (e1 = e0)
% 156.39/26.84 (67) op(e3, e1) = all_52_8
% 156.39/26.84 (68) ~ (all_6_2 = e2)
% 156.39/26.84 (69) all_56_14 = all_6_2
% 156.39/26.84 (70) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.39/26.84 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.39/26.84 (71) ~ (all_52_7 = all_4_2)
% 156.39/26.84 (72) ~ (all_52_7 = e1)
% 156.39/26.84 (73) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 156.39/26.84 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 156.39/26.84 (74) op(e0, e2) = all_52_7
% 156.39/26.84 (75) op(e1, e0) = all_52_14
% 156.39/26.84 (76) ~ (all_52_8 = e1)
% 156.39/26.84 (77) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.39/26.84 (78) ~ (all_52_14 = all_6_2)
% 156.39/26.84 (79) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.39/26.84 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.39/26.84 (80) ~ (all_52_12 = e1)
% 156.39/26.84 (81) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.84 (82) ~ (all_52_3 = all_52_11)
% 156.39/26.84 (83) all_58_8 = e0
% 156.39/26.84 (84) ~ (all_52_13 = all_52_14)
% 156.39/26.84 (85) ~ (e3 = e2)
% 156.39/26.84 (86) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.39/26.84 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.39/26.84 (87) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.39/26.84 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.39/26.84 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.39/26.84 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.39/26.84 (88) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.39/26.84 (89) all_54_12 = all_52_3
% 156.39/26.84 (90) ~ (all_52_14 = all_4_2)
% 156.39/26.84 (91) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.39/26.84 (92) all_58_3 = e1
% 156.39/26.84 (93) ~ (all_52_3 = all_52_7)
% 156.39/26.84 (94) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.39/26.84 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.39/26.84
% 156.39/26.84 Begin of proof
% 156.39/26.84 |
% 156.39/26.84 | BETA: splitting (5) gives:
% 156.39/26.84 |
% 156.39/26.84 | Case 1:
% 156.39/26.84 | |
% 156.39/26.84 | | (95) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 156.39/26.84 | | e1)
% 156.39/26.84 | |
% 156.39/26.84 | | REF_CLOSE: (35), (40), (58), (61), (81), (95) are inconsistent by sub-proof
% 156.39/26.84 | | #196.
% 156.39/26.84 | |
% 156.39/26.84 | Case 2:
% 156.39/26.84 | |
% 156.39/26.84 | | (96) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 156.39/26.84 | | e1)
% 156.39/26.84 | |
% 156.39/26.84 | | BETA: splitting (96) gives:
% 156.39/26.84 | |
% 156.39/26.84 | | Case 1:
% 156.39/26.84 | | |
% 156.39/26.84 | | | (97) all_58_8 = e1 & op(e1, e1) = e1
% 156.39/26.84 | | |
% 156.39/26.84 | | | ALPHA: (97) implies:
% 156.39/26.84 | | | (98) all_58_8 = e1
% 156.39/26.84 | | |
% 156.39/26.84 | | | REF_CLOSE: (66), (83), (98) are inconsistent by sub-proof #1445.
% 156.39/26.84 | | |
% 156.39/26.84 | | Case 2:
% 156.39/26.84 | | |
% 156.39/26.84 | | | (99) all_58_11 = e1 & op(e1, e0) = e1
% 156.39/26.84 | | |
% 156.39/26.84 | | | ALPHA: (99) implies:
% 156.39/26.84 | | | (100) all_58_11 = e1
% 156.39/26.84 | | | (101) op(e1, e0) = e1
% 156.39/26.84 | | |
% 156.39/26.84 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.39/26.84 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 156.39/26.84 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 156.39/26.84 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 156.39/26.84 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 156.39/26.84 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 156.39/26.84 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 156.39/26.84 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 156.39/26.84 | | | (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 156.39/26.84 | | | (94), (100), (101) are inconsistent by sub-proof #177.
% 156.39/26.84 | | |
% 156.39/26.84 | | End of split
% 156.39/26.84 | |
% 156.39/26.84 | End of split
% 156.39/26.84 |
% 156.39/26.84 End of proof
% 156.39/26.84
% 156.39/26.84 Sub-proof #177 shows that the following formulas are inconsistent:
% 156.39/26.84 ----------------------------------------------------------------
% 156.39/26.84 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 156.39/26.84 (2) all_58_5 = e2
% 156.39/26.84 (3) op(e0, e3) = all_52_3
% 156.39/26.84 (4) op(e3, e0) = all_52_12
% 156.39/26.84 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.39/26.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.39/26.84 (6) op(e3, e3) = all_10_2
% 156.39/26.84 (7) all_54_13 = all_52_7
% 156.39/26.84 (8) ~ (all_52_1 = e2)
% 156.39/26.84 (9) all_58_11 = e1
% 156.39/26.85 (10) op(e1, e1) = all_6_2
% 156.39/26.85 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.39/26.85 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 156.39/26.85 e1)
% 156.39/26.85 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.39/26.85 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.39/26.85 (13) ~ (all_52_6 = all_52_14)
% 156.39/26.85 (14) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.39/26.85 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.39/26.85 (15) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.39/26.85 (16) ~ (all_52_7 = all_52_11)
% 156.39/26.85 (17) ~ (all_52_12 = all_4_2)
% 156.39/26.85 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.39/26.85 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.39/26.85 (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.39/26.85 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.39/26.85 (20) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.39/26.85 (21) op(e3, e2) = all_52_4
% 156.39/26.85 (22) ~ (all_4_2 = e2)
% 156.39/26.85 (23) ~ (all_52_1 = all_52_13)
% 156.39/26.85 (24) ~ (all_52_12 = all_52_13)
% 156.39/26.85 (25) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 & op(e1, e1) =
% 156.39/26.85 all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e2) & op(e1,
% 156.39/26.85 e1) = all_32_1 & $i(all_32_1))
% 156.39/26.85 (26) op(all_6_2, e2) = all_8_0
% 156.39/26.85 (27) op(e2, e3) = all_52_1
% 156.39/26.85 (28) ~ (all_52_1 = all_52_3)
% 156.39/26.85 (29) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.39/26.85 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.39/26.85 (30) ~ (e3 = e0)
% 156.39/26.85 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.39/26.85 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.39/26.85 (32) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.39/26.85 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.39/26.85 e2)
% 156.39/26.85 (33) ~ (e2 = e0)
% 156.39/26.85 (34) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 156.39/26.85 (35) all_56_13 = e1
% 156.39/26.85 (36) op(e1, e3) = all_52_2
% 156.39/26.85 (37) op(e2, e0) = all_52_13
% 156.39/26.85 (38) ~ (e3 = e1)
% 156.39/26.85 (39) all_56_12 = e1
% 156.39/26.85 (40) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.39/26.85 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.39/26.85 (41) op(e1, e2) = all_52_6
% 156.39/26.85 (42) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.39/26.85 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.39/26.85 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.39/26.85 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.39/26.85 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.39/26.85 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.39/26.85 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.39/26.85 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.39/26.85 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.39/26.85 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.39/26.85 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.39/26.85 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.39/26.85 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.39/26.85 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.39/26.85 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.39/26.85 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.39/26.85 = e0)
% 156.39/26.85 (43) ~ (all_4_2 = e1)
% 156.39/26.85 (44) all_54_4 = all_52_1
% 156.39/26.85 (45) ~ (all_52_11 = e2)
% 156.39/26.85 (46) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e2) & op(all_50_1, e3) = all_50_0 &
% 156.39/26.85 op(e1, e1) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 156.39/26.85 e0) & op(e1, e1) = all_50_1 & $i(all_50_1))
% 156.39/26.85 (47) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.39/26.85 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 156.39/26.85 (48) ~ (all_6_2 = e3)
% 156.39/26.85 (49) op(e0, e0) = all_4_2
% 156.39/26.85 (50) all_54_7 = all_52_13
% 156.39/26.85 (51) ~ (all_52_1 = e1)
% 156.39/26.85 (52) op(e1, e0) = e1
% 156.39/26.85 (53) op(e3, e3) = e1
% 156.39/26.85 (54) ~ (all_52_13 = e2)
% 156.39/26.85 (55) all_50_2 = e1
% 156.39/26.85 (56) all_56_15 = all_4_2
% 156.39/26.85 (57) op(e0, e1) = all_52_11
% 156.39/26.85 (58) ~ (all_52_4 = e1)
% 156.39/26.85 (59) ~ (all_52_13 = all_4_2)
% 156.39/26.85 (60) ~ (all_52_2 = e1)
% 156.39/26.85 (61) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 156.39/26.85 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.39/26.85 (62) ~ (all_52_2 = all_52_14)
% 156.39/26.85 (63) ~ (all_52_6 = e1)
% 156.39/26.85 (64) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.39/26.85 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.39/26.85 (65) ~ (all_52_6 = all_52_7)
% 156.39/26.85 (66) ~ (all_10_2 = e2)
% 156.39/26.85 (67) ~ (e2 = e1)
% 156.39/26.85 (68) ~ (e1 = e0)
% 156.39/26.85 (69) op(e3, e1) = all_52_8
% 156.39/26.85 (70) ~ (all_6_2 = e2)
% 156.39/26.85 (71) all_56_14 = all_6_2
% 156.39/26.85 (72) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.39/26.85 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.39/26.85 (73) ~ (all_52_7 = all_4_2)
% 156.39/26.85 (74) ~ (all_52_7 = e1)
% 156.39/26.85 (75) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 156.39/26.85 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 156.39/26.85 (76) op(e0, e2) = all_52_7
% 156.39/26.85 (77) op(e1, e0) = all_52_14
% 156.39/26.85 (78) ~ (all_52_8 = e1)
% 156.39/26.85 (79) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.39/26.85 (80) ~ (all_52_14 = all_6_2)
% 156.39/26.85 (81) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.39/26.85 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.39/26.85 (82) ~ (all_52_12 = e1)
% 156.39/26.85 (83) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.85 (84) ~ (all_52_3 = all_52_11)
% 156.39/26.85 (85) ~ (all_52_13 = all_52_14)
% 156.39/26.85 (86) ~ (e3 = e2)
% 156.39/26.85 (87) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.39/26.85 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.39/26.85 (88) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.39/26.85 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.39/26.85 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.39/26.85 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.39/26.85 (89) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.39/26.85 (90) all_54_12 = all_52_3
% 156.39/26.85 (91) ~ (all_52_14 = all_4_2)
% 156.39/26.85 (92) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.39/26.85 (93) all_58_3 = e1
% 156.39/26.85 (94) ~ (all_52_3 = all_52_7)
% 156.39/26.85 (95) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.39/26.85 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.39/26.85
% 156.39/26.85 Begin of proof
% 156.39/26.85 |
% 156.39/26.85 | BETA: splitting (1) gives:
% 156.39/26.85 |
% 156.39/26.85 | Case 1:
% 156.39/26.85 | |
% 156.39/26.85 | | (96) ~ (all_56_12 = e1)
% 156.39/26.85 | |
% 156.39/26.85 | | REDUCE: (39), (96) imply:
% 156.39/26.85 | | (97) $false
% 156.39/26.85 | |
% 156.39/26.85 | | CLOSE: (97) is inconsistent.
% 156.39/26.85 | |
% 156.39/26.85 | Case 2:
% 156.39/26.85 | |
% 156.39/26.85 | | (98) all_56_1 = e3 & op(e3, e1) = e3
% 156.39/26.85 | |
% 156.39/26.85 | | ALPHA: (98) implies:
% 156.39/26.85 | | (99) op(e3, e1) = e3
% 156.39/26.85 | |
% 156.39/26.85 | | BETA: splitting (19) gives:
% 156.39/26.85 | |
% 156.39/26.85 | | Case 1:
% 156.39/26.85 | | |
% 156.39/26.85 | | | (100) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 156.39/26.85 | | | = e2)
% 156.39/26.85 | | |
% 156.39/26.85 | | | BETA: splitting (100) gives:
% 156.39/26.85 | | |
% 156.39/26.85 | | | Case 1:
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | (101) all_58_9 = e2 & op(e3, e0) = e2
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | ALPHA: (101) implies:
% 156.39/26.85 | | | | (102) all_58_9 = e2
% 156.39/26.85 | | | | (103) op(e3, e0) = e2
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | BETA: splitting (11) gives:
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | Case 1:
% 156.39/26.85 | | | | |
% 156.39/26.85 | | | | | (104) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 156.39/26.85 | | | | | e2) = e1)
% 156.39/26.85 | | | | |
% 156.39/26.85 | | | | | BETA: splitting (104) gives:
% 156.39/26.85 | | | | |
% 156.39/26.85 | | | | | Case 1:
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | (105) all_58_12 = e1 & op(e0, e3) = e1
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | ALPHA: (105) implies:
% 156.39/26.85 | | | | | | (106) all_58_12 = e1
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | REF_CLOSE: (2), (5), (6), (8), (10), (14), (18), (21), (27), (30),
% 156.39/26.85 | | | | | | (31), (33), (36), (38), (40), (41), (48), (53), (58),
% 156.39/26.85 | | | | | | (60), (61), (63), (66), (67), (68), (69), (72), (75),
% 156.39/26.85 | | | | | | (81), (83), (86), (87), (99), (102), (103), (105), (106)
% 156.39/26.85 | | | | | | are inconsistent by sub-proof #193.
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | Case 2:
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | (107) all_58_13 = e1 & op(e0, e2) = e1
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | REF_CLOSE: (74), (76), (83), (107) are inconsistent by sub-proof
% 156.39/26.85 | | | | | | #192.
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | End of split
% 156.39/26.85 | | | | |
% 156.39/26.85 | | | | Case 2:
% 156.39/26.85 | | | | |
% 156.39/26.85 | | | | | (108) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 156.39/26.85 | | | | | e0) = e1)
% 156.39/26.85 | | | | |
% 156.39/26.85 | | | | | BETA: splitting (108) gives:
% 156.39/26.85 | | | | |
% 156.39/26.85 | | | | | Case 1:
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | (109) all_58_14 = e1 & op(e0, e1) = e1
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | ALPHA: (109) implies:
% 156.39/26.85 | | | | | | (110) all_58_14 = e1
% 156.39/26.85 | | | | | | (111) op(e0, e1) = e1
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | BETA: splitting (14) gives:
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | Case 1:
% 156.39/26.85 | | | | | | |
% 156.39/26.85 | | | | | | | (112) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 156.39/26.85 | | | | | | | op(e2, e1) = e3)
% 156.39/26.85 | | | | | | |
% 156.39/26.85 | | | | | | | BETA: splitting (112) gives:
% 156.39/26.85 | | | | | | |
% 156.39/26.85 | | | | | | | Case 1:
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | (113) all_58_4 = e3 & op(e3, e1) = e3
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | ALPHA: (113) implies:
% 156.39/26.85 | | | | | | | | (114) all_58_4 = e3
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | BETA: splitting (25) gives:
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | Case 1:
% 156.39/26.85 | | | | | | | | |
% 156.39/26.85 | | | | | | | | | (115) ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 156.39/26.85 | | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) & $i(all_32_1)
% 156.39/26.85 | | | | | | | | |
% 156.39/26.85 | | | | | | | | | ALPHA: (115) implies:
% 156.39/26.85 | | | | | | | | | (116) op(e1, e1) = all_32_1
% 156.39/26.85 | | | | | | | | |
% 156.39/26.85 | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 156.39/26.85 | | | | | | | | | (13), (15), (16), (17), (18), (19), (20), (21),
% 156.39/26.85 | | | | | | | | | (23), (24), (26), (27), (28), (29), (30), (31),
% 156.39/26.85 | | | | | | | | | (32), (33), (34), (35), (36), (37), (38), (39),
% 156.39/26.85 | | | | | | | | | (40), (41), (42), (44), (45), (46), (47), (49),
% 156.39/26.85 | | | | | | | | | (50), (51), (52), (55), (56), (57), (58), (59),
% 156.39/26.85 | | | | | | | | | (61), (62), (64), (65), (66), (67), (68), (69),
% 156.39/26.85 | | | | | | | | | (70), (71), (72), (73), (76), (77), (78), (79),
% 156.39/26.85 | | | | | | | | | (80), (81), (82), (83), (84), (85), (87), (88),
% 156.39/26.85 | | | | | | | | | (89), (90), (91), (92), (93), (94), (95), (101),
% 156.39/26.85 | | | | | | | | | (102), (103), (110), (111), (113), (114), (116) are
% 156.39/26.85 | | | | | | | | | inconsistent by sub-proof #178.
% 156.39/26.85 | | | | | | | | |
% 156.39/26.85 | | | | | | | | Case 2:
% 156.39/26.85 | | | | | | | | |
% 156.39/26.85 | | | | | | | | | (117) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 156.39/26.85 | | | | | | | | | $i(all_32_1)
% 156.39/26.85 | | | | | | | | |
% 156.39/26.85 | | | | | | | | | ALPHA: (117) implies:
% 156.39/26.85 | | | | | | | | | (118) op(e1, e1) = all_32_1
% 156.39/26.85 | | | | | | | | |
% 156.39/26.85 | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 156.39/26.85 | | | | | | | | | (13), (15), (16), (17), (18), (19), (20), (21),
% 156.39/26.85 | | | | | | | | | (23), (24), (26), (27), (28), (29), (30), (31),
% 156.39/26.85 | | | | | | | | | (32), (33), (34), (35), (36), (37), (38), (39),
% 156.39/26.85 | | | | | | | | | (40), (41), (42), (44), (45), (46), (47), (49),
% 156.39/26.85 | | | | | | | | | (50), (51), (52), (55), (56), (57), (58), (59),
% 156.39/26.85 | | | | | | | | | (61), (62), (64), (65), (66), (67), (68), (69),
% 156.39/26.85 | | | | | | | | | (70), (71), (72), (73), (76), (77), (78), (79),
% 156.39/26.85 | | | | | | | | | (80), (81), (82), (83), (84), (85), (87), (88),
% 156.39/26.85 | | | | | | | | | (89), (90), (91), (92), (93), (94), (95), (101),
% 156.39/26.85 | | | | | | | | | (102), (103), (110), (111), (113), (114), (118) are
% 156.39/26.85 | | | | | | | | | inconsistent by sub-proof #178.
% 156.39/26.85 | | | | | | | | |
% 156.39/26.85 | | | | | | | | End of split
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | Case 2:
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | (119) all_58_5 = e3 & op(e2, e1) = e3
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | ALPHA: (119) implies:
% 156.39/26.85 | | | | | | | | (120) all_58_5 = e3
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | REF_CLOSE: (2), (86), (120) are inconsistent by sub-proof #897.
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | End of split
% 156.39/26.85 | | | | | | |
% 156.39/26.85 | | | | | | Case 2:
% 156.39/26.85 | | | | | | |
% 156.39/26.85 | | | | | | | (121) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 156.39/26.85 | | | | | | | op(e0, e1) = e3)
% 156.39/26.85 | | | | | | |
% 156.39/26.85 | | | | | | | BETA: splitting (121) gives:
% 156.39/26.85 | | | | | | |
% 156.39/26.85 | | | | | | | Case 1:
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | (122) all_58_8 = e3 & op(e1, e1) = e3
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | REF_CLOSE: (10), (48), (83), (122) are inconsistent by sub-proof
% 156.39/26.85 | | | | | | | | #1469.
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | Case 2:
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | (123) all_58_14 = e3 & op(e0, e1) = e3
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | | REF_CLOSE: (38), (110), (123) are inconsistent by sub-proof
% 156.39/26.85 | | | | | | | | #872.
% 156.39/26.85 | | | | | | | |
% 156.39/26.85 | | | | | | | End of split
% 156.39/26.85 | | | | | | |
% 156.39/26.85 | | | | | | End of split
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | Case 2:
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | (124) all_58_15 = e1 & op(e0, e0) = e1
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | | REF_CLOSE: (43), (49), (83), (124) are inconsistent by sub-proof
% 156.39/26.85 | | | | | | #1418.
% 156.39/26.85 | | | | | |
% 156.39/26.85 | | | | | End of split
% 156.39/26.85 | | | | |
% 156.39/26.85 | | | | End of split
% 156.39/26.85 | | | |
% 156.39/26.85 | | | Case 2:
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | (125) all_58_10 = e2 & op(e2, e0) = e2
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | ALPHA: (125) implies:
% 156.39/26.85 | | | | (126) op(e2, e0) = e2
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | REF_CLOSE: (37), (54), (83), (126) are inconsistent by sub-proof #1535.
% 156.39/26.85 | | | |
% 156.39/26.85 | | | End of split
% 156.39/26.85 | | |
% 156.39/26.85 | | Case 2:
% 156.39/26.85 | | |
% 156.39/26.85 | | | (127) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0)
% 156.39/26.85 | | | = e2)
% 156.39/26.85 | | |
% 156.39/26.85 | | | BETA: splitting (127) gives:
% 156.39/26.85 | | |
% 156.39/26.85 | | | Case 1:
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | (128) all_58_11 = e2 & op(e1, e0) = e2
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | REF_CLOSE: (9), (67), (128) are inconsistent by sub-proof #948.
% 156.39/26.85 | | | |
% 156.39/26.85 | | | Case 2:
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | (129) all_58_15 = e2 & op(e0, e0) = e2
% 156.39/26.85 | | | |
% 156.39/26.85 | | | | REF_CLOSE: (22), (49), (83), (129) are inconsistent by sub-proof #1452.
% 156.39/26.85 | | | |
% 156.39/26.85 | | | End of split
% 156.39/26.85 | | |
% 156.39/26.85 | | End of split
% 156.39/26.85 | |
% 156.39/26.85 | End of split
% 156.39/26.85 |
% 156.39/26.85 End of proof
% 156.39/26.85
% 156.39/26.85 Sub-proof #178 shows that the following formulas are inconsistent:
% 156.39/26.85 ----------------------------------------------------------------
% 156.39/26.85 (1) op(e1, e1) = all_32_1
% 156.39/26.85 (2) all_58_5 = e2
% 156.39/26.85 (3) op(e0, e3) = all_52_3
% 156.39/26.85 (4) op(e3, e0) = all_52_12
% 156.39/26.85 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.39/26.85 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.39/26.85 (6) op(e3, e3) = all_10_2
% 156.39/26.85 (7) all_54_13 = all_52_7
% 156.39/26.85 (8) ~ (all_52_1 = e2)
% 156.39/26.85 (9) all_58_11 = e1
% 156.39/26.85 (10) op(e1, e1) = all_6_2
% 156.39/26.85 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.39/26.85 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.39/26.85 (12) ~ (all_52_6 = all_52_14)
% 156.39/26.85 (13) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.39/26.85 (14) ~ (all_52_7 = all_52_11)
% 156.39/26.85 (15) ~ (all_52_12 = all_4_2)
% 156.39/26.85 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.39/26.85 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.39/26.85 (17) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.39/26.85 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.39/26.85 (18) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.39/26.85 (19) op(e3, e2) = all_52_4
% 156.39/26.85 (20) ~ (all_52_1 = all_52_13)
% 156.39/26.85 (21) all_58_9 = e2 & op(e3, e0) = e2
% 156.39/26.85 (22) ~ (all_52_12 = all_52_13)
% 156.39/26.85 (23) op(all_6_2, e2) = all_8_0
% 156.39/26.85 (24) op(e2, e3) = all_52_1
% 156.39/26.85 (25) all_58_14 = e1
% 156.39/26.85 (26) ~ (all_52_1 = all_52_3)
% 156.39/26.85 (27) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.39/26.85 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.39/26.85 (28) ~ (e3 = e0)
% 156.39/26.85 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.39/26.85 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.39/26.85 (30) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.39/26.85 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.39/26.85 e2)
% 156.39/26.85 (31) ~ (e2 = e0)
% 156.39/26.85 (32) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 156.39/26.85 (33) all_56_13 = e1
% 156.39/26.85 (34) op(e1, e3) = all_52_2
% 156.39/26.85 (35) op(e2, e0) = all_52_13
% 156.39/26.85 (36) ~ (e3 = e1)
% 156.39/26.85 (37) op(e0, e1) = e1
% 156.39/26.85 (38) all_56_12 = e1
% 156.39/26.85 (39) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.39/26.85 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.39/26.85 (40) op(e1, e2) = all_52_6
% 156.39/26.85 (41) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.39/26.85 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.39/26.85 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.39/26.85 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.39/26.85 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.39/26.85 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.39/26.85 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.39/26.85 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.39/26.85 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.39/26.85 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.39/26.85 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.39/26.85 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.39/26.85 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.39/26.85 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.39/26.85 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.39/26.85 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.39/26.85 = e0)
% 156.39/26.85 (42) all_54_4 = all_52_1
% 156.39/26.85 (43) ~ (all_52_11 = e2)
% 156.39/26.85 (44) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e2) & op(all_50_1, e3) = all_50_0 &
% 156.39/26.85 op(e1, e1) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 156.39/26.85 e0) & op(e1, e1) = all_50_1 & $i(all_50_1))
% 156.39/26.85 (45) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.39/26.85 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 156.39/26.85 (46) op(e0, e0) = all_4_2
% 156.39/26.85 (47) all_54_7 = all_52_13
% 156.39/26.85 (48) ~ (all_52_1 = e1)
% 156.39/26.85 (49) op(e1, e0) = e1
% 156.39/26.85 (50) all_50_2 = e1
% 156.39/26.85 (51) all_56_15 = all_4_2
% 156.39/26.85 (52) op(e3, e0) = e2
% 156.39/26.85 (53) op(e0, e1) = all_52_11
% 156.39/26.85 (54) ~ (all_52_4 = e1)
% 156.39/26.85 (55) ~ (all_52_13 = all_4_2)
% 156.39/26.85 (56) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 156.39/26.85 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.39/26.85 (57) ~ (all_52_2 = all_52_14)
% 156.39/26.85 (58) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.39/26.85 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.39/26.85 (59) ~ (all_52_6 = all_52_7)
% 156.39/26.85 (60) ~ (all_10_2 = e2)
% 156.39/26.85 (61) ~ (e2 = e1)
% 156.39/26.85 (62) ~ (e1 = e0)
% 156.39/26.85 (63) all_58_4 = e3
% 156.39/26.85 (64) op(e3, e1) = all_52_8
% 156.39/26.85 (65) ~ (all_6_2 = e2)
% 156.39/26.85 (66) all_56_14 = all_6_2
% 156.39/26.86 (67) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.39/26.86 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.39/26.86 (68) ~ (all_52_7 = all_4_2)
% 156.39/26.86 (69) all_58_9 = e2
% 156.39/26.86 (70) op(e0, e2) = all_52_7
% 156.39/26.86 (71) op(e1, e0) = all_52_14
% 156.39/26.86 (72) ~ (all_52_8 = e1)
% 156.39/26.86 (73) all_58_4 = e3 & op(e3, e1) = e3
% 156.39/26.86 (74) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.39/26.86 (75) ~ (all_52_14 = all_6_2)
% 156.39/26.86 (76) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.39/26.86 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.39/26.86 (77) ~ (all_52_12 = e1)
% 156.39/26.86 (78) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.86 (79) ~ (all_52_3 = all_52_11)
% 156.39/26.86 (80) ~ (all_52_13 = all_52_14)
% 156.39/26.86 (81) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.39/26.86 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.39/26.86 (82) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.39/26.86 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.39/26.86 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.39/26.86 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.39/26.86 (83) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.39/26.86 (84) all_54_12 = all_52_3
% 156.39/26.86 (85) ~ (all_52_14 = all_4_2)
% 156.39/26.86 (86) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.39/26.86 (87) all_58_3 = e1
% 156.39/26.86 (88) ~ (all_52_3 = all_52_7)
% 156.39/26.86 (89) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.39/26.86 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.39/26.86
% 156.39/26.86 Begin of proof
% 156.39/26.86 |
% 156.39/26.86 | BETA: splitting (39) gives:
% 156.39/26.86 |
% 156.39/26.86 | Case 1:
% 156.39/26.86 | |
% 156.39/26.86 | | (90) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 156.39/26.86 | | e0)
% 156.39/26.86 | |
% 156.39/26.86 | | BETA: splitting (90) gives:
% 156.39/26.86 | |
% 156.39/26.86 | | Case 1:
% 156.39/26.86 | | |
% 156.39/26.86 | | | (91) all_58_4 = e0 & op(e3, e1) = e0
% 156.39/26.86 | | |
% 156.39/26.86 | | | REF_CLOSE: (28), (63), (91) are inconsistent by sub-proof #1344.
% 156.39/26.86 | | |
% 156.39/26.86 | | Case 2:
% 156.39/26.86 | | |
% 156.39/26.86 | | | (92) all_58_5 = e0 & op(e2, e1) = e0
% 156.39/26.86 | | |
% 156.39/26.86 | | | REF_CLOSE: (2), (31), (92) are inconsistent by sub-proof #919.
% 156.39/26.86 | | |
% 156.39/26.86 | | End of split
% 156.39/26.86 | |
% 156.39/26.86 | Case 2:
% 156.39/26.86 | |
% 156.39/26.86 | | (93) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 156.39/26.86 | | e0)
% 156.39/26.86 | |
% 156.39/26.86 | | BETA: splitting (93) gives:
% 156.39/26.86 | |
% 156.39/26.86 | | Case 1:
% 156.39/26.86 | | |
% 156.39/26.86 | | | (94) all_58_8 = e0 & op(e1, e1) = e0
% 156.39/26.86 | | |
% 156.39/26.86 | | | ALPHA: (94) implies:
% 156.39/26.86 | | | (95) all_58_8 = e0
% 156.39/26.86 | | | (96) op(e1, e1) = e0
% 156.39/26.86 | | |
% 156.39/26.86 | | | BETA: splitting (67) gives:
% 156.39/26.86 | | |
% 156.39/26.86 | | | Case 1:
% 156.39/26.86 | | | |
% 156.39/26.86 | | | | (97) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 156.39/26.86 | | | | = e1)
% 156.39/26.86 | | | |
% 156.39/26.86 | | | | BETA: splitting (97) gives:
% 156.39/26.86 | | | |
% 156.39/26.86 | | | | Case 1:
% 156.39/26.86 | | | | |
% 156.39/26.86 | | | | | (98) all_58_0 = e1 & op(e3, e3) = e1
% 156.39/26.86 | | | | |
% 156.39/26.86 | | | | | ALPHA: (98) implies:
% 156.39/26.86 | | | | | (99) all_58_0 = e1
% 156.39/26.86 | | | | |
% 156.39/26.86 | | | | | BETA: splitting (81) gives:
% 156.39/26.86 | | | | |
% 156.39/26.86 | | | | | Case 1:
% 156.39/26.86 | | | | | |
% 156.39/26.86 | | | | | | (100) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 156.39/26.86 | | | | | | e2) = e0)
% 156.39/26.86 | | | | | |
% 156.39/26.86 | | | | | | BETA: splitting (100) gives:
% 156.39/26.86 | | | | | |
% 156.39/26.86 | | | | | | Case 1:
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | (101) all_58_0 = e0 & op(e3, e3) = e0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REF_CLOSE: (62), (99), (101) are inconsistent by sub-proof #1520.
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | Case 2:
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | (102) all_58_1 = e0 & op(e3, e2) = e0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | ALPHA: (102) implies:
% 156.39/26.86 | | | | | | | (103) op(e3, e2) = e0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | ALPHA: (73) implies:
% 156.39/26.86 | | | | | | | (104) op(e3, e1) = e3
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | GROUND_INST: instantiating (78) with all_52_11, e1, e1, e0,
% 156.39/26.86 | | | | | | | simplifying with (37), (53) gives:
% 156.39/26.86 | | | | | | | (105) all_52_11 = e1
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | GROUND_INST: instantiating (78) with all_52_14, e1, e0, e1,
% 156.39/26.86 | | | | | | | simplifying with (49), (71) gives:
% 156.39/26.86 | | | | | | | (106) all_52_14 = e1
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | GROUND_INST: instantiating (78) with all_6_2, all_32_1, e1, e1,
% 156.39/26.86 | | | | | | | simplifying with (1), (10) gives:
% 156.39/26.86 | | | | | | | (107) all_32_1 = all_6_2
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | GROUND_INST: instantiating (78) with e0, all_32_1, e1, e1,
% 156.39/26.86 | | | | | | | simplifying with (1), (96) gives:
% 156.39/26.86 | | | | | | | (108) all_32_1 = e0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | GROUND_INST: instantiating (78) with all_52_12, e2, e0, e3,
% 156.39/26.86 | | | | | | | simplifying with (4), (52) gives:
% 156.39/26.86 | | | | | | | (109) all_52_12 = e2
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | GROUND_INST: instantiating (78) with all_52_8, e3, e1, e3,
% 156.39/26.86 | | | | | | | simplifying with (64), (104) gives:
% 156.39/26.86 | | | | | | | (110) all_52_8 = e3
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | GROUND_INST: instantiating (78) with all_52_4, e0, e2, e3,
% 156.39/26.86 | | | | | | | simplifying with (19), (103) gives:
% 156.39/26.86 | | | | | | | (111) all_52_4 = e0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | COMBINE_EQS: (107), (108) imply:
% 156.39/26.86 | | | | | | | (112) all_6_2 = e0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | SIMP: (112) implies:
% 156.39/26.86 | | | | | | | (113) all_6_2 = e0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | COMBINE_EQS: (66), (113) imply:
% 156.39/26.86 | | | | | | | (114) all_56_14 = e0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (57), (106) imply:
% 156.39/26.86 | | | | | | | (115) ~ (all_52_2 = e1)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (79), (105) imply:
% 156.39/26.86 | | | | | | | (116) ~ (all_52_3 = e1)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (12), (106) imply:
% 156.39/26.86 | | | | | | | (117) ~ (all_52_6 = e1)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (14), (105) imply:
% 156.39/26.86 | | | | | | | (118) ~ (all_52_7 = e1)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (22), (109) imply:
% 156.39/26.86 | | | | | | | (119) ~ (all_52_13 = e2)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | SIMP: (119) implies:
% 156.39/26.86 | | | | | | | (120) ~ (all_52_13 = e2)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (15), (109) imply:
% 156.39/26.86 | | | | | | | (121) ~ (all_4_2 = e2)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | SIMP: (121) implies:
% 156.39/26.86 | | | | | | | (122) ~ (all_4_2 = e2)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (80), (106) imply:
% 156.39/26.86 | | | | | | | (123) ~ (all_52_13 = e1)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (85), (106) imply:
% 156.39/26.86 | | | | | | | (124) ~ (all_4_2 = e1)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | SIMP: (124) implies:
% 156.39/26.86 | | | | | | | (125) ~ (all_4_2 = e1)
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | REDUCE: (23), (113) imply:
% 156.39/26.86 | | | | | | | (126) op(e0, e2) = all_8_0
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | BETA: splitting (32) gives:
% 156.39/26.86 | | | | | | |
% 156.39/26.86 | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | |
% 156.39/26.86 | | | | | | | | (127) ~ (all_56_14 = e0)
% 156.39/26.86 | | | | | | | |
% 156.39/26.86 | | | | | | | | REDUCE: (114), (127) imply:
% 156.39/26.86 | | | | | | | | (128) $false
% 156.39/26.86 | | | | | | | |
% 156.39/26.86 | | | | | | | | CLOSE: (128) is inconsistent.
% 156.39/26.86 | | | | | | | |
% 156.39/26.86 | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | |
% 156.39/26.86 | | | | | | | | (129) all_56_8 = e1 & op(e1, e0) = e1
% 156.39/26.86 | | | | | | | |
% 156.39/26.86 | | | | | | | | ALPHA: (129) implies:
% 156.39/26.86 | | | | | | | | (130) all_56_8 = e1
% 156.39/26.86 | | | | | | | |
% 156.39/26.86 | | | | | | | | BETA: splitting (86) gives:
% 156.39/26.86 | | | | | | | |
% 156.39/26.86 | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | |
% 156.39/26.86 | | | | | | | | | (131) all_56_12 = e3
% 156.39/26.86 | | | | | | | | |
% 156.39/26.86 | | | | | | | | | COMBINE_EQS: (38), (131) imply:
% 156.39/26.86 | | | | | | | | | (132) e3 = e1
% 156.39/26.86 | | | | | | | | |
% 156.39/26.86 | | | | | | | | | REDUCE: (36), (132) imply:
% 156.39/26.86 | | | | | | | | | (133) $false
% 156.39/26.86 | | | | | | | | |
% 156.39/26.86 | | | | | | | | | CLOSE: (133) is inconsistent.
% 156.39/26.86 | | | | | | | | |
% 156.39/26.86 | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | |
% 156.39/26.86 | | | | | | | | | (134) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.39/26.86 | | | | | | | | |
% 156.39/26.86 | | | | | | | | | BETA: splitting (134) gives:
% 156.39/26.86 | | | | | | | | |
% 156.39/26.86 | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | (135) all_56_13 = e2
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | COMBINE_EQS: (33), (135) imply:
% 156.39/26.86 | | | | | | | | | | (136) e2 = e1
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | REDUCE: (61), (136) imply:
% 156.39/26.86 | | | | | | | | | | (137) $false
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | CLOSE: (137) is inconsistent.
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | (138) ~ (all_56_13 = e2)
% 156.39/26.86 | | | | | | | | | | (139) all_56_14 = e1 | all_56_15 = e0
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | REDUCE: (33), (138) imply:
% 156.39/26.86 | | | | | | | | | | (140) ~ (e2 = e1)
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | BETA: splitting (139) gives:
% 156.39/26.86 | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | (141) all_56_14 = e1
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | COMBINE_EQS: (114), (141) imply:
% 156.39/26.86 | | | | | | | | | | | (142) e1 = e0
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | REDUCE: (62), (142) imply:
% 156.39/26.86 | | | | | | | | | | | (143) $false
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | CLOSE: (143) is inconsistent.
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | (144) all_56_15 = e0
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | COMBINE_EQS: (51), (144) imply:
% 156.39/26.86 | | | | | | | | | | | (145) all_4_2 = e0
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | REDUCE: (68), (145) imply:
% 156.39/26.86 | | | | | | | | | | | (146) ~ (all_52_7 = e0)
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | REDUCE: (55), (145) imply:
% 156.39/26.86 | | | | | | | | | | | (147) ~ (all_52_13 = e0)
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | REDUCE: (122), (145) imply:
% 156.39/26.86 | | | | | | | | | | | (148) ~ (e2 = e0)
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | REDUCE: (125), (145) imply:
% 156.39/26.86 | | | | | | | | | | | (149) ~ (e1 = e0)
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | BETA: splitting (13) gives:
% 156.39/26.86 | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | (150) all_54_7 = e3
% 156.39/26.86 | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | COMBINE_EQS: (47), (150) imply:
% 156.39/26.86 | | | | | | | | | | | | (151) all_52_13 = e3
% 156.39/26.86 | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | REDUCE: (20), (151) imply:
% 156.39/26.86 | | | | | | | | | | | | (152) ~ (all_52_1 = e3)
% 156.39/26.86 | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | REDUCE: (120), (151) imply:
% 156.39/26.86 | | | | | | | | | | | | (153) ~ (e3 = e2)
% 156.39/26.86 | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | BETA: splitting (45) gives:
% 156.39/26.86 | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | (154) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 156.39/26.86 | | | | | | | | | | | | | & op(e2, e2) = e0)
% 156.39/26.86 | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | BETA: splitting (154) gives:
% 156.39/26.86 | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | (155) all_58_2 = e0 & op(e2, e3) = e0
% 156.39/26.86 | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | ALPHA: (155) implies:
% 156.39/26.86 | | | | | | | | | | | | | | (156) all_58_2 = e0
% 156.39/26.86 | | | | | | | | | | | | | | (157) op(e2, e3) = e0
% 156.39/26.86 | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 156.39/26.86 | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | (158) all_54_4 = e3
% 156.39/26.86 | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | COMBINE_EQS: (42), (158) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | (159) all_52_1 = e3
% 156.39/26.86 | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | REDUCE: (152), (159) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | (160) $false
% 156.39/26.86 | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 156.39/26.86 | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | (161) ~ (all_54_4 = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | (162) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.39/26.86 | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 156.39/26.86 | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | (163) all_54_4 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (163) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | (164) all_52_1 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | REDUCE: (8), (164) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | (165) $false
% 156.39/26.86 | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 156.39/26.86 | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | (166) ~ (all_54_4 = e2)
% 156.39/26.86 | | | | | | | | | | | | | | | | (167) all_54_4 = e1 | all_54_4 = e0
% 156.39/26.86 | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | (168) ~ (all_50_2 = e1)
% 156.39/26.86 | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | REDUCE: (50), (168) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | (169) $false
% 156.39/26.86 | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 156.39/26.86 | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | (170) ( ~ (all_50_0 = e2) & op(all_50_1, e3) = all_50_0
% 156.39/26.86 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_50_1 & $i(all_50_0) &
% 156.39/26.86 | | | | | | | | | | | | | | | | | $i(all_50_1)) | ( ~ (all_50_1 = e0) & op(e1, e1)
% 156.39/26.86 | | | | | | | | | | | | | | | | | = all_50_1 & $i(all_50_1))
% 156.39/26.86 | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | (171) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | (172) all_58_9 = e3 & op(e3, e0) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | (173) all_58_9 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (153), (173) are inconsistent by sub-proof
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | #1245.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | (174) all_58_10 = e3 & op(e2, e0) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | (175) all_58_10 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | (176) ~ (all_50_0 = e2) & op(all_50_1, e3) = all_50_0 &
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_50_1 & $i(all_50_0) &
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | $i(all_50_1)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | (177) ~ (all_50_0 = e2)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | (178) op(e1, e1) = all_50_1
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | (179) op(all_50_1, e3) = all_50_0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (180) all_54_4 = e1
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (180) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (181) all_52_1 = e1
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (181) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (182) $false
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (183) all_54_4 = e0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (183) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (184) all_52_1 = e0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (184) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (185) ~ (all_52_3 = e0)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | SIMP: (185) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (186) ~ (all_52_3 = e0)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_7, all_8_0, e2, e0,
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | simplifying with (70), (126) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (187) all_52_7 = all_8_0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with e0, all_50_1, e1, e1,
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | simplifying with (96), (178) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (188) all_50_1 = e0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (187) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (189) all_54_13 = all_8_0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (187) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (190) ~ (all_52_3 = all_8_0)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (187) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (191) ~ (all_8_0 = e1)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (187) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (192) ~ (all_8_0 = e0)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (188) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (193) op(e0, e3) = all_50_0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_3, all_50_0, e3,
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (3), (193) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (194) all_52_3 = all_50_0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (194) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (195) all_54_12 = all_50_0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (194) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (196) ~ (all_50_0 = all_8_0)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (194) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (197) ~ (all_50_0 = e1)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (194) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | (198) ~ (all_50_0 = e0)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | (199) all_54_12 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (199) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | (200) all_50_0 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | SIMP: (200) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | (201) all_50_0 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (201) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | (202) ~ (all_8_0 = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | SIMP: (202) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | (203) ~ (all_8_0 = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | (204) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (36), (78), (99), (152), (204) are
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #191.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | (205) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_6 = e3 & op(e1, e3) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | (207) all_58_6 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_54_13 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (189), (203), (208) are inconsistent by sub-proof
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | #190.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (17), (27), (40), (46), (59),
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | (61), (65), (69), (78), (118), (122), (146),
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | (153), (175), (207), (209) are inconsistent by
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #189.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_12 = e3 & op(e0, e3) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_12 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_54_13 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (189), (203), (212) are inconsistent by sub-proof
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | #190.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | (213) ~ (all_54_13 = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (215) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_6 = e2 & op(e1, e3) = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_58_6 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) op(e1, e3) = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (28), (36), (78), (87), (99), (103), (153),
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156), (211), (217), (219) are inconsistent by
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #188.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_7 = e3 & op(e1, e2) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_7 = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) op(e2, e3) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (78), (152), (226) are inconsistent by
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1183.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) op(e2, e3) = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (78), (157), (229) are inconsistent by
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1156.
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) ~ (all_56_14 = e1)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) op(e1, e3) = e3
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_54_13 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (189), (233) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_8_0 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (234) implies:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_8_0 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (235) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (e3 = e2)
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with e2, e3, e3, e1,
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (218), (232) gives:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) e3 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (237) imply:
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_12 = e2
% 156.39/26.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (16), (17), (27), (28), (29), (31),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (36), (46), (61), (62), (65), (69), (76), (78),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (153), (175), (222), (238) are inconsistent
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #200.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_54_13 = e1 | all_54_13 = e0
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (118), (146), (239) are inconsistent by
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #875.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (34), (52), (78), (115), (144), (240) are
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #187.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) op(e1, e2) = e2
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (40), (59), (78), (118), (146), (214), (244)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #209.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (40), (78), (117), (120), (245) are
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1129.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) op(e0, e2) = e0
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (70), (78), (118), (146), (214), (248) are
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #874.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (34), (36), (62), (78), (95), (115),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (130), (144), (222), (249) are inconsistent by
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #339.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_58_13 = e3 & op(e0, e2) = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_58_13 = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (28), (29), (30), (31), (36), (43), (46),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (61), (62), (76), (78), (122), (153), (217),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) are inconsistent by sub-proof #1174.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_58_7 = e2 & op(e1, e2) = e2
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) op(e1, e2) = e2
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (40), (59), (78), (118), (146), (214), (253)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #209.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (254) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (17), (46), (61), (65), (69), (78),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (153), (175), (254) are inconsistent by
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #204.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (255) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (116), (177), (186), (195), (255) are
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #186.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | (256) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 &
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | $i(all_50_1)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (96), (256) are inconsistent by sub-proof
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | #185.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | (257) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 156.39/26.87 | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 156.39/26.87 | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | (258) all_58_11 = e3 & op(e1, e0) = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | (259) op(e1, e0) = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (49), (78), (259) are inconsistent by
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | sub-proof #1275.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | (260) all_58_15 = e3 & op(e0, e0) = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | (261) all_58_15 = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | (262) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (36), (78), (87), (152), (262) are
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #213.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | (263) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | (264) all_58_5 = e3 & op(e2, e1) = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | (265) all_58_5 = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (153), (265) are inconsistent by sub-proof
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | #897.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | (266) all_58_10 = e3 & op(e2, e0) = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | (267) all_58_10 = e3
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (268) all_58_15 = e0 & op(e0, e0) = e0
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (269) all_58_15 = e0
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (269) imply:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (270) e3 = e0
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (270) imply:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (271) all_58_10 = e0
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (24), (28), (36), (58), (78), (87), (152),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (153), (271) are inconsistent by sub-proof #184.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (272) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (273) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (24), (25), (28), (31), (36), (56),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (60), (62), (70), (78), (99), (146), (152), (153),
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | | (157), (273) are inconsistent by sub-proof #181.
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | (274) all_58_3 = e0 & op(e2, e2) = e0
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | REF_CLOSE: (62), (87), (274) are inconsistent by sub-proof
% 156.39/26.87 | | | | | | | | | | | | | | #203.
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | (275) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 156.39/26.87 | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 156.39/26.87 | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | BETA: splitting (275) gives:
% 156.39/26.87 | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | Case 1:
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | (276) all_58_5 = e0 & op(e2, e1) = e0
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (276) are inconsistent by sub-proof
% 156.39/26.87 | | | | | | | | | | | | | | #180.
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | (277) all_58_10 = e0 & op(e2, e0) = e0
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | ALPHA: (277) implies:
% 156.39/26.87 | | | | | | | | | | | | | | (278) all_58_10 = e0
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | | REF_CLOSE: (2), (24), (28), (36), (58), (78), (87), (152),
% 156.39/26.87 | | | | | | | | | | | | | | (153), (278) are inconsistent by sub-proof #184.
% 156.39/26.87 | | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | Case 2:
% 156.39/26.87 | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | (279) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.39/26.87 | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | | REF_CLOSE: (47), (120), (123), (147), (279) are inconsistent
% 156.39/26.87 | | | | | | | | | | | | by sub-proof #179.
% 156.39/26.87 | | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | | |
% 156.39/26.87 | | | | | | | | | End of split
% 156.39/26.87 | | | | | | | | |
% 156.39/26.87 | | | | | | | | End of split
% 156.39/26.87 | | | | | | | |
% 156.39/26.87 | | | | | | | End of split
% 156.39/26.87 | | | | | | |
% 156.39/26.87 | | | | | | End of split
% 156.39/26.87 | | | | | |
% 156.39/26.87 | | | | | Case 2:
% 156.39/26.87 | | | | | |
% 156.39/26.87 | | | | | | (280) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 156.39/26.87 | | | | | | e0) = e0)
% 156.39/26.87 | | | | | |
% 156.39/26.87 | | | | | | REF_CLOSE: (28), (31), (52), (63), (78), (280) are inconsistent by
% 156.39/26.87 | | | | | | sub-proof #1499.
% 156.39/26.87 | | | | | |
% 156.39/26.87 | | | | | End of split
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | Case 2:
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | | (281) all_58_1 = e1 & op(e3, e2) = e1
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | | REF_CLOSE: (19), (54), (78), (281) are inconsistent by sub-proof
% 156.39/26.87 | | | | | #1284.
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | End of split
% 156.39/26.87 | | | |
% 156.39/26.87 | | | Case 2:
% 156.39/26.87 | | | |
% 156.39/26.87 | | | | (282) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 156.39/26.87 | | | | = e1)
% 156.39/26.87 | | | |
% 156.39/26.87 | | | | BETA: splitting (282) gives:
% 156.39/26.87 | | | |
% 156.39/26.87 | | | | Case 1:
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | | (283) all_58_4 = e1 & op(e3, e1) = e1
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | | REF_CLOSE: (36), (63), (283) are inconsistent by sub-proof #1345.
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | Case 2:
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | | (284) all_58_9 = e1 & op(e3, e0) = e1
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | | ALPHA: (284) implies:
% 156.39/26.87 | | | | | (285) all_58_9 = e1
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | | REF_CLOSE: (61), (69), (285) are inconsistent by sub-proof #1324.
% 156.39/26.87 | | | | |
% 156.39/26.87 | | | | End of split
% 156.39/26.87 | | | |
% 156.39/26.87 | | | End of split
% 156.39/26.87 | | |
% 156.39/26.87 | | Case 2:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (286) all_58_14 = e0 & op(e0, e1) = e0
% 156.39/26.87 | | |
% 156.39/26.87 | | | ALPHA: (286) implies:
% 156.39/26.87 | | | (287) all_58_14 = e0
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (25), (62), (287) are inconsistent by sub-proof #614.
% 156.39/26.87 | | |
% 156.39/26.87 | | End of split
% 156.39/26.87 | |
% 156.39/26.87 | End of split
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #179 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) all_54_7 = all_52_13
% 156.39/26.87 (2) ~ (all_52_13 = e2)
% 156.39/26.87 (3) ~ (all_52_13 = e0)
% 156.39/26.87 (4) ~ (all_52_13 = e1)
% 156.39/26.87 (5) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | BETA: splitting (5) gives:
% 156.39/26.87 |
% 156.39/26.87 | Case 1:
% 156.39/26.87 | |
% 156.39/26.87 | | (6) all_54_7 = e2
% 156.39/26.87 | |
% 156.39/26.87 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #1427.
% 156.39/26.87 | |
% 156.39/26.87 | Case 2:
% 156.39/26.87 | |
% 156.39/26.87 | | (7) all_54_7 = e1 | all_54_7 = e0
% 156.39/26.87 | |
% 156.39/26.87 | | BETA: splitting (7) gives:
% 156.39/26.87 | |
% 156.39/26.87 | | Case 1:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (8) all_54_7 = e1
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #1426.
% 156.39/26.87 | | |
% 156.39/26.87 | | Case 2:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (9) all_54_7 = e0
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1112.
% 156.39/26.87 | | |
% 156.39/26.87 | | End of split
% 156.39/26.87 | |
% 156.39/26.87 | End of split
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #180 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) all_58_5 = e0 & op(e2, e1) = e0
% 156.39/26.87 (2) all_58_5 = e2
% 156.39/26.87 (3) ~ (e2 = e0)
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | ALPHA: (1) implies:
% 156.39/26.87 | (4) all_58_5 = e0
% 156.39/26.87 |
% 156.39/26.87 | COMBINE_EQS: (2), (4) imply:
% 156.39/26.87 | (5) e2 = e0
% 156.39/26.87 |
% 156.39/26.87 | REDUCE: (3), (5) imply:
% 156.39/26.87 | (6) $false
% 156.39/26.87 |
% 156.39/26.87 | CLOSE: (6) is inconsistent.
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #181 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) op(e3, e3) = all_10_2
% 156.39/26.87 (2) all_58_0 = e1
% 156.39/26.87 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.39/26.87 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.39/26.87 (4) op(e2, e3) = all_52_1
% 156.39/26.87 (5) all_58_14 = e1
% 156.39/26.87 (6) ~ (e3 = e0)
% 156.39/26.87 (7) ~ (e2 = e0)
% 156.39/26.87 (8) ~ (e3 = e1)
% 156.39/26.87 (9) ~ (all_52_7 = e0)
% 156.39/26.87 (10) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.39/26.87 | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.39/26.87 (11) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 156.39/26.87 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.39/26.87 (12) ~ (all_10_2 = e2)
% 156.39/26.87 (13) ~ (e1 = e0)
% 156.39/26.87 (14) op(e0, e2) = all_52_7
% 156.39/26.87 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.87 (16) ~ (e3 = e2)
% 156.39/26.87 (17) op(e2, e3) = e0
% 156.39/26.87 (18) ~ (all_52_1 = e3)
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | BETA: splitting (10) gives:
% 156.39/26.87 |
% 156.39/26.87 | Case 1:
% 156.39/26.87 | |
% 156.39/26.87 | | (19) all_58_12 = e0 & op(e0, e3) = e0
% 156.39/26.87 | |
% 156.39/26.87 | | ALPHA: (19) implies:
% 156.39/26.87 | | (20) all_58_12 = e0
% 156.39/26.87 | |
% 156.39/26.87 | | BETA: splitting (11) gives:
% 156.39/26.87 | |
% 156.39/26.87 | | Case 1:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (21) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 156.39/26.87 | | | e2)
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (1), (7), (12), (15), (17), (21) are inconsistent by sub-proof
% 156.39/26.87 | | | #183.
% 156.39/26.87 | | |
% 156.39/26.87 | | Case 2:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 156.39/26.87 | | | e2)
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (15), (16), (18), (20), (22) are
% 156.39/26.87 | | | inconsistent by sub-proof #182.
% 156.39/26.87 | | |
% 156.39/26.87 | | End of split
% 156.39/26.87 | |
% 156.39/26.87 | Case 2:
% 156.39/26.87 | |
% 156.39/26.87 | | (23) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 156.39/26.87 | | e0)
% 156.39/26.87 | |
% 156.39/26.87 | | BETA: splitting (23) gives:
% 156.39/26.87 | |
% 156.39/26.87 | | Case 1:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (24) all_58_13 = e0 & op(e0, e2) = e0
% 156.39/26.87 | | |
% 156.39/26.87 | | | ALPHA: (24) implies:
% 156.39/26.87 | | | (25) op(e0, e2) = e0
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (9), (14), (15), (25) are inconsistent by sub-proof #1532.
% 156.39/26.87 | | |
% 156.39/26.87 | | Case 2:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (26) all_58_14 = e0 & op(e0, e1) = e0
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (5), (13), (26) are inconsistent by sub-proof #1135.
% 156.39/26.87 | | |
% 156.39/26.87 | | End of split
% 156.39/26.87 | |
% 156.39/26.87 | End of split
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #182 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) all_58_0 = e1
% 156.39/26.87 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.39/26.87 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.39/26.87 (3) all_58_12 = e0
% 156.39/26.87 (4) op(e2, e3) = all_52_1
% 156.39/26.87 (5) ~ (e3 = e0)
% 156.39/26.87 (6) ~ (e2 = e0)
% 156.39/26.87 (7) ~ (e3 = e1)
% 156.39/26.87 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.87 (9) ~ (e3 = e2)
% 156.39/26.87 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.39/26.87 (11) ~ (all_52_1 = e3)
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | BETA: splitting (10) gives:
% 156.39/26.87 |
% 156.39/26.87 | Case 1:
% 156.39/26.87 | |
% 156.39/26.87 | | (12) all_58_6 = e2 & op(e1, e3) = e2
% 156.39/26.87 | |
% 156.39/26.87 | | ALPHA: (12) implies:
% 156.39/26.87 | | (13) all_58_6 = e2
% 156.39/26.87 | |
% 156.39/26.87 | | BETA: splitting (2) gives:
% 156.39/26.87 | |
% 156.39/26.87 | | Case 1:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 156.39/26.87 | | | e3)
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (1), (4), (7), (8), (11), (14) are inconsistent by sub-proof
% 156.39/26.87 | | | #191.
% 156.39/26.87 | | |
% 156.39/26.87 | | Case 2:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 156.39/26.87 | | | e3)
% 156.39/26.87 | | |
% 156.39/26.87 | | | BETA: splitting (15) gives:
% 156.39/26.87 | | |
% 156.39/26.87 | | | Case 1:
% 156.39/26.87 | | | |
% 156.39/26.87 | | | | (16) all_58_6 = e3 & op(e1, e3) = e3
% 156.39/26.87 | | | |
% 156.39/26.87 | | | | REF_CLOSE: (9), (13), (16) are inconsistent by sub-proof #1517.
% 156.39/26.87 | | | |
% 156.39/26.87 | | | Case 2:
% 156.39/26.87 | | | |
% 156.39/26.87 | | | | (17) all_58_12 = e3 & op(e0, e3) = e3
% 156.39/26.87 | | | |
% 156.39/26.87 | | | | ALPHA: (17) implies:
% 156.39/26.87 | | | | (18) all_58_12 = e3
% 156.39/26.87 | | | |
% 156.39/26.87 | | | | REF_CLOSE: (3), (5), (18) are inconsistent by sub-proof #1463.
% 156.39/26.87 | | | |
% 156.39/26.87 | | | End of split
% 156.39/26.87 | | |
% 156.39/26.87 | | End of split
% 156.39/26.87 | |
% 156.39/26.87 | Case 2:
% 156.39/26.87 | |
% 156.39/26.87 | | (19) all_58_12 = e2 & op(e0, e3) = e2
% 156.39/26.87 | |
% 156.39/26.87 | | ALPHA: (19) implies:
% 156.39/26.87 | | (20) all_58_12 = e2
% 156.39/26.87 | |
% 156.39/26.87 | | REF_CLOSE: (3), (6), (20) are inconsistent by sub-proof #1482.
% 156.39/26.87 | |
% 156.39/26.87 | End of split
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #183 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 156.39/26.87 (2) op(e3, e3) = all_10_2
% 156.39/26.87 (3) ~ (e2 = e0)
% 156.39/26.87 (4) ~ (all_10_2 = e2)
% 156.39/26.87 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.87 (6) op(e2, e3) = e0
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | BETA: splitting (1) gives:
% 156.39/26.87 |
% 156.39/26.87 | Case 1:
% 156.39/26.87 | |
% 156.39/26.87 | | (7) all_58_0 = e2 & op(e3, e3) = e2
% 156.39/26.87 | |
% 156.39/26.87 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #1523.
% 156.39/26.87 | |
% 156.39/26.87 | Case 2:
% 156.39/26.87 | |
% 156.39/26.87 | | (8) all_58_2 = e2 & op(e2, e3) = e2
% 156.39/26.87 | |
% 156.39/26.87 | | ALPHA: (8) implies:
% 156.39/26.87 | | (9) op(e2, e3) = e2
% 156.39/26.87 | |
% 156.39/26.87 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #1156.
% 156.39/26.87 | |
% 156.39/26.87 | End of split
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #184 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) all_58_5 = e2
% 156.39/26.87 (2) op(e2, e3) = all_52_1
% 156.39/26.87 (3) ~ (e3 = e0)
% 156.39/26.87 (4) ~ (e3 = e1)
% 156.39/26.87 (5) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.39/26.87 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.39/26.87 (6) all_58_10 = e0
% 156.39/26.87 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.87 (8) ~ (e3 = e2)
% 156.39/26.87 (9) all_58_3 = e1
% 156.39/26.87 (10) ~ (all_52_1 = e3)
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | BETA: splitting (5) gives:
% 156.39/26.87 |
% 156.39/26.87 | Case 1:
% 156.39/26.87 | |
% 156.39/26.87 | | (11) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 156.39/26.87 | | e3)
% 156.39/26.87 | |
% 156.39/26.87 | | REF_CLOSE: (2), (4), (7), (9), (10), (11) are inconsistent by sub-proof
% 156.39/26.87 | | #213.
% 156.39/26.87 | |
% 156.39/26.87 | Case 2:
% 156.39/26.87 | |
% 156.39/26.87 | | (12) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 156.39/26.87 | | e3)
% 156.39/26.87 | |
% 156.39/26.87 | | BETA: splitting (12) gives:
% 156.39/26.87 | |
% 156.39/26.87 | | Case 1:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (13) all_58_5 = e3 & op(e2, e1) = e3
% 156.39/26.87 | | |
% 156.39/26.87 | | | ALPHA: (13) implies:
% 156.39/26.87 | | | (14) all_58_5 = e3
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #897.
% 156.39/26.87 | | |
% 156.39/26.87 | | Case 2:
% 156.39/26.87 | | |
% 156.39/26.87 | | | (15) all_58_10 = e3 & op(e2, e0) = e3
% 156.39/26.87 | | |
% 156.39/26.87 | | | ALPHA: (15) implies:
% 156.39/26.87 | | | (16) all_58_10 = e3
% 156.39/26.87 | | |
% 156.39/26.87 | | | REF_CLOSE: (3), (6), (16) are inconsistent by sub-proof #1061.
% 156.39/26.87 | | |
% 156.39/26.87 | | End of split
% 156.39/26.87 | |
% 156.39/26.87 | End of split
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #185 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 & $i(all_50_1)
% 156.39/26.87 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.87 (3) op(e1, e1) = e0
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | ALPHA: (1) implies:
% 156.39/26.87 | (4) ~ (all_50_1 = e0)
% 156.39/26.87 | (5) op(e1, e1) = all_50_1
% 156.39/26.87 |
% 156.39/26.87 | GROUND_INST: instantiating (2) with e0, all_50_1, e1, e1, simplifying with
% 156.39/26.87 | (3), (5) gives:
% 156.39/26.87 | (6) all_50_1 = e0
% 156.39/26.87 |
% 156.39/26.87 | REDUCE: (4), (6) imply:
% 156.39/26.87 | (7) $false
% 156.39/26.87 |
% 156.39/26.87 | CLOSE: (7) is inconsistent.
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #186 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) ~ (all_52_3 = e1)
% 156.39/26.87 (2) ~ (all_52_3 = e0)
% 156.39/26.87 (3) all_54_12 = all_50_0
% 156.39/26.87 (4) ~ (all_50_0 = e2)
% 156.39/26.87 (5) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.39/26.87 (6) all_54_12 = all_52_3
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | BETA: splitting (5) gives:
% 156.39/26.87 |
% 156.39/26.87 | Case 1:
% 156.39/26.87 | |
% 156.39/26.87 | | (7) all_54_12 = e2
% 156.39/26.87 | |
% 156.39/26.87 | | COMBINE_EQS: (3), (7) imply:
% 156.39/26.87 | | (8) all_50_0 = e2
% 156.39/26.87 | |
% 156.39/26.87 | | SIMP: (8) implies:
% 156.39/26.87 | | (9) all_50_0 = e2
% 156.39/26.87 | |
% 156.39/26.87 | | REDUCE: (4), (9) imply:
% 156.39/26.87 | | (10) $false
% 156.39/26.87 | |
% 156.39/26.87 | | CLOSE: (10) is inconsistent.
% 156.39/26.87 | |
% 156.39/26.87 | Case 2:
% 156.39/26.87 | |
% 156.39/26.87 | | (11) all_54_12 = e1 | all_54_12 = e0
% 156.39/26.87 | |
% 156.39/26.87 | | REF_CLOSE: (1), (2), (6), (11) are inconsistent by sub-proof #1222.
% 156.39/26.87 | |
% 156.39/26.87 | End of split
% 156.39/26.87 |
% 156.39/26.87 End of proof
% 156.39/26.87
% 156.39/26.87 Sub-proof #187 shows that the following formulas are inconsistent:
% 156.39/26.87 ----------------------------------------------------------------
% 156.39/26.87 (1) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.39/26.87 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0)
% 156.39/26.87 & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 &
% 156.39/26.87 ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.39/26.87 (2) ~ (e2 = e0)
% 156.39/26.87 (3) op(e1, e3) = all_52_2
% 156.39/26.87 (4) all_56_15 = e0
% 156.39/26.87 (5) op(e3, e0) = e2
% 156.39/26.87 (6) ~ (all_52_2 = e1)
% 156.39/26.87 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.87
% 156.39/26.87 Begin of proof
% 156.39/26.87 |
% 156.39/26.87 | BETA: splitting (1) gives:
% 156.39/26.87 |
% 156.39/26.87 | Case 1:
% 156.39/26.87 | |
% 156.39/26.88 | | (8) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1
% 156.39/26.88 | | & op(e1, e3) = e1
% 156.39/26.88 | |
% 156.39/26.88 | | ALPHA: (8) implies:
% 156.39/26.88 | | (9) op(e1, e3) = e1
% 156.39/26.88 | |
% 156.39/26.88 | | REF_CLOSE: (3), (6), (7), (9) are inconsistent by sub-proof #1412.
% 156.39/26.88 | |
% 156.39/26.88 | Case 2:
% 156.39/26.88 | |
% 156.39/26.88 | | (10) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 156.39/26.88 | | e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 156.39/26.88 | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.39/26.88 | |
% 156.39/26.88 | | BETA: splitting (10) gives:
% 156.39/26.88 | |
% 156.39/26.88 | | Case 1:
% 156.39/26.88 | | |
% 156.39/26.88 | | | (11) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) =
% 156.39/26.88 | | | e3 & op(e0, e3) = e3
% 156.39/26.88 | | |
% 156.39/26.88 | | | ALPHA: (11) implies:
% 156.39/26.88 | | | (12) ~ (all_56_15 = e0)
% 156.39/26.88 | | |
% 156.39/26.88 | | | REDUCE: (4), (12) imply:
% 156.39/26.88 | | | (13) $false
% 156.39/26.88 | | |
% 156.39/26.88 | | | CLOSE: (13) is inconsistent.
% 156.39/26.88 | | |
% 156.39/26.88 | | Case 2:
% 156.39/26.88 | | |
% 156.39/26.88 | | | (14) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 156.39/26.88 | | | e0 & op(e0, e3) = e0
% 156.39/26.88 | | |
% 156.39/26.88 | | | ALPHA: (14) implies:
% 156.39/26.88 | | | (15) op(e3, e0) = e0
% 156.39/26.88 | | |
% 156.39/26.88 | | | REF_CLOSE: (2), (5), (7), (15) are inconsistent by sub-proof #1500.
% 156.39/26.88 | | |
% 156.39/26.88 | | End of split
% 156.39/26.88 | |
% 156.39/26.88 | End of split
% 156.39/26.88 |
% 156.39/26.88 End of proof
% 156.39/26.88
% 156.39/26.88 Sub-proof #188 shows that the following formulas are inconsistent:
% 156.39/26.88 ----------------------------------------------------------------
% 156.39/26.88 (1) all_58_12 = e3
% 156.39/26.88 (2) all_58_0 = e1
% 156.39/26.88 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.39/26.88 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.39/26.88 (4) all_58_6 = e2
% 156.39/26.88 (5) ~ (e3 = e0)
% 156.39/26.88 (6) ~ (e3 = e1)
% 156.39/26.88 (7) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 156.39/26.88 (8) op(e3, e2) = e0
% 156.39/26.88 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.88 (10) ~ (e3 = e2)
% 156.39/26.88 (11) all_58_2 = e0
% 156.39/26.88 (12) all_58_3 = e1
% 156.39/26.88
% 156.39/26.88 Begin of proof
% 156.39/26.88 |
% 156.39/26.88 | BETA: splitting (7) gives:
% 156.39/26.88 |
% 156.39/26.88 | Case 1:
% 156.39/26.88 | |
% 156.39/26.88 | | (13) all_58_1 = e3 & op(e3, e2) = e3
% 156.39/26.88 | |
% 156.39/26.88 | | ALPHA: (13) implies:
% 156.39/26.88 | | (14) op(e3, e2) = e3
% 156.39/26.88 | |
% 156.39/26.88 | | REF_CLOSE: (5), (8), (9), (14) are inconsistent by sub-proof #1303.
% 156.39/26.88 | |
% 156.39/26.88 | Case 2:
% 156.39/26.88 | |
% 156.39/26.88 | | (15) all_58_3 = e3 & op(e2, e2) = e3
% 156.39/26.88 | |
% 156.39/26.88 | | ALPHA: (15) implies:
% 156.39/26.88 | | (16) all_58_3 = e3
% 156.39/26.88 | |
% 156.39/26.88 | | COMBINE_EQS: (12), (16) imply:
% 156.39/26.88 | | (17) e3 = e1
% 156.39/26.88 | |
% 156.39/26.88 | | SIMP: (17) implies:
% 156.39/26.88 | | (18) e3 = e1
% 156.39/26.88 | |
% 156.39/26.88 | | COMBINE_EQS: (1), (18) imply:
% 156.39/26.88 | | (19) all_58_12 = e1
% 156.39/26.88 | |
% 156.39/26.88 | | REF_CLOSE: (2), (3), (4), (5), (6), (10), (11), (19) are inconsistent by
% 156.39/26.88 | | sub-proof #1515.
% 156.39/26.88 | |
% 156.39/26.88 | End of split
% 156.39/26.88 |
% 156.39/26.88 End of proof
% 156.39/26.88
% 156.39/26.88 Sub-proof #189 shows that the following formulas are inconsistent:
% 156.39/26.88 ----------------------------------------------------------------
% 156.39/26.88 (1) all_54_13 = all_52_7
% 156.39/26.88 (2) all_58_11 = e1
% 156.39/26.88 (3) op(e1, e1) = all_6_2
% 156.39/26.88 (4) all_58_6 = e3
% 156.39/26.88 (5) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.39/26.88 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.39/26.88 (6) ~ (all_4_2 = e2)
% 156.39/26.88 (7) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.39/26.88 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.39/26.88 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.39/26.88 (9) op(e1, e2) = all_52_6
% 156.39/26.88 (10) ~ (all_52_7 = e0)
% 156.39/26.88 (11) op(e0, e0) = all_4_2
% 156.39/26.88 (12) ~ (all_52_6 = all_52_7)
% 156.39/26.88 (13) all_58_10 = e3
% 156.39/26.88 (14) ~ (e2 = e1)
% 156.39/26.88 (15) ~ (all_6_2 = e2)
% 156.39/26.88 (16) ~ (all_52_7 = e1)
% 156.39/26.88 (17) all_58_9 = e2
% 156.39/26.88 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.88 (19) ~ (e3 = e2)
% 156.39/26.88
% 156.39/26.88 Begin of proof
% 156.39/26.88 |
% 156.39/26.88 | BETA: splitting (8) gives:
% 156.39/26.88 |
% 156.39/26.88 | Case 1:
% 156.39/26.88 | |
% 156.39/26.88 | | (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 156.39/26.88 | | e2)
% 156.39/26.88 | |
% 156.39/26.88 | | BETA: splitting (20) gives:
% 156.39/26.88 | |
% 156.39/26.88 | | Case 1:
% 156.39/26.88 | | |
% 156.39/26.88 | | | (21) all_58_6 = e2 & op(e1, e3) = e2
% 156.39/26.88 | | |
% 156.39/26.88 | | | REF_CLOSE: (4), (19), (21) are inconsistent by sub-proof #1352.
% 156.39/26.88 | | |
% 156.39/26.88 | | Case 2:
% 156.39/26.88 | | |
% 156.39/26.88 | | | (22) all_58_7 = e2 & op(e1, e2) = e2
% 156.39/26.88 | | |
% 156.39/26.88 | | | ALPHA: (22) implies:
% 156.39/26.88 | | | (23) op(e1, e2) = e2
% 156.39/26.88 | | |
% 156.39/26.88 | | | REF_CLOSE: (1), (7), (9), (10), (12), (16), (18), (23) are inconsistent by
% 156.39/26.88 | | | sub-proof #209.
% 156.39/26.88 | | |
% 156.39/26.88 | | End of split
% 156.39/26.88 | |
% 156.39/26.88 | Case 2:
% 156.39/26.88 | |
% 156.39/26.88 | | (24) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 156.39/26.88 | | e2)
% 156.39/26.88 | |
% 156.39/26.88 | | REF_CLOSE: (2), (3), (5), (6), (11), (13), (14), (15), (17), (18), (19),
% 156.39/26.88 | | (24) are inconsistent by sub-proof #204.
% 156.39/26.88 | |
% 156.39/26.88 | End of split
% 156.39/26.88 |
% 156.39/26.88 End of proof
% 156.39/26.88
% 156.39/26.88 Sub-proof #190 shows that the following formulas are inconsistent:
% 156.39/26.88 ----------------------------------------------------------------
% 156.39/26.88 (1) all_54_13 = all_8_0
% 156.39/26.88 (2) all_54_13 = e3
% 156.39/26.88 (3) ~ (all_8_0 = e3)
% 156.39/26.88
% 156.39/26.88 Begin of proof
% 156.39/26.88 |
% 156.39/26.88 | COMBINE_EQS: (1), (2) imply:
% 156.39/26.88 | (4) all_8_0 = e3
% 156.39/26.88 |
% 156.39/26.88 | SIMP: (4) implies:
% 156.39/26.88 | (5) all_8_0 = e3
% 156.39/26.88 |
% 156.39/26.88 | REDUCE: (3), (5) imply:
% 156.39/26.88 | (6) $false
% 156.39/26.88 |
% 156.39/26.88 | CLOSE: (6) is inconsistent.
% 156.39/26.88 |
% 156.39/26.88 End of proof
% 156.39/26.88
% 156.39/26.88 Sub-proof #191 shows that the following formulas are inconsistent:
% 156.39/26.88 ----------------------------------------------------------------
% 156.39/26.88 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 156.39/26.88 (2) all_58_0 = e1
% 156.39/26.88 (3) op(e2, e3) = all_52_1
% 156.39/26.88 (4) ~ (e3 = e1)
% 156.39/26.88 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.88 (6) ~ (all_52_1 = e3)
% 156.39/26.88
% 156.39/26.88 Begin of proof
% 156.39/26.88 |
% 156.39/26.88 | BETA: splitting (1) gives:
% 156.39/26.88 |
% 156.39/26.88 | Case 1:
% 156.39/26.88 | |
% 156.39/26.88 | | (7) all_58_0 = e3 & op(e3, e3) = e3
% 156.39/26.88 | |
% 156.39/26.88 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #1519.
% 156.39/26.88 | |
% 156.39/26.88 | Case 2:
% 156.39/26.88 | |
% 156.39/26.88 | | (8) all_58_2 = e3 & op(e2, e3) = e3
% 156.39/26.88 | |
% 156.39/26.88 | | ALPHA: (8) implies:
% 156.39/26.88 | | (9) op(e2, e3) = e3
% 156.39/26.88 | |
% 156.39/26.88 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #1183.
% 156.39/26.88 | |
% 156.39/26.88 | End of split
% 156.39/26.88 |
% 156.39/26.88 End of proof
% 156.39/26.88
% 156.39/26.88 Sub-proof #192 shows that the following formulas are inconsistent:
% 156.39/26.88 ----------------------------------------------------------------
% 156.39/26.88 (1) all_58_13 = e1 & op(e0, e2) = e1
% 156.39/26.88 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.88 (3) op(e0, e2) = all_52_7
% 156.39/26.88 (4) ~ (all_52_7 = e1)
% 156.39/26.88
% 156.39/26.88 Begin of proof
% 156.39/26.88 |
% 156.39/26.88 | ALPHA: (1) implies:
% 156.39/26.88 | (5) op(e0, e2) = e1
% 156.39/26.88 |
% 156.39/26.88 | GROUND_INST: instantiating (2) with all_52_7, e1, e2, e0, simplifying with
% 156.39/26.88 | (3), (5) gives:
% 156.39/26.88 | (6) all_52_7 = e1
% 156.39/26.88 |
% 156.39/26.88 | REDUCE: (4), (6) imply:
% 156.39/26.88 | (7) $false
% 156.39/26.88 |
% 156.39/26.88 | CLOSE: (7) is inconsistent.
% 156.39/26.88 |
% 156.39/26.88 End of proof
% 156.39/26.88
% 156.39/26.88 Sub-proof #193 shows that the following formulas are inconsistent:
% 156.39/26.88 ----------------------------------------------------------------
% 156.39/26.88 (1) all_58_5 = e2
% 156.39/26.88 (2) op(e3, e1) = e3
% 156.39/26.88 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.39/26.88 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.39/26.88 (4) op(e3, e3) = all_10_2
% 156.39/26.88 (5) ~ (all_52_1 = e2)
% 156.39/26.88 (6) op(e1, e1) = all_6_2
% 156.39/26.88 (7) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.39/26.88 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.39/26.88 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.39/26.88 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.39/26.88 (9) op(e3, e2) = all_52_4
% 156.39/26.88 (10) op(e2, e3) = all_52_1
% 156.39/26.88 (11) ~ (e3 = e0)
% 156.39/26.88 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.39/26.88 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.39/26.88 (13) ~ (e2 = e0)
% 156.39/26.88 (14) op(e1, e3) = all_52_2
% 156.39/26.88 (15) ~ (e3 = e1)
% 156.39/26.88 (16) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.39/26.88 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.39/26.88 (17) op(e1, e2) = all_52_6
% 156.39/26.88 (18) ~ (all_6_2 = e3)
% 156.39/26.88 (19) op(e3, e3) = e1
% 156.39/26.88 (20) op(e3, e0) = e2
% 156.39/26.88 (21) ~ (all_52_4 = e1)
% 156.39/26.88 (22) ~ (all_52_2 = e1)
% 156.39/26.88 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 156.39/26.88 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 156.39/26.88 (24) ~ (all_52_6 = e1)
% 156.39/26.88 (25) ~ (all_10_2 = e2)
% 156.39/26.88 (26) ~ (e2 = e1)
% 156.39/26.88 (27) ~ (e1 = e0)
% 156.39/26.88 (28) op(e3, e1) = all_52_8
% 156.39/26.88 (29) all_58_12 = e1 & op(e0, e3) = e1
% 156.39/26.88 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.39/26.88 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.39/26.88 (31) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 156.39/26.88 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 156.39/26.88 (32) all_58_9 = e2
% 156.39/26.88 (33) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.39/26.88 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.39/26.88 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.39/26.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.39/26.88 (35) ~ (e3 = e2)
% 156.39/26.88 (36) all_58_12 = e1
% 156.39/26.88 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.39/26.88 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.39/26.88
% 156.39/26.88 Begin of proof
% 156.39/26.88 |
% 156.39/26.88 | BETA: splitting (30) gives:
% 156.39/26.88 |
% 156.39/26.88 | Case 1:
% 156.39/26.88 | |
% 156.39/26.88 | | (38) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 156.39/26.88 | | e1)
% 156.39/26.88 | |
% 156.39/26.88 | | BETA: splitting (38) gives:
% 156.39/26.88 | |
% 156.39/26.88 | | Case 1:
% 156.39/26.88 | | |
% 156.39/26.88 | | | (39) all_58_0 = e1 & op(e3, e3) = e1
% 156.39/26.88 | | |
% 156.39/26.88 | | | ALPHA: (39) implies:
% 156.39/26.88 | | | (40) all_58_0 = e1
% 156.39/26.88 | | |
% 156.39/26.88 | | | REF_CLOSE: (4), (5), (8), (10), (11), (13), (15), (23), (25), (26), (27),
% 156.39/26.88 | | | (33), (34), (35), (36), (40) are inconsistent by sub-proof
% 156.39/26.88 | | | #1510.
% 156.39/26.88 | | |
% 156.39/26.88 | | Case 2:
% 156.39/26.88 | | |
% 156.39/26.88 | | | (41) all_58_1 = e1 & op(e3, e2) = e1
% 156.39/26.88 | | |
% 156.39/26.88 | | | REF_CLOSE: (9), (21), (34), (41) are inconsistent by sub-proof #1284.
% 156.39/26.88 | | |
% 156.39/26.88 | | End of split
% 156.39/26.88 | |
% 156.39/26.88 | Case 2:
% 156.39/26.88 | |
% 156.39/26.88 | | (42) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 156.39/26.88 | | e1)
% 156.39/26.88 | |
% 156.39/26.88 | | BETA: splitting (42) gives:
% 156.39/26.88 | |
% 156.39/26.88 | | Case 1:
% 156.39/26.88 | | |
% 156.39/26.88 | | | (43) all_58_4 = e1 & op(e3, e1) = e1
% 156.39/26.88 | | |
% 156.39/26.88 | | | ALPHA: (43) implies:
% 156.39/26.88 | | | (44) all_58_4 = e1
% 156.39/26.88 | | | (45) op(e3, e1) = e1
% 156.39/26.88 | | |
% 156.39/26.88 | | | BETA: splitting (7) gives:
% 156.39/26.88 | | |
% 156.39/26.88 | | | Case 1:
% 156.39/26.88 | | | |
% 156.39/26.88 | | | | (46) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 156.39/26.88 | | | | = e3)
% 156.39/26.88 | | | |
% 156.39/26.88 | | | | BETA: splitting (46) gives:
% 156.39/26.88 | | | |
% 156.39/26.88 | | | | Case 1:
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | (47) all_58_4 = e3 & op(e3, e1) = e3
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | ALPHA: (47) implies:
% 156.39/26.88 | | | | | (48) all_58_4 = e3
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | REF_CLOSE: (15), (44), (48) are inconsistent by sub-proof #1282.
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | Case 2:
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | (49) all_58_5 = e3 & op(e2, e1) = e3
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | REF_CLOSE: (1), (35), (49) are inconsistent by sub-proof #890.
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | End of split
% 156.39/26.88 | | | |
% 156.39/26.88 | | | Case 2:
% 156.39/26.88 | | | |
% 156.39/26.88 | | | | (50) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 156.39/26.88 | | | | = e3)
% 156.39/26.88 | | | |
% 156.39/26.88 | | | | BETA: splitting (50) gives:
% 156.39/26.88 | | | |
% 156.39/26.88 | | | | Case 1:
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | (51) all_58_8 = e3 & op(e1, e1) = e3
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | REF_CLOSE: (6), (18), (34), (51) are inconsistent by sub-proof #1469.
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | Case 2:
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | (52) all_58_14 = e3 & op(e0, e1) = e3
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | ALPHA: (52) implies:
% 156.39/26.88 | | | | | (53) all_58_14 = e3
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | BETA: splitting (23) gives:
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | | Case 1:
% 156.39/26.88 | | | | | |
% 156.39/26.88 | | | | | | (54) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 156.39/26.88 | | | | | | e3) = e2)
% 156.39/26.88 | | | | | |
% 156.39/26.88 | | | | | | REF_CLOSE: (4), (5), (10), (25), (34), (54) are inconsistent by
% 156.39/26.88 | | | | | | sub-proof #1522.
% 156.39/26.88 | | | | | |
% 156.39/26.88 | | | | | Case 2:
% 156.39/26.88 | | | | | |
% 156.39/26.88 | | | | | | (55) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0,
% 156.39/26.88 | | | | | | e3) = e2)
% 156.39/26.88 | | | | | |
% 156.39/26.88 | | | | | | BETA: splitting (55) gives:
% 156.39/26.88 | | | | | |
% 156.39/26.88 | | | | | | Case 1:
% 156.39/26.88 | | | | | | |
% 156.39/26.88 | | | | | | | (56) all_58_6 = e2 & op(e1, e3) = e2
% 156.39/26.88 | | | | | | |
% 156.39/26.88 | | | | | | | ALPHA: (56) implies:
% 156.39/26.88 | | | | | | | (57) all_58_6 = e2
% 156.39/26.88 | | | | | | |
% 156.39/26.88 | | | | | | | BETA: splitting (31) gives:
% 156.39/26.88 | | | | | | |
% 156.39/26.88 | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | |
% 156.39/26.88 | | | | | | | | (58) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 156.39/26.88 | | | | | | | | op(e3, e2) = e3)
% 156.39/26.88 | | | | | | | |
% 156.39/26.88 | | | | | | | | BETA: splitting (58) gives:
% 156.39/26.88 | | | | | | | |
% 156.39/26.88 | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | (59) all_58_0 = e3 & op(e3, e3) = e3
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | ALPHA: (59) implies:
% 156.39/26.88 | | | | | | | | | (60) all_58_0 = e3
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | BETA: splitting (33) gives:
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | (61) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 156.39/26.88 | | | | | | | | | | op(e2, e3) = e0)
% 156.39/26.88 | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | BETA: splitting (61) gives:
% 156.39/26.88 | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | (62) all_58_0 = e0 & op(e3, e3) = e0
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | ALPHA: (62) implies:
% 156.39/26.88 | | | | | | | | | | | (63) all_58_0 = e0
% 156.39/26.88 | | | | | | | | | | | (64) op(e3, e3) = e0
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | REF_CLOSE: (8), (11), (12), (14), (15), (19), (22), (27),
% 156.39/26.88 | | | | | | | | | | | (29), (34), (35), (36), (57), (63), (64) are
% 156.39/26.88 | | | | | | | | | | | inconsistent by sub-proof #1276.
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | (65) all_58_2 = e0 & op(e2, e3) = e0
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | ALPHA: (65) implies:
% 156.39/26.88 | | | | | | | | | | | (66) all_58_2 = e0
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | BETA: splitting (3) gives:
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | (67) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 156.39/26.88 | | | | | | | | | | | | & op(e1, e2) = e1)
% 156.39/26.88 | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | REF_CLOSE: (14), (17), (22), (24), (34), (67) are
% 156.39/26.88 | | | | | | | | | | | | inconsistent by sub-proof #196.
% 156.39/26.88 | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | (68) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 156.39/26.88 | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 156.39/26.88 | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | BETA: splitting (68) gives:
% 156.39/26.88 | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | (69) all_58_8 = e1 & op(e1, e1) = e1
% 156.39/26.88 | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | ALPHA: (69) implies:
% 156.39/26.88 | | | | | | | | | | | | | (70) all_58_8 = e1
% 156.39/26.88 | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | BETA: splitting (16) gives:
% 156.39/26.88 | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | (71) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 156.39/26.88 | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 156.39/26.88 | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 156.39/26.88 | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | (72) all_58_4 = e0 & op(e3, e1) = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | ALPHA: (72) implies:
% 156.39/26.88 | | | | | | | | | | | | | | | (73) op(e3, e1) = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | REF_CLOSE: (27), (34), (45), (73) are inconsistent by
% 156.39/26.88 | | | | | | | | | | | | | | | sub-proof #1281.
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | (74) all_58_5 = e0 & op(e2, e1) = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (74) are inconsistent by sub-proof
% 156.39/26.88 | | | | | | | | | | | | | | | #919.
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | End of split
% 156.39/26.88 | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | (75) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 156.39/26.88 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 156.39/26.88 | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 156.39/26.88 | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | (76) all_58_8 = e0 & op(e1, e1) = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | REF_CLOSE: (27), (70), (76) are inconsistent by sub-proof
% 156.39/26.88 | | | | | | | | | | | | | | | #1271.
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | (77) all_58_14 = e0 & op(e0, e1) = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | ALPHA: (77) implies:
% 156.39/26.88 | | | | | | | | | | | | | | | (78) all_58_14 = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | COMBINE_EQS: (53), (78) imply:
% 156.39/26.88 | | | | | | | | | | | | | | | (79) e3 = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | SIMP: (79) implies:
% 156.39/26.88 | | | | | | | | | | | | | | | (80) e3 = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | COMBINE_EQS: (60), (80) imply:
% 156.39/26.88 | | | | | | | | | | | | | | | (81) all_58_0 = e0
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (15), (35), (36), (57), (66), (81) are
% 156.39/26.88 | | | | | | | | | | | | | | | inconsistent by sub-proof #1248.
% 156.39/26.88 | | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | | End of split
% 156.39/26.88 | | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | End of split
% 156.39/26.88 | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | | REF_CLOSE: (2), (8), (11), (15), (28), (34), (35), (36),
% 156.39/26.88 | | | | | | | | | | | | | (45), (57), (60), (66) are inconsistent by
% 156.39/26.88 | | | | | | | | | | | | | sub-proof #1261.
% 156.39/26.88 | | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | | End of split
% 156.39/26.88 | | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | | End of split
% 156.39/26.88 | | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | End of split
% 156.39/26.88 | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | (82) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0
% 156.39/26.88 | | | | | | | | | | & op(e0, e3) = e0)
% 156.39/26.88 | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | | REF_CLOSE: (13), (27), (36), (57), (82) are inconsistent by
% 156.39/26.88 | | | | | | | | | | sub-proof #1259.
% 156.39/26.88 | | | | | | | | | |
% 156.39/26.88 | | | | | | | | | End of split
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | (83) all_58_1 = e3 & op(e3, e2) = e3
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | ALPHA: (83) implies:
% 156.39/26.88 | | | | | | | | | (84) op(e3, e2) = e3
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | REF_CLOSE: (8), (11), (12), (13), (14), (15), (19), (20),
% 156.39/26.88 | | | | | | | | | (22), (27), (29), (33), (34), (35), (36), (37),
% 156.39/26.88 | | | | | | | | | (45), (57), (84) are inconsistent by sub-proof
% 156.39/26.88 | | | | | | | | | #1247.
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | End of split
% 156.39/26.88 | | | | | | | |
% 156.39/26.88 | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | |
% 156.39/26.88 | | | | | | | | (85) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 156.39/26.88 | | | | | | | | op(e3, e0) = e3)
% 156.39/26.88 | | | | | | | |
% 156.39/26.88 | | | | | | | | BETA: splitting (85) gives:
% 156.39/26.88 | | | | | | | |
% 156.39/26.88 | | | | | | | | Case 1:
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | (86) all_58_4 = e3 & op(e3, e1) = e3
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | REF_CLOSE: (15), (44), (86) are inconsistent by sub-proof
% 156.39/26.88 | | | | | | | | | #195.
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | Case 2:
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | (87) all_58_9 = e3 & op(e3, e0) = e3
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | | REF_CLOSE: (32), (35), (87) are inconsistent by sub-proof
% 156.39/26.88 | | | | | | | | | #194.
% 156.39/26.88 | | | | | | | | |
% 156.39/26.88 | | | | | | | | End of split
% 156.39/26.88 | | | | | | | |
% 156.39/26.88 | | | | | | | End of split
% 156.39/26.88 | | | | | | |
% 156.39/26.88 | | | | | | Case 2:
% 156.39/26.88 | | | | | | |
% 156.39/26.88 | | | | | | | (88) all_58_12 = e2 & op(e0, e3) = e2
% 156.39/26.88 | | | | | | |
% 156.39/26.88 | | | | | | | REF_CLOSE: (26), (36), (88) are inconsistent by sub-proof #1511.
% 156.39/26.88 | | | | | | |
% 156.39/26.88 | | | | | | End of split
% 156.39/26.88 | | | | | |
% 156.39/26.88 | | | | | End of split
% 156.39/26.88 | | | | |
% 156.39/26.88 | | | | End of split
% 156.39/26.88 | | | |
% 156.39/26.88 | | | End of split
% 156.39/26.88 | | |
% 156.39/26.88 | | Case 2:
% 156.39/26.88 | | |
% 156.39/26.88 | | | (89) all_58_9 = e1 & op(e3, e0) = e1
% 156.39/26.88 | | |
% 156.39/26.88 | | | ALPHA: (89) implies:
% 156.39/26.88 | | | (90) all_58_9 = e1
% 156.39/26.88 | | |
% 156.39/26.88 | | | REF_CLOSE: (26), (32), (90) are inconsistent by sub-proof #1324.
% 156.39/26.88 | | |
% 156.39/26.88 | | End of split
% 156.39/26.88 | |
% 156.39/26.88 | End of split
% 156.39/26.88 |
% 156.39/26.88 End of proof
% 156.39/26.88
% 156.39/26.88 Sub-proof #194 shows that the following formulas are inconsistent:
% 156.39/26.88 ----------------------------------------------------------------
% 156.39/26.88 (1) all_58_9 = e3 & op(e3, e0) = e3
% 156.39/26.88 (2) all_58_9 = e2
% 156.39/26.88 (3) ~ (e3 = e2)
% 156.39/26.88
% 156.39/26.88 Begin of proof
% 156.39/26.88 |
% 156.39/26.88 | ALPHA: (1) implies:
% 156.39/26.88 | (4) all_58_9 = e3
% 156.39/26.88 |
% 156.39/26.88 | COMBINE_EQS: (2), (4) imply:
% 156.39/26.88 | (5) e3 = e2
% 156.39/26.88 |
% 156.39/26.88 | REDUCE: (3), (5) imply:
% 156.39/26.88 | (6) $false
% 156.39/26.88 |
% 156.39/26.88 | CLOSE: (6) is inconsistent.
% 156.39/26.88 |
% 156.39/26.88 End of proof
% 156.39/26.88
% 156.39/26.88 Sub-proof #195 shows that the following formulas are inconsistent:
% 156.39/26.88 ----------------------------------------------------------------
% 156.39/26.88 (1) all_58_4 = e3 & op(e3, e1) = e3
% 156.39/26.88 (2) all_58_4 = e1
% 156.39/26.88 (3) ~ (e3 = e1)
% 156.39/26.88
% 156.39/26.88 Begin of proof
% 156.39/26.88 |
% 156.39/26.88 | ALPHA: (1) implies:
% 156.39/26.88 | (4) all_58_4 = e3
% 156.39/26.88 |
% 156.57/26.88 | COMBINE_EQS: (2), (4) imply:
% 156.57/26.88 | (5) e3 = e1
% 156.57/26.88 |
% 156.57/26.88 | REDUCE: (3), (5) imply:
% 156.57/26.88 | (6) $false
% 156.57/26.88 |
% 156.57/26.88 | CLOSE: (6) is inconsistent.
% 156.57/26.88 |
% 156.57/26.88 End of proof
% 156.57/26.88
% 156.57/26.88 Sub-proof #196 shows that the following formulas are inconsistent:
% 156.57/26.88 ----------------------------------------------------------------
% 156.57/26.88 (1) op(e1, e3) = all_52_2
% 156.57/26.88 (2) op(e1, e2) = all_52_6
% 156.57/26.88 (3) ~ (all_52_2 = e1)
% 156.57/26.88 (4) ~ (all_52_6 = e1)
% 156.57/26.88 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.88 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 156.57/26.88
% 156.57/26.88 Begin of proof
% 156.57/26.88 |
% 156.57/26.88 | BETA: splitting (6) gives:
% 156.57/26.88 |
% 156.57/26.88 | Case 1:
% 156.57/26.88 | |
% 156.57/26.88 | | (7) all_58_6 = e1 & op(e1, e3) = e1
% 156.57/26.88 | |
% 156.57/26.88 | | ALPHA: (7) implies:
% 156.57/26.88 | | (8) op(e1, e3) = e1
% 156.57/26.88 | |
% 156.57/26.88 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1412.
% 156.57/26.88 | |
% 156.57/26.88 | Case 2:
% 156.57/26.88 | |
% 156.57/26.88 | | (9) all_58_7 = e1 & op(e1, e2) = e1
% 156.57/26.88 | |
% 156.57/26.88 | | ALPHA: (9) implies:
% 156.57/26.88 | | (10) op(e1, e2) = e1
% 156.57/26.88 | |
% 156.57/26.88 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #1166.
% 156.57/26.88 | |
% 156.57/26.88 | End of split
% 156.57/26.88 |
% 156.57/26.88 End of proof
% 156.57/26.88
% 156.57/26.88 Sub-proof #197 shows that the following formulas are inconsistent:
% 156.57/26.88 ----------------------------------------------------------------
% 156.57/26.88 (1) op(e3, e2) = e2
% 156.57/26.88 (2) op(e3, e2) = all_52_4
% 156.57/26.88 (3) ~ (e3 = e1)
% 156.57/26.88 (4) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 156.57/26.88 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.88 (6) ~ (e3 = e2)
% 156.57/26.88 (7) all_58_3 = e1
% 156.57/26.88
% 156.57/26.88 Begin of proof
% 156.57/26.88 |
% 156.57/26.88 | BETA: splitting (4) gives:
% 156.57/26.88 |
% 156.57/26.88 | Case 1:
% 156.57/26.88 | |
% 156.57/26.88 | | (8) all_58_1 = e3 & op(e3, e2) = e3
% 156.57/26.88 | |
% 156.57/26.88 | | ALPHA: (8) implies:
% 156.57/26.88 | | (9) op(e3, e2) = e3
% 156.57/26.88 | |
% 156.57/26.88 | | REF_CLOSE: (1), (2), (5), (6), (9) are inconsistent by sub-proof #1094.
% 156.57/26.88 | |
% 156.57/26.88 | Case 2:
% 156.57/26.88 | |
% 156.57/26.88 | | (10) all_58_3 = e3 & op(e2, e2) = e3
% 156.57/26.88 | |
% 156.57/26.88 | | ALPHA: (10) implies:
% 156.57/26.88 | | (11) all_58_3 = e3
% 156.57/26.89 | |
% 156.57/26.89 | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #841.
% 156.57/26.89 | |
% 156.57/26.89 | End of split
% 156.57/26.89 |
% 156.57/26.89 End of proof
% 156.57/26.89
% 156.57/26.89 Sub-proof #198 shows that the following formulas are inconsistent:
% 156.57/26.89 ----------------------------------------------------------------
% 156.57/26.89 (1) op(e2, e0) = all_52_13
% 156.57/26.89 (2) ~ (all_52_13 = e2)
% 156.57/26.89 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.57/26.89 (4) ~ (e2 = e1)
% 156.57/26.89 (5) all_58_9 = e1
% 156.57/26.89 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.89
% 156.57/26.89 Begin of proof
% 156.57/26.89 |
% 156.57/26.89 | BETA: splitting (3) gives:
% 156.57/26.89 |
% 156.57/26.89 | Case 1:
% 156.57/26.89 | |
% 156.57/26.89 | | (7) all_58_9 = e2 & op(e3, e0) = e2
% 156.57/26.89 | |
% 156.57/26.89 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #931.
% 156.57/26.89 | |
% 156.57/26.89 | Case 2:
% 156.57/26.89 | |
% 156.57/26.89 | | (8) all_58_10 = e2 & op(e2, e0) = e2
% 156.57/26.89 | |
% 156.57/26.89 | | ALPHA: (8) implies:
% 156.57/26.89 | | (9) op(e2, e0) = e2
% 156.57/26.89 | |
% 156.57/26.89 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #1535.
% 156.57/26.89 | |
% 156.57/26.89 | End of split
% 156.57/26.89 |
% 156.57/26.89 End of proof
% 156.57/26.89
% 156.57/26.89 Sub-proof #199 shows that the following formulas are inconsistent:
% 156.57/26.89 ----------------------------------------------------------------
% 156.57/26.89 (1) all_58_5 = e2
% 156.57/26.89 (2) op(e3, e0) = all_52_12
% 156.57/26.89 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.57/26.89 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.57/26.89 (4) op(e3, e3) = all_10_2
% 156.57/26.89 (5) ~ (all_10_2 = e1)
% 156.57/26.89 (6) all_54_13 = all_52_7
% 156.57/26.89 (7) op(e1, e1) = all_6_2
% 156.57/26.89 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.57/26.89 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.57/26.89 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.57/26.89 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.57/26.89 (10) all_54_10 = all_6_2
% 156.57/26.89 (11) all_56_12 = all_10_2
% 156.57/26.89 (12) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.57/26.89 (13) ~ (all_52_7 = all_52_11)
% 156.57/26.89 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.57/26.89 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.57/26.89 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.57/26.89 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.57/26.89 (16) op(e3, e2) = all_52_4
% 156.57/26.89 (17) ~ (all_4_2 = e2)
% 156.57/26.89 (18) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 156.57/26.89 (19) ~ (all_52_12 = all_52_13)
% 156.57/26.89 (20) all_54_0 = all_10_2
% 156.57/26.89 (21) op(e2, e3) = all_52_1
% 156.57/26.89 (22) all_54_2 = all_52_8
% 156.57/26.89 (23) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.57/26.89 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.57/26.89 (24) ~ (all_10_2 = e0)
% 156.57/26.89 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.57/26.89 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.57/26.89 (26) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.57/26.89 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.57/26.89 (27) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.57/26.89 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.57/26.89 e2)
% 156.57/26.89 (28) ~ (e2 = e0)
% 156.57/26.89 (29) ~ (all_52_11 = all_6_2)
% 156.57/26.89 (30) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 156.57/26.89 (31) op(e2, e0) = all_52_13
% 156.57/26.89 (32) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.57/26.89 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.57/26.89 (33) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.57/26.89 (34) op(e1, e2) = all_52_6
% 156.57/26.89 (35) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.57/26.89 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.57/26.89 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.57/26.89 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.57/26.89 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.57/26.89 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.57/26.89 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.57/26.89 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.57/26.89 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.57/26.89 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.89 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.57/26.89 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.57/26.89 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.57/26.89 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.57/26.89 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.57/26.89 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.57/26.89 = e0)
% 156.57/26.89 (36) ~ (all_4_2 = e1)
% 156.57/26.89 (37) ~ (all_52_4 = all_10_2)
% 156.57/26.89 (38) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.57/26.89 (39) ~ (all_52_8 = e2)
% 156.57/26.89 (40) ~ (all_52_11 = e2)
% 156.57/26.89 (41) ~ (all_6_2 = e3)
% 156.57/26.89 (42) op(e0, e0) = all_4_2
% 156.57/26.89 (43) all_54_7 = all_52_13
% 156.57/26.89 (44) ~ (all_52_8 = all_10_2)
% 156.57/26.89 (45) ~ (all_52_13 = e2)
% 156.57/26.89 (46) all_56_15 = all_4_2
% 156.57/26.89 (47) op(e0, e1) = all_52_11
% 156.57/26.89 (48) ~ (all_52_13 = all_4_2)
% 156.57/26.89 (49) ~ (all_52_6 = e1)
% 156.57/26.89 (50) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.57/26.89 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.57/26.89 (51) ~ (all_52_6 = all_52_7)
% 156.57/26.89 (52) ~ (all_52_8 = all_6_2)
% 156.57/26.89 (53) ~ (all_10_2 = e2)
% 156.57/26.89 (54) ~ (e2 = e1)
% 156.57/26.89 (55) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.57/26.89 (56) ~ (all_52_8 = all_52_11)
% 156.57/26.89 (57) ~ (e1 = e0)
% 156.57/26.89 (58) op(e3, e1) = all_52_8
% 156.57/26.89 (59) ~ (all_6_2 = e2)
% 156.57/26.89 (60) ~ (all_52_13 = e1)
% 156.57/26.89 (61) all_56_14 = all_6_2
% 156.57/26.89 (62) ~ (all_52_1 = all_10_2)
% 156.57/26.89 (63) all_54_14 = all_52_11
% 156.57/26.89 (64) ~ (all_52_7 = all_4_2)
% 156.57/26.89 (65) ~ (all_52_7 = e1)
% 156.57/26.89 (66) op(e0, e2) = all_52_7
% 156.57/26.89 (67) all_54_15 = all_4_2
% 156.57/26.89 (68) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.57/26.89 (69) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.57/26.89 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.57/26.89 (70) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.89 (71) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.57/26.89 (72) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.57/26.89 (73) all_58_3 = e1
% 156.57/26.89 (74) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.57/26.89 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.57/26.89
% 156.57/26.89 Begin of proof
% 156.57/26.89 |
% 156.57/26.89 | BETA: splitting (33) gives:
% 156.57/26.89 |
% 156.57/26.89 | Case 1:
% 156.57/26.89 | |
% 156.57/26.89 | | (75) all_54_0 = e3
% 156.57/26.89 | |
% 156.57/26.89 | | COMBINE_EQS: (20), (75) imply:
% 156.57/26.89 | | (76) all_10_2 = e3
% 156.57/26.89 | |
% 156.57/26.89 | | COMBINE_EQS: (11), (76) imply:
% 156.57/26.89 | | (77) all_56_12 = e3
% 156.57/26.89 | |
% 156.57/26.89 | | REDUCE: (62), (76) imply:
% 156.57/26.89 | | (78) ~ (all_52_1 = e3)
% 156.57/26.89 | |
% 156.57/26.89 | | REDUCE: (37), (76) imply:
% 156.57/26.89 | | (79) ~ (all_52_4 = e3)
% 156.57/26.89 | |
% 156.57/26.89 | | REDUCE: (44), (76) imply:
% 156.57/26.89 | | (80) ~ (all_52_8 = e3)
% 156.57/26.89 | |
% 156.57/26.89 | | REDUCE: (53), (76) imply:
% 156.57/26.89 | | (81) ~ (e3 = e2)
% 156.57/26.89 | |
% 156.57/26.89 | | REDUCE: (5), (76) imply:
% 156.57/26.89 | | (82) ~ (e3 = e1)
% 156.57/26.89 | |
% 156.57/26.89 | | REDUCE: (24), (76) imply:
% 156.57/26.89 | | (83) ~ (e3 = e0)
% 156.57/26.89 | |
% 156.57/26.89 | | BETA: splitting (9) gives:
% 156.57/26.89 | |
% 156.57/26.89 | | Case 1:
% 156.57/26.89 | | |
% 156.57/26.89 | | | (84) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 156.57/26.89 | | | e3)
% 156.57/26.89 | | |
% 156.57/26.89 | | | BETA: splitting (84) gives:
% 156.57/26.89 | | |
% 156.57/26.89 | | | Case 1:
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | (85) all_58_4 = e3 & op(e3, e1) = e3
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | ALPHA: (85) implies:
% 156.57/26.89 | | | | (86) op(e3, e1) = e3
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | REF_CLOSE: (58), (70), (80), (86) are inconsistent by sub-proof #1538.
% 156.57/26.89 | | | |
% 156.57/26.89 | | | Case 2:
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | (87) all_58_5 = e3 & op(e2, e1) = e3
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | ALPHA: (87) implies:
% 156.57/26.89 | | | | (88) all_58_5 = e3
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | REF_CLOSE: (1), (81), (88) are inconsistent by sub-proof #897.
% 156.57/26.89 | | | |
% 156.57/26.89 | | | End of split
% 156.57/26.89 | | |
% 156.57/26.89 | | Case 2:
% 156.57/26.89 | | |
% 156.57/26.89 | | | (89) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 156.57/26.89 | | | e3)
% 156.57/26.89 | | |
% 156.57/26.89 | | | BETA: splitting (89) gives:
% 156.57/26.89 | | |
% 156.57/26.89 | | | Case 1:
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | (90) all_58_8 = e3 & op(e1, e1) = e3
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | REF_CLOSE: (7), (41), (70), (90) are inconsistent by sub-proof #1469.
% 156.57/26.89 | | | |
% 156.57/26.89 | | | Case 2:
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | (91) all_58_14 = e3 & op(e0, e1) = e3
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | ALPHA: (91) implies:
% 156.57/26.89 | | | | (92) all_58_14 = e3
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | BETA: splitting (8) gives:
% 156.57/26.89 | | | |
% 156.57/26.89 | | | | Case 1:
% 156.57/26.89 | | | | |
% 156.57/26.89 | | | | | (93) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 156.57/26.89 | | | | | e2) = e1)
% 156.57/26.89 | | | | |
% 156.57/26.89 | | | | | BETA: splitting (93) gives:
% 156.57/26.89 | | | | |
% 156.57/26.89 | | | | | Case 1:
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | (94) all_58_12 = e1 & op(e0, e3) = e1
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | ALPHA: (94) implies:
% 156.57/26.89 | | | | | | (95) all_58_12 = e1
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12), (13),
% 156.57/26.89 | | | | | | (14), (15), (16), (17), (18), (19), (21), (22), (23),
% 156.57/26.89 | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 156.57/26.89 | | | | | | (35), (36), (38), (39), (40), (41), (42), (43), (45),
% 156.57/26.89 | | | | | | (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 156.57/26.89 | | | | | | (55), (56), (57), (58), (59), (60), (61), (63), (64),
% 156.57/26.89 | | | | | | (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 156.57/26.89 | | | | | | (74), (77), (78), (79), (80), (81), (82), (83), (92),
% 156.57/26.89 | | | | | | (95) are inconsistent by sub-proof #201.
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | Case 2:
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | (96) all_58_13 = e1 & op(e0, e2) = e1
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | ALPHA: (96) implies:
% 156.57/26.89 | | | | | | (97) op(e0, e2) = e1
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | BETA: splitting (27) gives:
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | Case 1:
% 156.57/26.89 | | | | | | |
% 156.57/26.89 | | | | | | | (98) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 156.57/26.89 | | | | | | | op(e0, e2) = e2)
% 156.57/26.89 | | | | | | |
% 156.57/26.89 | | | | | | | BETA: splitting (98) gives:
% 156.57/26.89 | | | | | | |
% 156.57/26.89 | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | (99) all_58_12 = e2 & op(e0, e3) = e2
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | ALPHA: (99) implies:
% 156.57/26.89 | | | | | | | | (100) all_58_12 = e2
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | BETA: splitting (74) gives:
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | |
% 156.57/26.89 | | | | | | | | | (101) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 156.57/26.89 | | | | | | | | | op(e2, e2) = e3)
% 156.57/26.89 | | | | | | | | |
% 156.57/26.89 | | | | | | | | | REF_CLOSE: (16), (70), (73), (79), (82), (101) are
% 156.57/26.89 | | | | | | | | | inconsistent by sub-proof #214.
% 156.57/26.89 | | | | | | | | |
% 156.57/26.89 | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | |
% 156.57/26.89 | | | | | | | | | (102) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 &
% 156.57/26.89 | | | | | | | | | op(e0, e2) = e3)
% 156.57/26.89 | | | | | | | | |
% 156.57/26.89 | | | | | | | | | BETA: splitting (102) gives:
% 156.57/26.89 | | | | | | | | |
% 156.57/26.89 | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | (103) all_58_7 = e3 & op(e1, e2) = e3
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | ALPHA: (103) implies:
% 156.57/26.89 | | | | | | | | | | (104) all_58_7 = e3
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | BETA: splitting (32) gives:
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | (105) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 156.57/26.89 | | | | | | | | | | | & op(e2, e2) = e0)
% 156.57/26.89 | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | BETA: splitting (105) gives:
% 156.57/26.89 | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | (106) all_58_1 = e0 & op(e3, e2) = e0
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | ALPHA: (106) implies:
% 156.57/26.89 | | | | | | | | | | | | (107) all_58_1 = e0
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | BETA: splitting (50) gives:
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | (108) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 156.57/26.89 | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.57/26.89 | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | REF_CLOSE: (21), (70), (73), (78), (82), (108) are
% 156.57/26.89 | | | | | | | | | | | | | inconsistent by sub-proof #213.
% 156.57/26.89 | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | (109) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 156.57/26.89 | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 156.57/26.89 | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | BETA: splitting (109) gives:
% 156.57/26.89 | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | (110) all_58_5 = e3 & op(e2, e1) = e3
% 156.57/26.89 | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | REF_CLOSE: (1), (81), (110) are inconsistent by sub-proof
% 156.57/26.89 | | | | | | | | | | | | | | #890.
% 156.57/26.89 | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | (111) all_58_10 = e3 & op(e2, e0) = e3
% 156.57/26.89 | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | ALPHA: (111) implies:
% 156.57/26.89 | | | | | | | | | | | | | | (112) all_58_10 = e3
% 156.57/26.89 | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 156.57/26.89 | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | (113) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 156.57/26.89 | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 156.57/26.89 | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 156.57/26.89 | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | (114) all_58_0 = e2 & op(e3, e3) = e2
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 156.57/26.89 | | | | | | | | | | | | | | | | (115) all_58_0 = e2
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (28), (54), (57), (69), (81), (82),
% 156.57/26.89 | | | | | | | | | | | | | | | | (83), (100), (115) are inconsistent by sub-proof
% 156.57/26.89 | | | | | | | | | | | | | | | | #999.
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | (116) all_58_1 = e2 & op(e3, e2) = e2
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | REF_CLOSE: (28), (107), (116) are inconsistent by sub-proof
% 156.57/26.89 | | | | | | | | | | | | | | | | #801.
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | (117) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 156.57/26.89 | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 156.57/26.89 | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 156.57/26.89 | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | (118) all_58_4 = e2 & op(e3, e1) = e2
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 156.57/26.89 | | | | | | | | | | | | | | | | (119) op(e3, e1) = e2
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (58), (70), (119) are inconsistent by
% 156.57/26.89 | | | | | | | | | | | | | | | | sub-proof #1212.
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | (120) all_58_9 = e2 & op(e3, e0) = e2
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 156.57/26.89 | | | | | | | | | | | | | | | | (121) all_58_9 = e2
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | (122) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 156.57/26.89 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 156.57/26.89 | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 156.57/26.89 | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (123) all_58_9 = e1 & op(e3, e0) = e1
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (124) all_58_9 = e1
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (124) imply:
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (125) e2 = e1
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (125) imply:
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (126) all_58_12 = e1
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (13), (14), (15), (16), (17), (18), (19), (21),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (22), (23), (25), (26), (27), (28), (29), (30),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (31), (32), (34), (35), (36), (38), (39), (40),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (41), (42), (43), (45), (46), (47), (48), (49),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (57),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (58), (59), (60), (61), (63), (64), (65), (66),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (67), (68), (69), (70), (71), (72), (73), (74),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (92),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (126) are inconsistent by sub-proof #201.
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (127) all_58_10 = e1 & op(e2, e0) = e1
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (60), (70), (127) are inconsistent by
% 156.57/26.89 | | | | | | | | | | | | | | | | | | sub-proof #212.
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | (128) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 156.57/26.89 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 156.57/26.89 | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 156.57/26.89 | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (129) all_58_11 = e1 & op(e1, e0) = e1
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (130) all_58_11 = e1
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14), (15), (17), (23), (25), (28), (42),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (54), (57), (59), (69), (70), (81), (82), (83),
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (100), (104), (112), (121), (130) are inconsistent
% 156.57/26.89 | | | | | | | | | | | | | | | | | | by sub-proof #200.
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | (131) all_58_15 = e1 & op(e0, e0) = e1
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (42), (70), (131) are inconsistent by
% 156.57/26.89 | | | | | | | | | | | | | | | | | | sub-proof #1418.
% 156.57/26.89 | | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | (132) all_58_3 = e0 & op(e2, e2) = e0
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | REF_CLOSE: (57), (73), (132) are inconsistent by sub-proof
% 156.57/26.89 | | | | | | | | | | | | #203.
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | (133) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 156.57/26.89 | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 156.57/26.89 | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | BETA: splitting (133) gives:
% 156.57/26.89 | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | (134) all_58_7 = e0 & op(e1, e2) = e0
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | ALPHA: (134) implies:
% 156.57/26.89 | | | | | | | | | | | | (135) all_58_7 = e0
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | REF_CLOSE: (83), (104), (135) are inconsistent by sub-proof
% 156.57/26.89 | | | | | | | | | | | | #1477.
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | (136) all_58_13 = e0 & op(e0, e2) = e0
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | ALPHA: (136) implies:
% 156.57/26.89 | | | | | | | | | | | | (137) op(e0, e2) = e0
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | | REF_CLOSE: (57), (66), (70), (97), (137) are inconsistent by
% 156.57/26.89 | | | | | | | | | | | | sub-proof #1396.
% 156.57/26.89 | | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | (138) all_58_13 = e3 & op(e0, e2) = e3
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | ALPHA: (138) implies:
% 156.57/26.89 | | | | | | | | | | (139) all_58_13 = e3
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | | REF_CLOSE: (8), (36), (42), (54), (70), (82), (92), (100),
% 156.57/26.89 | | | | | | | | | | (139) are inconsistent by sub-proof #255.
% 156.57/26.89 | | | | | | | | | |
% 156.57/26.89 | | | | | | | | | End of split
% 156.57/26.89 | | | | | | | | |
% 156.57/26.89 | | | | | | | | End of split
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | (140) all_58_13 = e2 & op(e0, e2) = e2
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | ALPHA: (140) implies:
% 156.57/26.89 | | | | | | | | (141) op(e0, e2) = e2
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | REF_CLOSE: (54), (66), (70), (97), (141) are inconsistent by
% 156.57/26.89 | | | | | | | | sub-proof #1319.
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | End of split
% 156.57/26.89 | | | | | | |
% 156.57/26.89 | | | | | | Case 2:
% 156.57/26.89 | | | | | | |
% 156.57/26.89 | | | | | | | (142) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 156.57/26.89 | | | | | | | op(e0, e0) = e2)
% 156.57/26.89 | | | | | | |
% 156.57/26.89 | | | | | | | BETA: splitting (142) gives:
% 156.57/26.89 | | | | | | |
% 156.57/26.89 | | | | | | | Case 1:
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | (143) all_58_14 = e2 & op(e0, e1) = e2
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | REF_CLOSE: (40), (47), (70), (143) are inconsistent by sub-proof
% 156.57/26.89 | | | | | | | | #1175.
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | Case 2:
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | (144) all_58_15 = e2 & op(e0, e0) = e2
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | | REF_CLOSE: (17), (42), (70), (144) are inconsistent by sub-proof
% 156.57/26.89 | | | | | | | | #1452.
% 156.57/26.89 | | | | | | | |
% 156.57/26.89 | | | | | | | End of split
% 156.57/26.89 | | | | | | |
% 156.57/26.89 | | | | | | End of split
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | End of split
% 156.57/26.89 | | | | |
% 156.57/26.89 | | | | Case 2:
% 156.57/26.89 | | | | |
% 156.57/26.89 | | | | | (145) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 156.57/26.89 | | | | | e0) = e1)
% 156.57/26.89 | | | | |
% 156.57/26.89 | | | | | BETA: splitting (145) gives:
% 156.57/26.89 | | | | |
% 156.57/26.89 | | | | | Case 1:
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | (146) all_58_14 = e1 & op(e0, e1) = e1
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | REF_CLOSE: (82), (92), (146) are inconsistent by sub-proof #844.
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | Case 2:
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | (147) all_58_15 = e1 & op(e0, e0) = e1
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | | REF_CLOSE: (36), (42), (70), (147) are inconsistent by sub-proof
% 156.57/26.89 | | | | | | #1418.
% 156.57/26.89 | | | | | |
% 156.57/26.89 | | | | | End of split
% 156.57/26.89 | | | | |
% 156.57/26.89 | | | | End of split
% 156.57/26.89 | | | |
% 156.57/26.89 | | | End of split
% 156.57/26.89 | | |
% 156.57/26.89 | | End of split
% 156.57/26.89 | |
% 156.57/26.89 | Case 2:
% 156.57/26.89 | |
% 156.57/26.89 | | (148) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.57/26.89 | |
% 156.57/26.89 | | REF_CLOSE: (5), (20), (24), (53), (148) are inconsistent by sub-proof #1307.
% 156.57/26.89 | |
% 156.57/26.89 | End of split
% 156.57/26.89 |
% 156.57/26.89 End of proof
% 156.57/26.89
% 156.57/26.89 Sub-proof #200 shows that the following formulas are inconsistent:
% 156.57/26.89 ----------------------------------------------------------------
% 156.57/26.89 (1) all_58_12 = e2
% 156.57/26.89 (2) all_58_11 = e1
% 156.57/26.89 (3) op(e1, e1) = all_6_2
% 156.57/26.89 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.57/26.89 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.57/26.89 (5) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.57/26.89 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.57/26.89 (6) ~ (all_4_2 = e2)
% 156.57/26.89 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.57/26.89 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.57/26.89 (8) ~ (e3 = e0)
% 156.57/26.89 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.57/26.89 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.57/26.89 (10) ~ (e2 = e0)
% 156.57/26.89 (11) all_58_7 = e3
% 156.57/26.89 (12) ~ (e3 = e1)
% 156.57/26.89 (13) op(e0, e0) = all_4_2
% 156.57/26.90 (14) all_58_10 = e3
% 156.57/26.90 (15) ~ (e2 = e1)
% 156.57/26.90 (16) ~ (e1 = e0)
% 156.57/26.90 (17) ~ (all_6_2 = e2)
% 156.57/26.90 (18) all_58_9 = e2
% 156.57/26.90 (19) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.57/26.90 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.57/26.90 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.90 (21) ~ (e3 = e2)
% 156.57/26.90
% 156.57/26.90 Begin of proof
% 156.57/26.90 |
% 156.57/26.90 | BETA: splitting (7) gives:
% 156.57/26.90 |
% 156.57/26.90 | Case 1:
% 156.57/26.90 | |
% 156.57/26.90 | | (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 156.57/26.90 | | e2)
% 156.57/26.90 | |
% 156.57/26.90 | | BETA: splitting (22) gives:
% 156.57/26.90 | |
% 156.57/26.90 | | Case 1:
% 156.57/26.90 | | |
% 156.57/26.90 | | | (23) all_58_6 = e2 & op(e1, e3) = e2
% 156.57/26.90 | | |
% 156.57/26.90 | | | ALPHA: (23) implies:
% 156.57/26.90 | | | (24) all_58_6 = e2
% 156.57/26.90 | | |
% 156.57/26.90 | | | REF_CLOSE: (1), (4), (8), (9), (10), (12), (15), (16), (19), (20), (21),
% 156.57/26.90 | | | (24) are inconsistent by sub-proof #1481.
% 156.57/26.90 | | |
% 156.57/26.90 | | Case 2:
% 156.57/26.90 | | |
% 156.57/26.90 | | | (25) all_58_7 = e2 & op(e1, e2) = e2
% 156.57/26.90 | | |
% 156.57/26.90 | | | REF_CLOSE: (11), (21), (25) are inconsistent by sub-proof #1203.
% 156.57/26.90 | | |
% 156.57/26.90 | | End of split
% 156.57/26.90 | |
% 156.57/26.90 | Case 2:
% 156.57/26.90 | |
% 156.57/26.90 | | (26) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 156.57/26.90 | | e2)
% 156.57/26.90 | |
% 156.57/26.90 | | REF_CLOSE: (2), (3), (5), (6), (13), (14), (15), (17), (18), (20), (21),
% 156.57/26.90 | | (26) are inconsistent by sub-proof #204.
% 156.57/26.90 | |
% 156.57/26.90 | End of split
% 156.57/26.90 |
% 156.57/26.90 End of proof
% 156.57/26.90
% 156.57/26.90 Sub-proof #201 shows that the following formulas are inconsistent:
% 156.57/26.90 ----------------------------------------------------------------
% 156.57/26.90 (1) all_58_5 = e2
% 156.57/26.90 (2) op(e3, e0) = all_52_12
% 156.57/26.90 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.57/26.90 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.57/26.90 (4) op(e3, e3) = all_10_2
% 156.57/26.90 (5) all_58_14 = e3
% 156.57/26.90 (6) all_54_13 = all_52_7
% 156.57/26.90 (7) op(e1, e1) = all_6_2
% 156.57/26.90 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.57/26.90 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.57/26.90 (9) all_54_10 = all_6_2
% 156.57/26.90 (10) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.57/26.90 (11) ~ (all_52_7 = all_52_11)
% 156.57/26.90 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.57/26.90 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.57/26.90 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.57/26.90 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.57/26.90 (14) op(e3, e2) = all_52_4
% 156.57/26.90 (15) ~ (all_4_2 = e2)
% 156.57/26.90 (16) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 156.57/26.90 (17) ~ (all_52_12 = all_52_13)
% 156.57/26.90 (18) op(e2, e3) = all_52_1
% 156.57/26.90 (19) all_54_2 = all_52_8
% 156.57/26.90 (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.57/26.90 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.57/26.90 (21) ~ (e3 = e0)
% 156.57/26.90 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.57/26.90 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.57/26.90 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.57/26.90 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.57/26.90 (24) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.57/26.90 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.57/26.90 e2)
% 156.57/26.90 (25) ~ (e2 = e0)
% 156.57/26.90 (26) ~ (all_52_11 = all_6_2)
% 156.57/26.90 (27) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 156.57/26.90 (28) op(e2, e0) = all_52_13
% 156.57/26.90 (29) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.57/26.90 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.57/26.90 (30) ~ (e3 = e1)
% 156.57/26.90 (31) op(e1, e2) = all_52_6
% 156.57/26.90 (32) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.57/26.90 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.57/26.90 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.57/26.90 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.57/26.90 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.57/26.90 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.57/26.90 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.57/26.90 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.57/26.90 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.57/26.90 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.90 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.57/26.90 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.57/26.90 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.57/26.90 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.57/26.90 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.57/26.90 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.57/26.90 = e0)
% 156.57/26.90 (33) ~ (all_4_2 = e1)
% 156.57/26.90 (34) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.57/26.90 (35) ~ (all_52_8 = e2)
% 156.57/26.90 (36) ~ (all_52_11 = e2)
% 156.57/26.90 (37) ~ (all_6_2 = e3)
% 156.57/26.90 (38) op(e0, e0) = all_4_2
% 156.57/26.90 (39) all_54_7 = all_52_13
% 156.57/26.90 (40) all_56_12 = e3
% 156.57/26.90 (41) ~ (all_52_13 = e2)
% 156.57/26.90 (42) all_56_15 = all_4_2
% 156.57/26.90 (43) op(e0, e1) = all_52_11
% 156.57/26.90 (44) ~ (all_52_13 = all_4_2)
% 156.57/26.90 (45) ~ (all_52_6 = e1)
% 156.57/26.90 (46) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.57/26.90 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.57/26.90 (47) ~ (all_52_6 = all_52_7)
% 156.57/26.90 (48) ~ (all_52_4 = e3)
% 156.57/26.90 (49) ~ (all_52_8 = all_6_2)
% 156.57/26.90 (50) ~ (all_10_2 = e2)
% 156.57/26.90 (51) ~ (e2 = e1)
% 156.57/26.90 (52) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.57/26.90 (53) ~ (all_52_8 = all_52_11)
% 156.57/26.90 (54) ~ (e1 = e0)
% 156.57/26.90 (55) op(e3, e1) = all_52_8
% 156.57/26.90 (56) ~ (all_6_2 = e2)
% 156.57/26.90 (57) ~ (all_52_13 = e1)
% 156.57/26.90 (58) all_56_14 = all_6_2
% 156.57/26.90 (59) ~ (all_52_8 = e3)
% 156.57/26.90 (60) all_54_14 = all_52_11
% 156.57/26.90 (61) ~ (all_52_7 = all_4_2)
% 156.57/26.90 (62) ~ (all_52_7 = e1)
% 156.57/26.90 (63) op(e0, e2) = all_52_7
% 156.57/26.90 (64) all_54_15 = all_4_2
% 156.57/26.90 (65) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.57/26.90 (66) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.57/26.90 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.57/26.90 (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.90 (68) ~ (e3 = e2)
% 156.57/26.90 (69) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.57/26.90 (70) all_58_12 = e1
% 156.57/26.90 (71) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.57/26.90 (72) all_58_3 = e1
% 156.57/26.90 (73) ~ (all_52_1 = e3)
% 156.57/26.90 (74) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.57/26.90 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.57/26.90
% 156.57/26.90 Begin of proof
% 156.57/26.90 |
% 156.57/26.90 | BETA: splitting (24) gives:
% 156.57/26.90 |
% 156.57/26.90 | Case 1:
% 156.57/26.90 | |
% 156.57/26.90 | | (75) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 156.57/26.90 | | e2)
% 156.57/26.90 | |
% 156.57/26.90 | | BETA: splitting (75) gives:
% 156.57/26.90 | |
% 156.57/26.90 | | Case 1:
% 156.57/26.90 | | |
% 156.57/26.90 | | | (76) all_58_12 = e2 & op(e0, e3) = e2
% 156.57/26.90 | | |
% 156.57/26.90 | | | REF_CLOSE: (51), (70), (76) are inconsistent by sub-proof #1511.
% 156.57/26.90 | | |
% 156.57/26.90 | | Case 2:
% 156.57/26.90 | | |
% 156.57/26.90 | | | (77) all_58_13 = e2 & op(e0, e2) = e2
% 156.57/26.90 | | |
% 156.57/26.90 | | | ALPHA: (77) implies:
% 156.57/26.90 | | | (78) op(e0, e2) = e2
% 156.57/26.90 | | |
% 156.57/26.90 | | | BETA: splitting (74) gives:
% 156.57/26.90 | | |
% 156.57/26.90 | | | Case 1:
% 156.57/26.90 | | | |
% 156.57/26.90 | | | | (79) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2)
% 156.57/26.90 | | | | = e3)
% 156.57/26.90 | | | |
% 156.57/26.90 | | | | REF_CLOSE: (14), (30), (48), (67), (72), (79) are inconsistent by
% 156.57/26.90 | | | | sub-proof #214.
% 156.57/26.90 | | | |
% 156.57/26.90 | | | Case 2:
% 156.57/26.90 | | | |
% 156.57/26.90 | | | | (80) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2)
% 156.57/26.90 | | | | = e3)
% 156.57/26.90 | | | |
% 156.57/26.90 | | | | BETA: splitting (80) gives:
% 156.57/26.90 | | | |
% 156.57/26.90 | | | | Case 1:
% 156.57/26.90 | | | | |
% 156.57/26.90 | | | | | (81) all_58_7 = e3 & op(e1, e2) = e3
% 156.57/26.90 | | | | |
% 156.57/26.90 | | | | | ALPHA: (81) implies:
% 156.57/26.90 | | | | | (82) all_58_7 = e3
% 156.57/26.90 | | | | |
% 156.57/26.90 | | | | | BETA: splitting (29) gives:
% 156.57/26.90 | | | | |
% 156.57/26.90 | | | | | Case 1:
% 156.57/26.90 | | | | | |
% 156.57/26.90 | | | | | | (83) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 156.57/26.90 | | | | | | e2) = e0)
% 156.57/26.90 | | | | | |
% 156.57/26.90 | | | | | | BETA: splitting (83) gives:
% 156.57/26.90 | | | | | |
% 156.57/26.90 | | | | | | Case 1:
% 156.57/26.90 | | | | | | |
% 156.57/26.90 | | | | | | | (84) all_58_1 = e0 & op(e3, e2) = e0
% 156.57/26.90 | | | | | | |
% 156.57/26.90 | | | | | | | ALPHA: (84) implies:
% 156.57/26.90 | | | | | | | (85) all_58_1 = e0
% 156.57/26.90 | | | | | | |
% 156.57/26.90 | | | | | | | BETA: splitting (46) gives:
% 156.57/26.90 | | | | | | |
% 156.57/26.90 | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | |
% 156.57/26.90 | | | | | | | | (86) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 &
% 156.57/26.90 | | | | | | | | op(e2, e2) = e3)
% 156.57/26.90 | | | | | | | |
% 156.57/26.90 | | | | | | | | REF_CLOSE: (18), (30), (67), (72), (73), (86) are inconsistent
% 156.57/26.90 | | | | | | | | by sub-proof #213.
% 156.57/26.90 | | | | | | | |
% 156.57/26.90 | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | |
% 156.57/26.90 | | | | | | | | (87) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 156.57/26.90 | | | | | | | | op(e2, e0) = e3)
% 156.57/26.90 | | | | | | | |
% 156.57/26.90 | | | | | | | | BETA: splitting (87) gives:
% 156.57/26.90 | | | | | | | |
% 156.57/26.90 | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | |
% 156.57/26.90 | | | | | | | | | (88) all_58_5 = e3 & op(e2, e1) = e3
% 156.57/26.90 | | | | | | | | |
% 156.57/26.90 | | | | | | | | | REF_CLOSE: (1), (68), (88) are inconsistent by sub-proof #890.
% 156.57/26.90 | | | | | | | | |
% 156.57/26.90 | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | |
% 156.57/26.90 | | | | | | | | | (89) all_58_10 = e3 & op(e2, e0) = e3
% 156.57/26.90 | | | | | | | | |
% 156.57/26.90 | | | | | | | | | ALPHA: (89) implies:
% 156.57/26.90 | | | | | | | | | (90) all_58_10 = e3
% 156.57/26.90 | | | | | | | | | (91) op(e2, e0) = e3
% 156.57/26.90 | | | | | | | | |
% 156.57/26.90 | | | | | | | | | BETA: splitting (10) gives:
% 156.57/26.90 | | | | | | | | |
% 156.57/26.90 | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | (92) all_54_7 = e3
% 156.57/26.90 | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | COMBINE_EQS: (39), (92) imply:
% 156.57/26.90 | | | | | | | | | | (93) all_52_13 = e3
% 156.57/26.90 | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | SIMP: (93) implies:
% 156.57/26.90 | | | | | | | | | | (94) all_52_13 = e3
% 156.57/26.90 | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | REDUCE: (17), (94) imply:
% 156.57/26.90 | | | | | | | | | | (95) ~ (all_52_12 = e3)
% 156.57/26.90 | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | REDUCE: (44), (94) imply:
% 156.57/26.90 | | | | | | | | | | (96) ~ (all_4_2 = e3)
% 156.57/26.90 | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | SIMP: (96) implies:
% 156.57/26.90 | | | | | | | | | | (97) ~ (all_4_2 = e3)
% 156.57/26.90 | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | BETA: splitting (69) gives:
% 156.57/26.90 | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | (98) all_54_15 = e3
% 156.57/26.90 | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | REF_CLOSE: (64), (97), (98) are inconsistent by sub-proof
% 156.57/26.90 | | | | | | | | | | | #1543.
% 156.57/26.90 | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | (99) ~ (all_54_15 = e3)
% 156.57/26.90 | | | | | | | | | | | (100) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.57/26.90 | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | BETA: splitting (23) gives:
% 156.57/26.90 | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | (101) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 156.57/26.90 | | | | | | | | | | | | & op(e3, e2) = e2)
% 156.57/26.90 | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | BETA: splitting (101) gives:
% 156.57/26.90 | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | (102) all_58_0 = e2 & op(e3, e3) = e2
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | REF_CLOSE: (4), (50), (67), (102) are inconsistent by
% 156.57/26.90 | | | | | | | | | | | | | sub-proof #1523.
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | (103) all_58_1 = e2 & op(e3, e2) = e2
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | REF_CLOSE: (25), (85), (103) are inconsistent by sub-proof
% 156.57/26.90 | | | | | | | | | | | | | #801.
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | (104) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 156.57/26.90 | | | | | | | | | | | | & op(e3, e0) = e2)
% 156.57/26.90 | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | BETA: splitting (104) gives:
% 156.57/26.90 | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | (105) all_58_4 = e2 & op(e3, e1) = e2
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | ALPHA: (105) implies:
% 156.57/26.90 | | | | | | | | | | | | | (106) op(e3, e1) = e2
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | REF_CLOSE: (35), (55), (67), (106) are inconsistent by
% 156.57/26.90 | | | | | | | | | | | | | sub-proof #1212.
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | (107) all_58_9 = e2 & op(e3, e0) = e2
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | ALPHA: (107) implies:
% 156.57/26.90 | | | | | | | | | | | | | (108) all_58_9 = e2
% 156.57/26.90 | | | | | | | | | | | | | (109) op(e3, e0) = e2
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | BETA: splitting (3) gives:
% 156.57/26.90 | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | (110) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 156.57/26.90 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 156.57/26.90 | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 156.57/26.90 | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | (111) all_58_9 = e1 & op(e3, e0) = e1
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | REF_CLOSE: (51), (108), (111) are inconsistent by sub-proof
% 156.57/26.90 | | | | | | | | | | | | | | | #1325.
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | (112) all_58_10 = e1 & op(e2, e0) = e1
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | REF_CLOSE: (28), (57), (67), (112) are inconsistent by
% 156.57/26.90 | | | | | | | | | | | | | | | sub-proof #212.
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | (113) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 156.57/26.90 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 156.57/26.90 | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 156.57/26.90 | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | (114) all_58_11 = e1 & op(e1, e0) = e1
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 156.57/26.90 | | | | | | | | | | | | | | | (115) all_58_11 = e1
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 156.57/26.90 | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | (116) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 156.57/26.90 | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 156.57/26.90 | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | (117) all_58_6 = e2 & op(e1, e3) = e2
% 156.57/26.90 | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 156.57/26.90 | | | | | | | | | | | | | | | | | (118) all_58_6 = e2
% 156.57/26.90 | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | (119) all_54_15 = e2
% 156.57/26.90 | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (25), (42), (63), (64), (67), (78), (119)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #287.
% 156.57/26.90 | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | (120) ~ (all_54_15 = e2)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | (121) all_54_15 = e1 | all_54_15 = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (122) all_54_15 = e1
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (122) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (123) all_4_2 = e1
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | REDUCE: (33), (123) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (124) $false
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (125) all_54_15 = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (125) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (126) all_4_2 = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (126) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (127) all_56_15 = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | REDUCE: (61), (126) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (128) ~ (all_52_7 = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | REDUCE: (97), (126) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (129) ~ (e3 = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | REDUCE: (15), (126) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (130) ~ (e2 = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | REDUCE: (33), (126) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | (131) ~ (e1 = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (132) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (133) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (134) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (135) op(e2, e3) = e3
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (67), (73), (135) are inconsistent by
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1183.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (136) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (18), (21), (22), (25), (30), (51), (54),
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (55), (59), (66), (67), (68), (118), (136) are
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #211.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (137) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (138) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (139) ~ (all_56_12 = e3)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (139) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (140) $false
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (141) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | (142) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | (143) op(e3, e0) = e3
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (95), (143) are inconsistent by
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #210.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | (144) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | (145) op(e3, e0) = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (67), (109), (145) are inconsistent by
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1500.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (146) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (147) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (148) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (149) ~ (all_56_14 = e1)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (150) op(e1, e2) = e2
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (149) imply:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (151) ~ (all_6_2 = e1)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | (152) all_54_10 = e3
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (37), (152) are inconsistent by sub-proof
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | #1531.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | (153) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | | (154) all_54_10 = e2
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (56), (154) are inconsistent by sub-proof
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | | #1530.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | | (155) all_54_10 = e1 | all_54_10 = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11), (19), (26), (31), (34), (35),
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | | (36), (47), (49), (53), (59), (60), (62), (65),
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | | (67), (71), (128), (150), (151), (155) are
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #206.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (156) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (31), (41), (45), (67), (156) are
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1129.
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (157) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (158) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | | (159) op(e0, e2) = e0
% 156.57/26.90 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (63), (67), (78), (159) are inconsistent by
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1040.
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | (160) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | (161) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | (162) ~ (all_56_15 = e0)
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (162) imply:
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | (163) $false
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (163) is inconsistent.
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | (164) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (27), (37), (52), (54), (56), (58), (164) are
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #205.
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.91 | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | (165) all_58_7 = e2 & op(e1, e2) = e2
% 156.57/26.91 | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (82), (165) are inconsistent by sub-proof
% 156.57/26.91 | | | | | | | | | | | | | | | | | #1203.
% 156.57/26.91 | | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | Case 2:
% 156.57/26.91 | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | (166) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 156.57/26.91 | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 156.57/26.91 | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (15), (38), (51), (56), (67), (68),
% 156.57/26.91 | | | | | | | | | | | | | | | | (90), (108), (115), (166) are inconsistent by
% 156.57/26.91 | | | | | | | | | | | | | | | | sub-proof #204.
% 156.57/26.91 | | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | Case 2:
% 156.57/26.91 | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | (167) all_58_15 = e1 & op(e0, e0) = e1
% 156.57/26.91 | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | | REF_CLOSE: (33), (38), (67), (167) are inconsistent by
% 156.57/26.91 | | | | | | | | | | | | | | | sub-proof #1418.
% 156.57/26.91 | | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | Case 2:
% 156.57/26.91 | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | (168) ~ (all_54_7 = e3)
% 156.57/26.91 | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | REDUCE: (39), (168) imply:
% 156.57/26.91 | | | | | | | | | | (169) ~ (all_52_13 = e3)
% 156.57/26.91 | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | | REF_CLOSE: (28), (67), (91), (169) are inconsistent by
% 156.57/26.91 | | | | | | | | | | sub-proof #1364.
% 156.57/26.91 | | | | | | | | | |
% 156.57/26.91 | | | | | | | | | End of split
% 156.57/26.91 | | | | | | | | |
% 156.57/26.91 | | | | | | | | End of split
% 156.57/26.91 | | | | | | | |
% 156.57/26.91 | | | | | | | End of split
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | Case 2:
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | | (170) all_58_3 = e0 & op(e2, e2) = e0
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | | REF_CLOSE: (54), (72), (170) are inconsistent by sub-proof #203.
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | End of split
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | Case 2:
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | (171) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 156.57/26.91 | | | | | | op(e0, e2) = e0)
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | BETA: splitting (171) gives:
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | Case 1:
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | | (172) all_58_7 = e0 & op(e1, e2) = e0
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | | ALPHA: (172) implies:
% 156.57/26.91 | | | | | | | (173) all_58_7 = e0
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | | REF_CLOSE: (21), (82), (173) are inconsistent by sub-proof #1477.
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | Case 2:
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | | (174) all_58_13 = e0 & op(e0, e2) = e0
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | | ALPHA: (174) implies:
% 156.57/26.91 | | | | | | | (175) op(e0, e2) = e0
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | | REF_CLOSE: (25), (63), (67), (78), (175) are inconsistent by
% 156.57/26.91 | | | | | | | sub-proof #1040.
% 156.57/26.91 | | | | | | |
% 156.57/26.91 | | | | | | End of split
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | End of split
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | Case 2:
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | (176) all_58_13 = e3 & op(e0, e2) = e3
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | ALPHA: (176) implies:
% 156.57/26.91 | | | | | (177) all_58_13 = e3
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | REF_CLOSE: (5), (8), (15), (24), (30), (33), (38), (51), (67), (68),
% 156.57/26.91 | | | | | (177) are inconsistent by sub-proof #202.
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | End of split
% 156.57/26.91 | | | |
% 156.57/26.91 | | | End of split
% 156.57/26.91 | | |
% 156.57/26.91 | | End of split
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (178) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.57/26.91 | | e2)
% 156.57/26.91 | |
% 156.57/26.91 | | BETA: splitting (178) gives:
% 156.57/26.91 | |
% 156.57/26.91 | | Case 1:
% 156.57/26.91 | | |
% 156.57/26.91 | | | (179) all_58_14 = e2 & op(e0, e1) = e2
% 156.57/26.91 | | |
% 156.57/26.91 | | | REF_CLOSE: (36), (43), (67), (179) are inconsistent by sub-proof #1175.
% 156.57/26.91 | | |
% 156.57/26.91 | | Case 2:
% 156.57/26.91 | | |
% 156.57/26.91 | | | (180) all_58_15 = e2 & op(e0, e0) = e2
% 156.57/26.91 | | |
% 156.57/26.91 | | | REF_CLOSE: (15), (38), (67), (180) are inconsistent by sub-proof #1452.
% 156.57/26.91 | | |
% 156.57/26.91 | | End of split
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #202 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_58_14 = e3
% 156.57/26.91 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.57/26.91 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.57/26.91 (3) ~ (all_4_2 = e2)
% 156.57/26.91 (4) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 156.57/26.91 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.57/26.91 (5) ~ (e3 = e1)
% 156.57/26.91 (6) all_58_13 = e3
% 156.57/26.91 (7) ~ (all_4_2 = e1)
% 156.57/26.91 (8) op(e0, e0) = all_4_2
% 156.57/26.91 (9) ~ (e2 = e1)
% 156.57/26.91 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91 (11) ~ (e3 = e2)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | BETA: splitting (4) gives:
% 156.57/26.91 |
% 156.57/26.91 | Case 1:
% 156.57/26.91 | |
% 156.57/26.91 | | (12) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 156.57/26.91 | | e2)
% 156.57/26.91 | |
% 156.57/26.91 | | BETA: splitting (12) gives:
% 156.57/26.91 | |
% 156.57/26.91 | | Case 1:
% 156.57/26.91 | | |
% 156.57/26.91 | | | (13) all_58_12 = e2 & op(e0, e3) = e2
% 156.57/26.91 | | |
% 156.57/26.91 | | | ALPHA: (13) implies:
% 156.57/26.91 | | | (14) all_58_12 = e2
% 156.57/26.91 | | |
% 156.57/26.91 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (14) are inconsistent
% 156.57/26.91 | | | by sub-proof #255.
% 156.57/26.91 | | |
% 156.57/26.91 | | Case 2:
% 156.57/26.91 | | |
% 156.57/26.91 | | | (15) all_58_13 = e2 & op(e0, e2) = e2
% 156.57/26.91 | | |
% 156.57/26.91 | | | REF_CLOSE: (6), (11), (15) are inconsistent by sub-proof #1177.
% 156.57/26.91 | | |
% 156.57/26.91 | | End of split
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (16) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.57/26.91 | | e2)
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (1), (3), (8), (10), (11), (16) are inconsistent by sub-proof
% 156.57/26.91 | | #936.
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #203 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_58_3 = e0 & op(e2, e2) = e0
% 156.57/26.91 (2) all_58_3 = e1
% 156.57/26.91 (3) ~ (e1 = e0)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | ALPHA: (1) implies:
% 156.57/26.91 | (4) all_58_3 = e0
% 156.57/26.91 |
% 156.57/26.91 | COMBINE_EQS: (2), (4) imply:
% 156.57/26.91 | (5) e1 = e0
% 156.57/26.91 |
% 156.57/26.91 | REDUCE: (3), (5) imply:
% 156.57/26.91 | (6) $false
% 156.57/26.91 |
% 156.57/26.91 | CLOSE: (6) is inconsistent.
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #204 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_58_11 = e1
% 156.57/26.91 (2) op(e1, e1) = all_6_2
% 156.57/26.91 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.57/26.91 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.57/26.91 (4) ~ (all_4_2 = e2)
% 156.57/26.91 (5) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.57/26.91 (6) op(e0, e0) = all_4_2
% 156.57/26.91 (7) all_58_10 = e3
% 156.57/26.91 (8) ~ (e2 = e1)
% 156.57/26.91 (9) ~ (all_6_2 = e2)
% 156.57/26.91 (10) all_58_9 = e2
% 156.57/26.91 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91 (12) ~ (e3 = e2)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | BETA: splitting (5) gives:
% 156.57/26.91 |
% 156.57/26.91 | Case 1:
% 156.57/26.91 | |
% 156.57/26.91 | | (13) all_58_8 = e2 & op(e1, e1) = e2
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (2), (9), (11), (13) are inconsistent by sub-proof #1440.
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (14) all_58_11 = e2 & op(e1, e0) = e2
% 156.57/26.91 | |
% 156.57/26.91 | | ALPHA: (14) implies:
% 156.57/26.91 | | (15) all_58_11 = e2
% 156.57/26.91 | |
% 156.57/26.91 | | COMBINE_EQS: (1), (15) imply:
% 156.57/26.91 | | (16) e2 = e1
% 156.57/26.91 | |
% 156.57/26.91 | | SIMP: (16) implies:
% 156.57/26.91 | | (17) e2 = e1
% 156.57/26.91 | |
% 156.57/26.91 | | COMBINE_EQS: (10), (17) imply:
% 156.57/26.91 | | (18) all_58_9 = e1
% 156.57/26.91 | |
% 156.57/26.91 | | BETA: splitting (3) gives:
% 156.57/26.91 | |
% 156.57/26.91 | | Case 1:
% 156.57/26.91 | | |
% 156.57/26.91 | | | (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 156.57/26.91 | | | e2)
% 156.57/26.91 | | |
% 156.57/26.91 | | | BETA: splitting (19) gives:
% 156.57/26.91 | | |
% 156.57/26.91 | | | Case 1:
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | (20) all_58_9 = e2 & op(e3, e0) = e2
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | REF_CLOSE: (8), (10), (18) are inconsistent by sub-proof #1324.
% 156.57/26.91 | | | |
% 156.57/26.91 | | | Case 2:
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | (21) all_58_10 = e2 & op(e2, e0) = e2
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | REF_CLOSE: (7), (12), (21) are inconsistent by sub-proof #1050.
% 156.57/26.91 | | | |
% 156.57/26.91 | | | End of split
% 156.57/26.91 | | |
% 156.57/26.91 | | Case 2:
% 156.57/26.91 | | |
% 156.57/26.91 | | | (22) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0)
% 156.57/26.91 | | | = e2)
% 156.57/26.91 | | |
% 156.57/26.91 | | | REF_CLOSE: (1), (4), (6), (8), (11), (22) are inconsistent by sub-proof
% 156.57/26.91 | | | #942.
% 156.57/26.91 | | |
% 156.57/26.91 | | End of split
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #205 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_54_10 = all_6_2
% 156.57/26.91 (2) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 156.57/26.91 (3) ~ (all_6_2 = e3)
% 156.57/26.91 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.57/26.91 (5) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 &
% 156.57/26.91 op(e0, e1) = e0
% 156.57/26.91 (6) ~ (e1 = e0)
% 156.57/26.91 (7) ~ (all_6_2 = e2)
% 156.57/26.91 (8) all_56_14 = all_6_2
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | ALPHA: (5) implies:
% 156.57/26.91 | (9) all_56_8 = e0
% 156.57/26.91 | (10) ~ (all_56_14 = e1)
% 156.57/26.91 |
% 156.57/26.91 | REDUCE: (8), (10) imply:
% 156.57/26.91 | (11) ~ (all_6_2 = e1)
% 156.57/26.91 |
% 156.57/26.91 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11) are inconsistent by
% 156.57/26.91 | sub-proof #1525.
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #206 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_54_13 = all_52_7
% 156.57/26.91 (2) all_54_10 = all_6_2
% 156.57/26.91 (3) ~ (all_52_7 = all_52_11)
% 156.57/26.91 (4) ~ (all_6_2 = e1)
% 156.57/26.91 (5) op(e1, e2) = e2
% 156.57/26.91 (6) all_54_2 = all_52_8
% 156.57/26.91 (7) ~ (all_52_11 = all_6_2)
% 156.57/26.91 (8) op(e1, e2) = all_52_6
% 156.57/26.91 (9) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.57/26.91 (10) ~ (all_52_8 = e2)
% 156.57/26.91 (11) ~ (all_52_11 = e2)
% 156.57/26.91 (12) ~ (all_52_7 = e0)
% 156.57/26.91 (13) all_54_10 = e1 | all_54_10 = e0
% 156.57/26.91 (14) ~ (all_52_6 = all_52_7)
% 156.57/26.91 (15) ~ (all_52_8 = all_6_2)
% 156.57/26.91 (16) ~ (all_52_8 = all_52_11)
% 156.57/26.91 (17) ~ (all_52_8 = e3)
% 156.57/26.91 (18) all_54_14 = all_52_11
% 156.57/26.91 (19) ~ (all_52_7 = e1)
% 156.57/26.91 (20) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.57/26.91 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91 (22) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | BETA: splitting (13) gives:
% 156.57/26.91 |
% 156.57/26.91 | Case 1:
% 156.57/26.91 | |
% 156.57/26.91 | | (23) all_54_10 = e1
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (2), (4), (23) are inconsistent by sub-proof #1529.
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (24) all_54_10 = e0
% 156.57/26.91 | |
% 156.57/26.91 | | COMBINE_EQS: (2), (24) imply:
% 156.57/26.91 | | (25) all_6_2 = e0
% 156.57/26.91 | |
% 156.57/26.91 | | SIMP: (25) implies:
% 156.57/26.91 | | (26) all_6_2 = e0
% 156.57/26.91 | |
% 156.57/26.91 | | REDUCE: (15), (26) imply:
% 156.57/26.91 | | (27) ~ (all_52_8 = e0)
% 156.57/26.91 | |
% 156.57/26.91 | | REDUCE: (7), (26) imply:
% 156.57/26.91 | | (28) ~ (all_52_11 = e0)
% 156.57/26.91 | |
% 156.57/26.91 | | BETA: splitting (9) gives:
% 156.57/26.91 | |
% 156.57/26.91 | | Case 1:
% 156.57/26.91 | | |
% 156.57/26.91 | | | (29) all_54_2 = e3
% 156.57/26.91 | | |
% 156.57/26.91 | | | REF_CLOSE: (6), (17), (29) are inconsistent by sub-proof #1210.
% 156.57/26.91 | | |
% 156.57/26.91 | | Case 2:
% 156.57/26.91 | | |
% 156.57/26.91 | | | (30) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.57/26.91 | | |
% 156.57/26.91 | | | BETA: splitting (30) gives:
% 156.57/26.91 | | |
% 156.57/26.91 | | | Case 1:
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | (31) all_54_2 = e2
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | REF_CLOSE: (6), (10), (31) are inconsistent by sub-proof #1209.
% 156.57/26.91 | | | |
% 156.57/26.91 | | | Case 2:
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | (32) all_54_2 = e1 | all_54_2 = e0
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | BETA: splitting (32) gives:
% 156.57/26.91 | | | |
% 156.57/26.91 | | | | Case 1:
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | (33) all_54_2 = e1
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | COMBINE_EQS: (6), (33) imply:
% 156.57/26.91 | | | | | (34) all_52_8 = e1
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | SIMP: (34) implies:
% 156.57/26.91 | | | | | (35) all_52_8 = e1
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | REDUCE: (16), (35) imply:
% 156.57/26.91 | | | | | (36) ~ (all_52_11 = e1)
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | SIMP: (36) implies:
% 156.57/26.91 | | | | | (37) ~ (all_52_11 = e1)
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | BETA: splitting (22) gives:
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | Case 1:
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | (38) all_54_14 = e3
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | COMBINE_EQS: (18), (38) imply:
% 156.57/26.91 | | | | | | (39) all_52_11 = e3
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | SIMP: (39) implies:
% 156.57/26.91 | | | | | | (40) all_52_11 = e3
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | REDUCE: (3), (40) imply:
% 156.57/26.91 | | | | | | (41) ~ (all_52_7 = e3)
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | REF_CLOSE: (1), (5), (8), (12), (14), (19), (20), (21), (41) are
% 156.57/26.91 | | | | | | inconsistent by sub-proof #208.
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | Case 2:
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | (42) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | | REF_CLOSE: (11), (18), (28), (37), (42) are inconsistent by
% 156.57/26.91 | | | | | | sub-proof #1149.
% 156.57/26.91 | | | | | |
% 156.57/26.91 | | | | | End of split
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | Case 2:
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | (43) all_54_2 = e0
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | | REF_CLOSE: (6), (27), (43) are inconsistent by sub-proof #207.
% 156.57/26.91 | | | | |
% 156.57/26.91 | | | | End of split
% 156.57/26.91 | | | |
% 156.57/26.91 | | | End of split
% 156.57/26.91 | | |
% 156.57/26.91 | | End of split
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #207 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_54_2 = all_52_8
% 156.57/26.91 (2) all_54_2 = e0
% 156.57/26.91 (3) ~ (all_52_8 = e0)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | COMBINE_EQS: (1), (2) imply:
% 156.57/26.91 | (4) all_52_8 = e0
% 156.57/26.91 |
% 156.57/26.91 | SIMP: (4) implies:
% 156.57/26.91 | (5) all_52_8 = e0
% 156.57/26.91 |
% 156.57/26.91 | REDUCE: (3), (5) imply:
% 156.57/26.91 | (6) $false
% 156.57/26.91 |
% 156.57/26.91 | CLOSE: (6) is inconsistent.
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #208 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_54_13 = all_52_7
% 156.57/26.91 (2) ~ (all_52_7 = e3)
% 156.57/26.91 (3) op(e1, e2) = e2
% 156.57/26.91 (4) op(e1, e2) = all_52_6
% 156.57/26.91 (5) ~ (all_52_7 = e0)
% 156.57/26.91 (6) ~ (all_52_6 = all_52_7)
% 156.57/26.91 (7) ~ (all_52_7 = e1)
% 156.57/26.91 (8) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.57/26.91 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | BETA: splitting (8) gives:
% 156.57/26.91 |
% 156.57/26.91 | Case 1:
% 156.57/26.91 | |
% 156.57/26.91 | | (10) all_54_13 = e3
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #1435.
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (11) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11) are inconsistent by
% 156.57/26.91 | | sub-proof #209.
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #209 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_54_13 = all_52_7
% 156.57/26.91 (2) op(e1, e2) = e2
% 156.57/26.91 (3) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.57/26.91 (4) op(e1, e2) = all_52_6
% 156.57/26.91 (5) ~ (all_52_7 = e0)
% 156.57/26.91 (6) ~ (all_52_6 = all_52_7)
% 156.57/26.91 (7) ~ (all_52_7 = e1)
% 156.57/26.91 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | BETA: splitting (3) gives:
% 156.57/26.91 |
% 156.57/26.91 | Case 1:
% 156.57/26.91 | |
% 156.57/26.91 | | (9) all_54_13 = e2
% 156.57/26.91 | |
% 156.57/26.91 | | COMBINE_EQS: (1), (9) imply:
% 156.57/26.91 | | (10) all_52_7 = e2
% 156.57/26.91 | |
% 156.57/26.91 | | SIMP: (10) implies:
% 156.57/26.91 | | (11) all_52_7 = e2
% 156.57/26.91 | |
% 156.57/26.91 | | REDUCE: (6), (11) imply:
% 156.57/26.91 | | (12) ~ (all_52_6 = e2)
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (2), (4), (8), (12) are inconsistent by sub-proof #1536.
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (13) all_54_13 = e1 | all_54_13 = e0
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (1), (5), (7), (13) are inconsistent by sub-proof #875.
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #210 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91 (2) op(e3, e0) = all_52_12
% 156.57/26.91 (3) op(e3, e0) = e3
% 156.57/26.91 (4) ~ (all_52_12 = e3)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | GROUND_INST: instantiating (1) with all_52_12, e3, e0, e3, simplifying with
% 156.57/26.91 | (2), (3) gives:
% 156.57/26.91 | (5) all_52_12 = e3
% 156.57/26.91 |
% 156.57/26.91 | REDUCE: (4), (5) imply:
% 156.57/26.91 | (6) $false
% 156.57/26.91 |
% 156.57/26.91 | CLOSE: (6) is inconsistent.
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #211 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.57/26.91 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.57/26.91 (2) op(e2, e3) = all_52_1
% 156.57/26.91 (3) all_58_6 = e2
% 156.57/26.91 (4) ~ (e3 = e0)
% 156.57/26.91 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.57/26.91 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.57/26.91 (6) ~ (e2 = e0)
% 156.57/26.91 (7) ~ (e3 = e1)
% 156.57/26.91 (8) ~ (e2 = e1)
% 156.57/26.91 (9) ~ (e1 = e0)
% 156.57/26.91 (10) op(e3, e1) = all_52_8
% 156.57/26.91 (11) ~ (all_52_8 = e3)
% 156.57/26.91 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.57/26.91 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.57/26.91 (13) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 &
% 156.57/26.91 op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.57/26.91 e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.57/26.91 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91 (15) ~ (e3 = e2)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | BETA: splitting (13) gives:
% 156.57/26.91 |
% 156.57/26.91 | Case 1:
% 156.57/26.91 | |
% 156.57/26.91 | | (16) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) =
% 156.57/26.91 | | e2 & op(e2, e3) = e2
% 156.57/26.91 | |
% 156.57/26.91 | | ALPHA: (16) implies:
% 156.57/26.91 | | (17) op(e2, e3) = e2
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (15),
% 156.57/26.91 | | (17) are inconsistent by sub-proof #1152.
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (18) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) =
% 156.57/26.91 | | e3 & op(e1, e3) = e3
% 156.57/26.91 | |
% 156.57/26.91 | | ALPHA: (18) implies:
% 156.57/26.91 | | (19) op(e3, e1) = e3
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (10), (11), (14), (19) are inconsistent by sub-proof #1538.
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #212 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_58_10 = e1 & op(e2, e0) = e1
% 156.57/26.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91 (3) op(e2, e0) = all_52_13
% 156.57/26.91 (4) ~ (all_52_13 = e1)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | ALPHA: (1) implies:
% 156.57/26.91 | (5) op(e2, e0) = e1
% 156.57/26.91 |
% 156.57/26.91 | GROUND_INST: instantiating (2) with all_52_13, e1, e0, e2, simplifying with
% 156.57/26.91 | (3), (5) gives:
% 156.57/26.91 | (6) all_52_13 = e1
% 156.57/26.91 |
% 156.57/26.91 | REDUCE: (4), (6) imply:
% 156.57/26.91 | (7) $false
% 156.57/26.91 |
% 156.57/26.91 | CLOSE: (7) is inconsistent.
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #213 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 156.57/26.91 (2) op(e2, e3) = all_52_1
% 156.57/26.91 (3) ~ (e3 = e1)
% 156.57/26.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91 (5) all_58_3 = e1
% 156.57/26.91 (6) ~ (all_52_1 = e3)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | BETA: splitting (1) gives:
% 156.57/26.91 |
% 156.57/26.91 | Case 1:
% 156.57/26.91 | |
% 156.57/26.91 | | (7) all_58_2 = e3 & op(e2, e3) = e3
% 156.57/26.91 | |
% 156.57/26.91 | | ALPHA: (7) implies:
% 156.57/26.91 | | (8) op(e2, e3) = e3
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1183.
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (9) all_58_3 = e3 & op(e2, e2) = e3
% 156.57/26.91 | |
% 156.57/26.91 | | ALPHA: (9) implies:
% 156.57/26.91 | | (10) all_58_3 = e3
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #841.
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #214 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) op(e3, e2) = all_52_4
% 156.57/26.91 (2) ~ (e3 = e1)
% 156.57/26.91 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 156.57/26.91 (4) ~ (all_52_4 = e3)
% 156.57/26.91 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.91 (6) all_58_3 = e1
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.91 |
% 156.57/26.91 | BETA: splitting (3) gives:
% 156.57/26.91 |
% 156.57/26.91 | Case 1:
% 156.57/26.91 | |
% 156.57/26.91 | | (7) all_58_1 = e3 & op(e3, e2) = e3
% 156.57/26.91 | |
% 156.57/26.91 | | ALPHA: (7) implies:
% 156.57/26.91 | | (8) op(e3, e2) = e3
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1540.
% 156.57/26.91 | |
% 156.57/26.91 | Case 2:
% 156.57/26.91 | |
% 156.57/26.91 | | (9) all_58_3 = e3 & op(e2, e2) = e3
% 156.57/26.91 | |
% 156.57/26.91 | | ALPHA: (9) implies:
% 156.57/26.91 | | (10) all_58_3 = e3
% 156.57/26.91 | |
% 156.57/26.91 | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #841.
% 156.57/26.91 | |
% 156.57/26.91 | End of split
% 156.57/26.91 |
% 156.57/26.91 End of proof
% 156.57/26.91
% 156.57/26.91 Sub-proof #215 shows that the following formulas are inconsistent:
% 156.57/26.91 ----------------------------------------------------------------
% 156.57/26.91 (1) all_58_3 = e2 & op(e2, e2) = e2
% 156.57/26.91 (2) all_58_3 = e1
% 156.57/26.91 (3) ~ (e2 = e1)
% 156.57/26.91
% 156.57/26.91 Begin of proof
% 156.57/26.92 |
% 156.57/26.92 | ALPHA: (1) implies:
% 156.57/26.92 | (4) all_58_3 = e2
% 156.57/26.92 |
% 156.57/26.92 | COMBINE_EQS: (2), (4) imply:
% 156.57/26.92 | (5) e2 = e1
% 156.57/26.92 |
% 156.57/26.92 | SIMP: (5) implies:
% 156.57/26.92 | (6) e2 = e1
% 156.57/26.92 |
% 156.57/26.92 | REDUCE: (3), (6) imply:
% 156.57/26.92 | (7) $false
% 156.57/26.92 |
% 156.57/26.92 | CLOSE: (7) is inconsistent.
% 156.57/26.92 |
% 156.57/26.92 End of proof
% 156.57/26.92
% 156.57/26.92 Sub-proof #216 shows that the following formulas are inconsistent:
% 156.57/26.92 ----------------------------------------------------------------
% 156.57/26.92 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 156.57/26.92 (2) ~ (all_56_13 = e3) | (all_56_3 = e2 & op(e2, e3) = e2)
% 156.57/26.92 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 156.57/26.92 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 156.57/26.92 (5) op(e0, e3) = all_52_3
% 156.57/26.92 (6) op(e3, e0) = all_52_12
% 156.57/26.92 (7) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.57/26.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.57/26.92 (8) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.57/26.92 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.57/26.92 (9) all_14_2 = all_8_2
% 156.57/26.92 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.57/26.92 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.57/26.92 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.57/26.92 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 156.57/26.92 (12) op(e3, e3) = all_10_2
% 156.57/26.92 (13) op(e0, e0) = all_10_1
% 156.57/26.92 (14) all_54_13 = all_52_7
% 156.57/26.92 (15) op(e1, e1) = all_6_2
% 156.57/26.92 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.57/26.92 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 156.57/26.92 e1)
% 156.57/26.92 (17) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.57/26.92 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.57/26.92 (18) ~ (all_52_6 = all_52_14)
% 156.57/26.92 (19) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 156.57/26.92 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 156.57/26.92 (20) all_54_10 = all_6_2
% 156.57/26.92 (21) ~ (all_52_2 = all_52_3)
% 156.57/26.92 (22) ~ (all_52_4 = all_52_6)
% 156.57/26.92 (23) all_56_12 = all_10_2
% 156.57/26.92 (24) ~ (all_52_2 = all_10_2)
% 156.57/26.92 (25) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 156.57/26.92 (26) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 156.57/26.92 (27) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 156.57/26.92 op(e1, e1) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 156.57/26.92 e2) & op(e1, e1) = all_32_1 & $i(all_32_1))
% 156.57/26.92 (28) ~ (all_52_7 = all_52_11)
% 156.57/26.92 (29) ~ (all_52_12 = all_4_2)
% 156.57/26.92 (30) ~ (all_24_2 = e0) | ( ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 &
% 156.57/26.92 op(e0, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 156.57/26.92 e2) & op(e0, e0) = all_24_1 & $i(all_24_1))
% 156.57/26.92 (31) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 156.57/26.92 (32) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.57/26.92 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.57/26.92 (33) ~ (all_52_1 = all_8_2)
% 156.57/26.92 (34) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 156.57/26.92 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 156.57/26.92 (35) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.57/26.92 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.57/26.92 (36) ~ (all_14_2 = e3) | ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 156.57/26.92 op(e3, e3) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 =
% 156.57/26.92 e0) & op(e3, e3) = all_14_1 & $i(all_14_1))
% 156.57/26.92 (37) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.57/26.92 (38) all_54_1 = all_52_4
% 156.57/26.92 (39) op(e3, e2) = all_52_4
% 156.57/26.92 (40) ~ (all_52_1 = all_52_13)
% 156.57/26.92 (41) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 156.57/26.92 (42) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 156.57/26.92 (43) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.57/26.92 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.57/26.92 (44) ~ (all_52_12 = all_52_13)
% 156.57/26.92 (45) all_56_13 = all_8_2
% 156.57/26.92 (46) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 156.57/26.92 (47) ~ (all_52_4 = all_52_12)
% 156.57/26.92 (48) all_54_0 = all_10_2
% 156.57/26.92 (49) op(e2, e1) = all_52_9
% 156.57/26.92 (50) all_24_2 = e0
% 156.57/26.92 (51) op(e2, e3) = all_52_1
% 156.57/26.92 (52) ~ (all_52_1 = all_52_3)
% 156.57/26.92 (53) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 156.57/26.92 op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 156.57/26.92 e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 156.57/26.92 (54) all_54_2 = all_52_8
% 156.57/26.92 (55) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 156.57/26.92 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 156.57/26.92 (56) ~ (all_52_8 = all_52_9)
% 156.57/26.92 (57) ~ (all_52_2 = all_6_2)
% 156.57/26.92 (58) all_56_12 = e0
% 156.57/26.92 (59) ~ (e3 = e0)
% 156.57/26.92 (60) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.57/26.92 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.57/26.92 (61) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.57/26.92 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.57/26.92 (62) ~ (all_52_9 = all_52_13)
% 156.57/26.92 (63) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.57/26.92 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.57/26.92 e2)
% 156.57/26.92 (64) ~ (e2 = e0)
% 156.57/26.92 (65) ~ (all_52_11 = all_6_2)
% 156.57/26.92 (66) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 156.57/26.92 (67) ~ (all_52_2 = all_52_6)
% 156.57/26.92 (68) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.57/26.92 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.57/26.92 (69) ~ (all_56_12 = e0) | (all_56_2 = e3 & op(e3, e0) = e3)
% 156.57/26.92 (70) ~ (all_52_8 = e0)
% 156.57/26.92 (71) all_32_2 = all_10_2
% 156.57/26.92 (72) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 &
% 156.57/26.92 op(e3, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 156.57/26.92 e0) & op(e3, e3) = all_28_1 & $i(all_28_1))
% 156.57/26.92 (73) all_30_2 = all_8_2
% 156.57/26.92 (74) op(e1, e3) = all_52_2
% 156.57/26.92 (75) ~ (all_52_6 = all_6_2)
% 156.57/26.92 (76) op(e2, e0) = all_52_13
% 156.57/26.92 (77) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 156.57/26.92 (78) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.57/26.92 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.57/26.92 (79) ~ (all_52_8 = all_52_12)
% 156.57/26.92 (80) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 156.57/26.92 (81) ~ (all_52_6 = all_8_2)
% 156.57/26.92 (82) ~ (e3 = e1)
% 156.57/26.92 (83) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.57/26.92 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.57/26.92 (84) op(e1, e2) = all_52_6
% 156.57/26.92 (85) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.57/26.92 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.57/26.92 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.57/26.92 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.57/26.92 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.57/26.92 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.57/26.92 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.57/26.92 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 156.57/26.92 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 156.57/26.92 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.92 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 156.57/26.92 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 156.57/26.92 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 156.57/26.92 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 156.57/26.92 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 156.57/26.92 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 156.57/26.92 = e0)
% 156.57/26.92 (86) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.57/26.92 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.57/26.92 (87) all_54_4 = all_52_1
% 156.57/26.92 (88) ~ (all_52_4 = all_10_2)
% 156.57/26.92 (89) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 156.57/26.92 (90) ~ (all_52_4 = e0)
% 156.57/26.92 (91) ~ (all_52_3 = all_4_2)
% 156.57/26.92 (92) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.57/26.92 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 156.57/26.92 (93) ~ (all_52_3 = all_10_2)
% 156.57/26.92 (94) ~ (all_52_9 = all_6_2)
% 156.57/26.92 (95) op(e0, e0) = all_4_2
% 156.57/26.92 (96) all_54_8 = all_52_2
% 156.57/26.92 (97) all_54_7 = all_52_13
% 156.57/26.92 (98) ~ (all_52_8 = all_10_2)
% 156.57/26.92 (99) ~ (all_36_2 = e3) | ( ~ (all_36_0 = e0) & op(all_36_1, e1) = all_36_0 &
% 156.57/26.92 op(e3, e3) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 156.57/26.92 e2) & op(e3, e3) = all_36_1 & $i(all_36_1))
% 156.57/26.92 (100) all_56_15 = all_4_2
% 156.57/26.92 (101) op(e0, e1) = all_52_11
% 156.57/26.92 (102) ~ (all_52_9 = all_52_11)
% 156.57/26.92 (103) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 156.57/26.92 (104) ~ (all_52_13 = all_4_2)
% 156.57/26.92 (105) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0
% 156.57/26.92 & op(e2, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 156.57/26.92 (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1))
% 156.57/26.92 (106) ~ (all_52_4 = all_8_2)
% 156.57/26.92 (107) all_28_2 = all_6_2
% 156.57/26.92 (108) ~ (all_52_2 = all_52_14)
% 156.57/26.92 (109) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.57/26.92 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.57/26.92 (110) ~ (all_52_6 = all_52_7)
% 156.57/26.92 (111) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.57/26.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.57/26.92 (112) ~ (all_52_8 = all_6_2)
% 156.57/26.92 (113) all_54_6 = all_52_9
% 156.57/26.92 (114) ~ (e2 = e1)
% 156.57/26.92 (115) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 156.57/26.92 (116) all_54_3 = all_52_12
% 156.57/26.92 (117) all_22_2 = all_8_2
% 156.57/26.92 (118) ~ (all_52_4 = all_52_7)
% 156.57/26.92 (119) ~ (all_52_12 = e0)
% 156.57/26.92 (120) ~ (all_52_8 = all_52_11)
% 156.57/26.92 (121) ~ (all_52_12 = all_10_2)
% 156.57/26.92 (122) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 156.57/26.92 (123) ~ (e1 = e0)
% 156.57/26.92 (124) ~ (all_8_2 = e1)
% 156.57/26.92 (125) ~ (all_52_1 = e0)
% 156.57/26.92 (126) ~ (all_52_7 = all_8_2)
% 156.57/26.92 (127) ~ (all_56_13 = e0) | (all_56_5 = e2 & op(e2, e0) = e2)
% 156.57/26.92 (128) op(e3, e1) = all_52_8
% 156.57/26.92 (129) ~ (all_6_2 = e2)
% 156.57/26.92 (130) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.57/26.92 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 156.57/26.92 e3)
% 156.57/26.92 (131) all_56_14 = all_6_2
% 156.57/26.92 (132) ~ (all_52_1 = all_10_2)
% 156.57/26.92 (133) ~ (all_52_12 = all_52_14)
% 156.57/26.92 (134) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.57/26.92 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.57/26.92 (135) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0
% 156.57/26.92 & op(e0, e0) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~
% 156.57/26.92 (all_30_1 = e1) & op(e0, e0) = all_30_1 & $i(all_30_1))
% 156.57/26.92 (136) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.57/26.92 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.57/26.92 (137) all_54_14 = all_52_11
% 156.57/26.92 (138) ~ (all_52_7 = all_4_2)
% 156.57/26.92 (139) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 156.57/26.92 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 156.57/26.92 (140) op(e0, e2) = all_52_7
% 156.57/26.92 (141) op(e1, e0) = all_52_14
% 156.57/26.92 (142) ~ (all_52_1 = all_52_2)
% 156.57/26.92 (143) all_54_15 = all_4_2
% 156.57/26.92 (144) all_20_2 = all_4_2
% 156.57/26.92 (145) op(e2, e2) = all_8_2
% 156.57/26.92 (146) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 156.57/26.92 (147) ~ (all_52_14 = all_6_2)
% 156.57/26.92 (148) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 156.57/26.92 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 156.57/26.92 (149) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.57/26.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.57/26.92 (150) all_54_5 = all_8_2
% 156.57/26.92 (151) ~ (all_52_3 = all_52_11)
% 156.57/26.92 (152) ~ (all_52_11 = all_4_2)
% 156.57/26.92 (153) ~ (all_52_9 = all_8_2)
% 156.57/26.92 (154) all_36_2 = all_6_2
% 156.57/26.92 (155) all_54_11 = all_52_14
% 156.57/26.92 (156) ~ (all_52_13 = all_52_14)
% 156.57/26.92 (157) ~ (e3 = e2)
% 156.57/26.92 (158) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.57/26.92 (159) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 156.57/26.92 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 156.57/26.92 (160) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 156.57/26.92 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 156.57/26.92 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 156.57/26.92 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 156.57/26.92 e0)))
% 156.57/26.92 (161) all_54_9 = all_52_6
% 156.57/26.92 (162) ~ (all_52_13 = all_8_2)
% 156.57/26.92 (163) ~ (all_52_4 = all_52_8)
% 156.57/26.92 (164) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 156.57/26.92 (165) all_54_12 = all_52_3
% 156.57/26.92 (166) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 156.57/26.92 (167) ~ (all_10_1 = e1)
% 156.57/26.92 (168) ~ (all_52_14 = all_4_2)
% 156.57/26.92 (169) ~ (all_52_1 = all_52_9)
% 156.57/26.92 (170) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 156.57/26.92 (171) ~ (all_52_3 = all_52_7)
% 156.57/26.92 (172) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.57/26.92 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 156.57/26.92
% 156.57/26.92 Begin of proof
% 156.57/26.92 |
% 156.57/26.92 | BETA: splitting (69) gives:
% 156.57/26.92 |
% 156.57/26.92 | Case 1:
% 156.57/26.92 | |
% 156.57/26.92 | | (173) ~ (all_56_12 = e0)
% 156.57/26.92 | |
% 156.57/26.92 | | REDUCE: (58), (173) imply:
% 156.57/26.92 | | (174) $false
% 156.57/26.92 | |
% 156.57/26.92 | | CLOSE: (174) is inconsistent.
% 156.57/26.92 | |
% 156.57/26.92 | Case 2:
% 156.57/26.92 | |
% 156.57/26.92 | | (175) all_56_2 = e3 & op(e3, e0) = e3
% 156.57/26.92 | |
% 156.57/26.92 | | ALPHA: (175) implies:
% 156.57/26.92 | | (176) all_56_2 = e3
% 156.57/26.92 | | (177) op(e3, e0) = e3
% 156.57/26.92 | |
% 156.57/26.92 | | BETA: splitting (159) gives:
% 156.57/26.92 | |
% 156.57/26.92 | | Case 1:
% 156.57/26.92 | | |
% 156.57/26.92 | | | (178) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 156.57/26.92 | | | e0)
% 156.57/26.92 | | |
% 156.57/26.92 | | | BETA: splitting (178) gives:
% 156.57/26.92 | | |
% 156.57/26.92 | | | Case 1:
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | (179) all_58_0 = e0 & op(e3, e3) = e0
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | ALPHA: (179) implies:
% 156.57/26.92 | | | | (180) all_58_0 = e0
% 156.57/26.92 | | | | (181) op(e3, e3) = e0
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | GROUND_INST: instantiating (149) with all_4_2, all_10_1, e0, e0,
% 156.57/26.92 | | | | simplifying with (13), (95) gives:
% 156.57/26.92 | | | | (182) all_10_1 = all_4_2
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | GROUND_INST: instantiating (149) with all_52_12, e3, e0, e3, simplifying
% 156.57/26.92 | | | | with (6), (177) gives:
% 156.57/26.92 | | | | (183) all_52_12 = e3
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | REDUCE: (47), (183) imply:
% 156.57/26.92 | | | | (184) ~ (all_52_4 = e3)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | REDUCE: (79), (183) imply:
% 156.57/26.92 | | | | (185) ~ (all_52_8 = e3)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | REDUCE: (44), (183) imply:
% 156.57/26.92 | | | | (186) ~ (all_52_13 = e3)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | SIMP: (186) implies:
% 156.57/26.92 | | | | (187) ~ (all_52_13 = e3)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | REDUCE: (133), (183) imply:
% 156.57/26.92 | | | | (188) ~ (all_52_14 = e3)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | SIMP: (188) implies:
% 156.57/26.92 | | | | (189) ~ (all_52_14 = e3)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | REDUCE: (29), (183) imply:
% 156.57/26.92 | | | | (190) ~ (all_4_2 = e3)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | SIMP: (190) implies:
% 156.57/26.92 | | | | (191) ~ (all_4_2 = e3)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | REDUCE: (167), (182) imply:
% 156.57/26.92 | | | | (192) ~ (all_4_2 = e1)
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | BETA: splitting (139) gives:
% 156.57/26.92 | | | |
% 156.57/26.92 | | | | Case 1:
% 156.57/26.92 | | | | |
% 156.57/26.92 | | | | | (193) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 156.57/26.92 | | | | | e2) = e3)
% 156.57/26.92 | | | | |
% 156.57/26.92 | | | | | REF_CLOSE: (39), (59), (149), (181), (184), (193) are inconsistent by
% 156.57/26.92 | | | | | sub-proof #353.
% 156.57/26.92 | | | | |
% 156.57/26.92 | | | | Case 2:
% 156.57/26.92 | | | | |
% 156.57/26.92 | | | | | (194) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 156.57/26.92 | | | | | e0) = e3)
% 156.57/26.92 | | | | |
% 156.57/26.92 | | | | | BETA: splitting (194) gives:
% 156.57/26.92 | | | | |
% 156.57/26.92 | | | | | Case 1:
% 156.57/26.92 | | | | | |
% 156.57/26.92 | | | | | | (195) all_58_4 = e3 & op(e3, e1) = e3
% 156.57/26.92 | | | | | |
% 156.57/26.92 | | | | | | ALPHA: (195) implies:
% 156.57/26.92 | | | | | | (196) op(e3, e1) = e3
% 156.57/26.92 | | | | | |
% 156.57/26.92 | | | | | | REF_CLOSE: (128), (149), (185), (196) are inconsistent by sub-proof
% 156.57/26.92 | | | | | | #1538.
% 156.57/26.92 | | | | | |
% 156.57/26.92 | | | | | Case 2:
% 156.57/26.92 | | | | | |
% 156.57/26.92 | | | | | | (197) all_58_9 = e3 & op(e3, e0) = e3
% 156.57/26.92 | | | | | |
% 156.57/26.92 | | | | | | ALPHA: (197) implies:
% 156.57/26.92 | | | | | | (198) all_58_9 = e3
% 156.57/26.92 | | | | | |
% 156.57/26.92 | | | | | | BETA: splitting (36) gives:
% 156.57/26.92 | | | | | |
% 156.57/26.92 | | | | | | Case 1:
% 156.57/26.92 | | | | | | |
% 156.57/26.92 | | | | | | | (199) ~ (all_14_2 = e3)
% 156.57/26.92 | | | | | | |
% 156.57/26.92 | | | | | | | REDUCE: (9), (199) imply:
% 156.57/26.92 | | | | | | | (200) ~ (all_8_2 = e3)
% 156.57/26.92 | | | | | | |
% 156.57/26.92 | | | | | | | BETA: splitting (105) gives:
% 156.57/26.92 | | | | | | |
% 156.57/26.92 | | | | | | | Case 1:
% 156.57/26.92 | | | | | | | |
% 156.57/26.92 | | | | | | | | (201) ~ (all_20_2 = e2)
% 156.57/26.92 | | | | | | | |
% 156.57/26.92 | | | | | | | | REDUCE: (144), (201) imply:
% 156.57/26.92 | | | | | | | | (202) ~ (all_4_2 = e2)
% 156.57/26.92 | | | | | | | |
% 156.57/26.92 | | | | | | | | BETA: splitting (30) gives:
% 156.57/26.92 | | | | | | | |
% 156.57/26.92 | | | | | | | | Case 1:
% 156.57/26.92 | | | | | | | | |
% 156.57/26.92 | | | | | | | | | (203) ~ (all_24_2 = e0)
% 156.57/26.92 | | | | | | | | |
% 156.57/26.92 | | | | | | | | | REDUCE: (50), (203) imply:
% 156.57/26.92 | | | | | | | | | (204) $false
% 156.57/26.92 | | | | | | | | |
% 156.57/26.92 | | | | | | | | | CLOSE: (204) is inconsistent.
% 156.57/26.92 | | | | | | | | |
% 156.57/26.92 | | | | | | | | Case 2:
% 156.57/26.92 | | | | | | | | |
% 156.57/26.92 | | | | | | | | | (205) ( ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 &
% 156.57/26.92 | | | | | | | | | op(e0, e0) = all_24_1 & $i(all_24_0) &
% 156.57/26.92 | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e2) & op(e0, e0) =
% 156.57/26.92 | | | | | | | | | all_24_1 & $i(all_24_1))
% 156.57/26.92 | | | | | | | | |
% 156.57/26.92 | | | | | | | | | BETA: splitting (205) gives:
% 156.57/26.92 | | | | | | | | |
% 156.57/26.92 | | | | | | | | | Case 1:
% 156.57/26.92 | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | (206) ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 &
% 156.57/26.92 | | | | | | | | | | op(e0, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)
% 156.57/26.92 | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | ALPHA: (206) implies:
% 156.57/26.92 | | | | | | | | | | (207) op(e0, e0) = all_24_1
% 156.57/26.92 | | | | | | | | | | (208) op(all_24_1, e3) = all_24_0
% 156.57/26.92 | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | BETA: splitting (158) gives:
% 156.57/26.92 | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | Case 1:
% 156.57/26.92 | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | (209) all_54_15 = e3
% 156.57/26.92 | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | REF_CLOSE: (143), (191), (209) are inconsistent by sub-proof
% 156.57/26.92 | | | | | | | | | | | #1543.
% 156.57/26.92 | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | Case 2:
% 156.57/26.92 | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | (210) ~ (all_54_15 = e3)
% 156.57/26.92 | | | | | | | | | | | (211) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.57/26.92 | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | BETA: splitting (211) gives:
% 156.57/26.92 | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | Case 1:
% 156.57/26.92 | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | (212) all_54_15 = e2
% 156.57/26.92 | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | REF_CLOSE: (143), (202), (212) are inconsistent by sub-proof
% 156.57/26.92 | | | | | | | | | | | | #1542.
% 156.57/26.92 | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | Case 2:
% 156.57/26.92 | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | (213) ~ (all_54_15 = e2)
% 156.57/26.92 | | | | | | | | | | | | (214) all_54_15 = e1 | all_54_15 = e0
% 156.57/26.92 | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | BETA: splitting (214) gives:
% 156.57/26.92 | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | Case 1:
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | (215) all_54_15 = e1
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | REF_CLOSE: (143), (192), (215) are inconsistent by sub-proof
% 156.57/26.92 | | | | | | | | | | | | | #1541.
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | Case 2:
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | (216) all_54_15 = e0
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | COMBINE_EQS: (143), (216) imply:
% 156.57/26.92 | | | | | | | | | | | | | (217) all_4_2 = e0
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | SIMP: (217) implies:
% 156.57/26.92 | | | | | | | | | | | | | (218) all_4_2 = e0
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | COMBINE_EQS: (100), (218) imply:
% 156.57/26.92 | | | | | | | | | | | | | (219) all_56_15 = e0
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | REDUCE: (91), (218) imply:
% 156.57/26.92 | | | | | | | | | | | | | (220) ~ (all_52_3 = e0)
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | REDUCE: (138), (218) imply:
% 156.57/26.92 | | | | | | | | | | | | | (221) ~ (all_52_7 = e0)
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | REDUCE: (104), (218) imply:
% 156.57/26.92 | | | | | | | | | | | | | (222) ~ (all_52_13 = e0)
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | REDUCE: (191), (218) imply:
% 156.57/26.92 | | | | | | | | | | | | | (223) ~ (e3 = e0)
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | REDUCE: (202), (218) imply:
% 156.57/26.92 | | | | | | | | | | | | | (224) ~ (e2 = e0)
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | REDUCE: (192), (218) imply:
% 156.57/26.92 | | | | | | | | | | | | | (225) ~ (e1 = e0)
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | REDUCE: (95), (218) imply:
% 156.57/26.92 | | | | | | | | | | | | | (226) op(e0, e0) = e0
% 156.57/26.92 | | | | | | | | | | | | |
% 156.57/26.92 | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e0, all_24_1, e0, e0,
% 156.57/26.92 | | | | | | | | | | | | | simplifying with (207), (226) gives:
% 156.57/26.93 | | | | | | | | | | | | | (227) all_24_1 = e0
% 156.57/26.93 | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | REDUCE: (208), (227) imply:
% 156.57/26.93 | | | | | | | | | | | | | (228) op(e0, e3) = all_24_0
% 156.57/26.93 | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_3, all_24_0, e3,
% 156.57/26.93 | | | | | | | | | | | | | e0, simplifying with (5), (228) gives:
% 156.57/26.93 | | | | | | | | | | | | | (229) all_52_3 = all_24_0
% 156.57/26.93 | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | REDUCE: (220), (229) imply:
% 156.57/26.93 | | | | | | | | | | | | | (230) ~ (all_24_0 = e0)
% 156.57/26.93 | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | BETA: splitting (72) gives:
% 156.57/26.93 | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | (231) ~ (all_28_2 = e3)
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | REDUCE: (107), (231) imply:
% 156.57/26.93 | | | | | | | | | | | | | | (232) ~ (all_6_2 = e3)
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (11), (14), (15), (16), (18),
% 156.57/26.93 | | | | | | | | | | | | | | (19), (32), (33), (34), (35), (38), (39), (41),
% 156.57/26.93 | | | | | | | | | | | | | | (43), (45), (49), (51), (55), (59), (60), (61),
% 156.57/26.93 | | | | | | | | | | | | | | (62), (63), (64), (66), (68), (73), (74), (76),
% 156.57/26.93 | | | | | | | | | | | | | | (77), (81), (82), (83), (84), (85), (86), (90),
% 156.57/26.93 | | | | | | | | | | | | | | (92), (95), (101), (106), (108), (109), (110),
% 156.57/26.93 | | | | | | | | | | | | | | (114), (118), (122), (123), (124), (125), (126),
% 156.57/26.93 | | | | | | | | | | | | | | (127), (128), (129), (131), (134), (135), (140),
% 156.57/26.93 | | | | | | | | | | | | | | (141), (145), (146), (147), (149), (150), (153),
% 156.57/26.93 | | | | | | | | | | | | | | (155), (156), (157), (162), (172), (177), (180),
% 156.57/26.93 | | | | | | | | | | | | | | (181), (184), (185), (187), (189), (192), (198),
% 156.57/26.93 | | | | | | | | | | | | | | (200), (202), (219), (221), (232) are inconsistent
% 156.57/26.93 | | | | | | | | | | | | | | by sub-proof #239.
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | (233) all_28_2 = e3
% 156.57/26.93 | | | | | | | | | | | | | | (234) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0
% 156.57/26.93 | | | | | | | | | | | | | | & op(e3, e3) = all_28_1 & $i(all_28_0) &
% 156.57/26.93 | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3, e3)
% 156.57/26.93 | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | COMBINE_EQS: (107), (233) imply:
% 156.57/26.93 | | | | | | | | | | | | | | (235) all_6_2 = e3
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | SIMP: (235) implies:
% 156.57/26.93 | | | | | | | | | | | | | | (236) all_6_2 = e3
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | COMBINE_EQS: (131), (236) imply:
% 156.57/26.93 | | | | | | | | | | | | | | (237) all_56_14 = e3
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | REDUCE: (75), (236) imply:
% 156.57/26.93 | | | | | | | | | | | | | | (238) ~ (all_52_6 = e3)
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | REDUCE: (94), (236) imply:
% 156.57/26.93 | | | | | | | | | | | | | | (239) ~ (all_52_9 = e3)
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | REDUCE: (15), (236) imply:
% 156.57/26.93 | | | | | | | | | | | | | | (240) op(e1, e1) = e3
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 156.57/26.93 | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | (241) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 156.57/26.93 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.57/26.93 | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | REF_CLOSE: (39), (145), (149), (184), (200), (241) are
% 156.57/26.93 | | | | | | | | | | | | | | | inconsistent by sub-proof #1436.
% 156.57/26.93 | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | (242) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 156.57/26.93 | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 156.57/26.93 | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | (243) all_58_7 = e3 & op(e1, e2) = e3
% 156.57/26.93 | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | REF_CLOSE: (84), (149), (238), (243) are inconsistent by
% 156.57/26.93 | | | | | | | | | | | | | | | | sub-proof #1184.
% 156.57/26.93 | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | (244) all_58_13 = e3 & op(e0, e2) = e3
% 156.57/26.93 | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | (245) all_58_13 = e3
% 156.57/26.93 | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | (246) ~ (all_56_14 = e3)
% 156.57/26.93 | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | REDUCE: (237), (246) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | (247) $false
% 156.57/26.93 | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 156.57/26.93 | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | (248) all_56_6 = e1 & op(e1, e3) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | (249) op(e1, e3) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | (250) ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 &
% 156.57/26.93 | | | | | | | | | | | | | | | | | | op(e3, e3) = all_28_1 & $i(all_28_0) &
% 156.57/26.93 | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | (251) op(e3, e3) = all_28_1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | (252) op(all_28_1, e1) = all_28_0
% 156.57/26.93 | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | (253) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | (254) all_58_2 = e3 & op(e2, e3) = e3
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | (255) op(e2, e3) = e3
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | (256) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (123), (149), (180), (255), (256) are
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1493.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | (257) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | (258) all_58_6 = e1 & op(e1, e3) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | (259) all_58_6 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | (260) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | (261) all_58_4 = e0 & op(e3, e1) = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (82), (114), (123), (134), (149),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | (157), (180), (198), (261) are inconsistent by
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #348.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | (262) all_58_5 = e0 & op(e2, e1) = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_5 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | (264) op(e2, e1) = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | (265) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (124), (145), (149), (255), (265) are
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1122.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | (266) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_5 = e1 & op(e2, e1) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (263), (267) are inconsistent by sub-proof
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | #1121.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_58_10 = e1 & op(e2, e0) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_10 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (270) op(e2, e0) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (157), (198), (269), (271) are inconsistent
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #301.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_11 = e2 & op(e1, e0) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_58_11 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_58_12 = e1 & op(e0, e3) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_12 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (17), (35), (39), (43), (51),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (59), (61), (63), (64), (68), (74), (78), (82),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (86), (90), (95), (101), (111), (114),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (124), (140), (145), (149), (157), (160),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180), (192), (198), (202), (221), (238), (245),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (255), (263), (269), (274), (277) are
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_58_13 = e1 & op(e0, e2) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (245), (278) are inconsistent by sub-proof
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1165.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_14 = e1 & op(e0, e1) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) op(e0, e1) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_58_12 = e2 & op(e0, e3) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_58_12 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) op(e0, e3) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_58_4 = e2 & op(e3, e1) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_4 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (82), (84), (149), (238), (249), (289) are
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_58_8 = e3 & op(e1, e1) = e3
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_58_8 = e3
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_2 = e2 & op(e2, e3) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) op(e2, e3) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (51), (59), (82), (149), (157), (180),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259), (284), (295) are inconsistent by sub-proof
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1067.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_58_3 = e2 & op(e2, e2) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_3 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) op(e2, e2) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_11, e1, e1, e0,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (101), (281) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_52_11 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_24_0, e2, e3, e0,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (228), (285) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_24_0 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_2, e1, e3, e1,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (74), (249) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_52_2 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_13, e1, e0, e2,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (76), (270) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_52_13 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_9, e0, e1, e2,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (49), (264) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_52_9 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_8_2, e2, e2, e2,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (145), (298) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_8_2 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e0, all_28_1, e3, e3,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (181), (251) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_28_1 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (304) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_56_13 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (302) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) ~ (e3 = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (304) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) ~ (e3 = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (252), (305) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) op(e0, e1) = all_28_0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (32), (35), (39), (43), (51),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (59), (61), (64), (68), (74), (78), (82), (84),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (95), (114), (123), (124), (134), (140),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (149), (157), (177), (180), (192), (198),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (219), (221), (238), (245), (249), (259),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274), (284), (288), (292), (297), (310) are
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) ~ (all_56_14 = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) op(e2, e1) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e0, e2, e1, e2,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (264), (315) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) e2 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (316) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_11 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (64), (82), (95), (114), (123), (149),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (192), (198), (202), (317) are inconsistent
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #240.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (219), (306), (318) are inconsistent by sub-proof
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #233.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) op(e0, e2) = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (149), (221), (321) are inconsistent by
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1532.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) ~ (all_56_15 = e0)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (219), (324) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) $false
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (325) is inconsistent.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) ~ (all_56_14 = e1)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) op(e0, e1) = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e1, all_28_0, e1, e0,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (281), (309) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_28_0 = e1
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e0, all_28_0, e1, e0,
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (309), (328) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_28_0 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (330) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) e1 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (331) imply:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_58_10 = e0
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (82), (95), (114), (123), (149), (192),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (274), (332) are inconsistent by sub-proof
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #350.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (64), (82), (95), (114), (123), (149),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (192), (198), (202), (263), (274), (333)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #236.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_11 = e3 & op(e1, e0) = e3
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (82), (95), (114), (149), (157),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (198), (202), (334) are inconsistent by
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #243.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_58_5 = e2 & op(e2, e1) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (64), (82), (95), (114), (123), (149),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (192), (198), (202), (263), (274), (335)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #237.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_58_8 = e2 & op(e1, e1) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_58_8 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (43), (59), (64), (68), (82), (84), (114),
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (149), (157), (238), (274), (338) are
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1068.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_58_14 = e2 & op(e0, e1) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) op(e0, e1) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (114), (149), (281), (340) are inconsistent
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1473.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_58_13 = e2 & op(e0, e2) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_58_13 = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (245), (342) are inconsistent by sub-proof
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #320.
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_58_14 = e2 & op(e0, e1) = e2
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) op(e0, e1) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (114), (149), (281), (345) are inconsistent
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1473.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_58_15 = e2 & op(e0, e0) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (346) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_58_15 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (59), (64), (82), (114), (123), (160),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (274), (347) are inconsistent by sub-proof
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1453.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_58_15 = e1 & op(e0, e0) = e1
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (149), (192), (348) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1418.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_58_15 = e2 & op(e0, e0) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (149), (202), (349) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1452.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | (350) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (350) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_8 = e0 & op(e1, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (351) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (352) op(e1, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (149), (240), (352) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1466.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_14 = e0 & op(e0, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_14 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (355) op(e0, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | (356) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (356) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_58_6 = e0 & op(e1, e3) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (357) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_6 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (259), (358) are inconsistent by sub-proof
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | #735.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_58_7 = e0 & op(e1, e2) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (359) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_58_7 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (361) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_12 = e2 & op(e0, e3) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (362) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_58_12 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (82), (84), (149), (238), (249), (364) are
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_58_8 = e3 & op(e1, e1) = e3
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_58_8 = e3
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_58_0 = e2 & op(e3, e3) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (369) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_58_0 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (59), (64), (82), (123), (148), (157),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259), (363), (370) are inconsistent by sub-proof
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1333.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_58_1 = e2 & op(e3, e2) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_58_1 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (82), (114), (123), (124), (145), (149),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245), (360), (372) are inconsistent by sub-proof
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #322.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_58_4 = e2 & op(e3, e1) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_4 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_58_6 = e2 & op(e1, e3) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_58_6 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (82), (114), (123), (149), (180), (255),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363), (378) are inconsistent by sub-proof #1491.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_58_7 = e2 & op(e1, e2) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (360), (379) are inconsistent by sub-proof
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #746.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (380) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_58_8 = e2 & op(e1, e1) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (129), (149), (381) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1440.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_58_11 = e2 & op(e1, e0) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_58_11 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (384) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_58_1 = e2 & op(e3, e2) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (114), (123), (134), (180), (198), (375),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) are inconsistent by sub-proof #276.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_58_3 = e2 & op(e2, e2) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_58_3 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (388) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_58_2 = e0 & op(e2, e3) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (125), (149), (389) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1433.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_58_3 = e0 & op(e2, e2) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_58_3 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (391) imply:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) e2 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (383), (392) imply:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_58_11 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (64), (82), (95), (114), (123), (149),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (192), (198), (202), (393) are inconsistent
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #240.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (394) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_58_5 = e0 & op(e2, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_58_5 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (16), (17), (35), (39),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (51), (59), (61), (63), (64), (68), (74),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (82), (84), (86), (90), (95), (101), (111),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (123), (124), (140), (145), (149), (157),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (180), (192), (198), (202), (221), (238),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245), (249), (255), (354), (396) are inconsistent
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #230.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_58_10 = e0 & op(e2, e0) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (397) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_58_10 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (82), (95), (114), (123), (149), (192),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (383), (398) are inconsistent by sub-proof
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #350.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_58_7 = e2 & op(e1, e2) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (400) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_58_7 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (360), (401) imply:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) e2 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (383), (402) imply:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_58_11 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (64), (82), (95), (114), (123), (149),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (192), (198), (202), (403) are inconsistent
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #240.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_58_13 = e2 & op(e0, e2) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (43), (59), (64), (68), (82), (84), (114),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (149), (157), (238), (245), (367), (383),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) are inconsistent by sub-proof #229.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_58_9 = e2 & op(e3, e0) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (405) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_58_9 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (198), (406) are inconsistent by sub-proof
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1245.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_58_11 = e3 & op(e1, e0) = e3
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (82), (95), (114), (149), (157),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (198), (202), (407) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #243.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_58_13 = e2 & op(e0, e2) = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (408) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_58_13 = e2
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (245), (409) are inconsistent by sub-proof
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #320.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (95), (101), (149), (202), (355), (410) are
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #334.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | (411) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (411) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_58_8 = e0 & op(e1, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (412) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (413) op(e1, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (149), (240), (413) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1466.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_58_11 = e0 & op(e1, e0) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (414) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_58_11 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (64), (82), (95), (114), (123), (149),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (192), (198), (202), (415) are inconsistent
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #240.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | (416) all_58_12 = e1 & op(e0, e3) = e1
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (416) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | (417) all_58_12 = e1
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | (418) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (418) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (419) all_58_4 = e0 & op(e3, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (82), (114), (123), (134), (149),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (157), (180), (198), (419) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #348.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (420) all_58_5 = e0 & op(e2, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (420) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (421) all_58_5 = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (17), (35), (39), (43),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (51), (59), (61), (63), (64), (68), (74), (78),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (82), (84), (86), (90), (95), (101), (111), (114),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (123), (124), (140), (145), (149), (157), (160),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (180), (192), (198), (202), (221), (238), (245),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (249), (255), (417), (421) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #232.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | (422) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (422) gives:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (423) all_58_8 = e0 & op(e1, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (424) op(e1, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (149), (240), (424) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1466.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (425) all_58_14 = e0 & op(e0, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (425) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (426) op(e0, e1) = e0
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (64), (95), (101), (114), (149), (157),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | (202), (245), (417), (426) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #228.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | (427) all_58_3 = e3 & op(e2, e2) = e3
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (149), (200), (427) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | | sub-proof #1437.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | (428) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (49), (82), (95), (114), (149), (157),
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | (192), (198), (202), (239), (428) are inconsistent
% 156.57/26.94 | | | | | | | | | | | | | | | | | | | by sub-proof #295.
% 156.57/26.94 | | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | (429) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 156.57/26.94 | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 156.57/26.94 | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | ALPHA: (429) implies:
% 156.57/26.94 | | | | | | | | | | | | | | | | | | (430) ~ (all_28_1 = e0)
% 156.57/26.94 | | | | | | | | | | | | | | | | | | (431) op(e3, e3) = all_28_1
% 156.57/26.94 | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (181), (430), (431) are inconsistent by
% 156.57/26.94 | | | | | | | | | | | | | | | | | | sub-proof #227.
% 156.57/26.94 | | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | End of split
% 156.57/26.94 | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | Case 2:
% 156.57/26.94 | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | (432) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 156.57/26.94 | | | | | | | | | | $i(all_24_1)
% 156.57/26.94 | | | | | | | | | |
% 156.57/26.94 | | | | | | | | | | ALPHA: (432) implies:
% 156.81/26.94 | | | | | | | | | | (433) ~ (all_24_1 = e2)
% 156.81/26.94 | | | | | | | | | | (434) op(e0, e0) = all_24_1
% 156.81/26.94 | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | BETA: splitting (158) gives:
% 156.81/26.94 | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | Case 1:
% 156.81/26.94 | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | (435) all_54_15 = e3
% 156.81/26.94 | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | REF_CLOSE: (143), (191), (435) are inconsistent by sub-proof
% 156.81/26.94 | | | | | | | | | | | #1543.
% 156.81/26.94 | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | Case 2:
% 156.81/26.94 | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | (436) ~ (all_54_15 = e3)
% 156.81/26.94 | | | | | | | | | | | (437) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 156.81/26.94 | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | BETA: splitting (437) gives:
% 156.81/26.94 | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | Case 1:
% 156.81/26.94 | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | (438) all_54_15 = e2
% 156.81/26.94 | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | REF_CLOSE: (143), (202), (438) are inconsistent by sub-proof
% 156.81/26.94 | | | | | | | | | | | | #1542.
% 156.81/26.94 | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | Case 2:
% 156.81/26.94 | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | (439) ~ (all_54_15 = e2)
% 156.81/26.94 | | | | | | | | | | | | (440) all_54_15 = e1 | all_54_15 = e0
% 156.81/26.94 | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | BETA: splitting (440) gives:
% 156.81/26.94 | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | Case 1:
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | (441) all_54_15 = e1
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | REF_CLOSE: (143), (192), (441) are inconsistent by sub-proof
% 156.81/26.94 | | | | | | | | | | | | | #1541.
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | Case 2:
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | (442) all_54_15 = e0
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | COMBINE_EQS: (143), (442) imply:
% 156.81/26.94 | | | | | | | | | | | | | (443) all_4_2 = e0
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | SIMP: (443) implies:
% 156.81/26.94 | | | | | | | | | | | | | (444) all_4_2 = e0
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | COMBINE_EQS: (100), (444) imply:
% 156.81/26.94 | | | | | | | | | | | | | (445) all_56_15 = e0
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | REDUCE: (138), (444) imply:
% 156.81/26.94 | | | | | | | | | | | | | (446) ~ (all_52_7 = e0)
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | REDUCE: (104), (444) imply:
% 156.81/26.94 | | | | | | | | | | | | | (447) ~ (all_52_13 = e0)
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | REDUCE: (168), (444) imply:
% 156.81/26.94 | | | | | | | | | | | | | (448) ~ (all_52_14 = e0)
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | REDUCE: (191), (444) imply:
% 156.81/26.94 | | | | | | | | | | | | | (449) ~ (e3 = e0)
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | REDUCE: (192), (444) imply:
% 156.81/26.94 | | | | | | | | | | | | | (450) ~ (e1 = e0)
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | REDUCE: (95), (444) imply:
% 156.81/26.94 | | | | | | | | | | | | | (451) op(e0, e0) = e0
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e0, all_24_1, e0, e0,
% 156.81/26.94 | | | | | | | | | | | | | simplifying with (434), (451) gives:
% 156.81/26.94 | | | | | | | | | | | | | (452) all_24_1 = e0
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | REDUCE: (433), (452) imply:
% 156.81/26.94 | | | | | | | | | | | | | (453) ~ (e2 = e0)
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | BETA: splitting (72) gives:
% 156.81/26.94 | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | Case 1:
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | (454) ~ (all_28_2 = e3)
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | REDUCE: (107), (454) imply:
% 156.81/26.94 | | | | | | | | | | | | | | (455) ~ (all_6_2 = e3)
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (11), (14), (15), (16), (18),
% 156.81/26.94 | | | | | | | | | | | | | | (19), (32), (33), (34), (35), (38), (39), (41),
% 156.81/26.94 | | | | | | | | | | | | | | (43), (45), (49), (51), (55), (59), (60), (61),
% 156.81/26.94 | | | | | | | | | | | | | | (62), (63), (64), (66), (68), (73), (74), (76),
% 156.81/26.94 | | | | | | | | | | | | | | (77), (81), (82), (83), (84), (85), (86), (90),
% 156.81/26.94 | | | | | | | | | | | | | | (92), (95), (101), (106), (108), (109), (110),
% 156.81/26.94 | | | | | | | | | | | | | | (114), (118), (122), (123), (124), (125), (126),
% 156.81/26.94 | | | | | | | | | | | | | | (127), (128), (129), (131), (134), (135), (140),
% 156.81/26.94 | | | | | | | | | | | | | | (141), (145), (146), (147), (149), (150), (153),
% 156.81/26.94 | | | | | | | | | | | | | | (155), (156), (157), (162), (172), (177), (180),
% 156.81/26.94 | | | | | | | | | | | | | | (181), (184), (185), (187), (189), (192), (198),
% 156.81/26.94 | | | | | | | | | | | | | | (200), (202), (445), (446), (455) are inconsistent
% 156.81/26.94 | | | | | | | | | | | | | | by sub-proof #239.
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | Case 2:
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | (456) all_28_2 = e3
% 156.81/26.94 | | | | | | | | | | | | | | (457) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0
% 156.81/26.94 | | | | | | | | | | | | | | & op(e3, e3) = all_28_1 & $i(all_28_0) &
% 156.81/26.94 | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3, e3)
% 156.81/26.94 | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | COMBINE_EQS: (107), (456) imply:
% 156.81/26.94 | | | | | | | | | | | | | | (458) all_6_2 = e3
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | SIMP: (458) implies:
% 156.81/26.94 | | | | | | | | | | | | | | (459) all_6_2 = e3
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | COMBINE_EQS: (154), (459) imply:
% 156.81/26.94 | | | | | | | | | | | | | | (460) all_36_2 = e3
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | COMBINE_EQS: (131), (459) imply:
% 156.81/26.94 | | | | | | | | | | | | | | (461) all_56_14 = e3
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | REDUCE: (75), (459) imply:
% 156.81/26.94 | | | | | | | | | | | | | | (462) ~ (all_52_6 = e3)
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | REDUCE: (94), (459) imply:
% 156.81/26.94 | | | | | | | | | | | | | | (463) ~ (all_52_9 = e3)
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | REDUCE: (15), (459) imply:
% 156.81/26.94 | | | | | | | | | | | | | | (464) op(e1, e1) = e3
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 156.81/26.94 | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | Case 1:
% 156.81/26.94 | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | (465) ~ (all_36_2 = e3)
% 156.81/26.94 | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | REDUCE: (460), (465) imply:
% 156.81/26.94 | | | | | | | | | | | | | | | (466) $false
% 156.81/26.94 | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | CLOSE: (466) is inconsistent.
% 156.81/26.94 | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | Case 2:
% 156.81/26.94 | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | (467) ( ~ (all_36_0 = e0) & op(all_36_1, e1) = all_36_0
% 156.81/26.94 | | | | | | | | | | | | | | | & op(e3, e3) = all_36_1 & $i(all_36_0) &
% 156.81/26.94 | | | | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e2) & op(e3, e3)
% 156.81/26.94 | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 156.81/26.94 | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 156.81/26.94 | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | Case 1:
% 156.81/26.94 | | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | | (468) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 156.81/26.94 | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.81/26.94 | | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (145), (149), (184), (200), (468) are
% 156.81/26.94 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1436.
% 156.81/26.94 | | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | Case 2:
% 156.81/26.94 | | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | | (469) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 156.81/26.94 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 156.81/26.94 | | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | | BETA: splitting (469) gives:
% 156.81/26.94 | | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.94 | | | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | | | (470) all_58_7 = e3 & op(e1, e2) = e3
% 156.81/26.94 | | | | | | | | | | | | | | | | |
% 156.81/26.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (149), (462), (470) are inconsistent by
% 156.81/26.94 | | | | | | | | | | | | | | | | | sub-proof #1184.
% 156.81/26.95 | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | (471) all_58_13 = e3 & op(e0, e2) = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | ALPHA: (471) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | (472) all_58_13 = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | BETA: splitting (467) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | (473) ~ (all_36_0 = e0) & op(all_36_1, e1) = all_36_0 &
% 156.81/26.95 | | | | | | | | | | | | | | | | | | op(e3, e3) = all_36_1 & $i(all_36_0) &
% 156.81/26.95 | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | ALPHA: (473) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | (474) op(e3, e3) = all_36_1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | (475) op(all_36_1, e1) = all_36_0
% 156.81/26.95 | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | (476) ~ (all_56_14 = e3)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | REDUCE: (461), (476) imply:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | (477) $false
% 156.81/26.95 | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | CLOSE: (477) is inconsistent.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | (478) all_56_6 = e1 & op(e1, e3) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | ALPHA: (478) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | (479) op(e1, e3) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | (480) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (480) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (481) all_58_6 = e0 & op(e1, e3) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (481) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (482) all_58_6 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (16), (17), (35), (39),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (43), (49), (51), (59), (60), (61), (63), (64),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (68), (74), (78), (82), (83), (84), (86), (90),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (95), (101), (109), (111), (114), (123), (124),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (134), (140), (145), (149), (157), (160), (180),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (192), (198), (200), (202), (446), (462), (463),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (464), (472), (479), (482) are inconsistent by
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | sub-proof #222.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (483) all_58_7 = e0 & op(e1, e2) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | (484) all_58_7 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | (485) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (485) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | (486) all_58_2 = e3 & op(e2, e3) = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (486) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | (487) op(e2, e3) = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | (488) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (488) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_58_4 = e0 & op(e3, e1) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (82), (114), (123), (134), (149),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | (157), (180), (198), (489) are inconsistent by
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #348.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | (490) all_58_5 = e0 & op(e2, e1) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (490) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_58_5 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | (492) op(e2, e1) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (493) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (493) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_58_0 = e2 & op(e3, e3) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (180), (494) are inconsistent by sub-proof
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_58_1 = e2 & op(e3, e2) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (495) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_58_1 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (82), (114), (123), (124), (145), (149),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (472), (484), (496) are inconsistent by sub-proof
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | #322.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (497) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (497) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_58_4 = e2 & op(e3, e1) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (498) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_58_4 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) op(e3, e1) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (82), (84), (149), (462), (479), (501) are
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_58_8 = e3 & op(e1, e1) = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (503) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_58_8 = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (124), (145), (149), (487), (505) are
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1122.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (506) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_58_5 = e1 & op(e2, e1) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (491), (507) are inconsistent by sub-proof
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1121.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_58_10 = e1 & op(e2, e0) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (508) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_58_10 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) op(e2, e0) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (123), (149), (491), (500), (511) are
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #299.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (512) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_58_8 = e1 & op(e1, e1) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (513) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) all_58_8 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (504), (514) are inconsistent by sub-proof
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #950.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_58_14 = e1 & op(e0, e1) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (515) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_58_14 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) op(e0, e1) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (157), (198), (509), (518) are inconsistent
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #221.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (519) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_58_11 = e2 & op(e1, e0) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (520) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) all_58_11 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) op(e1, e0) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (523) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_58_6 = e1 & op(e1, e3) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (524) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_58_6 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_58_12 = e2 & op(e0, e3) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (527) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_58_12 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_2 = e2 & op(e2, e3) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (530) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) op(e2, e3) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (51), (59), (82), (149), (157), (180),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525), (528), (531) are inconsistent by sub-proof
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1067.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_58_3 = e2 & op(e2, e2) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) all_58_3 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) op(e2, e2) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_11, e1, e1, e0,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (101), (517) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_52_11 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_14, e2, e0, e1,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (141), (522) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_52_14 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_2, e1, e3, e1,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (74), (479) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_52_2 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_13, e1, e0, e2,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (76), (510) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_52_13 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_9, e0, e1, e2,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (49), (492) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_52_9 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_8_2, e2, e2, e2,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (145), (534) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_8_2 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_1, e3, e3, e2,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (51), (487) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) all_52_1 = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e0, all_36_1, e3, e3,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (181), (474) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_36_1 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (540) imply:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_56_13 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (538) imply:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) ~ (e3 = e1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (540) imply:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) ~ (e3 = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (475), (542) imply:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) op(e0, e1) = all_36_0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (32), (35), (39), (43), (51),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (59), (61), (64), (68), (74), (78), (82), (84),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (95), (114), (123), (124), (134), (140),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (149), (157), (177), (180), (192), (198),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (445), (446), (462), (472), (479), (499),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504), (521), (525), (528), (533), (547) are
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (548) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (549) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (550) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) op(e2, e1) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (64), (114), (149), (157), (181), (198),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433), (434), (457), (492), (509), (521), (551)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #220.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (445), (543), (552) are inconsistent by sub-proof
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #233.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (553) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) op(e0, e2) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (149), (446), (555) are inconsistent by
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1532.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (556) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (557) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) ~ (all_56_15 = e0)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (445), (558) imply:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) $false
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (559) is inconsistent.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) ~ (all_56_14 = e1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) op(e0, e1) = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e1, all_36_0, e1, e0,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (517), (546) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_36_0 = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e0, all_36_0, e1, e0,
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (546), (562) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) all_36_0 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (563), (564) imply:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) e1 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (565) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) e1 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (525), (566) imply:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_58_6 = e0
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (16), (17), (35), (39),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (51), (59), (60), (61), (63), (64), (68),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (74), (78), (82), (84), (86), (90), (95), (101),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (114), (123), (124), (140), (145), (149),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (160), (180), (192), (198), (202), (446),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462), (472), (479), (487), (491), (516), (567)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #225.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (568) gives:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) all_58_5 = e2 & op(e2, e1) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (569) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) op(e2, e1) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (64), (114), (149), (157), (181), (198),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433), (434), (457), (492), (509), (521), (570)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #220.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_58_10 = e2 & op(e2, e0) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (571) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) all_58_10 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (82), (95), (114), (149), (192), (198),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (572) are inconsistent by sub-proof #248.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_58_13 = e2 & op(e0, e2) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (43), (59), (64), (68), (82), (84), (114),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (149), (157), (462), (472), (504), (521),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) are inconsistent by sub-proof #229.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (17), (43), (59), (64), (68), (82),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (101), (111), (114), (123), (149), (157),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (198), (462), (491), (500), (504), (509),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (574) are inconsistent by sub-proof #219.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_58_7 = e1 & op(e1, e2) = e1
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (82), (95), (114), (123), (149), (192),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (484), (509), (521), (575) are inconsistent
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #218.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (43), (59), (64), (68), (82), (84),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (123), (149), (157), (160), (198), (462),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504), (509), (521), (576) are inconsistent by
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #217.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_58_15 = e2 & op(e0, e0) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (577) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) op(e0, e0) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (433), (434), (578) are inconsistent by
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #317.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_58_11 = e3 & op(e1, e0) = e3
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (82), (95), (114), (149), (157),
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (198), (433), (434), (579) are inconsistent
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #316.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_58_9 = e2 & op(e3, e0) = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (580) implies:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_58_9 = e2
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (198), (581) are inconsistent by sub-proof
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1245.
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | (582) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 156.81/26.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (59), (63), (64), (82), (95), (101), (114),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | | | (123), (149), (157), (192), (202), (464), (472),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | | | (582) are inconsistent by sub-proof #223.
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | | (583) all_58_3 = e3 & op(e2, e2) = e3
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (149), (200), (583) are inconsistent by
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1437.
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | (584) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (49), (82), (95), (114), (149), (157),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | (192), (198), (202), (463), (584) are inconsistent
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #295.
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | (585) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (59), (64), (82), (95), (114), (123),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | (149), (157), (192), (198), (433), (434), (464),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | (585) are inconsistent by sub-proof #296.
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | End of split
% 156.81/26.96 | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.96 | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | (586) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 &
% 156.81/26.96 | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 156.81/26.96 | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | ALPHA: (586) implies:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | (587) ~ (all_36_1 = e2)
% 156.81/26.96 | | | | | | | | | | | | | | | | | | (588) op(e3, e3) = all_36_1
% 156.81/26.96 | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 156.81/26.96 | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | (589) ~ (all_56_14 = e3)
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | REDUCE: (461), (589) imply:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | (590) $false
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | CLOSE: (590) is inconsistent.
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | (591) all_56_6 = e1 & op(e1, e3) = e1
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | ALPHA: (591) implies:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | (592) op(e1, e3) = e1
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | (593) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (593) gives:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (594) all_58_6 = e0 & op(e1, e3) = e0
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (595) all_58_6 = e0
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (16), (17), (35), (39),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (43), (49), (51), (59), (60), (61), (63), (64),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (68), (74), (78), (82), (83), (84), (86), (90),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (95), (101), (109), (111), (114), (123), (124),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (134), (140), (145), (149), (157), (160), (180),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (192), (198), (200), (202), (446), (462), (463),
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (464), (472), (592), (595) are inconsistent by
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | sub-proof #222.
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.81/26.96 | | | | | | | | | | | | | | | | | | | | | (596) all_58_7 = e0 & op(e1, e2) = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | (597) all_58_7 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | (598) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (598) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | (599) all_58_2 = e3 & op(e2, e3) = e3
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (599) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | (600) op(e2, e3) = e3
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | (601) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (601) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | (602) all_58_4 = e0 & op(e3, e1) = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (82), (114), (123), (134), (149),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | (157), (180), (198), (602) are inconsistent by
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #348.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | (603) all_58_5 = e0 & op(e2, e1) = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (603) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_58_5 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | (605) op(e2, e1) = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (606) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (606) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_58_0 = e2 & op(e3, e3) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (607) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) op(e3, e3) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (587), (588), (608) are inconsistent by
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #951.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_58_1 = e2 & op(e3, e2) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (609) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_58_1 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (82), (114), (123), (124), (145), (149),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (472), (597), (610) are inconsistent by sub-proof
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | #322.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (611) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_58_4 = e2 & op(e3, e1) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (612) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_58_4 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) op(e3, e1) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (82), (84), (149), (462), (592), (615) are
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (616) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_58_8 = e3 & op(e1, e1) = e3
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (617) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) all_58_8 = e3
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (124), (145), (149), (600), (619) are
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1122.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (620) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_58_5 = e1 & op(e2, e1) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (604), (621) are inconsistent by sub-proof
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1121.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_58_10 = e1 & op(e2, e0) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (622) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_58_10 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) op(e2, e0) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (123), (149), (604), (614), (625) are
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #299.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_58_8 = e1 & op(e1, e1) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (627) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_58_8 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (618), (628) are inconsistent by sub-proof
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #950.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_58_14 = e1 & op(e0, e1) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (629) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) op(e0, e1) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (157), (198), (623), (631) are inconsistent
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #221.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (632) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_58_11 = e2 & op(e1, e0) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (633) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_58_11 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (635) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) all_58_6 = e1 & op(e1, e3) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (636) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) all_58_6 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_58_12 = e2 & op(e0, e3) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (639) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) all_58_12 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (641) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_58_2 = e2 & op(e2, e3) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (642) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) op(e2, e3) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (51), (59), (82), (149), (157), (180),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (640), (643) are inconsistent by sub-proof
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1067.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) all_58_3 = e2 & op(e2, e2) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (644) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_58_3 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) op(e2, e2) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_11, e1, e1, e0,
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (101), (630) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) all_52_11 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_2, e1, e3, e1,
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (74), (592) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_52_2 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_13, e1, e0, e2,
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (76), (624) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_52_13 = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_9, e0, e1, e2,
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (49), (605) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_52_9 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_8_2, e2, e2, e2,
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (145), (646) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_8_2 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e0, all_36_1, e3, e3,
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (181), (588) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_36_1 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (651) imply:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_56_13 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (649) imply:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) ~ (e3 = e1)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (651) imply:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) ~ (e3 = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (32), (35), (39), (43), (51),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (59), (61), (64), (68), (74), (78), (82), (84),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (95), (114), (123), (124), (134), (140),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (149), (157), (177), (180), (192), (198),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (445), (446), (462), (472), (592), (613),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618), (634), (637), (640), (645), (656) are
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (657) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (658) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (659) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) op(e2, e1) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (64), (114), (149), (157), (181), (198),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433), (434), (457), (605), (623), (634), (660)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #220.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (445), (653), (661) are inconsistent by sub-proof
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #233.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (662) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (663) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) op(e0, e2) = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (149), (446), (664) are inconsistent by
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1532.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (665) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (666) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) ~ (all_56_15 = e0)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (445), (667) imply:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) $false
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (668) is inconsistent.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (669) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) ~ (all_56_14 = e1)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) op(e0, e1) = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e1, e0, e1, e0,
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (630), (671) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) e1 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (623), (672) imply:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_58_10 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (82), (95), (114), (123), (149), (192),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (634), (673) are inconsistent by sub-proof
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #350.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (674) gives:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_58_5 = e2 & op(e2, e1) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (675) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) all_58_5 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (604), (676) imply:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) e2 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (677) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) e2 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (634), (678) imply:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_58_11 = e0
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (64), (114), (149), (157), (198), (433),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434), (623), (679) are inconsistent by sub-proof
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_58_10 = e2 & op(e2, e0) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (680) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_58_10 = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (82), (95), (114), (149), (192), (198),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (681) are inconsistent by sub-proof #248.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_58_13 = e2 & op(e0, e2) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (43), (59), (64), (68), (82), (84), (114),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (149), (157), (462), (472), (618), (634),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) are inconsistent by sub-proof #229.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (17), (43), (59), (64), (68), (82),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (101), (111), (114), (123), (149), (157),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (198), (462), (604), (614), (618), (623),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (683) are inconsistent by sub-proof #219.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) all_58_7 = e1 & op(e1, e2) = e1
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (82), (95), (114), (123), (149), (192),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (597), (623), (634), (684) are inconsistent
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #218.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (43), (59), (64), (68), (82), (84),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (123), (149), (157), (160), (198), (462),
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618), (623), (634), (685) are inconsistent by
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #217.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_58_15 = e2 & op(e0, e0) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (686) implies:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) op(e0, e0) = e2
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (433), (434), (687) are inconsistent by
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #317.
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) all_58_11 = e3 & op(e1, e0) = e3
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (82), (95), (114), (149), (157),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (198), (433), (434), (688) are inconsistent
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #316.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) all_58_9 = e2 & op(e3, e0) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (689) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) all_58_9 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (198), (690) are inconsistent by sub-proof
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1245.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | (691) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (59), (63), (64), (82), (95), (101), (114),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | (123), (149), (157), (192), (202), (464), (472),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | (691) are inconsistent by sub-proof #223.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | (692) all_58_3 = e3 & op(e2, e2) = e3
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (149), (200), (692) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1437.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | (693) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (49), (82), (95), (114), (149), (157),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | (192), (198), (202), (463), (693) are inconsistent
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #295.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | (694) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (59), (64), (82), (95), (114), (123),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | (149), (157), (192), (198), (433), (434), (464),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | (694) are inconsistent by sub-proof #296.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | End of split
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | (695) all_20_2 = e2
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | COMBINE_EQS: (144), (695) imply:
% 156.85/26.97 | | | | | | | | (696) all_4_2 = e2
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | COMBINE_EQS: (100), (696) imply:
% 156.85/26.97 | | | | | | | | (697) all_56_15 = e2
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | REDUCE: (152), (696) imply:
% 156.85/26.97 | | | | | | | | (698) ~ (all_52_11 = e2)
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | REDUCE: (104), (696) imply:
% 156.85/26.97 | | | | | | | | (699) ~ (all_52_13 = e2)
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | REDUCE: (168), (696) imply:
% 156.85/26.97 | | | | | | | | (700) ~ (all_52_14 = e2)
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | REDUCE: (95), (696) imply:
% 156.85/26.97 | | | | | | | | (701) op(e0, e0) = e2
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | BETA: splitting (30) gives:
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | | (702) ~ (all_24_2 = e0)
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | | REDUCE: (50), (702) imply:
% 156.85/26.97 | | | | | | | | | (703) $false
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | | CLOSE: (703) is inconsistent.
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | | (704) ( ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 &
% 156.85/26.97 | | | | | | | | | op(e0, e0) = all_24_1 & $i(all_24_0) &
% 156.85/26.97 | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e2) & op(e0, e0) =
% 156.85/26.97 | | | | | | | | | all_24_1 & $i(all_24_1))
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | | BETA: splitting (42) gives:
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | (705) ~ (all_56_15 = e2)
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | REDUCE: (697), (705) imply:
% 156.85/26.97 | | | | | | | | | | (706) $false
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | CLOSE: (706) is inconsistent.
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | (707) all_56_10 = e0 & op(e0, e2) = e0
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | ALPHA: (707) implies:
% 156.85/26.97 | | | | | | | | | | (708) op(e0, e2) = e0
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | BETA: splitting (704) gives:
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | (709) ~ (all_24_0 = e1) & op(all_24_1, e3) = all_24_0 &
% 156.85/26.97 | | | | | | | | | | | op(e0, e0) = all_24_1 & $i(all_24_0) &
% 156.85/26.97 | | | | | | | | | | | $i(all_24_1)
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | ALPHA: (709) implies:
% 156.85/26.97 | | | | | | | | | | | (710) ~ (all_24_0 = e1)
% 156.85/26.97 | | | | | | | | | | | (711) op(e0, e0) = all_24_1
% 156.85/26.97 | | | | | | | | | | | (712) op(all_24_1, e3) = all_24_0
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | BETA: splitting (127) gives:
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | (713) ~ (all_56_13 = e0)
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | REDUCE: (45), (713) imply:
% 156.85/26.97 | | | | | | | | | | | | (714) ~ (all_8_2 = e0)
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | BETA: splitting (77) gives:
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | (715) all_54_5 = e3
% 156.85/26.97 | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | REF_CLOSE: (150), (200), (715) are inconsistent by sub-proof
% 156.85/26.97 | | | | | | | | | | | | | #1161.
% 156.85/26.97 | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | (716) ~ (all_54_5 = e3)
% 156.85/26.97 | | | | | | | | | | | | | (717) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 156.85/26.97 | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | BETA: splitting (717) gives:
% 156.85/26.97 | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | (718) all_54_5 = e2
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | COMBINE_EQS: (150), (718) imply:
% 156.85/26.97 | | | | | | | | | | | | | | (719) all_8_2 = e2
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | SIMP: (719) implies:
% 156.85/26.97 | | | | | | | | | | | | | | (720) all_8_2 = e2
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | COMBINE_EQS: (45), (720) imply:
% 156.85/26.97 | | | | | | | | | | | | | | (721) all_56_13 = e2
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | REDUCE: (33), (720) imply:
% 156.85/26.97 | | | | | | | | | | | | | | (722) ~ (all_52_1 = e2)
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | REDUCE: (106), (720) imply:
% 156.85/26.97 | | | | | | | | | | | | | | (723) ~ (all_52_4 = e2)
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | REDUCE: (81), (720) imply:
% 156.85/26.97 | | | | | | | | | | | | | | (724) ~ (all_52_6 = e2)
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | REDUCE: (126), (720) imply:
% 156.85/26.97 | | | | | | | | | | | | | | (725) ~ (all_52_7 = e2)
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | REDUCE: (153), (720) imply:
% 156.85/26.97 | | | | | | | | | | | | | | (726) ~ (all_52_9 = e2)
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | REDUCE: (200), (720) imply:
% 156.85/26.97 | | | | | | | | | | | | | | (727) ~ (e3 = e2)
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | (728) all_54_1 = e3
% 156.85/26.97 | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | REF_CLOSE: (38), (184), (728) are inconsistent by sub-proof
% 156.85/26.97 | | | | | | | | | | | | | | | #1305.
% 156.85/26.97 | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | (729) ~ (all_54_1 = e3)
% 156.85/26.97 | | | | | | | | | | | | | | | (730) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 156.85/26.97 | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 156.85/26.97 | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | (731) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | BETA: splitting (731) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | (732) all_58_2 = e2 & op(e2, e3) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | ALPHA: (732) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | (733) op(e2, e3) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (149), (722), (733) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | | | | | | sub-proof #1544.
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | (734) all_58_3 = e2 & op(e2, e2) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | ALPHA: (734) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | (735) all_58_3 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | (736) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 156.85/26.97 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (149), (157), (198), (699), (736) are
% 156.85/26.97 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #294.
% 156.85/26.97 | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | (737) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 156.85/26.97 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | BETA: splitting (737) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | (738) all_58_11 = e2 & op(e1, e0) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | ALPHA: (738) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | (739) op(e1, e0) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (149), (700), (739) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | sub-proof #1389.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | (740) all_58_15 = e2 & op(e0, e0) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | ALPHA: (740) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | (741) all_58_15 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | (742) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (742) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | (743) all_58_4 = e2 & op(e3, e1) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (743) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | (744) all_58_4 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | (745) op(e3, e1) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | (746) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (746) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | (747) all_58_6 = e2 & op(e1, e3) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (747) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | (748) all_58_6 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | (749) op(e1, e3) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | (750) all_54_1 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (723), (750) are inconsistent by sub-proof
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | #1304.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | (751) ~ (all_54_1 = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | (752) all_54_1 = e1 | all_54_1 = e0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_54_1 = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (753) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_52_4 = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (754) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_52_4 = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (755) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (756) ~ (all_52_6 = e1)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (756) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (757) ~ (all_52_6 = e1)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (755) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (758) ~ (all_52_7 = e1)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (758) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (759) ~ (all_52_7 = e1)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (755) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (760) ~ (e3 = e1)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (723), (755) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (761) ~ (e2 = e1)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (762) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (762) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_58_0 = e1 & op(e3, e3) = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (180), (763) are inconsistent by sub-proof
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1495.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_58_1 = e1 & op(e3, e2) = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (764) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_58_1 = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with e2, all_24_1, e0, e0,
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (701), (711) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_24_1 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_7, e0, e2, e0,
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (140), (708) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) all_52_7 = e0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_2, e2, e3, e1,
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (74), (749) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) all_52_2 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (768) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) ~ (all_52_3 = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (769) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) ~ (all_52_3 = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (768) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) ~ (all_52_6 = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (768) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) ~ (all_6_2 = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (767) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) ~ (all_52_3 = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (767) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) ~ (all_52_6 = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (767) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) ~ (all_52_11 = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (775) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) ~ (all_52_11 = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (725), (767) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) ~ (e2 = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (759), (767) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) ~ (e1 = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (712), (766) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) op(e2, e3) = all_24_0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) ~ (all_56_14 = e3)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (780) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) ~ (all_6_2 = e3)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_52_1, all_24_0, e3,
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (51), (779) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_52_1 = all_24_0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (782) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_54_4 = all_24_0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (782) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) ~ (all_52_3 = all_24_0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (784) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) ~ (all_52_3 = all_24_0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (782) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) ~ (all_52_9 = all_24_0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (786) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) ~ (all_52_9 = all_24_0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (722), (782) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) ~ (all_24_0 = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (782) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) ~ (all_24_0 = e0)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_54_4 = e3
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (783), (790) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_24_0 = e3
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (785), (791) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) ~ (all_52_3 = e3)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (787), (791) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) ~ (all_52_9 = e3)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (779), (791) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) op(e2, e3) = e3
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (11), (15), (16), (19), (20), (32),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (49), (59), (60), (64), (65), (66), (76),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (82), (84), (85), (92), (101), (102), (109),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (115), (123), (124), (129), (131), (134),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (140), (145), (149), (151), (157), (164),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (166), (176), (180), (198), (200), (698),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699), (701), (708), (721), (723), (724), (735),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744), (745), (748), (757), (765), (770), (773),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776), (781), (792), (793), (794) are inconsistent
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #291.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (795) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_54_4 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (783), (796) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_24_0 = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (788), (797) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) $false
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (798) is inconsistent.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) all_54_4 = e1 | all_54_4 = e0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (799) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) all_54_4 = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (783), (800) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) all_24_0 = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (710), (801) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) $false
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (802) is inconsistent.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) all_54_4 = e0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (783), (803) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) all_24_0 = e0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (789), (804) imply:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) $false
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (805) is inconsistent.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_56_14 = e3
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (22), (38), (41), (75), (90), (131), (161),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (723), (724), (774), (806) are inconsistent
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (807) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (114), (149), (198), (745), (807) are
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #289.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_54_1 = e0
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (90), (808) are inconsistent by sub-proof
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | | #1115.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | (809) all_58_7 = e2 & op(e1, e2) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (809) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | (810) op(e1, e2) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (149), (724), (810) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1536.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | (811) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (15), (59), (64), (82), (114), (123), (129),
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | (149), (160), (198), (741), (811) are inconsistent
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #656.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | (812) all_58_5 = e2 & op(e2, e1) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (812) implies:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | (813) op(e2, e1) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (149), (726), (813) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | sub-proof #1441.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | (814) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (814) gives:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | (815) all_58_8 = e2 & op(e1, e1) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (129), (149), (815) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | sub-proof #1440.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | (816) all_58_14 = e2 & op(e0, e1) = e2
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (149), (698), (816) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | | sub-proof #1175.
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | (817) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 156.85/26.97 | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 156.85/26.97 | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | | REF_CLOSE: (49), (76), (149), (699), (726), (817) are
% 156.85/26.97 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1240.
% 156.85/26.97 | | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | (818) all_54_5 = e1 | all_54_5 = e0
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | | REF_CLOSE: (124), (150), (714), (818) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | | | sub-proof #1239.
% 156.85/26.97 | | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | (819) all_56_5 = e2 & op(e2, e0) = e2
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | ALPHA: (819) implies:
% 156.85/26.97 | | | | | | | | | | | | (820) op(e2, e0) = e2
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | | REF_CLOSE: (76), (149), (699), (820) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | | sub-proof #1535.
% 156.85/26.97 | | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | Case 2:
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | (821) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 156.85/26.97 | | | | | | | | | | | $i(all_24_1)
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | ALPHA: (821) implies:
% 156.85/26.97 | | | | | | | | | | | (822) ~ (all_24_1 = e2)
% 156.85/26.97 | | | | | | | | | | | (823) op(e0, e0) = all_24_1
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | | REF_CLOSE: (149), (701), (822), (823) are inconsistent by
% 156.85/26.97 | | | | | | | | | | | sub-proof #317.
% 156.85/26.97 | | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | | |
% 156.85/26.97 | | | | | | | | | End of split
% 156.85/26.97 | | | | | | | | |
% 156.85/26.97 | | | | | | | | End of split
% 156.85/26.97 | | | | | | | |
% 156.85/26.97 | | | | | | | End of split
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | Case 2:
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | (824) all_14_2 = e3
% 156.85/26.97 | | | | | | | (825) ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 156.85/26.97 | | | | | | | op(e3, e3) = all_14_1 & $i(all_14_0) & $i(all_14_1)) |
% 156.85/26.97 | | | | | | | ( ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 &
% 156.85/26.97 | | | | | | | $i(all_14_1))
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | COMBINE_EQS: (9), (824) imply:
% 156.85/26.97 | | | | | | | (826) all_8_2 = e3
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | SIMP: (826) implies:
% 156.85/26.97 | | | | | | | (827) all_8_2 = e3
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | COMBINE_EQS: (117), (827) imply:
% 156.85/26.97 | | | | | | | (828) all_22_2 = e3
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | COMBINE_EQS: (45), (827) imply:
% 156.85/26.97 | | | | | | | (829) all_56_13 = e3
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | REDUCE: (33), (827) imply:
% 156.85/26.97 | | | | | | | (830) ~ (all_52_1 = e3)
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | REDUCE: (81), (827) imply:
% 156.85/26.97 | | | | | | | (831) ~ (all_52_6 = e3)
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | REDUCE: (126), (827) imply:
% 156.85/26.97 | | | | | | | (832) ~ (all_52_7 = e3)
% 156.85/26.97 | | | | | | |
% 156.85/26.97 | | | | | | | REDUCE: (153), (827) imply:
% 156.85/26.97 | | | | | | | (833) ~ (all_52_9 = e3)
% 156.85/26.97 | | | | | | |
% 156.85/26.98 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11),
% 156.85/26.98 | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 156.85/26.98 | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 156.85/26.98 | | | | | | | (31), (32), (34), (35), (38), (39), (40), (41), (42),
% 156.85/26.98 | | | | | | | (43), (44), (46), (47), (48), (49), (51), (52), (53),
% 156.85/26.98 | | | | | | | (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 156.85/26.98 | | | | | | | (63), (64), (65), (66), (67), (68), (70), (71), (72),
% 156.85/26.98 | | | | | | | (74), (75), (76), (78), (79), (80), (82), (83), (84),
% 156.85/26.98 | | | | | | | (85), (86), (88), (89), (90), (91), (92), (93), (94),
% 156.85/26.98 | | | | | | | (95), (96), (97), (98), (100), (101), (102), (103),
% 156.85/26.98 | | | | | | | (104), (105), (107), (108), (109), (110), (111), (112),
% 156.85/26.98 | | | | | | | (113), (114), (115), (116), (118), (120), (121), (122),
% 156.85/26.98 | | | | | | | (123), (124), (125), (128), (129), (130), (131), (132),
% 156.85/26.98 | | | | | | | (133), (134), (136), (137), (138), (139), (140), (141),
% 156.85/26.98 | | | | | | | (142), (143), (144), (145), (146), (147), (148), (149),
% 156.85/26.98 | | | | | | | (151), (152), (155), (156), (158), (159), (160), (161),
% 156.85/26.98 | | | | | | | (163), (164), (165), (166), (168), (169), (170), (171),
% 156.85/26.98 | | | | | | | (172), (176), (180), (181), (184), (185), (187), (191),
% 156.85/26.98 | | | | | | | (192), (198), (825), (828), (829), (830), (831), (832),
% 156.85/26.98 | | | | | | | (833) are inconsistent by sub-proof #260.
% 156.85/26.98 | | | | | | |
% 156.85/26.98 | | | | | | End of split
% 156.85/26.98 | | | | | |
% 156.85/26.98 | | | | | End of split
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | End of split
% 156.85/26.98 | | | |
% 156.85/26.98 | | | Case 2:
% 156.85/26.98 | | | |
% 156.85/26.98 | | | | (834) all_58_1 = e0 & op(e3, e2) = e0
% 156.85/26.98 | | | |
% 156.85/26.98 | | | | REF_CLOSE: (39), (90), (149), (834) are inconsistent by sub-proof #1221.
% 156.85/26.98 | | | |
% 156.85/26.98 | | | End of split
% 156.85/26.98 | | |
% 156.85/26.98 | | Case 2:
% 156.85/26.98 | | |
% 156.85/26.98 | | | (835) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 156.85/26.98 | | | e0)
% 156.85/26.98 | | |
% 156.85/26.98 | | | REF_CLOSE: (6), (59), (70), (128), (149), (177), (835) are inconsistent by
% 156.85/26.98 | | | sub-proof #257.
% 156.85/26.98 | | |
% 156.85/26.98 | | End of split
% 156.85/26.98 | |
% 156.85/26.98 | End of split
% 156.85/26.98 |
% 156.85/26.98 End of proof
% 156.85/26.98
% 156.85/26.98 Sub-proof #217 shows that the following formulas are inconsistent:
% 156.85/26.98 ----------------------------------------------------------------
% 156.85/26.98 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/26.98 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/26.98 (2) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/26.98 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/26.98 (3) all_58_8 = e3
% 156.85/26.98 (4) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/26.98 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/26.98 (5) ~ (e3 = e0)
% 156.85/26.98 (6) ~ (e2 = e0)
% 156.85/26.98 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/26.98 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/26.98 (8) all_58_9 = e3
% 156.85/26.98 (9) ~ (e3 = e1)
% 156.85/26.98 (10) op(e1, e2) = all_52_6
% 156.85/26.98 (11) all_58_10 = e1
% 156.85/26.98 (12) all_58_11 = e2
% 156.85/26.98 (13) ~ (e2 = e1)
% 156.85/26.98 (14) ~ (e1 = e0)
% 156.85/26.98 (15) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/26.98 (16) ~ (all_52_6 = e3)
% 156.85/26.98 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.98 (18) ~ (e3 = e2)
% 156.85/26.98 (19) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/26.98 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/26.98 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/26.98 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/26.98
% 156.85/26.98 Begin of proof
% 156.85/26.98 |
% 156.85/26.98 | BETA: splitting (15) gives:
% 156.85/26.98 |
% 156.85/26.98 | Case 1:
% 156.85/26.98 | |
% 156.85/26.98 | | (20) all_58_8 = e1 & op(e1, e1) = e1
% 156.85/26.98 | |
% 156.85/26.98 | | ALPHA: (20) implies:
% 156.85/26.98 | | (21) all_58_8 = e1
% 156.85/26.98 | |
% 156.85/26.98 | | COMBINE_EQS: (3), (21) imply:
% 156.85/26.98 | | (22) e3 = e1
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.85/26.98 | | (13), (14), (16), (17), (18), (19), (22) are inconsistent by
% 156.85/26.98 | | sub-proof #297.
% 156.85/26.98 | |
% 156.85/26.98 | Case 2:
% 156.85/26.98 | |
% 156.85/26.98 | | (23) all_58_11 = e1 & op(e1, e0) = e1
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (12), (13), (23) are inconsistent by sub-proof #1455.
% 156.85/26.98 | |
% 156.85/26.98 | End of split
% 156.85/26.98 |
% 156.85/26.98 End of proof
% 156.85/26.98
% 156.85/26.98 Sub-proof #218 shows that the following formulas are inconsistent:
% 156.85/26.98 ----------------------------------------------------------------
% 156.85/26.98 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/26.98 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.98 (2) all_58_7 = e0
% 156.85/26.98 (3) all_58_9 = e3
% 156.85/26.98 (4) all_58_7 = e1 & op(e1, e2) = e1
% 156.85/26.98 (5) ~ (e3 = e1)
% 156.85/26.98 (6) ~ (all_4_2 = e1)
% 156.85/26.98 (7) all_58_10 = e1
% 156.85/26.98 (8) op(e0, e0) = all_4_2
% 156.85/26.98 (9) all_58_11 = e2
% 156.85/26.98 (10) ~ (e2 = e1)
% 156.85/26.98 (11) ~ (e1 = e0)
% 156.85/26.98 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.98
% 156.85/26.98 Begin of proof
% 156.85/26.98 |
% 156.85/26.98 | ALPHA: (4) implies:
% 156.85/26.98 | (13) all_58_7 = e1
% 156.85/26.98 |
% 156.85/26.98 | COMBINE_EQS: (2), (13) imply:
% 156.85/26.98 | (14) e1 = e0
% 156.85/26.98 |
% 156.85/26.98 | COMBINE_EQS: (7), (14) imply:
% 156.85/26.98 | (15) all_58_10 = e0
% 156.85/26.98 |
% 156.85/26.98 | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (15) are
% 156.85/26.98 | inconsistent by sub-proof #350.
% 156.85/26.98 |
% 156.85/26.98 End of proof
% 156.85/26.98
% 156.85/26.98 Sub-proof #219 shows that the following formulas are inconsistent:
% 156.85/26.98 ----------------------------------------------------------------
% 156.85/26.98 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/26.98 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/26.98 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/26.98 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.98 (3) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/26.98 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/26.98 (4) all_58_8 = e3
% 156.85/26.98 (5) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/26.98 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/26.98 (6) op(e3, e1) = e2
% 156.85/26.98 (7) ~ (e3 = e0)
% 156.85/26.98 (8) ~ (e2 = e0)
% 156.85/26.98 (9) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/26.98 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/26.98 (10) all_58_9 = e3
% 156.85/26.98 (11) ~ (e3 = e1)
% 156.85/26.98 (12) op(e1, e2) = all_52_6
% 156.85/26.98 (13) all_58_10 = e1
% 156.85/26.98 (14) all_58_5 = e0
% 156.85/26.98 (15) op(e0, e1) = all_52_11
% 156.85/26.98 (16) all_58_11 = e2
% 156.85/26.98 (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.85/26.98 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.85/26.98 (18) ~ (e2 = e1)
% 156.85/26.98 (19) ~ (e1 = e0)
% 156.85/26.98 (20) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.98 (21) ~ (all_52_6 = e3)
% 156.85/26.98 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.98 (23) ~ (e3 = e2)
% 156.85/26.98 (24) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/26.98 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/26.98 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/26.98 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/26.98
% 156.85/26.98 Begin of proof
% 156.85/26.98 |
% 156.85/26.98 | BETA: splitting (20) gives:
% 156.85/26.98 |
% 156.85/26.98 | Case 1:
% 156.85/26.98 | |
% 156.85/26.98 | | (25) all_58_14 = e2 & op(e0, e1) = e2
% 156.85/26.98 | |
% 156.85/26.98 | | ALPHA: (25) implies:
% 156.85/26.98 | | (26) op(e0, e1) = e2
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 156.85/26.98 | | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (26)
% 156.85/26.98 | | are inconsistent by sub-proof #298.
% 156.85/26.98 | |
% 156.85/26.98 | Case 2:
% 156.85/26.98 | |
% 156.85/26.98 | | (27) all_58_15 = e2 & op(e0, e0) = e2
% 156.85/26.98 | |
% 156.85/26.98 | | ALPHA: (27) implies:
% 156.85/26.98 | | (28) all_58_15 = e2
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (2), (7), (8), (10), (11), (16), (18), (19), (24), (28) are
% 156.85/26.98 | | inconsistent by sub-proof #1453.
% 156.85/26.98 | |
% 156.85/26.98 | End of split
% 156.85/26.98 |
% 156.85/26.98 End of proof
% 156.85/26.98
% 156.85/26.98 Sub-proof #220 shows that the following formulas are inconsistent:
% 156.85/26.98 ----------------------------------------------------------------
% 156.85/26.98 (1) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/26.98 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.98 (2) ~ (e2 = e0)
% 156.85/26.98 (3) op(e3, e3) = e0
% 156.85/26.98 (4) all_58_9 = e3
% 156.85/26.98 (5) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) = all_28_1
% 156.85/26.98 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3, e3) =
% 156.85/26.98 all_28_1 & $i(all_28_1))
% 156.85/26.98 (6) ~ (all_24_1 = e2)
% 156.85/26.98 (7) all_58_10 = e1
% 156.85/26.98 (8) all_58_11 = e2
% 156.85/26.98 (9) ~ (e2 = e1)
% 156.85/26.98 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.98 (11) op(e2, e1) = e2
% 156.85/26.98 (12) op(e2, e1) = e0
% 156.85/26.98 (13) ~ (e3 = e2)
% 156.85/26.98 (14) op(e0, e0) = all_24_1
% 156.85/26.98
% 156.85/26.98 Begin of proof
% 156.85/26.98 |
% 156.85/26.98 | BETA: splitting (5) gives:
% 156.85/26.98 |
% 156.85/26.98 | Case 1:
% 156.85/26.98 | |
% 156.85/26.98 | |
% 156.85/26.98 | | GROUND_INST: instantiating (10) with e0, e2, e1, e2, simplifying with (11),
% 156.85/26.98 | | (12) gives:
% 156.85/26.98 | | (15) e2 = e0
% 156.85/26.98 | |
% 156.85/26.98 | | COMBINE_EQS: (8), (15) imply:
% 156.85/26.98 | | (16) all_58_11 = e0
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (10), (13), (14), (16) are
% 156.85/26.98 | | inconsistent by sub-proof #306.
% 156.85/26.98 | |
% 156.85/26.98 | Case 2:
% 156.85/26.98 | |
% 156.85/26.98 | | (17) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1)
% 156.85/26.98 | |
% 156.85/26.98 | | ALPHA: (17) implies:
% 156.85/26.98 | | (18) ~ (all_28_1 = e0)
% 156.85/26.98 | | (19) op(e3, e3) = all_28_1
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (3), (10), (18), (19) are inconsistent by sub-proof #227.
% 156.85/26.98 | |
% 156.85/26.98 | End of split
% 156.85/26.98 |
% 156.85/26.98 End of proof
% 156.85/26.98
% 156.85/26.98 Sub-proof #221 shows that the following formulas are inconsistent:
% 156.85/26.98 ----------------------------------------------------------------
% 156.85/26.98 (1) all_58_9 = e3
% 156.85/26.98 (2) all_58_10 = e1
% 156.85/26.98 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/26.98 (4) ~ (e2 = e1)
% 156.85/26.98 (5) ~ (e3 = e2)
% 156.85/26.98
% 156.85/26.98 Begin of proof
% 156.85/26.98 |
% 156.85/26.98 | BETA: splitting (3) gives:
% 156.85/26.98 |
% 156.85/26.98 | Case 1:
% 156.85/26.98 | |
% 156.85/26.98 | | (6) all_58_9 = e2 & op(e3, e0) = e2
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #1353.
% 156.85/26.98 | |
% 156.85/26.98 | Case 2:
% 156.85/26.98 | |
% 156.85/26.98 | | (7) all_58_10 = e2 & op(e2, e0) = e2
% 156.85/26.98 | |
% 156.85/26.98 | | ALPHA: (7) implies:
% 156.85/26.98 | | (8) all_58_10 = e2
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #1091.
% 156.85/26.98 | |
% 156.85/26.98 | End of split
% 156.85/26.98 |
% 156.85/26.98 End of proof
% 156.85/26.98
% 156.85/26.98 Sub-proof #222 shows that the following formulas are inconsistent:
% 156.85/26.98 ----------------------------------------------------------------
% 156.85/26.98 (1) op(e1, e1) = e3
% 156.85/26.98 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/26.98 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/26.98 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/26.98 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/26.98 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/26.98 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.98 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/26.98 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 156.85/26.98 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.85/26.98 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.98 (7) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/26.98 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/26.98 (8) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/26.98 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.98 (9) op(e3, e2) = all_52_4
% 156.85/26.98 (10) ~ (all_4_2 = e2)
% 156.85/26.98 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/26.98 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/26.98 (12) op(e2, e1) = all_52_9
% 156.85/26.98 (13) op(e2, e3) = all_52_1
% 156.85/26.98 (14) ~ (e3 = e0)
% 156.85/26.98 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.85/26.98 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.85/26.98 (16) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/26.98 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/26.98 (17) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.85/26.98 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/26.98 e2)
% 156.85/26.98 (18) ~ (e2 = e0)
% 156.85/26.98 (19) ~ (all_52_9 = e3)
% 156.85/26.98 (20) ~ (all_8_2 = e3)
% 156.85/26.98 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/26.98 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/26.98 (22) all_58_6 = e0
% 156.85/26.98 (23) all_58_9 = e3
% 156.85/26.98 (24) op(e1, e3) = all_52_2
% 156.85/26.98 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/26.98 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/26.98 (26) ~ (e3 = e1)
% 156.85/26.98 (27) all_58_13 = e3
% 156.85/26.98 (28) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 156.85/26.98 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.85/26.98 (29) op(e1, e2) = all_52_6
% 156.85/26.98 (30) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.85/26.98 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/26.98 (31) ~ (all_4_2 = e1)
% 156.85/26.98 (32) ~ (all_52_4 = e0)
% 156.85/26.98 (33) ~ (all_52_7 = e0)
% 156.85/26.98 (34) op(e0, e0) = all_4_2
% 156.85/26.98 (35) op(e0, e1) = all_52_11
% 156.85/26.98 (36) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 156.85/26.98 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 156.85/26.98 (37) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.85/26.98 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.85/26.98 (38) ~ (e2 = e1)
% 156.85/26.98 (39) ~ (e1 = e0)
% 156.85/26.98 (40) ~ (all_8_2 = e1)
% 156.85/26.98 (41) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.85/26.98 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.85/26.98 (42) op(e1, e3) = e1
% 156.85/26.98 (43) op(e0, e2) = all_52_7
% 156.85/26.98 (44) all_58_0 = e0
% 156.85/26.98 (45) op(e2, e2) = all_8_2
% 156.85/26.98 (46) ~ (all_52_6 = e3)
% 156.85/26.98 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.98 (48) ~ (e3 = e2)
% 156.85/26.98 (49) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/26.98 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/26.98 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/26.98 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/26.98
% 156.85/26.98 Begin of proof
% 156.85/26.98 |
% 156.85/26.98 | BETA: splitting (36) gives:
% 156.85/26.98 |
% 156.85/26.98 | Case 1:
% 156.85/26.98 | |
% 156.85/26.98 | | (50) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 156.85/26.98 | | e3)
% 156.85/26.98 | |
% 156.85/26.98 | | BETA: splitting (50) gives:
% 156.85/26.98 | |
% 156.85/26.98 | | Case 1:
% 156.85/26.98 | | |
% 156.85/26.98 | | | (51) all_58_2 = e3 & op(e2, e3) = e3
% 156.85/26.98 | | |
% 156.85/26.98 | | | ALPHA: (51) implies:
% 156.85/26.98 | | | (52) op(e2, e3) = e3
% 156.85/26.98 | | |
% 156.85/26.98 | | | BETA: splitting (28) gives:
% 156.85/26.98 | | |
% 156.85/26.98 | | | Case 1:
% 156.85/26.98 | | | |
% 156.85/26.98 | | | | (53) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 156.85/26.98 | | | | = e0)
% 156.85/26.98 | | | |
% 156.85/26.98 | | | | BETA: splitting (53) gives:
% 156.85/26.98 | | | |
% 156.85/26.98 | | | | Case 1:
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | | (54) all_58_4 = e0 & op(e3, e1) = e0
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | | REF_CLOSE: (16), (18), (23), (26), (38), (39), (41), (44), (47), (48),
% 156.85/26.98 | | | | | (54) are inconsistent by sub-proof #348.
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | Case 2:
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | | (55) all_58_5 = e0 & op(e2, e1) = e0
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | | ALPHA: (55) implies:
% 156.85/26.98 | | | | | (56) all_58_5 = e0
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | | BETA: splitting (6) gives:
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | | Case 1:
% 156.85/26.98 | | | | | |
% 156.85/26.98 | | | | | | (57) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 156.85/26.98 | | | | | | op(e0, e2) = e1)
% 156.85/26.98 | | | | | |
% 156.85/26.98 | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (13),
% 156.85/26.98 | | | | | | (14), (16), (17), (18), (21), (23), (24), (25), (26),
% 156.85/26.98 | | | | | | (27), (29), (30), (31), (32), (33), (34), (35), (37),
% 156.85/26.98 | | | | | | (38), (39), (40), (42), (43), (44), (45), (46), (47),
% 156.85/26.98 | | | | | | (48), (49), (52), (56), (57) are inconsistent by
% 156.85/26.98 | | | | | | sub-proof #231.
% 156.85/26.98 | | | | | |
% 156.85/26.98 | | | | | Case 2:
% 156.85/26.98 | | | | | |
% 156.85/26.98 | | | | | | (58) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 156.85/26.98 | | | | | | op(e0, e0) = e1)
% 156.85/26.98 | | | | | |
% 156.85/26.98 | | | | | | BETA: splitting (58) gives:
% 156.85/26.98 | | | | | |
% 156.85/26.98 | | | | | | Case 1:
% 156.85/26.98 | | | | | | |
% 156.85/26.98 | | | | | | | (59) all_58_14 = e1 & op(e0, e1) = e1
% 156.85/26.98 | | | | | | |
% 156.85/26.98 | | | | | | | ALPHA: (59) implies:
% 156.85/26.98 | | | | | | | (60) all_58_14 = e1
% 156.85/26.98 | | | | | | |
% 156.85/26.98 | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 156.85/26.98 | | | | | | | (13), (14), (15), (16), (17), (18), (21), (22), (23),
% 156.85/26.98 | | | | | | | (24), (25), (26), (27), (29), (30), (31), (32), (33),
% 156.85/26.98 | | | | | | | (34), (35), (37), (38), (39), (40), (42), (43), (44),
% 156.85/26.98 | | | | | | | (45), (46), (47), (48), (49), (52), (56), (60) are
% 156.85/26.98 | | | | | | | inconsistent by sub-proof #225.
% 156.85/26.98 | | | | | | |
% 156.85/26.98 | | | | | | Case 2:
% 156.85/26.98 | | | | | | |
% 156.85/26.98 | | | | | | | (61) all_58_15 = e1 & op(e0, e0) = e1
% 156.85/26.98 | | | | | | |
% 156.85/26.98 | | | | | | | REF_CLOSE: (31), (34), (47), (61) are inconsistent by sub-proof
% 156.85/26.98 | | | | | | | #1418.
% 156.85/26.98 | | | | | | |
% 156.85/26.98 | | | | | | End of split
% 156.85/26.98 | | | | | |
% 156.85/26.98 | | | | | End of split
% 156.85/26.98 | | | | |
% 156.85/26.98 | | | | End of split
% 156.85/26.98 | | | |
% 156.85/26.98 | | | Case 2:
% 156.85/26.98 | | | |
% 156.85/26.98 | | | | (62) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1)
% 156.85/26.98 | | | | = e0)
% 156.85/26.98 | | | |
% 156.85/26.98 | | | | REF_CLOSE: (1), (6), (10), (14), (17), (18), (26), (27), (31), (34),
% 156.85/26.98 | | | | (35), (38), (39), (47), (48), (62) are inconsistent by
% 156.85/26.98 | | | | sub-proof #223.
% 156.85/26.98 | | | |
% 156.85/26.98 | | | End of split
% 156.85/26.98 | | |
% 156.85/26.98 | | Case 2:
% 156.85/26.98 | | |
% 156.85/26.98 | | | (63) all_58_3 = e3 & op(e2, e2) = e3
% 156.85/26.98 | | |
% 156.85/26.98 | | | REF_CLOSE: (20), (45), (47), (63) are inconsistent by sub-proof #1437.
% 156.85/26.98 | | |
% 156.85/26.98 | | End of split
% 156.85/26.98 | |
% 156.85/26.98 | Case 2:
% 156.85/26.98 | |
% 156.85/26.98 | | (64) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 156.85/26.98 | | e3)
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (4), (8), (10), (12), (19), (23), (26), (31), (34), (38), (47),
% 156.85/26.98 | | (48), (64) are inconsistent by sub-proof #295.
% 156.85/26.98 | |
% 156.85/26.98 | End of split
% 156.85/26.98 |
% 156.85/26.98 End of proof
% 156.85/26.98
% 156.85/26.98 Sub-proof #223 shows that the following formulas are inconsistent:
% 156.85/26.98 ----------------------------------------------------------------
% 156.85/26.98 (1) op(e1, e1) = e3
% 156.85/26.98 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.85/26.98 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.98 (3) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 156.85/26.98 (4) ~ (all_4_2 = e2)
% 156.85/26.98 (5) ~ (e3 = e0)
% 156.85/26.98 (6) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 156.85/26.98 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.98 (7) ~ (e2 = e0)
% 156.85/26.98 (8) ~ (e3 = e1)
% 156.85/26.98 (9) all_58_13 = e3
% 156.85/26.98 (10) ~ (all_4_2 = e1)
% 156.85/26.98 (11) op(e0, e0) = all_4_2
% 156.85/26.98 (12) op(e0, e1) = all_52_11
% 156.85/26.98 (13) ~ (e2 = e1)
% 156.85/26.98 (14) ~ (e1 = e0)
% 156.85/26.98 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.98 (16) ~ (e3 = e2)
% 156.85/26.98
% 156.85/26.98 Begin of proof
% 156.85/26.98 |
% 156.85/26.98 | BETA: splitting (3) gives:
% 156.85/26.98 |
% 156.85/26.98 | Case 1:
% 156.85/26.98 | |
% 156.85/26.98 | | (17) all_58_8 = e0 & op(e1, e1) = e0
% 156.85/26.98 | |
% 156.85/26.98 | | ALPHA: (17) implies:
% 156.85/26.98 | | (18) op(e1, e1) = e0
% 156.85/26.98 | |
% 156.85/26.98 | | REF_CLOSE: (1), (5), (15), (18) are inconsistent by sub-proof #1466.
% 156.85/26.98 | |
% 156.85/26.98 | Case 2:
% 156.85/26.98 | |
% 156.85/26.98 | | (19) all_58_14 = e0 & op(e0, e1) = e0
% 156.85/26.98 | |
% 156.85/26.98 | | ALPHA: (19) implies:
% 156.85/26.99 | | (20) all_58_14 = e0
% 156.85/26.99 | | (21) op(e0, e1) = e0
% 156.85/26.99 | |
% 156.85/26.99 | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 156.85/26.99 | | (16), (20), (21) are inconsistent by sub-proof #224.
% 156.85/26.99 | |
% 156.85/26.99 | End of split
% 156.85/26.99 |
% 156.85/26.99 End of proof
% 156.85/26.99
% 156.85/26.99 Sub-proof #224 shows that the following formulas are inconsistent:
% 156.85/26.99 ----------------------------------------------------------------
% 156.85/26.99 (1) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.85/26.99 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.99 (2) all_58_14 = e0
% 156.85/26.99 (3) ~ (all_4_2 = e2)
% 156.85/26.99 (4) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 156.85/26.99 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.99 (5) ~ (e2 = e0)
% 156.85/26.99 (6) ~ (e3 = e1)
% 156.85/26.99 (7) all_58_13 = e3
% 156.85/26.99 (8) ~ (all_4_2 = e1)
% 156.85/26.99 (9) op(e0, e0) = all_4_2
% 156.85/26.99 (10) op(e0, e1) = all_52_11
% 156.85/26.99 (11) ~ (e2 = e1)
% 156.85/26.99 (12) ~ (e1 = e0)
% 156.85/26.99 (13) op(e0, e1) = e0
% 156.85/26.99 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.99 (15) ~ (e3 = e2)
% 156.85/26.99
% 156.85/26.99 Begin of proof
% 156.85/26.99 |
% 156.85/26.99 | BETA: splitting (1) gives:
% 156.85/26.99 |
% 156.85/26.99 | Case 1:
% 156.85/26.99 | |
% 156.85/26.99 | | (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 156.85/26.99 | | e1)
% 156.85/26.99 | |
% 156.85/26.99 | | BETA: splitting (16) gives:
% 156.85/26.99 | |
% 156.85/26.99 | | Case 1:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (17) all_58_12 = e1 & op(e0, e3) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | ALPHA: (17) implies:
% 156.85/26.99 | | | (18) all_58_12 = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (3), (4), (5), (7), (9), (10), (11), (13), (14), (15), (18) are
% 156.85/26.99 | | | inconsistent by sub-proof #228.
% 156.85/26.99 | | |
% 156.85/26.99 | | Case 2:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (19) all_58_13 = e1 & op(e0, e2) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | ALPHA: (19) implies:
% 156.85/26.99 | | | (20) all_58_13 = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (6), (7), (20) are inconsistent by sub-proof #1264.
% 156.85/26.99 | | |
% 156.85/26.99 | | End of split
% 156.85/26.99 | |
% 156.85/26.99 | Case 2:
% 156.85/26.99 | |
% 156.85/26.99 | | (21) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 156.85/26.99 | | e1)
% 156.85/26.99 | |
% 156.85/26.99 | | BETA: splitting (21) gives:
% 156.85/26.99 | |
% 156.85/26.99 | | Case 1:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (22) all_58_14 = e1 & op(e0, e1) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (2), (12), (22) are inconsistent by sub-proof #482.
% 156.85/26.99 | | |
% 156.85/26.99 | | Case 2:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (23) all_58_15 = e1 & op(e0, e0) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (8), (9), (14), (23) are inconsistent by sub-proof #1418.
% 156.85/26.99 | | |
% 156.85/26.99 | | End of split
% 156.85/26.99 | |
% 156.85/26.99 | End of split
% 156.85/26.99 |
% 156.85/26.99 End of proof
% 156.85/26.99
% 156.85/26.99 Sub-proof #225 shows that the following formulas are inconsistent:
% 156.85/26.99 ----------------------------------------------------------------
% 156.85/26.99 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/26.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/26.99 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/26.99 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/26.99 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/26.99 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.99 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/26.99 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 156.85/26.99 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.85/26.99 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.99 (6) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/26.99 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/26.99 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/26.99 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.99 (8) op(e2, e3) = e3
% 156.85/26.99 (9) op(e3, e2) = all_52_4
% 156.85/26.99 (10) ~ (all_4_2 = e2)
% 156.85/26.99 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/26.99 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/26.99 (12) op(e2, e3) = all_52_1
% 156.85/26.99 (13) all_58_14 = e1
% 156.85/26.99 (14) ~ (e3 = e0)
% 156.85/26.99 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 156.85/26.99 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 156.85/26.99 (16) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/26.99 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/26.99 (17) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.85/26.99 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/26.99 e2)
% 156.85/26.99 (18) ~ (e2 = e0)
% 156.85/26.99 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/26.99 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/26.99 (20) all_58_6 = e0
% 156.85/26.99 (21) all_58_9 = e3
% 156.85/26.99 (22) op(e1, e3) = all_52_2
% 156.85/26.99 (23) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/26.99 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/26.99 (24) ~ (e3 = e1)
% 156.85/26.99 (25) all_58_13 = e3
% 156.85/26.99 (26) op(e1, e2) = all_52_6
% 156.85/26.99 (27) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.85/26.99 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/26.99 (28) ~ (all_4_2 = e1)
% 156.85/26.99 (29) ~ (all_52_4 = e0)
% 156.85/26.99 (30) ~ (all_52_7 = e0)
% 156.85/26.99 (31) op(e0, e0) = all_4_2
% 156.85/26.99 (32) all_58_5 = e0
% 156.85/26.99 (33) op(e0, e1) = all_52_11
% 156.85/26.99 (34) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.85/26.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.85/26.99 (35) ~ (e2 = e1)
% 156.85/26.99 (36) ~ (e1 = e0)
% 156.85/26.99 (37) ~ (all_8_2 = e1)
% 156.85/26.99 (38) op(e1, e3) = e1
% 156.85/26.99 (39) op(e0, e2) = all_52_7
% 156.85/26.99 (40) all_58_0 = e0
% 156.85/26.99 (41) op(e2, e2) = all_8_2
% 156.85/26.99 (42) ~ (all_52_6 = e3)
% 156.85/26.99 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.99 (44) ~ (e3 = e2)
% 156.85/26.99 (45) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/26.99 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/26.99 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/26.99 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/26.99
% 156.85/26.99 Begin of proof
% 156.85/26.99 |
% 156.85/26.99 | BETA: splitting (15) gives:
% 156.85/26.99 |
% 156.85/26.99 | Case 1:
% 156.85/26.99 | |
% 156.85/26.99 | | (46) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 156.85/26.99 | | e1)
% 156.85/26.99 | |
% 156.85/26.99 | | BETA: splitting (46) gives:
% 156.85/26.99 | |
% 156.85/26.99 | | Case 1:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (47) all_58_0 = e1 & op(e3, e3) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | ALPHA: (47) implies:
% 156.85/26.99 | | | (48) all_58_0 = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | COMBINE_EQS: (40), (48) imply:
% 156.85/26.99 | | | (49) e1 = e0
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.85/26.99 | | | (13), (14), (16), (17), (18), (19), (21), (22), (23), (24),
% 156.85/26.99 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 156.85/26.99 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 156.85/26.99 | | | (45), (49) are inconsistent by sub-proof #226.
% 156.85/26.99 | | |
% 156.85/26.99 | | Case 2:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (50) all_58_2 = e1 & op(e2, e3) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | ALPHA: (50) implies:
% 156.85/26.99 | | | (51) op(e2, e3) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (8), (24), (43), (51) are inconsistent by sub-proof #1494.
% 156.85/26.99 | | |
% 156.85/26.99 | | End of split
% 156.85/26.99 | |
% 156.85/26.99 | Case 2:
% 156.85/26.99 | |
% 156.85/26.99 | | (52) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 156.85/26.99 | | e1)
% 156.85/26.99 | |
% 156.85/26.99 | | BETA: splitting (52) gives:
% 156.85/26.99 | |
% 156.85/26.99 | | Case 1:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (53) all_58_6 = e1 & op(e1, e3) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | ALPHA: (53) implies:
% 156.85/26.99 | | | (54) all_58_6 = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | COMBINE_EQS: (20), (54) imply:
% 156.85/26.99 | | | (55) e1 = e0
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.85/26.99 | | | (13), (14), (16), (17), (18), (19), (21), (22), (23), (24),
% 156.85/26.99 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 156.85/26.99 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 156.85/26.99 | | | (45), (55) are inconsistent by sub-proof #226.
% 156.85/26.99 | | |
% 156.85/26.99 | | Case 2:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (56) all_58_12 = e1 & op(e0, e3) = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | ALPHA: (56) implies:
% 156.85/26.99 | | | (57) all_58_12 = e1
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 156.85/26.99 | | | (16), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 156.85/26.99 | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 156.85/26.99 | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (57) are
% 156.85/26.99 | | | inconsistent by sub-proof #232.
% 156.85/26.99 | | |
% 156.85/26.99 | | End of split
% 156.85/26.99 | |
% 156.85/26.99 | End of split
% 156.85/26.99 |
% 156.85/26.99 End of proof
% 156.85/26.99
% 156.85/26.99 Sub-proof #226 shows that the following formulas are inconsistent:
% 156.85/26.99 ----------------------------------------------------------------
% 156.85/26.99 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/26.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/26.99 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/26.99 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/26.99 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/26.99 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.99 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/26.99 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 156.85/26.99 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.85/26.99 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.99 (6) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/26.99 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/26.99 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/26.99 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.99 (8) op(e2, e3) = e3
% 156.85/26.99 (9) op(e3, e2) = all_52_4
% 156.85/26.99 (10) ~ (all_4_2 = e2)
% 156.85/26.99 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/26.99 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/26.99 (12) e1 = e0
% 156.85/26.99 (13) op(e2, e3) = all_52_1
% 156.85/26.99 (14) all_58_14 = e1
% 156.85/26.99 (15) ~ (e3 = e0)
% 156.85/26.99 (16) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/26.99 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/26.99 (17) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.85/26.99 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/26.99 e2)
% 156.85/26.99 (18) ~ (e2 = e0)
% 156.85/26.99 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/26.99 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/26.99 (20) all_58_9 = e3
% 156.85/26.99 (21) op(e1, e3) = all_52_2
% 156.85/26.99 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/26.99 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/26.99 (23) ~ (e3 = e1)
% 156.85/26.99 (24) all_58_13 = e3
% 156.85/26.99 (25) op(e1, e2) = all_52_6
% 156.85/26.99 (26) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.85/26.99 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/26.99 (27) ~ (all_4_2 = e1)
% 156.85/26.99 (28) ~ (all_52_4 = e0)
% 156.85/26.99 (29) ~ (all_52_7 = e0)
% 156.85/26.99 (30) op(e0, e0) = all_4_2
% 156.85/26.99 (31) all_58_5 = e0
% 156.85/26.99 (32) op(e0, e1) = all_52_11
% 156.85/26.99 (33) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.85/26.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.85/26.99 (34) ~ (e2 = e1)
% 156.85/26.99 (35) ~ (e1 = e0)
% 156.85/26.99 (36) ~ (all_8_2 = e1)
% 156.85/26.99 (37) op(e1, e3) = e1
% 156.85/26.99 (38) op(e0, e2) = all_52_7
% 156.85/26.99 (39) all_58_0 = e0
% 156.85/26.99 (40) op(e2, e2) = all_8_2
% 156.85/26.99 (41) ~ (all_52_6 = e3)
% 156.85/26.99 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.99 (43) ~ (e3 = e2)
% 156.85/26.99 (44) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/26.99 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/26.99 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/26.99 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/26.99
% 156.85/26.99 Begin of proof
% 156.85/26.99 |
% 156.85/26.99 | SIMP: (12) implies:
% 156.85/26.99 | (45) e1 = e0
% 156.85/26.99 |
% 156.85/26.99 | COMBINE_EQS: (14), (45) imply:
% 156.85/26.99 | (46) all_58_14 = e0
% 156.85/26.99 |
% 156.85/26.99 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 156.85/26.99 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 156.85/26.99 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 156.85/26.99 | (37), (38), (39), (40), (41), (42), (43), (44), (46) are
% 156.85/26.99 | inconsistent by sub-proof #230.
% 156.85/26.99 |
% 156.85/26.99 End of proof
% 156.85/26.99
% 156.85/26.99 Sub-proof #227 shows that the following formulas are inconsistent:
% 156.85/26.99 ----------------------------------------------------------------
% 156.85/26.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.99 (2) op(e3, e3) = all_28_1
% 156.85/26.99 (3) op(e3, e3) = e0
% 156.85/26.99 (4) ~ (all_28_1 = e0)
% 156.85/26.99
% 156.85/26.99 Begin of proof
% 156.85/26.99 |
% 156.85/26.99 | GROUND_INST: instantiating (1) with e0, all_28_1, e3, e3, simplifying with
% 156.85/26.99 | (2), (3) gives:
% 156.85/26.99 | (5) all_28_1 = e0
% 156.85/26.99 |
% 156.85/26.99 | REDUCE: (4), (5) imply:
% 156.85/26.99 | (6) $false
% 156.85/26.99 |
% 156.85/26.99 | CLOSE: (6) is inconsistent.
% 156.85/26.99 |
% 156.85/26.99 End of proof
% 156.85/26.99
% 156.85/26.99 Sub-proof #228 shows that the following formulas are inconsistent:
% 156.85/26.99 ----------------------------------------------------------------
% 156.85/26.99 (1) ~ (all_4_2 = e2)
% 156.85/26.99 (2) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 156.85/26.99 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.99 (3) ~ (e2 = e0)
% 156.85/26.99 (4) all_58_13 = e3
% 156.85/26.99 (5) op(e0, e0) = all_4_2
% 156.85/26.99 (6) op(e0, e1) = all_52_11
% 156.85/26.99 (7) ~ (e2 = e1)
% 156.85/26.99 (8) op(e0, e1) = e0
% 156.85/26.99 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.99 (10) ~ (e3 = e2)
% 156.85/26.99 (11) all_58_12 = e1
% 156.85/26.99
% 156.85/26.99 Begin of proof
% 156.85/26.99 |
% 156.85/26.99 | BETA: splitting (2) gives:
% 156.85/26.99 |
% 156.85/26.99 | Case 1:
% 156.85/26.99 | |
% 156.85/26.99 | | (12) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 156.85/26.99 | | e2)
% 156.85/26.99 | |
% 156.85/26.99 | | BETA: splitting (12) gives:
% 156.85/26.99 | |
% 156.85/26.99 | | Case 1:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (13) all_58_12 = e2 & op(e0, e3) = e2
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (7), (11), (13) are inconsistent by sub-proof #1511.
% 156.85/26.99 | | |
% 156.85/26.99 | | Case 2:
% 156.85/26.99 | | |
% 156.85/26.99 | | | (14) all_58_13 = e2 & op(e0, e2) = e2
% 156.85/26.99 | | |
% 156.85/26.99 | | | ALPHA: (14) implies:
% 156.85/26.99 | | | (15) all_58_13 = e2
% 156.85/26.99 | | |
% 156.85/26.99 | | | REF_CLOSE: (4), (10), (15) are inconsistent by sub-proof #320.
% 156.85/26.99 | | |
% 156.85/26.99 | | End of split
% 156.85/26.99 | |
% 156.85/26.99 | Case 2:
% 156.85/26.99 | |
% 156.85/26.99 | | (16) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/26.99 | | e2)
% 156.85/26.99 | |
% 156.85/26.99 | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (16) are inconsistent by sub-proof
% 156.85/26.99 | | #334.
% 156.85/26.99 | |
% 156.85/26.99 | End of split
% 156.85/26.99 |
% 156.85/26.99 End of proof
% 156.85/26.99
% 156.85/26.99 Sub-proof #229 shows that the following formulas are inconsistent:
% 156.85/26.99 ----------------------------------------------------------------
% 156.85/26.99 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/26.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/26.99 (2) all_58_8 = e3
% 156.85/26.99 (3) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/26.99 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/26.99 (4) ~ (e3 = e0)
% 156.85/26.99 (5) ~ (e2 = e0)
% 156.85/26.99 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/26.99 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/26.99 (7) ~ (e3 = e1)
% 156.85/26.99 (8) all_58_13 = e3
% 156.85/26.99 (9) op(e1, e2) = all_52_6
% 156.85/26.99 (10) all_58_13 = e2 & op(e0, e2) = e2
% 156.85/26.99 (11) all_58_11 = e2
% 156.85/26.99 (12) ~ (e2 = e1)
% 156.85/26.99 (13) ~ (e1 = e0)
% 156.85/26.99 (14) ~ (all_52_6 = e3)
% 156.85/26.99 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/26.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/26.99 (16) ~ (e3 = e2)
% 156.85/26.99
% 156.85/26.99 Begin of proof
% 156.85/26.99 |
% 156.85/26.99 | ALPHA: (10) implies:
% 156.85/26.99 | (17) all_58_13 = e2
% 156.85/26.99 |
% 156.85/26.99 | COMBINE_EQS: (8), (17) imply:
% 156.85/26.99 | (18) e3 = e2
% 156.85/26.99 |
% 156.85/26.99 | SIMP: (18) implies:
% 156.85/26.99 | (19) e3 = e2
% 156.85/26.99 |
% 156.85/26.99 | COMBINE_EQS: (2), (19) imply:
% 156.85/26.99 | (20) all_58_8 = e2
% 156.85/26.99 |
% 156.85/26.99 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 156.85/26.99 | (16), (20) are inconsistent by sub-proof #1068.
% 156.85/26.99 |
% 156.85/26.99 End of proof
% 156.85/26.99
% 156.85/26.99 Sub-proof #230 shows that the following formulas are inconsistent:
% 156.85/26.99 ----------------------------------------------------------------
% 156.85/26.99 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/26.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/26.99 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/26.99 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/26.99 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/26.99 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.99 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/26.99 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 156.85/26.99 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 156.85/26.99 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/26.99 (6) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/26.99 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/26.99 (7) all_58_14 = e0
% 156.85/26.99 (8) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/26.99 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/26.99 (9) op(e2, e3) = e3
% 156.85/26.99 (10) op(e3, e2) = all_52_4
% 156.85/26.99 (11) ~ (all_4_2 = e2)
% 156.85/26.99 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/26.99 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/26.99 (13) op(e2, e3) = all_52_1
% 156.85/26.99 (14) ~ (e3 = e0)
% 156.85/26.99 (15) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/26.99 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/27.00 (16) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.85/27.00 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/27.00 e2)
% 156.85/27.00 (17) ~ (e2 = e0)
% 156.85/27.00 (18) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/27.00 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/27.00 (19) all_58_9 = e3
% 156.85/27.00 (20) op(e1, e3) = all_52_2
% 156.85/27.00 (21) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/27.00 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/27.00 (22) ~ (e3 = e1)
% 156.85/27.00 (23) all_58_13 = e3
% 156.85/27.00 (24) op(e1, e2) = all_52_6
% 156.85/27.00 (25) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.85/27.00 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/27.00 (26) ~ (all_4_2 = e1)
% 156.85/27.00 (27) ~ (all_52_4 = e0)
% 156.85/27.00 (28) ~ (all_52_7 = e0)
% 156.85/27.00 (29) op(e0, e0) = all_4_2
% 156.85/27.00 (30) all_58_5 = e0
% 156.85/27.00 (31) op(e0, e1) = all_52_11
% 156.85/27.00 (32) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.85/27.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.85/27.00 (33) ~ (e2 = e1)
% 156.85/27.00 (34) ~ (e1 = e0)
% 156.85/27.00 (35) ~ (all_8_2 = e1)
% 156.85/27.00 (36) op(e1, e3) = e1
% 156.85/27.00 (37) op(e0, e2) = all_52_7
% 156.85/27.00 (38) all_58_0 = e0
% 156.85/27.00 (39) op(e2, e2) = all_8_2
% 156.85/27.00 (40) ~ (all_52_6 = e3)
% 156.85/27.00 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/27.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/27.00 (42) ~ (e3 = e2)
% 156.85/27.00 (43) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/27.00 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/27.00 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/27.00 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/27.00
% 156.85/27.00 Begin of proof
% 156.85/27.00 |
% 156.85/27.00 | BETA: splitting (5) gives:
% 156.85/27.00 |
% 156.85/27.00 | Case 1:
% 156.85/27.00 | |
% 156.85/27.00 | | (44) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 156.85/27.00 | | e1)
% 156.85/27.00 | |
% 156.85/27.00 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 156.85/27.00 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 156.85/27.00 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 156.85/27.00 | | (37), (38), (39), (40), (41), (42), (43), (44) are inconsistent
% 156.85/27.00 | | by sub-proof #231.
% 156.85/27.00 | |
% 156.85/27.00 | Case 2:
% 156.85/27.00 | |
% 156.85/27.00 | | (45) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 156.85/27.00 | | e1)
% 156.85/27.00 | |
% 156.85/27.00 | | BETA: splitting (45) gives:
% 156.85/27.00 | |
% 156.85/27.00 | | Case 1:
% 156.85/27.00 | | |
% 156.85/27.00 | | | (46) all_58_14 = e1 & op(e0, e1) = e1
% 156.85/27.00 | | |
% 156.85/27.00 | | | REF_CLOSE: (7), (34), (46) are inconsistent by sub-proof #482.
% 156.85/27.00 | | |
% 156.85/27.00 | | Case 2:
% 156.85/27.00 | | |
% 156.85/27.00 | | | (47) all_58_15 = e1 & op(e0, e0) = e1
% 156.85/27.00 | | |
% 156.85/27.00 | | | REF_CLOSE: (26), (29), (41), (47) are inconsistent by sub-proof #1418.
% 156.85/27.00 | | |
% 156.85/27.00 | | End of split
% 156.85/27.00 | |
% 156.85/27.00 | End of split
% 156.85/27.00 |
% 156.85/27.00 End of proof
% 156.85/27.00
% 156.85/27.00 Sub-proof #231 shows that the following formulas are inconsistent:
% 156.85/27.00 ----------------------------------------------------------------
% 156.85/27.00 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/27.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/27.00 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/27.00 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/27.00 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/27.00 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/27.00 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/27.00 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 156.85/27.00 (5) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/27.00 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/27.00 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/27.00 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/27.00 (7) op(e2, e3) = e3
% 156.85/27.00 (8) op(e3, e2) = all_52_4
% 156.85/27.00 (9) ~ (all_4_2 = e2)
% 156.85/27.00 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/27.00 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/27.00 (11) op(e2, e3) = all_52_1
% 156.85/27.00 (12) ~ (e3 = e0)
% 156.85/27.00 (13) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/27.00 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/27.00 (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/27.00 (15) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.85/27.00 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/27.00 e2)
% 156.85/27.00 (16) ~ (e2 = e0)
% 156.85/27.00 (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/27.00 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/27.00 (18) all_58_9 = e3
% 156.85/27.00 (19) op(e1, e3) = all_52_2
% 156.85/27.00 (20) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/27.00 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/27.00 (21) ~ (e3 = e1)
% 156.85/27.00 (22) all_58_13 = e3
% 156.85/27.00 (23) op(e1, e2) = all_52_6
% 156.85/27.00 (24) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.85/27.00 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/27.00 (25) ~ (all_4_2 = e1)
% 156.85/27.00 (26) ~ (all_52_4 = e0)
% 156.85/27.00 (27) ~ (all_52_7 = e0)
% 156.85/27.00 (28) op(e0, e0) = all_4_2
% 156.85/27.00 (29) all_58_5 = e0
% 156.85/27.00 (30) op(e0, e1) = all_52_11
% 156.85/27.00 (31) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.85/27.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.85/27.00 (32) ~ (e2 = e1)
% 156.85/27.00 (33) ~ (e1 = e0)
% 156.85/27.00 (34) ~ (all_8_2 = e1)
% 156.85/27.00 (35) op(e1, e3) = e1
% 156.85/27.00 (36) op(e0, e2) = all_52_7
% 156.85/27.00 (37) all_58_0 = e0
% 156.85/27.00 (38) op(e2, e2) = all_8_2
% 156.85/27.00 (39) ~ (all_52_6 = e3)
% 156.85/27.00 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/27.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/27.00 (41) ~ (e3 = e2)
% 156.85/27.00 (42) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/27.00 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/27.00 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/27.00 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/27.00
% 156.85/27.00 Begin of proof
% 156.85/27.00 |
% 156.85/27.00 | BETA: splitting (14) gives:
% 156.85/27.00 |
% 156.85/27.00 | Case 1:
% 156.85/27.00 | |
% 156.85/27.00 | | (43) all_58_12 = e1 & op(e0, e3) = e1
% 156.85/27.00 | |
% 156.85/27.00 | | ALPHA: (43) implies:
% 156.85/27.00 | | (44) all_58_12 = e1
% 156.85/27.00 | |
% 156.85/27.00 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.85/27.00 | | (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 156.85/27.00 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 156.85/27.00 | | (36), (37), (38), (39), (40), (41), (42), (44) are inconsistent
% 156.85/27.00 | | by sub-proof #232.
% 156.85/27.00 | |
% 156.85/27.00 | Case 2:
% 156.85/27.00 | |
% 156.85/27.00 | | (45) all_58_13 = e1 & op(e0, e2) = e1
% 156.85/27.00 | |
% 156.85/27.00 | | ALPHA: (45) implies:
% 156.85/27.00 | | (46) all_58_13 = e1
% 156.85/27.00 | |
% 156.85/27.00 | | REF_CLOSE: (21), (22), (46) are inconsistent by sub-proof #1264.
% 156.85/27.00 | |
% 156.85/27.00 | End of split
% 156.85/27.00 |
% 156.85/27.00 End of proof
% 156.85/27.00
% 156.85/27.00 Sub-proof #232 shows that the following formulas are inconsistent:
% 156.85/27.00 ----------------------------------------------------------------
% 156.85/27.00 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/27.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/27.00 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/27.00 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/27.00 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/27.00 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/27.00 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/27.00 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 156.85/27.00 (5) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/27.00 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/27.00 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/27.00 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/27.00 (7) op(e2, e3) = e3
% 156.85/27.00 (8) op(e3, e2) = all_52_4
% 156.85/27.00 (9) ~ (all_4_2 = e2)
% 156.85/27.00 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/27.00 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/27.00 (11) op(e2, e3) = all_52_1
% 156.85/27.00 (12) ~ (e3 = e0)
% 156.85/27.00 (13) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/27.00 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/27.00 (14) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.85/27.00 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/27.00 e2)
% 156.85/27.00 (15) ~ (e2 = e0)
% 156.85/27.00 (16) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/27.00 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/27.00 (17) all_58_9 = e3
% 156.85/27.00 (18) op(e1, e3) = all_52_2
% 156.85/27.00 (19) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/27.00 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/27.00 (20) ~ (e3 = e1)
% 156.85/27.00 (21) all_58_13 = e3
% 156.85/27.00 (22) op(e1, e2) = all_52_6
% 156.85/27.00 (23) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.85/27.00 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/27.00 (24) ~ (all_4_2 = e1)
% 156.85/27.00 (25) ~ (all_52_4 = e0)
% 156.85/27.00 (26) ~ (all_52_7 = e0)
% 156.85/27.00 (27) op(e0, e0) = all_4_2
% 156.85/27.00 (28) all_58_5 = e0
% 156.85/27.00 (29) op(e0, e1) = all_52_11
% 156.85/27.00 (30) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.85/27.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.85/27.00 (31) ~ (e2 = e1)
% 156.85/27.00 (32) ~ (e1 = e0)
% 156.85/27.00 (33) ~ (all_8_2 = e1)
% 156.85/27.00 (34) op(e1, e3) = e1
% 156.85/27.00 (35) op(e0, e2) = all_52_7
% 156.85/27.00 (36) all_58_0 = e0
% 156.85/27.00 (37) op(e2, e2) = all_8_2
% 156.85/27.00 (38) ~ (all_52_6 = e3)
% 156.85/27.00 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/27.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/27.00 (40) ~ (e3 = e2)
% 156.85/27.00 (41) all_58_12 = e1
% 156.85/27.00 (42) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/27.00 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/27.00 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/27.00 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/27.00
% 156.85/27.00 Begin of proof
% 156.85/27.00 |
% 156.85/27.00 | BETA: splitting (4) gives:
% 156.85/27.00 |
% 156.85/27.00 | Case 1:
% 156.85/27.00 | |
% 156.85/27.00 | | (43) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 156.85/27.00 | | e1)
% 156.85/27.00 | |
% 156.85/27.00 | | REF_CLOSE: (7), (20), (33), (37), (39), (43) are inconsistent by sub-proof
% 156.85/27.00 | | #1122.
% 156.85/27.00 | |
% 156.85/27.00 | Case 2:
% 156.85/27.00 | |
% 156.85/27.00 | | (44) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 156.85/27.00 | | e1)
% 156.85/27.00 | |
% 156.85/27.00 | | BETA: splitting (44) gives:
% 156.85/27.00 | |
% 156.85/27.00 | | Case 1:
% 156.85/27.00 | | |
% 156.85/27.00 | | | (45) all_58_5 = e1 & op(e2, e1) = e1
% 156.85/27.00 | | |
% 156.85/27.00 | | | REF_CLOSE: (28), (32), (45) are inconsistent by sub-proof #1121.
% 156.85/27.00 | | |
% 156.85/27.00 | | Case 2:
% 156.85/27.00 | | |
% 156.85/27.00 | | | (46) all_58_10 = e1 & op(e2, e0) = e1
% 156.85/27.00 | | |
% 156.85/27.00 | | | ALPHA: (46) implies:
% 156.85/27.00 | | | (47) all_58_10 = e1
% 156.85/27.00 | | |
% 156.85/27.00 | | | BETA: splitting (6) gives:
% 156.85/27.00 | | |
% 156.85/27.00 | | | Case 1:
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | (48) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 156.85/27.00 | | | | = e2)
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | REF_CLOSE: (17), (31), (40), (47), (48) are inconsistent by sub-proof
% 156.85/27.00 | | | | #301.
% 156.85/27.00 | | | |
% 156.85/27.00 | | | Case 2:
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | (49) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 156.85/27.00 | | | | e0) = e2)
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | BETA: splitting (49) gives:
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | Case 1:
% 156.85/27.00 | | | | |
% 156.85/27.00 | | | | | (50) all_58_11 = e2 & op(e1, e0) = e2
% 156.85/27.00 | | | | |
% 156.85/27.00 | | | | | ALPHA: (50) implies:
% 156.85/27.00 | | | | | (51) all_58_11 = e2
% 156.85/27.00 | | | | |
% 156.85/27.00 | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.85/27.00 | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 156.85/27.00 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 156.85/27.00 | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 156.85/27.00 | | | | | (47), (51) are inconsistent by sub-proof #235.
% 156.85/27.00 | | | | |
% 156.85/27.00 | | | | Case 2:
% 156.85/27.00 | | | | |
% 156.85/27.00 | | | | | (52) all_58_15 = e2 & op(e0, e0) = e2
% 156.85/27.00 | | | | |
% 156.85/27.00 | | | | | REF_CLOSE: (9), (27), (39), (52) are inconsistent by sub-proof #1452.
% 156.85/27.00 | | | | |
% 156.85/27.00 | | | | End of split
% 156.85/27.00 | | | |
% 156.85/27.00 | | | End of split
% 156.85/27.00 | | |
% 156.85/27.00 | | End of split
% 156.85/27.00 | |
% 156.85/27.00 | End of split
% 156.85/27.00 |
% 156.85/27.00 End of proof
% 156.85/27.00
% 156.85/27.00 Sub-proof #233 shows that the following formulas are inconsistent:
% 156.85/27.00 ----------------------------------------------------------------
% 156.85/27.00 (1) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 &
% 156.85/27.00 op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 156.85/27.00 e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 156.85/27.00 (2) all_56_13 = e2
% 156.85/27.00 (3) all_56_15 = e0
% 156.85/27.00
% 156.85/27.00 Begin of proof
% 156.85/27.00 |
% 156.85/27.00 | BETA: splitting (1) gives:
% 156.85/27.00 |
% 156.85/27.00 | Case 1:
% 156.85/27.00 | |
% 156.85/27.00 | | (4) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1
% 156.85/27.00 | | & op(e1, e2) = e1
% 156.85/27.00 | |
% 156.85/27.00 | | ALPHA: (4) implies:
% 156.85/27.00 | | (5) ~ (all_56_13 = e2)
% 156.85/27.00 | |
% 156.85/27.00 | | REDUCE: (2), (5) imply:
% 156.85/27.00 | | (6) $false
% 156.85/27.00 | |
% 156.85/27.00 | | CLOSE: (6) is inconsistent.
% 156.85/27.00 | |
% 156.85/27.00 | Case 2:
% 156.85/27.00 | |
% 156.85/27.00 | | (7) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) =
% 156.85/27.00 | | e2 & op(e0, e2) = e2
% 156.85/27.00 | |
% 156.85/27.00 | | ALPHA: (7) implies:
% 156.85/27.00 | | (8) ~ (all_56_15 = e0)
% 156.85/27.00 | |
% 156.85/27.00 | | REDUCE: (3), (8) imply:
% 156.85/27.00 | | (9) $false
% 156.85/27.00 | |
% 156.85/27.00 | | CLOSE: (9) is inconsistent.
% 156.85/27.00 | |
% 156.85/27.00 | End of split
% 156.85/27.00 |
% 156.85/27.00 End of proof
% 156.85/27.00
% 156.85/27.00 Sub-proof #234 shows that the following formulas are inconsistent:
% 156.85/27.00 ----------------------------------------------------------------
% 156.85/27.00 (1) all_58_12 = e2
% 156.85/27.00 (2) op(e3, e0) = all_52_12
% 156.85/27.00 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/27.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/27.00 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/27.00 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/27.00 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/27.00 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/27.00 (6) all_58_8 = e3
% 156.85/27.00 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 156.85/27.00 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 156.85/27.00 (8) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/27.00 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/27.00 (9) op(e3, e2) = all_52_4
% 156.85/27.00 (10) ~ (all_4_2 = e2)
% 156.85/27.00 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/27.00 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/27.00 (12) all_58_6 = e1
% 156.85/27.00 (13) op(e2, e3) = all_52_1
% 156.85/27.00 (14) ~ (e3 = e0)
% 156.85/27.00 (15) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/27.00 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/27.00 (16) ~ (e2 = e0)
% 156.85/27.00 (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/27.00 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/27.00 (18) all_58_9 = e3
% 156.85/27.00 (19) op(e1, e3) = all_52_2
% 156.85/27.00 (20) all_56_15 = e0
% 156.85/27.00 (21) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/27.00 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/27.00 (22) ~ (e3 = e1)
% 156.85/27.00 (23) all_58_13 = e3
% 156.85/27.00 (24) op(e1, e2) = all_52_6
% 156.85/27.00 (25) ~ (all_4_2 = e1)
% 156.85/27.00 (26) ~ (all_52_4 = e0)
% 156.85/27.00 (27) ~ (all_52_7 = e0)
% 156.85/27.00 (28) op(e0, e0) = all_4_2
% 156.85/27.00 (29) all_58_11 = e2
% 156.85/27.00 (30) all_58_4 = e2
% 156.85/27.00 (31) ~ (e2 = e1)
% 156.85/27.00 (32) ~ (e1 = e0)
% 156.85/27.00 (33) ~ (all_8_2 = e1)
% 156.85/27.00 (34) op(e3, e0) = e3
% 156.85/27.00 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 156.85/27.00 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 156.85/27.00 (36) op(e1, e3) = e1
% 156.85/27.00 (37) op(e0, e2) = all_52_7
% 156.85/27.00 (38) all_58_0 = e0
% 156.85/27.00 (39) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 156.85/27.00 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 156.85/27.00 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 156.85/27.00 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 156.85/27.00 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 156.85/27.00 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 156.85/27.00 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 156.85/27.00 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.85/27.00 (40) op(e2, e2) = all_8_2
% 156.85/27.00 (41) ~ (all_52_6 = e3)
% 156.85/27.00 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/27.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/27.00 (43) ~ (e3 = e2)
% 156.85/27.00 (44) all_58_3 = e2
% 156.85/27.00
% 156.85/27.00 Begin of proof
% 156.85/27.00 |
% 156.85/27.00 | BETA: splitting (39) gives:
% 156.85/27.00 |
% 156.85/27.00 | Case 1:
% 156.85/27.00 | |
% 156.85/27.00 | | (45) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) =
% 156.85/27.00 | | e3 & op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~
% 156.85/27.00 | | (all_56_12 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1
% 156.85/27.00 | | = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 &
% 156.85/27.00 | | op(e1, e3) = e3)
% 156.85/27.00 | |
% 156.85/27.00 | | BETA: splitting (45) gives:
% 156.85/27.00 | |
% 156.85/27.00 | | Case 1:
% 156.85/27.00 | | |
% 156.85/27.00 | | | (46) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) =
% 156.85/27.00 | | | e3 & op(e2, e3) = e3
% 156.85/27.00 | | |
% 156.85/27.00 | | | ALPHA: (46) implies:
% 156.85/27.00 | | | (47) op(e3, e2) = e3
% 156.85/27.00 | | |
% 156.85/27.00 | | | REF_CLOSE: (18), (22), (30), (31), (32), (35), (38), (42), (47) are
% 156.85/27.00 | | | inconsistent by sub-proof #1126.
% 156.85/27.00 | | |
% 156.85/27.00 | | Case 2:
% 156.85/27.00 | | |
% 156.85/27.00 | | | (48) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2)
% 156.85/27.00 | | | = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~
% 156.85/27.00 | | | (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 156.85/27.00 | | |
% 156.85/27.00 | | | BETA: splitting (48) gives:
% 156.85/27.00 | | |
% 156.85/27.00 | | | Case 1:
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | (49) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2)
% 156.85/27.00 | | | | = e2 & op(e2, e3) = e2
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | ALPHA: (49) implies:
% 156.85/27.00 | | | | (50) op(e2, e3) = e2
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | REF_CLOSE: (1), (7), (12), (13), (14), (22), (38), (42), (43), (50) are
% 156.85/27.00 | | | | inconsistent by sub-proof #1067.
% 156.85/27.00 | | | |
% 156.85/27.00 | | | Case 2:
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | (51) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1)
% 156.85/27.00 | | | | = e3 & op(e1, e3) = e3
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | ALPHA: (51) implies:
% 156.85/27.00 | | | | (52) op(e1, e3) = e3
% 156.85/27.00 | | | |
% 156.85/27.00 | | | | REF_CLOSE: (19), (22), (36), (42), (52) are inconsistent by sub-proof
% 156.85/27.00 | | | | #1164.
% 156.85/27.00 | | | |
% 156.85/27.00 | | | End of split
% 156.85/27.00 | | |
% 156.85/27.00 | | End of split
% 156.85/27.00 | |
% 156.85/27.00 | Case 2:
% 156.85/27.00 | |
% 156.85/27.00 | | (53) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) =
% 156.85/27.00 | | e1 & op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~
% 156.85/27.00 | | (all_56_15 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2
% 156.85/27.00 | | = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 &
% 156.85/27.00 | | op(e0, e3) = e0)
% 156.85/27.00 | |
% 156.85/27.00 | | BETA: splitting (53) gives:
% 156.85/27.00 | |
% 156.85/27.00 | | Case 1:
% 156.85/27.00 | | |
% 156.85/27.00 | | | (54) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) =
% 156.85/27.00 | | | e1 & op(e1, e3) = e1
% 156.85/27.00 | | |
% 156.85/27.00 | | | ALPHA: (54) implies:
% 156.85/27.00 | | | (55) op(e3, e1) = e1
% 156.85/27.00 | | |
% 156.85/27.00 | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (14), (15), (16),
% 156.85/27.00 | | | (17), (18), (21), (22), (23), (24), (25), (26), (27), (28),
% 156.85/27.00 | | | (29), (31), (32), (33), (37), (38), (40), (41), (42), (43),
% 156.85/27.00 | | | (44), (55) are inconsistent by sub-proof #238.
% 156.85/27.00 | | |
% 156.85/27.00 | | Case 2:
% 156.85/27.00 | | |
% 156.85/27.00 | | | (56) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0)
% 156.85/27.00 | | | = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 156.85/27.00 | | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 156.85/27.00 | | |
% 156.85/27.00 | | | REF_CLOSE: (2), (14), (20), (34), (42), (56) are inconsistent by sub-proof
% 156.85/27.00 | | | #242.
% 156.85/27.00 | | |
% 156.85/27.00 | | End of split
% 156.85/27.00 | |
% 156.85/27.00 | End of split
% 156.85/27.00 |
% 156.85/27.00 End of proof
% 156.85/27.00
% 156.85/27.00 Sub-proof #235 shows that the following formulas are inconsistent:
% 156.85/27.00 ----------------------------------------------------------------
% 156.85/27.00 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/27.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/27.00 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/27.00 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/27.00 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/27.00 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/27.01 (4) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 156.85/27.01 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 156.85/27.01 (5) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/27.01 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/27.01 (6) op(e2, e3) = e3
% 156.85/27.01 (7) op(e3, e2) = all_52_4
% 156.85/27.01 (8) ~ (all_4_2 = e2)
% 156.85/27.01 (9) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/27.01 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/27.01 (10) op(e2, e3) = all_52_1
% 156.85/27.01 (11) ~ (e3 = e0)
% 156.85/27.01 (12) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/27.01 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/27.01 (13) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 156.85/27.01 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/27.01 e2)
% 156.85/27.01 (14) ~ (e2 = e0)
% 156.85/27.01 (15) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/27.01 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/27.01 (16) all_58_9 = e3
% 156.85/27.01 (17) op(e1, e3) = all_52_2
% 156.85/27.01 (18) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/27.01 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/27.01 (19) ~ (e3 = e1)
% 156.85/27.01 (20) all_58_13 = e3
% 156.85/27.01 (21) op(e1, e2) = all_52_6
% 156.85/27.01 (22) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 156.85/27.01 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/27.01 (23) ~ (all_4_2 = e1)
% 156.85/27.01 (24) ~ (all_52_4 = e0)
% 156.85/27.01 (25) all_58_10 = e1
% 156.85/27.01 (26) ~ (all_52_7 = e0)
% 156.85/27.01 (27) op(e0, e0) = all_4_2
% 156.85/27.01 (28) all_58_5 = e0
% 156.85/27.01 (29) op(e0, e1) = all_52_11
% 156.85/27.01 (30) all_58_11 = e2
% 156.85/27.01 (31) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 156.85/27.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 156.85/27.01 (32) ~ (e2 = e1)
% 156.85/27.01 (33) ~ (e1 = e0)
% 156.85/27.01 (34) ~ (all_8_2 = e1)
% 156.85/27.01 (35) op(e1, e3) = e1
% 156.85/27.01 (36) op(e0, e2) = all_52_7
% 156.85/27.01 (37) all_58_0 = e0
% 156.85/27.01 (38) op(e2, e2) = all_8_2
% 156.85/27.01 (39) ~ (all_52_6 = e3)
% 156.85/27.01 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/27.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/27.01 (41) ~ (e3 = e2)
% 156.85/27.01 (42) all_58_12 = e1
% 156.85/27.01 (43) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 156.85/27.01 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 156.85/27.01 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 156.85/27.01 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 156.85/27.01
% 156.85/27.01 Begin of proof
% 156.85/27.01 |
% 156.85/27.01 | BETA: splitting (13) gives:
% 156.85/27.01 |
% 156.85/27.01 | Case 1:
% 156.85/27.01 | |
% 156.85/27.01 | | (44) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 156.85/27.01 | | e2)
% 156.85/27.01 | |
% 156.85/27.01 | | BETA: splitting (44) gives:
% 156.85/27.01 | |
% 156.85/27.01 | | Case 1:
% 156.85/27.01 | | |
% 156.85/27.01 | | | (45) all_58_12 = e2 & op(e0, e3) = e2
% 156.85/27.01 | | |
% 156.85/27.01 | | | ALPHA: (45) implies:
% 156.85/27.01 | | | (46) all_58_12 = e2
% 156.85/27.01 | | |
% 156.85/27.01 | | | REF_CLOSE: (32), (42), (46) are inconsistent by sub-proof #1486.
% 156.85/27.01 | | |
% 156.85/27.01 | | Case 2:
% 156.85/27.01 | | |
% 156.85/27.01 | | | (47) all_58_13 = e2 & op(e0, e2) = e2
% 156.85/27.01 | | |
% 156.85/27.01 | | | REF_CLOSE: (20), (41), (47) are inconsistent by sub-proof #1177.
% 156.85/27.01 | | |
% 156.85/27.01 | | End of split
% 156.85/27.01 | |
% 156.85/27.01 | Case 2:
% 156.85/27.01 | |
% 156.85/27.01 | | (48) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 156.85/27.01 | | e2)
% 156.85/27.01 | |
% 156.85/27.01 | | BETA: splitting (48) gives:
% 156.85/27.01 | |
% 156.85/27.01 | | Case 1:
% 156.85/27.01 | | |
% 156.85/27.01 | | | (49) all_58_14 = e2 & op(e0, e1) = e2
% 156.85/27.01 | | |
% 156.85/27.01 | | | ALPHA: (49) implies:
% 156.85/27.01 | | | (50) op(e0, e1) = e2
% 156.85/27.01 | | |
% 156.85/27.01 | | | BETA: splitting (9) gives:
% 156.85/27.01 | | |
% 156.85/27.01 | | | Case 1:
% 156.85/27.01 | | | |
% 156.85/27.01 | | | | (51) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 156.85/27.01 | | | | = e3)
% 156.85/27.01 | | | |
% 156.85/27.01 | | | | REF_CLOSE: (17), (19), (21), (35), (39), (40), (51) are inconsistent by
% 156.85/27.01 | | | | sub-proof #300.
% 156.85/27.01 | | | |
% 156.85/27.01 | | | Case 2:
% 156.85/27.01 | | | |
% 156.85/27.01 | | | | (52) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 156.85/27.01 | | | | = e3)
% 156.85/27.01 | | | |
% 156.85/27.01 | | | | BETA: splitting (52) gives:
% 156.85/27.01 | | | |
% 156.85/27.01 | | | | Case 1:
% 156.85/27.01 | | | | |
% 156.85/27.01 | | | | | (53) all_58_8 = e3 & op(e1, e1) = e3
% 156.85/27.01 | | | | |
% 156.85/27.01 | | | | | ALPHA: (53) implies:
% 156.85/27.01 | | | | | (54) all_58_8 = e3
% 156.85/27.01 | | | | |
% 156.85/27.01 | | | | | BETA: splitting (31) gives:
% 156.85/27.01 | | | | |
% 156.85/27.01 | | | | | Case 1:
% 156.85/27.01 | | | | | |
% 156.85/27.01 | | | | | | (55) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 156.85/27.01 | | | | | | e1) = e1)
% 156.85/27.01 | | | | | |
% 156.85/27.01 | | | | | | BETA: splitting (55) gives:
% 156.85/27.01 | | | | | |
% 156.85/27.01 | | | | | | Case 1:
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | (56) all_58_4 = e1 & op(e3, e1) = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | ALPHA: (56) implies:
% 156.85/27.01 | | | | | | | (57) op(e3, e1) = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | BETA: splitting (22) gives:
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | Case 1:
% 156.85/27.01 | | | | | | | |
% 156.85/27.01 | | | | | | | | (58) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 156.85/27.01 | | | | | | | | op(e2, e2) = e2)
% 156.85/27.01 | | | | | | | |
% 156.85/27.01 | | | | | | | | BETA: splitting (58) gives:
% 156.85/27.01 | | | | | | | |
% 156.85/27.01 | | | | | | | | Case 1:
% 156.85/27.01 | | | | | | | | |
% 156.85/27.01 | | | | | | | | | (59) all_58_2 = e2 & op(e2, e3) = e2
% 156.85/27.01 | | | | | | | | |
% 156.85/27.01 | | | | | | | | | ALPHA: (59) implies:
% 156.85/27.01 | | | | | | | | | (60) op(e2, e3) = e2
% 156.85/27.01 | | | | | | | | |
% 156.85/27.01 | | | | | | | | | REF_CLOSE: (6), (10), (40), (41), (60) are inconsistent by
% 156.85/27.01 | | | | | | | | | sub-proof #1159.
% 156.85/27.01 | | | | | | | | |
% 156.85/27.01 | | | | | | | | Case 2:
% 156.85/27.01 | | | | | | | | |
% 156.85/27.01 | | | | | | | | | (61) all_58_3 = e2 & op(e2, e2) = e2
% 156.85/27.01 | | | | | | | | |
% 156.85/27.01 | | | | | | | | | ALPHA: (61) implies:
% 156.85/27.01 | | | | | | | | | (62) all_58_3 = e2
% 156.85/27.01 | | | | | | | | |
% 156.85/27.01 | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (12),
% 156.85/27.01 | | | | | | | | | (14), (15), (16), (18), (19), (20), (21), (23),
% 156.85/27.01 | | | | | | | | | (24), (26), (27), (30), (32), (33), (34), (36),
% 156.85/27.01 | | | | | | | | | (37), (38), (39), (40), (41), (54), (57), (62) are
% 156.85/27.01 | | | | | | | | | inconsistent by sub-proof #238.
% 156.85/27.01 | | | | | | | | |
% 156.85/27.01 | | | | | | | | End of split
% 156.85/27.01 | | | | | | | |
% 156.85/27.01 | | | | | | | Case 2:
% 156.85/27.01 | | | | | | | |
% 156.85/27.01 | | | | | | | | (63) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 156.85/27.01 | | | | | | | | op(e2, e0) = e2)
% 156.85/27.01 | | | | | | | |
% 156.85/27.01 | | | | | | | | REF_CLOSE: (3), (5), (8), (14), (16), (19), (23), (27), (28),
% 156.85/27.01 | | | | | | | | (30), (32), (33), (40), (41), (63) are inconsistent
% 156.85/27.01 | | | | | | | | by sub-proof #236.
% 156.85/27.01 | | | | | | | |
% 156.85/27.01 | | | | | | | End of split
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | Case 2:
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | (64) all_58_5 = e1 & op(e2, e1) = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | ALPHA: (64) implies:
% 156.85/27.01 | | | | | | | (65) all_58_5 = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | COMBINE_EQS: (28), (65) imply:
% 156.85/27.01 | | | | | | | (66) e1 = e0
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | COMBINE_EQS: (25), (66) imply:
% 156.85/27.01 | | | | | | | (67) all_58_10 = e0
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | REF_CLOSE: (3), (16), (19), (23), (27), (30), (32), (33), (40),
% 156.85/27.01 | | | | | | | (67) are inconsistent by sub-proof #350.
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | End of split
% 156.85/27.01 | | | | | |
% 156.85/27.01 | | | | | Case 2:
% 156.85/27.01 | | | | | |
% 156.85/27.01 | | | | | | (68) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 156.85/27.01 | | | | | | e1) = e1)
% 156.85/27.01 | | | | | |
% 156.85/27.01 | | | | | | BETA: splitting (68) gives:
% 156.85/27.01 | | | | | |
% 156.85/27.01 | | | | | | Case 1:
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | (69) all_58_8 = e1 & op(e1, e1) = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | ALPHA: (69) implies:
% 156.85/27.01 | | | | | | | (70) all_58_8 = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | COMBINE_EQS: (54), (70) imply:
% 156.85/27.01 | | | | | | | (71) e3 = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | REF_CLOSE: (1), (4), (9), (11), (14), (15), (16), (19), (21),
% 156.85/27.01 | | | | | | | (25), (30), (32), (33), (39), (40), (41), (43), (54),
% 156.85/27.01 | | | | | | | (71) are inconsistent by sub-proof #297.
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | Case 2:
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | (72) all_58_14 = e1 & op(e0, e1) = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | ALPHA: (72) implies:
% 156.85/27.01 | | | | | | | (73) op(e0, e1) = e1
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | | REF_CLOSE: (29), (32), (40), (50), (73) are inconsistent by
% 156.85/27.01 | | | | | | | sub-proof #1473.
% 156.85/27.01 | | | | | | |
% 156.85/27.01 | | | | | | End of split
% 156.85/27.01 | | | | | |
% 156.85/27.01 | | | | | End of split
% 156.85/27.01 | | | | |
% 156.85/27.01 | | | | Case 2:
% 156.85/27.01 | | | | |
% 156.85/27.01 | | | | | (74) all_58_11 = e3 & op(e1, e0) = e3
% 156.85/27.01 | | | | |
% 156.85/27.01 | | | | | REF_CLOSE: (3), (5), (8), (16), (19), (23), (27), (32), (40), (41),
% 156.85/27.01 | | | | | (74) are inconsistent by sub-proof #243.
% 156.85/27.01 | | | | |
% 156.85/27.01 | | | | End of split
% 156.85/27.01 | | | |
% 156.85/27.01 | | | End of split
% 156.85/27.01 | | |
% 156.85/27.01 | | Case 2:
% 156.85/27.01 | | |
% 156.85/27.01 | | | (75) all_58_15 = e2 & op(e0, e0) = e2
% 156.85/27.01 | | |
% 156.85/27.01 | | | ALPHA: (75) implies:
% 156.85/27.01 | | | (76) all_58_15 = e2
% 156.85/27.01 | | |
% 156.85/27.01 | | | REF_CLOSE: (3), (11), (14), (16), (19), (30), (32), (33), (43), (76) are
% 156.85/27.01 | | | inconsistent by sub-proof #1453.
% 156.85/27.01 | | |
% 156.85/27.01 | | End of split
% 156.85/27.01 | |
% 156.85/27.01 | End of split
% 156.85/27.01 |
% 156.85/27.01 End of proof
% 156.85/27.01
% 156.85/27.01 Sub-proof #236 shows that the following formulas are inconsistent:
% 156.85/27.01 ----------------------------------------------------------------
% 156.85/27.01 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/27.01 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/27.01 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/27.01 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/27.01 (3) ~ (all_4_2 = e2)
% 156.85/27.01 (4) ~ (e2 = e0)
% 156.85/27.01 (5) all_58_9 = e3
% 156.85/27.01 (6) ~ (e3 = e1)
% 156.85/27.01 (7) ~ (all_4_2 = e1)
% 156.85/27.01 (8) op(e0, e0) = all_4_2
% 156.85/27.01 (9) all_58_5 = e0
% 156.85/27.01 (10) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 156.85/27.01 (11) all_58_11 = e2
% 156.85/27.01 (12) ~ (e2 = e1)
% 156.85/27.01 (13) ~ (e1 = e0)
% 156.85/27.01 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/27.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/27.01 (15) ~ (e3 = e2)
% 156.85/27.01
% 156.85/27.01 Begin of proof
% 156.85/27.01 |
% 156.85/27.01 | BETA: splitting (10) gives:
% 156.85/27.01 |
% 156.85/27.01 | Case 1:
% 156.85/27.01 | |
% 156.85/27.01 | | (16) all_58_5 = e2 & op(e2, e1) = e2
% 156.85/27.01 | |
% 156.85/27.01 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 156.85/27.01 | | (14), (15), (16) are inconsistent by sub-proof #237.
% 156.85/27.01 | |
% 156.85/27.01 | Case 2:
% 156.85/27.01 | |
% 156.85/27.01 | | (17) all_58_10 = e2 & op(e2, e0) = e2
% 156.85/27.01 | |
% 156.85/27.01 | | ALPHA: (17) implies:
% 156.85/27.01 | | (18) all_58_10 = e2
% 156.85/27.01 | |
% 156.85/27.01 | | REF_CLOSE: (1), (5), (6), (7), (8), (11), (12), (14), (18) are inconsistent
% 156.85/27.01 | | by sub-proof #248.
% 156.85/27.01 | |
% 156.85/27.01 | End of split
% 156.85/27.01 |
% 156.85/27.01 End of proof
% 156.85/27.01
% 156.85/27.01 Sub-proof #237 shows that the following formulas are inconsistent:
% 156.85/27.01 ----------------------------------------------------------------
% 156.85/27.01 (1) all_58_5 = e2 & op(e2, e1) = e2
% 156.85/27.01 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/27.01 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/27.01 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/27.01 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/27.01 (4) ~ (all_4_2 = e2)
% 156.85/27.01 (5) ~ (e2 = e0)
% 156.85/27.01 (6) all_58_9 = e3
% 156.85/27.01 (7) ~ (e3 = e1)
% 156.85/27.01 (8) ~ (all_4_2 = e1)
% 156.85/27.01 (9) op(e0, e0) = all_4_2
% 156.85/27.01 (10) all_58_5 = e0
% 156.85/27.01 (11) all_58_11 = e2
% 156.85/27.01 (12) ~ (e2 = e1)
% 156.85/27.01 (13) ~ (e1 = e0)
% 156.85/27.01 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 156.85/27.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 156.85/27.01 (15) ~ (e3 = e2)
% 156.85/27.01
% 156.85/27.01 Begin of proof
% 156.85/27.01 |
% 156.85/27.01 | ALPHA: (1) implies:
% 156.85/27.01 | (16) all_58_5 = e2
% 156.85/27.01 |
% 156.85/27.01 | COMBINE_EQS: (10), (16) imply:
% 156.85/27.01 | (17) e2 = e0
% 156.85/27.01 |
% 156.85/27.01 | SIMP: (17) implies:
% 156.85/27.01 | (18) e2 = e0
% 156.85/27.01 |
% 156.85/27.01 | COMBINE_EQS: (11), (18) imply:
% 156.85/27.01 | (19) all_58_11 = e0
% 156.85/27.01 |
% 156.85/27.01 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14), (15),
% 156.85/27.01 | (19) are inconsistent by sub-proof #240.
% 156.85/27.01 |
% 156.85/27.01 End of proof
% 156.85/27.01
% 156.85/27.01 Sub-proof #238 shows that the following formulas are inconsistent:
% 156.85/27.01 ----------------------------------------------------------------
% 156.85/27.01 (1) op(e3, e1) = e1
% 156.85/27.01 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 156.85/27.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 156.85/27.01 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 156.85/27.01 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 156.85/27.01 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 156.85/27.01 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 156.85/27.01 (5) all_58_8 = e3
% 156.85/27.01 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 156.85/27.01 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 156.85/27.01 (7) op(e3, e2) = all_52_4
% 156.85/27.01 (8) ~ (all_4_2 = e2)
% 156.85/27.01 (9) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 156.85/27.01 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 156.85/27.01 (10) ~ (e3 = e0)
% 156.85/27.01 (11) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 156.85/27.01 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 156.85/27.01 (12) ~ (e2 = e0)
% 156.85/27.01 (13) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 156.85/27.01 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 156.85/27.01 (14) all_58_9 = e3
% 156.85/27.01 (15) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 156.85/27.01 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 156.85/27.01 (16) ~ (e3 = e1)
% 156.85/27.01 (17) all_58_13 = e3
% 156.85/27.01 (18) op(e1, e2) = all_52_6
% 156.85/27.01 (19) ~ (all_4_2 = e1)
% 156.85/27.01 (20) ~ (all_52_4 = e0)
% 156.85/27.01 (21) ~ (all_52_7 = e0)
% 156.85/27.01 (22) op(e0, e0) = all_4_2
% 156.85/27.01 (23) all_58_11 = e2
% 156.85/27.01 (24) ~ (e2 = e1)
% 157.00/27.01 (25) ~ (e1 = e0)
% 157.00/27.01 (26) ~ (all_8_2 = e1)
% 157.00/27.01 (27) op(e0, e2) = all_52_7
% 157.00/27.01 (28) all_58_0 = e0
% 157.00/27.01 (29) op(e2, e2) = all_8_2
% 157.00/27.01 (30) ~ (all_52_6 = e3)
% 157.00/27.01 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.01 (32) ~ (e3 = e2)
% 157.00/27.01 (33) all_58_3 = e2
% 157.00/27.01
% 157.00/27.01 Begin of proof
% 157.00/27.01 |
% 157.00/27.01 | BETA: splitting (15) gives:
% 157.00/27.01 |
% 157.00/27.01 | Case 1:
% 157.00/27.01 | |
% 157.00/27.01 | | (34) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 157.00/27.01 | | e0)
% 157.00/27.01 | |
% 157.00/27.01 | | BETA: splitting (34) gives:
% 157.00/27.01 | |
% 157.00/27.01 | | Case 1:
% 157.00/27.01 | | |
% 157.00/27.01 | | | (35) all_58_1 = e0 & op(e3, e2) = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | REF_CLOSE: (7), (20), (31), (35) are inconsistent by sub-proof #1221.
% 157.00/27.01 | | |
% 157.00/27.01 | | Case 2:
% 157.00/27.01 | | |
% 157.00/27.01 | | | (36) all_58_3 = e0 & op(e2, e2) = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | ALPHA: (36) implies:
% 157.00/27.01 | | | (37) all_58_3 = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | COMBINE_EQS: (33), (37) imply:
% 157.00/27.01 | | | (38) e2 = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | SIMP: (38) implies:
% 157.00/27.01 | | | (39) e2 = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | COMBINE_EQS: (23), (39) imply:
% 157.00/27.01 | | | (40) all_58_11 = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | REF_CLOSE: (4), (6), (8), (12), (14), (16), (19), (22), (24), (25), (31),
% 157.00/27.01 | | | (32), (40) are inconsistent by sub-proof #240.
% 157.00/27.01 | | |
% 157.00/27.01 | | End of split
% 157.00/27.01 | |
% 157.00/27.01 | Case 2:
% 157.00/27.01 | |
% 157.00/27.01 | | (41) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 157.00/27.01 | | e0)
% 157.00/27.01 | |
% 157.00/27.01 | | BETA: splitting (41) gives:
% 157.00/27.01 | |
% 157.00/27.01 | | Case 1:
% 157.00/27.01 | | |
% 157.00/27.01 | | | (42) all_58_7 = e0 & op(e1, e2) = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | ALPHA: (42) implies:
% 157.00/27.01 | | | (43) all_58_7 = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | BETA: splitting (11) gives:
% 157.00/27.01 | | |
% 157.00/27.01 | | | Case 1:
% 157.00/27.01 | | | |
% 157.00/27.01 | | | | (44) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 157.00/27.01 | | | | = e2)
% 157.00/27.01 | | | |
% 157.00/27.01 | | | | BETA: splitting (44) gives:
% 157.00/27.01 | | | |
% 157.00/27.01 | | | | Case 1:
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | (45) all_58_0 = e2 & op(e3, e3) = e2
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | ALPHA: (45) implies:
% 157.00/27.01 | | | | | (46) all_58_0 = e2
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | COMBINE_EQS: (28), (46) imply:
% 157.00/27.01 | | | | | (47) e2 = e0
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | SIMP: (47) implies:
% 157.00/27.01 | | | | | (48) e2 = e0
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | COMBINE_EQS: (23), (48) imply:
% 157.00/27.01 | | | | | (49) all_58_11 = e0
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | REF_CLOSE: (4), (6), (8), (12), (14), (16), (19), (22), (24), (25),
% 157.00/27.01 | | | | | (31), (32), (49) are inconsistent by sub-proof #240.
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | Case 2:
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | (50) all_58_1 = e2 & op(e3, e2) = e2
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | ALPHA: (50) implies:
% 157.00/27.01 | | | | | (51) all_58_1 = e2
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | REF_CLOSE: (3), (16), (17), (24), (25), (26), (29), (31), (43), (51)
% 157.00/27.01 | | | | | are inconsistent by sub-proof #322.
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | End of split
% 157.00/27.01 | | | |
% 157.00/27.01 | | | Case 2:
% 157.00/27.01 | | | |
% 157.00/27.01 | | | | (52) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 157.00/27.01 | | | | = e2)
% 157.00/27.01 | | | |
% 157.00/27.01 | | | | BETA: splitting (52) gives:
% 157.00/27.01 | | | |
% 157.00/27.01 | | | | Case 1:
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | (53) all_58_4 = e2 & op(e3, e1) = e2
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | ALPHA: (53) implies:
% 157.00/27.01 | | | | | (54) op(e3, e1) = e2
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | REF_CLOSE: (1), (24), (31), (54) are inconsistent by sub-proof #338.
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | Case 2:
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | (55) all_58_9 = e2 & op(e3, e0) = e2
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | | REF_CLOSE: (2), (5), (9), (10), (12), (13), (14), (16), (18), (23),
% 157.00/27.01 | | | | | (24), (25), (30), (31), (32), (55) are inconsistent by
% 157.00/27.01 | | | | | sub-proof #500.
% 157.00/27.01 | | | | |
% 157.00/27.01 | | | | End of split
% 157.00/27.01 | | | |
% 157.00/27.01 | | | End of split
% 157.00/27.01 | | |
% 157.00/27.01 | | Case 2:
% 157.00/27.01 | | |
% 157.00/27.01 | | | (56) all_58_13 = e0 & op(e0, e2) = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | ALPHA: (56) implies:
% 157.00/27.01 | | | (57) op(e0, e2) = e0
% 157.00/27.01 | | |
% 157.00/27.01 | | | REF_CLOSE: (21), (27), (31), (57) are inconsistent by sub-proof #1532.
% 157.00/27.01 | | |
% 157.00/27.01 | | End of split
% 157.00/27.01 | |
% 157.00/27.01 | End of split
% 157.00/27.01 |
% 157.00/27.01 End of proof
% 157.00/27.01
% 157.00/27.01 Sub-proof #239 shows that the following formulas are inconsistent:
% 157.00/27.01 ----------------------------------------------------------------
% 157.00/27.01 (1) op(e3, e0) = all_52_12
% 157.00/27.01 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.00/27.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.00/27.01 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.01 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.01 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.00/27.01 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.00/27.01 (5) all_54_13 = all_52_7
% 157.00/27.01 (6) op(e1, e1) = all_6_2
% 157.00/27.01 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.00/27.01 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.01 (8) ~ (all_52_6 = all_52_14)
% 157.00/27.01 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.00/27.01 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.00/27.01 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.00/27.01 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.00/27.01 (11) ~ (all_52_1 = all_8_2)
% 157.00/27.01 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.00/27.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.00/27.01 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.00/27.01 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.00/27.01 (14) ~ (all_52_14 = e3)
% 157.00/27.01 (15) all_54_1 = all_52_4
% 157.00/27.01 (16) op(e3, e2) = all_52_4
% 157.00/27.01 (17) ~ (all_4_2 = e2)
% 157.00/27.01 (18) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.00/27.01 (19) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.00/27.01 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.00/27.01 (20) all_56_13 = all_8_2
% 157.00/27.01 (21) op(e2, e1) = all_52_9
% 157.00/27.01 (22) op(e2, e3) = all_52_1
% 157.00/27.01 (23) ~ (all_52_13 = e3)
% 157.00/27.01 (24) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.00/27.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.00/27.01 (25) ~ (e3 = e0)
% 157.00/27.01 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.00/27.01 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.00/27.01 (27) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.00/27.01 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.00/27.01 (28) ~ (all_52_9 = all_52_13)
% 157.00/27.01 (29) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.00/27.01 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.00/27.01 e2)
% 157.00/27.01 (30) ~ (e2 = e0)
% 157.00/27.01 (31) ~ (all_8_2 = e3)
% 157.00/27.01 (32) op(e3, e3) = e0
% 157.00/27.01 (33) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.00/27.01 (34) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.00/27.01 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.00/27.01 (35) all_58_9 = e3
% 157.00/27.01 (36) all_30_2 = all_8_2
% 157.00/27.01 (37) op(e1, e3) = all_52_2
% 157.00/27.01 (38) op(e2, e0) = all_52_13
% 157.00/27.01 (39) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 157.00/27.02 (40) all_56_15 = e0
% 157.00/27.02 (41) ~ (all_52_6 = all_8_2)
% 157.00/27.02 (42) ~ (e3 = e1)
% 157.00/27.02 (43) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.00/27.02 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.00/27.02 (44) op(e1, e2) = all_52_6
% 157.00/27.02 (45) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.00/27.02 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.00/27.02 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.00/27.02 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.00/27.02 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.00/27.02 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.00/27.02 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.00/27.02 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.00/27.02 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.00/27.02 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.00/27.02 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.00/27.02 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.00/27.02 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.00/27.02 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.00/27.02 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.00/27.02 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.00/27.02 = e0)
% 157.00/27.02 (46) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.00/27.02 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.00/27.02 (47) ~ (all_4_2 = e1)
% 157.00/27.02 (48) ~ (all_52_4 = e0)
% 157.00/27.02 (49) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.00/27.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.00/27.02 (50) ~ (all_52_7 = e0)
% 157.00/27.02 (51) ~ (all_6_2 = e3)
% 157.00/27.02 (52) op(e0, e0) = all_4_2
% 157.00/27.02 (53) op(e0, e1) = all_52_11
% 157.00/27.02 (54) ~ (all_52_4 = all_8_2)
% 157.00/27.02 (55) ~ (all_52_2 = all_52_14)
% 157.00/27.02 (56) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.00/27.02 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.00/27.02 (57) ~ (all_52_6 = all_52_7)
% 157.00/27.02 (58) ~ (all_52_4 = e3)
% 157.00/27.02 (59) ~ (e2 = e1)
% 157.00/27.02 (60) ~ (all_52_4 = all_52_7)
% 157.00/27.02 (61) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.00/27.02 (62) ~ (e1 = e0)
% 157.00/27.02 (63) ~ (all_8_2 = e1)
% 157.00/27.02 (64) ~ (all_52_1 = e0)
% 157.00/27.02 (65) ~ (all_52_7 = all_8_2)
% 157.00/27.02 (66) ~ (all_56_13 = e0) | (all_56_5 = e2 & op(e2, e0) = e2)
% 157.00/27.02 (67) op(e3, e1) = all_52_8
% 157.00/27.02 (68) ~ (all_6_2 = e2)
% 157.00/27.02 (69) all_56_14 = all_6_2
% 157.00/27.02 (70) op(e3, e0) = e3
% 157.00/27.02 (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.00/27.02 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.00/27.02 (72) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e3) & op(all_30_1, e2) = all_30_0 &
% 157.00/27.02 op(e0, e0) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 157.00/27.02 e1) & op(e0, e0) = all_30_1 & $i(all_30_1))
% 157.00/27.02 (73) ~ (all_52_8 = e3)
% 157.00/27.02 (74) op(e0, e2) = all_52_7
% 157.00/27.02 (75) op(e1, e0) = all_52_14
% 157.00/27.02 (76) all_58_0 = e0
% 157.00/27.02 (77) op(e2, e2) = all_8_2
% 157.00/27.02 (78) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.00/27.02 (79) ~ (all_52_14 = all_6_2)
% 157.00/27.02 (80) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.02 (81) all_54_5 = all_8_2
% 157.00/27.02 (82) ~ (all_52_9 = all_8_2)
% 157.00/27.02 (83) all_54_11 = all_52_14
% 157.00/27.02 (84) ~ (all_52_13 = all_52_14)
% 157.00/27.02 (85) ~ (e3 = e2)
% 157.00/27.02 (86) ~ (all_52_13 = all_8_2)
% 157.00/27.02 (87) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.00/27.02 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.00/27.02
% 157.00/27.02 Begin of proof
% 157.00/27.02 |
% 157.00/27.02 | BETA: splitting (72) gives:
% 157.00/27.02 |
% 157.00/27.02 | Case 1:
% 157.00/27.02 | |
% 157.00/27.02 | | (88) ~ (all_30_2 = e0)
% 157.00/27.02 | |
% 157.00/27.02 | | REDUCE: (36), (88) imply:
% 157.00/27.02 | | (89) ~ (all_8_2 = e0)
% 157.00/27.02 | |
% 157.00/27.02 | | BETA: splitting (49) gives:
% 157.00/27.02 | |
% 157.00/27.02 | | Case 1:
% 157.00/27.02 | | |
% 157.00/27.02 | | | (90) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 157.00/27.02 | | | e0)
% 157.00/27.02 | | |
% 157.00/27.02 | | | BETA: splitting (90) gives:
% 157.00/27.02 | | |
% 157.00/27.02 | | | Case 1:
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | (91) all_58_2 = e0 & op(e2, e3) = e0
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | REF_CLOSE: (22), (64), (80), (91) are inconsistent by sub-proof #1433.
% 157.00/27.02 | | | |
% 157.00/27.02 | | | Case 2:
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | (92) all_58_3 = e0 & op(e2, e2) = e0
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | REF_CLOSE: (11), (21), (22), (31), (38), (39), (46), (63), (80), (81),
% 157.00/27.02 | | | | (82), (86), (89), (92) are inconsistent by sub-proof #323.
% 157.00/27.02 | | | |
% 157.00/27.02 | | | End of split
% 157.00/27.02 | | |
% 157.00/27.02 | | Case 2:
% 157.00/27.02 | | |
% 157.00/27.02 | | | (93) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 157.00/27.02 | | | e0)
% 157.00/27.02 | | |
% 157.00/27.02 | | | BETA: splitting (93) gives:
% 157.00/27.02 | | |
% 157.00/27.02 | | | Case 1:
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | (94) all_58_5 = e0 & op(e2, e1) = e0
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | ALPHA: (94) implies:
% 157.00/27.02 | | | | (95) all_58_5 = e0
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | BETA: splitting (39) gives:
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | Case 1:
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | (96) all_54_5 = e3
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | REF_CLOSE: (31), (81), (96) are inconsistent by sub-proof #1161.
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | Case 2:
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | (97) ~ (all_54_5 = e3)
% 157.00/27.02 | | | | | (98) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | BETA: splitting (98) gives:
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | Case 1:
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | (99) all_54_5 = e2
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | COMBINE_EQS: (81), (99) imply:
% 157.00/27.02 | | | | | | (100) all_8_2 = e2
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | SIMP: (100) implies:
% 157.00/27.02 | | | | | | (101) all_8_2 = e2
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | REDUCE: (54), (101) imply:
% 157.00/27.02 | | | | | | (102) ~ (all_52_4 = e2)
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | REDUCE: (65), (101) imply:
% 157.00/27.02 | | | | | | (103) ~ (all_52_7 = e2)
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | REDUCE: (82), (101) imply:
% 157.00/27.02 | | | | | | (104) ~ (all_52_9 = e2)
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | REDUCE: (31), (101) imply:
% 157.00/27.02 | | | | | | (105) ~ (e3 = e2)
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | BETA: splitting (9) gives:
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | Case 1:
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | (106) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 157.00/27.02 | | | | | | | op(e2, e1) = e3)
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | BETA: splitting (106) gives:
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | (107) all_58_4 = e3 & op(e3, e1) = e3
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | ALPHA: (107) implies:
% 157.00/27.02 | | | | | | | | (108) op(e3, e1) = e3
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | REF_CLOSE: (67), (73), (80), (108) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | #1538.
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | (109) all_58_5 = e3 & op(e2, e1) = e3
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | ALPHA: (109) implies:
% 157.00/27.02 | | | | | | | | (110) all_58_5 = e3
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | REF_CLOSE: (25), (95), (110) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | #1392.
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | End of split
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | Case 2:
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | (111) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 157.00/27.02 | | | | | | | op(e0, e1) = e3)
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | BETA: splitting (111) gives:
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | (112) all_58_8 = e3 & op(e1, e1) = e3
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | REF_CLOSE: (6), (51), (80), (112) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | #1469.
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | (113) all_58_14 = e3 & op(e0, e1) = e3
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | ALPHA: (113) implies:
% 157.00/27.02 | | | | | | | | (114) all_58_14 = e3
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | BETA: splitting (12) gives:
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | (115) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 157.00/27.02 | | | | | | | | | op(e2, e1) = e2)
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | BETA: splitting (115) gives:
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | (116) all_58_4 = e2 & op(e3, e1) = e2
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | ALPHA: (116) implies:
% 157.00/27.02 | | | | | | | | | | (117) all_58_4 = e2
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | BETA: splitting (18) gives:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | (118) all_54_1 = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | REF_CLOSE: (15), (58), (118) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | #1305.
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | (119) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | BETA: splitting (119) gives:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | (120) all_54_1 = e2
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | REF_CLOSE: (15), (102), (120) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | #1304.
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | (121) ~ (all_54_1 = e2)
% 157.00/27.02 | | | | | | | | | | | | (122) all_54_1 = e1 | all_54_1 = e0
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | BETA: splitting (122) gives:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | (123) all_54_1 = e1
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | COMBINE_EQS: (15), (123) imply:
% 157.00/27.02 | | | | | | | | | | | | | (124) all_52_4 = e1
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | SIMP: (124) implies:
% 157.00/27.02 | | | | | | | | | | | | | (125) all_52_4 = e1
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | REDUCE: (60), (125) imply:
% 157.00/27.02 | | | | | | | | | | | | | (126) ~ (all_52_7 = e1)
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | SIMP: (126) implies:
% 157.00/27.02 | | | | | | | | | | | | | (127) ~ (all_52_7 = e1)
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | REDUCE: (102), (125) imply:
% 157.00/27.02 | | | | | | | | | | | | | (128) ~ (e2 = e1)
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | BETA: splitting (29) gives:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | (129) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 157.00/27.02 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | (130) all_58_12 = e2 & op(e0, e3) = e2
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | (131) all_58_12 = e2
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | (132) all_54_13 = e3
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (132) imply:
% 157.00/27.02 | | | | | | | | | | | | | | | | (133) all_52_7 = e3
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | SIMP: (133) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | | (134) all_52_7 = e3
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | REDUCE: (57), (134) imply:
% 157.00/27.02 | | | | | | | | | | | | | | | | (135) ~ (all_52_6 = e3)
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | (136) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 157.00/27.02 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | (137) all_58_1 = e3 & op(e3, e2) = e3
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | | | | (138) op(e3, e2) = e3
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (42), (59), (62), (71), (76), (80), (117),
% 157.00/27.02 | | | | | | | | | | | | | | | | | | (138) are inconsistent by sub-proof #1126.
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | (139) all_58_3 = e3 & op(e2, e2) = e3
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (77), (80), (139) are inconsistent by
% 157.00/27.02 | | | | | | | | | | | | | | | | | | sub-proof #1437.
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | (140) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 157.00/27.02 | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | (141) all_58_7 = e3 & op(e1, e2) = e3
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (80), (135), (141) are inconsistent by
% 157.00/27.02 | | | | | | | | | | | | | | | | | | sub-proof #1184.
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | (142) all_58_13 = e3 & op(e0, e2) = e3
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | | | | (143) all_58_13 = e3
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (47), (52), (59), (80), (114), (131),
% 157.00/27.02 | | | | | | | | | | | | | | | | | | (143) are inconsistent by sub-proof #255.
% 157.00/27.02 | | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | (144) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (50), (103), (127), (144) are inconsistent by
% 157.00/27.02 | | | | | | | | | | | | | | | | sub-proof #254.
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | (145) all_58_13 = e2 & op(e0, e2) = e2
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | (146) op(e0, e2) = e2
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | REF_CLOSE: (74), (80), (103), (146) are inconsistent by
% 157.00/27.02 | | | | | | | | | | | | | | | sub-proof #1479.
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | (147) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 157.00/27.02 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | (148) all_58_14 = e2 & op(e0, e1) = e2
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | REF_CLOSE: (85), (114), (148) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | | | #1439.
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | (149) all_58_15 = e2 & op(e0, e0) = e2
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (80), (149) are inconsistent by
% 157.00/27.02 | | | | | | | | | | | | | | | sub-proof #1452.
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | (150) all_54_1 = e0
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | REF_CLOSE: (15), (48), (150) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | #1115.
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | (151) all_58_5 = e2 & op(e2, e1) = e2
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | ALPHA: (151) implies:
% 157.00/27.02 | | | | | | | | | | (152) op(e2, e1) = e2
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | REF_CLOSE: (21), (80), (104), (152) are inconsistent by
% 157.00/27.02 | | | | | | | | | | sub-proof #1441.
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | (153) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 157.00/27.02 | | | | | | | | | op(e0, e1) = e2)
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | BETA: splitting (153) gives:
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | (154) all_58_8 = e2 & op(e1, e1) = e2
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | REF_CLOSE: (6), (68), (80), (154) are inconsistent by
% 157.00/27.02 | | | | | | | | | | sub-proof #1440.
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | (155) all_58_14 = e2 & op(e0, e1) = e2
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | REF_CLOSE: (85), (114), (155) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | #1439.
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | End of split
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | End of split
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | End of split
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | Case 2:
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | (156) all_54_5 = e1 | all_54_5 = e0
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | REF_CLOSE: (63), (81), (89), (156) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | #1239.
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | End of split
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | End of split
% 157.00/27.02 | | | |
% 157.00/27.02 | | | Case 2:
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | (157) all_58_10 = e0 & op(e2, e0) = e0
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | REF_CLOSE: (3), (13), (17), (30), (35), (38), (42), (47), (52), (59),
% 157.00/27.02 | | | | (62), (80), (85), (157) are inconsistent by sub-proof #253.
% 157.00/27.02 | | | |
% 157.00/27.02 | | | End of split
% 157.00/27.02 | | |
% 157.00/27.02 | | End of split
% 157.00/27.02 | |
% 157.00/27.02 | Case 2:
% 157.00/27.02 | |
% 157.00/27.02 | | (158) all_30_2 = e0
% 157.00/27.02 | |
% 157.00/27.02 | | COMBINE_EQS: (36), (158) imply:
% 157.00/27.02 | | (159) all_8_2 = e0
% 157.00/27.02 | |
% 157.00/27.02 | | COMBINE_EQS: (20), (159) imply:
% 157.00/27.02 | | (160) all_56_13 = e0
% 157.00/27.02 | |
% 157.00/27.02 | | REDUCE: (41), (159) imply:
% 157.00/27.02 | | (161) ~ (all_52_6 = e0)
% 157.00/27.02 | |
% 157.00/27.02 | | REDUCE: (82), (159) imply:
% 157.00/27.02 | | (162) ~ (all_52_9 = e0)
% 157.00/27.02 | |
% 157.00/27.02 | | REDUCE: (31), (159) imply:
% 157.00/27.02 | | (163) ~ (e3 = e0)
% 157.00/27.02 | |
% 157.00/27.02 | | REDUCE: (63), (159) imply:
% 157.00/27.02 | | (164) ~ (e1 = e0)
% 157.00/27.02 | |
% 157.00/27.02 | | BETA: splitting (49) gives:
% 157.00/27.02 | |
% 157.00/27.02 | | Case 1:
% 157.00/27.02 | | |
% 157.00/27.02 | | | (165) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 157.00/27.02 | | | e0)
% 157.00/27.02 | | |
% 157.00/27.02 | | | BETA: splitting (165) gives:
% 157.00/27.02 | | |
% 157.00/27.02 | | | Case 1:
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | (166) all_58_2 = e0 & op(e2, e3) = e0
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | REF_CLOSE: (22), (64), (80), (166) are inconsistent by sub-proof #1433.
% 157.00/27.02 | | | |
% 157.00/27.02 | | | Case 2:
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | (167) all_58_3 = e0 & op(e2, e2) = e0
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | ALPHA: (167) implies:
% 157.00/27.02 | | | | (168) all_58_3 = e0
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | BETA: splitting (66) gives:
% 157.00/27.02 | | | |
% 157.00/27.02 | | | | Case 1:
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | (169) ~ (all_56_13 = e0)
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | REDUCE: (160), (169) imply:
% 157.00/27.02 | | | | | (170) $false
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | CLOSE: (170) is inconsistent.
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | Case 2:
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | (171) all_56_5 = e2 & op(e2, e0) = e2
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | ALPHA: (171) implies:
% 157.00/27.02 | | | | | (172) op(e2, e0) = e2
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | BETA: splitting (34) gives:
% 157.00/27.02 | | | | |
% 157.00/27.02 | | | | | Case 1:
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | (173) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 157.00/27.02 | | | | | | e2) = e0)
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | BETA: splitting (173) gives:
% 157.00/27.02 | | | | | |
% 157.00/27.02 | | | | | | Case 1:
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | (174) all_58_6 = e0 & op(e1, e3) = e0
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | ALPHA: (174) implies:
% 157.00/27.02 | | | | | | | (175) all_58_6 = e0
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | BETA: splitting (43) gives:
% 157.00/27.02 | | | | | | |
% 157.00/27.02 | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | (176) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 157.00/27.02 | | | | | | | | op(e2, e1) = e0)
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | REF_CLOSE: (21), (27), (30), (35), (42), (59), (62), (71), (76),
% 157.00/27.02 | | | | | | | | (80), (85), (162), (176) are inconsistent by
% 157.00/27.02 | | | | | | | | sub-proof #315.
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | (177) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 157.00/27.02 | | | | | | | | op(e0, e1) = e0)
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | BETA: splitting (177) gives:
% 157.00/27.02 | | | | | | | |
% 157.00/27.02 | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | (178) all_58_8 = e0 & op(e1, e1) = e0
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | ALPHA: (178) implies:
% 157.00/27.02 | | | | | | | | | (179) all_58_8 = e0
% 157.00/27.02 | | | | | | | | | (180) op(e1, e1) = e0
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | BETA: splitting (19) gives:
% 157.00/27.02 | | | | | | | | |
% 157.00/27.02 | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | (181) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 157.00/27.02 | | | | | | | | | | & op(e1, e2) = e3)
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | BETA: splitting (181) gives:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | (182) all_58_6 = e3 & op(e1, e3) = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | ALPHA: (182) implies:
% 157.00/27.02 | | | | | | | | | | | (183) all_58_6 = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | REF_CLOSE: (25), (175), (183) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | #1321.
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | (184) all_58_7 = e3 & op(e1, e2) = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | ALPHA: (184) implies:
% 157.00/27.02 | | | | | | | | | | | (185) all_58_7 = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | BETA: splitting (24) gives:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | (186) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 157.00/27.02 | | | | | | | | | | | | & op(e1, e2) = e2)
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | BETA: splitting (186) gives:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | (187) all_58_6 = e2 & op(e1, e3) = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | ALPHA: (187) implies:
% 157.00/27.02 | | | | | | | | | | | | | (188) all_58_6 = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | REF_CLOSE: (30), (175), (188) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | #1514.
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | (189) all_58_7 = e2 & op(e1, e2) = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | ALPHA: (189) implies:
% 157.00/27.02 | | | | | | | | | | | | | (190) all_58_7 = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | REF_CLOSE: (85), (185), (190) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | #1215.
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | (191) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 157.00/27.02 | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | BETA: splitting (191) gives:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | (192) all_58_8 = e2 & op(e1, e1) = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | REF_CLOSE: (6), (68), (80), (192) are inconsistent by
% 157.00/27.02 | | | | | | | | | | | | | sub-proof #1440.
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | (193) all_58_11 = e2 & op(e1, e0) = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | ALPHA: (193) implies:
% 157.00/27.02 | | | | | | | | | | | | | (194) all_58_11 = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | BETA: splitting (3) gives:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | (195) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 157.00/27.02 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | (196) all_58_9 = e1 & op(e3, e0) = e1
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | (197) all_58_9 = e1
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | REF_CLOSE: (35), (42), (197) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | | | #1461.
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | (198) all_58_10 = e1 & op(e2, e0) = e1
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | (199) all_58_10 = e1
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | (200) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 157.00/27.02 | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | (201) all_58_6 = e1 & op(e1, e3) = e1
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | | | (202) all_58_6 = e1
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (202) imply:
% 157.00/27.02 | | | | | | | | | | | | | | | | | (203) e1 = e0
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | SIMP: (203) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | | | (204) e1 = e0
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (204) imply:
% 157.00/27.02 | | | | | | | | | | | | | | | | | (205) all_58_10 = e0
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (35), (42), (47), (52), (59), (62), (80),
% 157.00/27.02 | | | | | | | | | | | | | | | | | (194), (205) are inconsistent by sub-proof #350.
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | (206) all_58_7 = e1 & op(e1, e2) = e1
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | | | (207) all_58_7 = e1
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (185), (207) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | | | | | #1330.
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | (208) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 157.00/27.02 | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | (209) all_58_8 = e1 & op(e1, e1) = e1
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 157.00/27.02 | | | | | | | | | | | | | | | | | (210) all_58_8 = e1
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (210) imply:
% 157.00/27.02 | | | | | | | | | | | | | | | | | (211) e1 = e0
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (211) imply:
% 157.00/27.02 | | | | | | | | | | | | | | | | | (212) all_58_10 = e0
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (35), (42), (47), (52), (59), (62), (80),
% 157.00/27.02 | | | | | | | | | | | | | | | | | (194), (212) are inconsistent by sub-proof #350.
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | (213) all_58_11 = e1 & op(e1, e0) = e1
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (194), (213) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | | | | | #1455.
% 157.00/27.02 | | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | (214) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 157.00/27.02 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | (215) all_58_11 = e1 & op(e1, e0) = e1
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | REF_CLOSE: (59), (194), (215) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | | | #1455.
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | (216) all_58_15 = e1 & op(e0, e0) = e1
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | | REF_CLOSE: (47), (52), (80), (216) are inconsistent by
% 157.00/27.02 | | | | | | | | | | | | | | | sub-proof #1418.
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | End of split
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | (217) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3
% 157.00/27.02 | | | | | | | | | | & op(e1, e0) = e3)
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | BETA: splitting (217) gives:
% 157.00/27.02 | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | (218) all_58_8 = e3 & op(e1, e1) = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | ALPHA: (218) implies:
% 157.00/27.02 | | | | | | | | | | | (219) op(e1, e1) = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | REF_CLOSE: (25), (80), (180), (219) are inconsistent by
% 157.00/27.02 | | | | | | | | | | | sub-proof #1466.
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | (220) all_58_11 = e3 & op(e1, e0) = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | ALPHA: (220) implies:
% 157.00/27.02 | | | | | | | | | | | (221) all_58_11 = e3
% 157.00/27.02 | | | | | | | | | | | (222) op(e1, e0) = e3
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | BETA: splitting (24) gives:
% 157.00/27.02 | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | (223) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 157.00/27.02 | | | | | | | | | | | | & op(e1, e2) = e2)
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | BETA: splitting (223) gives:
% 157.00/27.02 | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | (224) all_58_6 = e2 & op(e1, e3) = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | ALPHA: (224) implies:
% 157.00/27.02 | | | | | | | | | | | | | (225) all_58_6 = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | REF_CLOSE: (30), (175), (225) are inconsistent by sub-proof
% 157.00/27.02 | | | | | | | | | | | | | #1514.
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | Case 2:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | (226) all_58_7 = e2 & op(e1, e2) = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | ALPHA: (226) implies:
% 157.00/27.02 | | | | | | | | | | | | | (227) op(e1, e2) = e2
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | BETA: splitting (2) gives:
% 157.00/27.02 | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | (228) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 157.00/27.02 | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 157.00/27.02 | | | | | | | | | | | | | |
% 157.00/27.02 | | | | | | | | | | | | | | Case 1:
% 157.00/27.02 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (229) all_58_6 = e1 & op(e1, e3) = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | (230) all_58_6 = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REF_CLOSE: (62), (175), (230) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | #735.
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (231) all_58_7 = e1 & op(e1, e2) = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | (232) op(e1, e2) = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REF_CLOSE: (59), (80), (227), (232) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | | | | sub-proof #1088.
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | (233) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 157.00/27.03 | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (234) all_58_8 = e1 & op(e1, e1) = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REF_CLOSE: (62), (179), (234) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | #1474.
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (235) all_58_11 = e1 & op(e1, e0) = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | (236) op(e1, e0) = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REF_CLOSE: (42), (80), (222), (236) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | | | | sub-proof #1275.
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | (237) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 157.00/27.03 | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | REF_CLOSE: (6), (68), (80), (85), (221), (237) are
% 157.00/27.03 | | | | | | | | | | | | inconsistent by sub-proof #431.
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | (238) all_58_14 = e0 & op(e0, e1) = e0
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | ALPHA: (238) implies:
% 157.00/27.03 | | | | | | | | | (239) all_58_14 = e0
% 157.00/27.03 | | | | | | | | | (240) op(e0, e1) = e0
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | BETA: splitting (26) gives:
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | (241) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.00/27.03 | | | | | | | | | | & op(e2, e3) = e1)
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | BETA: splitting (241) gives:
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | (242) all_58_0 = e1 & op(e3, e3) = e1
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | REF_CLOSE: (62), (76), (242) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | #1495.
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | (243) all_58_2 = e1 & op(e2, e3) = e1
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | ALPHA: (243) implies:
% 157.00/27.03 | | | | | | | | | | | (244) op(e2, e3) = e1
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | BETA: splitting (56) gives:
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | (245) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 157.00/27.03 | | | | | | | | | | | | & op(e2, e2) = e3)
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | REF_CLOSE: (31), (42), (77), (80), (244), (245) are
% 157.00/27.03 | | | | | | | | | | | | inconsistent by sub-proof #884.
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | (246) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 157.00/27.03 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | BETA: splitting (246) gives:
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | (247) all_58_5 = e3 & op(e2, e1) = e3
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | ALPHA: (247) implies:
% 157.00/27.03 | | | | | | | | | | | | | (248) all_58_5 = e3
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | BETA: splitting (19) gives:
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | (249) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 157.00/27.03 | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (250) all_58_6 = e3 & op(e1, e3) = e3
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REF_CLOSE: (25), (175), (250) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | #749.
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (251) all_58_7 = e3 & op(e1, e2) = e3
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | (252) all_58_7 = e3
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | (253) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (254) all_58_12 = e1 & op(e0, e3) = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (10), (19), (22), (24), (25),
% 157.00/27.03 | | | | | | | | | | | | | | | | | (30), (32), (35), (42), (46), (47), (49), (51),
% 157.00/27.03 | | | | | | | | | | | | | | | | | (52), (59), (62), (63), (67), (68), (73), (77),
% 157.00/27.03 | | | | | | | | | | | | | | | | | (80), (85), (175), (239), (254) are inconsistent
% 157.00/27.03 | | | | | | | | | | | | | | | | | by sub-proof #244.
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (255) all_58_13 = e1 & op(e0, e2) = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | (256) op(e0, e2) = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (257) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (258) all_58_12 = e2 & op(e0, e3) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (259) all_58_12 = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | (260) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | (261) all_58_2 = e2 & op(e2, e3) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | (262) op(e2, e3) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (80), (244), (262) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | sub-proof #1430.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | (263) all_58_3 = e2 & op(e2, e2) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (168), (263) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | #1051.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | (264) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | (265) all_58_5 = e2 & op(e2, e1) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (248), (265) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | #250.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | (266) all_58_10 = e2 & op(e2, e0) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | (267) all_58_10 = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | (268) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_6 = e2 & op(e1, e3) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_6 = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (25), (26), (42), (59), (62), (76), (80),
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | (85), (259), (270) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | #1488.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_7 = e2 & op(e1, e2) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | (272) all_58_7 = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (252), (272) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | | #1215.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | (273) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (35), (42), (47), (52), (59), (68),
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | (80), (267), (273) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | | #247.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (274) all_58_13 = e2 & op(e0, e2) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (275) op(e0, e2) = e2
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (74), (80), (256), (275) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | sub-proof #1319.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (276) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (30), (52), (53), (80), (240), (276) are
% 157.00/27.03 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #334.
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | (277) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (278) all_58_14 = e1 & op(e0, e1) = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | (279) all_58_14 = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (239), (279) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | | | #614.
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (280) all_58_15 = e1 & op(e0, e0) = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (52), (80), (280) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | | | | | | sub-proof #1418.
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | (281) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 157.00/27.03 | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (282) all_58_8 = e3 & op(e1, e1) = e3
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (80), (282) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | | | | sub-proof #1469.
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (283) all_58_11 = e3 & op(e1, e0) = e3
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (17), (35), (42), (47), (52), (59),
% 157.00/27.03 | | | | | | | | | | | | | | | (80), (85), (283) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | #243.
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | (284) all_58_10 = e3 & op(e2, e0) = e3
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | REF_CLOSE: (3), (13), (17), (35), (42), (47), (52), (59),
% 157.00/27.03 | | | | | | | | | | | | | (80), (85), (284) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | #331.
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | (285) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 157.00/27.03 | | | | | | | | | | & op(e0, e3) = e1)
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | BETA: splitting (285) gives:
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | (286) all_58_6 = e1 & op(e1, e3) = e1
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | ALPHA: (286) implies:
% 157.00/27.03 | | | | | | | | | | | (287) all_58_6 = e1
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | REF_CLOSE: (62), (175), (287) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | #735.
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | (288) all_58_12 = e1 & op(e0, e3) = e1
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (10), (19), (22), (24), (25),
% 157.00/27.03 | | | | | | | | | | | (30), (32), (35), (42), (46), (47), (49), (51),
% 157.00/27.03 | | | | | | | | | | | (52), (59), (62), (63), (67), (68), (73), (77),
% 157.00/27.03 | | | | | | | | | | | (80), (85), (175), (239), (288) are inconsistent
% 157.00/27.03 | | | | | | | | | | | by sub-proof #244.
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | End of split
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | End of split
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | Case 2:
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | (289) all_58_7 = e0 & op(e1, e2) = e0
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | REF_CLOSE: (44), (80), (161), (289) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | #1301.
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | End of split
% 157.00/27.03 | | | | | |
% 157.00/27.03 | | | | | Case 2:
% 157.00/27.03 | | | | | |
% 157.00/27.03 | | | | | | (290) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 157.00/27.03 | | | | | | op(e1, e0) = e0)
% 157.00/27.03 | | | | | |
% 157.00/27.03 | | | | | | BETA: splitting (290) gives:
% 157.00/27.03 | | | | | |
% 157.00/27.03 | | | | | | Case 1:
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | (291) all_58_8 = e0 & op(e1, e1) = e0
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | ALPHA: (291) implies:
% 157.00/27.03 | | | | | | | (292) op(e1, e1) = e0
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | GROUND_INST: instantiating (80) with all_6_2, e0, e1, e1,
% 157.00/27.03 | | | | | | | simplifying with (6), (292) gives:
% 157.00/27.03 | | | | | | | (293) all_6_2 = e0
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | GROUND_INST: instantiating (80) with all_52_13, e2, e0, e2,
% 157.00/27.03 | | | | | | | simplifying with (38), (172) gives:
% 157.00/27.03 | | | | | | | (294) all_52_13 = e2
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | COMBINE_EQS: (69), (293) imply:
% 157.00/27.03 | | | | | | | (295) all_56_14 = e0
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | REDUCE: (28), (294) imply:
% 157.00/27.03 | | | | | | | (296) ~ (all_52_9 = e2)
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | REDUCE: (84), (294) imply:
% 157.00/27.03 | | | | | | | (297) ~ (all_52_14 = e2)
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | SIMP: (297) implies:
% 157.00/27.03 | | | | | | | (298) ~ (all_52_14 = e2)
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | REDUCE: (23), (294) imply:
% 157.00/27.03 | | | | | | | (299) ~ (e3 = e2)
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | REDUCE: (79), (293) imply:
% 157.00/27.03 | | | | | | | (300) ~ (all_52_14 = e0)
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | REDUCE: (68), (293) imply:
% 157.00/27.03 | | | | | | | (301) ~ (e2 = e0)
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | BETA: splitting (33) gives:
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | | (302) ~ (all_56_14 = e0)
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | | REDUCE: (295), (302) imply:
% 157.00/27.03 | | | | | | | | (303) $false
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | | CLOSE: (303) is inconsistent.
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | | (304) all_56_8 = e1 & op(e1, e0) = e1
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | | ALPHA: (304) implies:
% 157.00/27.03 | | | | | | | | (305) all_56_8 = e1
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | | BETA: splitting (13) gives:
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | (306) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 157.00/27.03 | | | | | | | | | op(e2, e0) = e2)
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | BETA: splitting (306) gives:
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | (307) all_58_9 = e2 & op(e3, e0) = e2
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | REF_CLOSE: (35), (85), (307) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | #1353.
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | (308) all_58_10 = e2 & op(e2, e0) = e2
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | ALPHA: (308) implies:
% 157.00/27.03 | | | | | | | | | | (309) all_58_10 = e2
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | BETA: splitting (3) gives:
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | (310) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 157.00/27.03 | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | REF_CLOSE: (35), (42), (59), (309), (310) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | sub-proof #329.
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | (311) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 157.00/27.03 | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | BETA: splitting (311) gives:
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | (312) all_58_11 = e1 & op(e1, e0) = e1
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | ALPHA: (312) implies:
% 157.00/27.03 | | | | | | | | | | | | (313) all_58_11 = e1
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | BETA: splitting (61) gives:
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | (314) all_54_11 = e3
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | REF_CLOSE: (14), (83), (314) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | #1415.
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | (315) ~ (all_54_11 = e3)
% 157.00/27.03 | | | | | | | | | | | | | (316) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | BETA: splitting (316) gives:
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | (317) all_54_11 = e2
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | REF_CLOSE: (83), (298), (317) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | #1414.
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | (318) ~ (all_54_11 = e2)
% 157.00/27.03 | | | | | | | | | | | | | | (319) all_54_11 = e1 | all_54_11 = e0
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (320) all_54_11 = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | COMBINE_EQS: (83), (320) imply:
% 157.00/27.03 | | | | | | | | | | | | | | | (321) all_52_14 = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | SIMP: (321) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | (322) all_52_14 = e1
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REDUCE: (55), (322) imply:
% 157.00/27.03 | | | | | | | | | | | | | | | (323) ~ (all_52_2 = e1)
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REDUCE: (8), (322) imply:
% 157.00/27.03 | | | | | | | | | | | | | | | (324) ~ (all_52_6 = e1)
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REDUCE: (14), (322) imply:
% 157.00/27.03 | | | | | | | | | | | | | | | (325) ~ (e3 = e1)
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REDUCE: (298), (322) imply:
% 157.00/27.03 | | | | | | | | | | | | | | | (326) ~ (e2 = e1)
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | (327) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (328) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (22), (25), (30), (42), (49), (56),
% 157.00/27.03 | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (67), (73), (77), (80),
% 157.00/27.03 | | | | | | | | | | | | | | | | | (85), (309), (328) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | | | #311.
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (329) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (330) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (331) op(e1, e3) = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (80), (323), (331) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | | | | | | | sub-proof #1412.
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (332) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (25), (40), (70), (80), (332) are
% 157.00/27.03 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #242.
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | (333) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.00/27.03 | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.00/27.03 | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (334) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (40), (44), (80), (296), (324), (334) are
% 157.00/27.03 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (335) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (336) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (337) op(e0, e2) = e0
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (74), (80), (337) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | | | | | | | sub-proof #1532.
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (338) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives:
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | Case 1:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (339) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (340) ~ (all_56_15 = e0)
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | REDUCE: (40), (340) imply:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (341) $false
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | CLOSE: (341) is inconsistent.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (342) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (343) all_56_8 = e0
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (343) imply:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (344) e1 = e0
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | SIMP: (344) implies:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (345) e1 = e0
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (345) imply:
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (346) all_58_11 = e0
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (35), (42), (47), (52), (59), (62), (80),
% 157.00/27.03 | | | | | | | | | | | | | | | | | | | (309), (346) are inconsistent by sub-proof #241.
% 157.00/27.03 | | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | (347) all_54_11 = e0
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | | REF_CLOSE: (83), (300), (347) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | | | | | | | | | #1394.
% 157.00/27.03 | | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | (348) all_58_15 = e1 & op(e0, e0) = e1
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | | REF_CLOSE: (47), (52), (80), (348) are inconsistent by
% 157.00/27.03 | | | | | | | | | | | | sub-proof #1418.
% 157.00/27.03 | | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | | |
% 157.00/27.03 | | | | | | | | | End of split
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | Case 2:
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | (349) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2
% 157.00/27.03 | | | | | | | | | & op(e0, e0) = e2)
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | | REF_CLOSE: (17), (52), (75), (80), (298), (349) are
% 157.00/27.03 | | | | | | | | | inconsistent by sub-proof #1185.
% 157.00/27.03 | | | | | | | | |
% 157.00/27.03 | | | | | | | | End of split
% 157.00/27.03 | | | | | | | |
% 157.00/27.03 | | | | | | | End of split
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | Case 2:
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | (350) all_58_11 = e0 & op(e1, e0) = e0
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | ALPHA: (350) implies:
% 157.00/27.03 | | | | | | | (351) all_58_11 = e0
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | | REF_CLOSE: (3), (13), (17), (30), (35), (42), (47), (52), (59),
% 157.00/27.03 | | | | | | | (62), (80), (85), (351) are inconsistent by sub-proof
% 157.00/27.03 | | | | | | | #240.
% 157.00/27.03 | | | | | | |
% 157.00/27.03 | | | | | | End of split
% 157.00/27.03 | | | | | |
% 157.00/27.03 | | | | | End of split
% 157.00/27.03 | | | | |
% 157.00/27.03 | | | | End of split
% 157.00/27.03 | | | |
% 157.00/27.03 | | | End of split
% 157.00/27.03 | | |
% 157.00/27.03 | | Case 2:
% 157.00/27.03 | | |
% 157.00/27.03 | | | (352) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 157.00/27.03 | | | = e0)
% 157.00/27.03 | | |
% 157.00/27.03 | | | BETA: splitting (352) gives:
% 157.00/27.03 | | |
% 157.00/27.03 | | | Case 1:
% 157.00/27.03 | | | |
% 157.00/27.03 | | | | (353) all_58_5 = e0 & op(e2, e1) = e0
% 157.00/27.03 | | | |
% 157.00/27.03 | | | | ALPHA: (353) implies:
% 157.00/27.03 | | | | (354) op(e2, e1) = e0
% 157.00/27.03 | | | |
% 157.00/27.03 | | | | REF_CLOSE: (21), (80), (162), (354) are inconsistent by sub-proof #1300.
% 157.00/27.03 | | | |
% 157.00/27.03 | | | Case 2:
% 157.00/27.03 | | | |
% 157.00/27.03 | | | | (355) all_58_10 = e0 & op(e2, e0) = e0
% 157.00/27.03 | | | |
% 157.00/27.03 | | | | REF_CLOSE: (3), (13), (17), (30), (35), (38), (42), (47), (52), (59),
% 157.00/27.03 | | | | (62), (80), (85), (355) are inconsistent by sub-proof #253.
% 157.00/27.03 | | | |
% 157.00/27.03 | | | End of split
% 157.00/27.03 | | |
% 157.00/27.03 | | End of split
% 157.00/27.03 | |
% 157.00/27.03 | End of split
% 157.00/27.03 |
% 157.00/27.03 End of proof
% 157.00/27.03
% 157.00/27.03 Sub-proof #240 shows that the following formulas are inconsistent:
% 157.00/27.03 ----------------------------------------------------------------
% 157.00/27.03 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.03 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.03 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.00/27.03 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.00/27.03 (3) ~ (all_4_2 = e2)
% 157.00/27.03 (4) ~ (e2 = e0)
% 157.00/27.03 (5) all_58_9 = e3
% 157.00/27.03 (6) ~ (e3 = e1)
% 157.00/27.03 (7) ~ (all_4_2 = e1)
% 157.00/27.03 (8) op(e0, e0) = all_4_2
% 157.00/27.03 (9) ~ (e2 = e1)
% 157.00/27.03 (10) ~ (e1 = e0)
% 157.00/27.03 (11) all_58_11 = e0
% 157.00/27.03 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.03 (13) ~ (e3 = e2)
% 157.00/27.03
% 157.00/27.03 Begin of proof
% 157.00/27.03 |
% 157.00/27.03 | BETA: splitting (2) gives:
% 157.00/27.03 |
% 157.00/27.03 | Case 1:
% 157.00/27.03 | |
% 157.00/27.03 | | (14) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 157.00/27.03 | | e2)
% 157.00/27.03 | |
% 157.00/27.03 | | BETA: splitting (14) gives:
% 157.00/27.03 | |
% 157.00/27.03 | | Case 1:
% 157.00/27.03 | | |
% 157.00/27.03 | | | (15) all_58_9 = e2 & op(e3, e0) = e2
% 157.00/27.03 | | |
% 157.00/27.03 | | | REF_CLOSE: (5), (13), (15) are inconsistent by sub-proof #1353.
% 157.00/27.03 | | |
% 157.00/27.03 | | Case 2:
% 157.00/27.03 | | |
% 157.00/27.03 | | | (16) all_58_10 = e2 & op(e2, e0) = e2
% 157.00/27.03 | | |
% 157.00/27.03 | | | ALPHA: (16) implies:
% 157.00/27.03 | | | (17) all_58_10 = e2
% 157.00/27.03 | | |
% 157.00/27.03 | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (17) are
% 157.00/27.03 | | | inconsistent by sub-proof #241.
% 157.00/27.03 | | |
% 157.00/27.03 | | End of split
% 157.00/27.03 | |
% 157.00/27.03 | Case 2:
% 157.00/27.03 | |
% 157.00/27.03 | | (18) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.00/27.03 | | e2)
% 157.00/27.03 | |
% 157.00/27.03 | | REF_CLOSE: (3), (4), (8), (11), (12), (18) are inconsistent by sub-proof
% 157.00/27.03 | | #330.
% 157.00/27.03 | |
% 157.00/27.03 | End of split
% 157.00/27.03 |
% 157.00/27.03 End of proof
% 157.00/27.03
% 157.00/27.03 Sub-proof #241 shows that the following formulas are inconsistent:
% 157.00/27.03 ----------------------------------------------------------------
% 157.00/27.03 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.03 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.03 (2) all_58_10 = e2
% 157.00/27.03 (3) all_58_9 = e3
% 157.00/27.03 (4) ~ (e3 = e1)
% 157.00/27.03 (5) ~ (all_4_2 = e1)
% 157.00/27.03 (6) op(e0, e0) = all_4_2
% 157.00/27.03 (7) ~ (e2 = e1)
% 157.00/27.03 (8) ~ (e1 = e0)
% 157.00/27.03 (9) all_58_11 = e0
% 157.00/27.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.03
% 157.00/27.03 Begin of proof
% 157.00/27.03 |
% 157.00/27.03 | BETA: splitting (1) gives:
% 157.00/27.03 |
% 157.00/27.03 | Case 1:
% 157.00/27.03 | |
% 157.00/27.03 | | (11) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.00/27.03 | | e1)
% 157.00/27.03 | |
% 157.00/27.03 | | REF_CLOSE: (2), (3), (4), (7), (11) are inconsistent by sub-proof #319.
% 157.00/27.03 | |
% 157.00/27.03 | Case 2:
% 157.00/27.03 | |
% 157.00/27.03 | | (12) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.00/27.03 | | e1)
% 157.00/27.03 | |
% 157.00/27.03 | | BETA: splitting (12) gives:
% 157.00/27.03 | |
% 157.00/27.03 | | Case 1:
% 157.00/27.03 | | |
% 157.00/27.03 | | | (13) all_58_11 = e1 & op(e1, e0) = e1
% 157.00/27.03 | | |
% 157.00/27.03 | | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #459.
% 157.00/27.03 | | |
% 157.00/27.03 | | Case 2:
% 157.00/27.03 | | |
% 157.00/27.03 | | | (14) all_58_15 = e1 & op(e0, e0) = e1
% 157.00/27.03 | | |
% 157.00/27.03 | | | REF_CLOSE: (5), (6), (10), (14) are inconsistent by sub-proof #1418.
% 157.00/27.03 | | |
% 157.00/27.03 | | End of split
% 157.00/27.03 | |
% 157.00/27.03 | End of split
% 157.00/27.03 |
% 157.00/27.03 End of proof
% 157.00/27.03
% 157.00/27.03 Sub-proof #242 shows that the following formulas are inconsistent:
% 157.00/27.03 ----------------------------------------------------------------
% 157.00/27.03 (1) op(e3, e0) = all_52_12
% 157.00/27.03 (2) ~ (e3 = e0)
% 157.00/27.03 (3) all_56_15 = e0
% 157.00/27.03 (4) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 &
% 157.00/27.03 op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3)
% 157.00/27.03 & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.00/27.03 (5) op(e3, e0) = e3
% 157.00/27.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.03
% 157.00/27.03 Begin of proof
% 157.00/27.03 |
% 157.00/27.03 | BETA: splitting (4) gives:
% 157.00/27.03 |
% 157.00/27.03 | Case 1:
% 157.00/27.03 | |
% 157.00/27.04 | | (7) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3
% 157.00/27.04 | | & op(e0, e3) = e3
% 157.00/27.04 | |
% 157.00/27.04 | | ALPHA: (7) implies:
% 157.00/27.04 | | (8) ~ (all_56_15 = e0)
% 157.00/27.04 | |
% 157.00/27.04 | | REDUCE: (3), (8) imply:
% 157.00/27.04 | | (9) $false
% 157.00/27.04 | |
% 157.00/27.04 | | CLOSE: (9) is inconsistent.
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (10) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 157.00/27.04 | | e0 & op(e0, e3) = e0
% 157.00/27.04 | |
% 157.00/27.04 | | ALPHA: (10) implies:
% 157.00/27.04 | | (11) op(e3, e0) = e0
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (1), (2), (5), (6), (11) are inconsistent by sub-proof #258.
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #243 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.04 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.04 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.00/27.04 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.00/27.04 (3) all_58_11 = e3 & op(e1, e0) = e3
% 157.00/27.04 (4) ~ (all_4_2 = e2)
% 157.00/27.04 (5) all_58_9 = e3
% 157.00/27.04 (6) ~ (e3 = e1)
% 157.00/27.04 (7) ~ (all_4_2 = e1)
% 157.00/27.04 (8) op(e0, e0) = all_4_2
% 157.00/27.04 (9) ~ (e2 = e1)
% 157.00/27.04 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04 (11) ~ (e3 = e2)
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | ALPHA: (3) implies:
% 157.00/27.04 | (12) all_58_11 = e3
% 157.00/27.04 | (13) op(e1, e0) = e3
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (2) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (14) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 157.00/27.04 | | e2)
% 157.00/27.04 | |
% 157.00/27.04 | | BETA: splitting (14) gives:
% 157.00/27.04 | |
% 157.00/27.04 | | Case 1:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (15) all_58_9 = e2 & op(e3, e0) = e2
% 157.00/27.04 | | |
% 157.00/27.04 | | | ALPHA: (15) implies:
% 157.00/27.04 | | | (16) all_58_9 = e2
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (5), (11), (16) are inconsistent by sub-proof #1245.
% 157.00/27.04 | | |
% 157.00/27.04 | | Case 2:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (17) all_58_10 = e2 & op(e2, e0) = e2
% 157.00/27.04 | | |
% 157.00/27.04 | | | ALPHA: (17) implies:
% 157.00/27.04 | | | (18) all_58_10 = e2
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (13), (18) are inconsistent
% 157.00/27.04 | | | by sub-proof #246.
% 157.00/27.04 | | |
% 157.00/27.04 | | End of split
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (19) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.00/27.04 | | e2)
% 157.00/27.04 | |
% 157.00/27.04 | | BETA: splitting (19) gives:
% 157.00/27.04 | |
% 157.00/27.04 | | Case 1:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (20) all_58_11 = e2 & op(e1, e0) = e2
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (11), (12), (20) are inconsistent by sub-proof #852.
% 157.00/27.04 | | |
% 157.00/27.04 | | Case 2:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (21) all_58_15 = e2 & op(e0, e0) = e2
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (4), (8), (10), (21) are inconsistent by sub-proof #1452.
% 157.00/27.04 | | |
% 157.00/27.04 | | End of split
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #244 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.04 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.04 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.00/27.04 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.00/27.04 (3) op(e1, e1) = all_6_2
% 157.00/27.04 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.00/27.04 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.00/27.04 (5) all_58_14 = e0
% 157.00/27.04 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.00/27.04 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.00/27.04 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.00/27.04 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.00/27.04 (8) op(e2, e3) = all_52_1
% 157.00/27.04 (9) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.00/27.04 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.00/27.04 (10) ~ (e3 = e0)
% 157.00/27.04 (11) ~ (e2 = e0)
% 157.00/27.04 (12) op(e3, e3) = e0
% 157.00/27.04 (13) all_58_6 = e0
% 157.00/27.04 (14) all_58_9 = e3
% 157.00/27.04 (15) ~ (e3 = e1)
% 157.00/27.04 (16) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.00/27.04 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.00/27.04 (17) ~ (all_4_2 = e1)
% 157.00/27.04 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.00/27.04 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.00/27.04 (19) ~ (all_6_2 = e3)
% 157.00/27.04 (20) op(e0, e0) = all_4_2
% 157.00/27.04 (21) ~ (e2 = e1)
% 157.00/27.04 (22) ~ (e1 = e0)
% 157.00/27.04 (23) ~ (all_8_2 = e1)
% 157.00/27.04 (24) op(e3, e1) = all_52_8
% 157.00/27.04 (25) ~ (all_6_2 = e2)
% 157.00/27.04 (26) all_58_12 = e1 & op(e0, e3) = e1
% 157.00/27.04 (27) ~ (all_52_8 = e3)
% 157.00/27.04 (28) op(e2, e2) = all_8_2
% 157.00/27.04 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04 (30) ~ (e3 = e2)
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | ALPHA: (26) implies:
% 157.00/27.04 | (31) all_58_12 = e1
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (6) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (32) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 157.00/27.04 | | e3)
% 157.00/27.04 | |
% 157.00/27.04 | | BETA: splitting (32) gives:
% 157.00/27.04 | |
% 157.00/27.04 | | Case 1:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (33) all_58_0 = e3 & op(e3, e3) = e3
% 157.00/27.04 | | |
% 157.00/27.04 | | | ALPHA: (33) implies:
% 157.00/27.04 | | | (34) op(e3, e3) = e3
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (10), (12), (29), (34) are inconsistent by sub-proof #1521.
% 157.00/27.04 | | |
% 157.00/27.04 | | Case 2:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (35) all_58_2 = e3 & op(e2, e3) = e3
% 157.00/27.04 | | |
% 157.00/27.04 | | | ALPHA: (35) implies:
% 157.00/27.04 | | | (36) all_58_2 = e3
% 157.00/27.04 | | | (37) op(e2, e3) = e3
% 157.00/27.04 | | |
% 157.00/27.04 | | | BETA: splitting (4) gives:
% 157.00/27.04 | | |
% 157.00/27.04 | | | Case 1:
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | (38) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 157.00/27.04 | | | | = e3)
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | BETA: splitting (38) gives:
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | Case 1:
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | | (39) all_58_4 = e3 & op(e3, e1) = e3
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | | ALPHA: (39) implies:
% 157.00/27.04 | | | | | (40) op(e3, e1) = e3
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | | REF_CLOSE: (24), (27), (29), (40) are inconsistent by sub-proof #1538.
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | Case 2:
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | | (41) all_58_5 = e3 & op(e2, e1) = e3
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | | ALPHA: (41) implies:
% 157.00/27.04 | | | | | (42) all_58_5 = e3
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | | BETA: splitting (7) gives:
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | | Case 1:
% 157.00/27.04 | | | | | |
% 157.00/27.04 | | | | | | (43) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 157.00/27.04 | | | | | | e2) = e3)
% 157.00/27.04 | | | | | |
% 157.00/27.04 | | | | | | BETA: splitting (43) gives:
% 157.00/27.04 | | | | | |
% 157.00/27.04 | | | | | | Case 1:
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | (44) all_58_6 = e3 & op(e1, e3) = e3
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | REF_CLOSE: (10), (13), (44) are inconsistent by sub-proof #749.
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | Case 2:
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | (45) all_58_7 = e3 & op(e1, e2) = e3
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | ALPHA: (45) implies:
% 157.00/27.04 | | | | | | | (46) all_58_7 = e3
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | BETA: splitting (16) gives:
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | Case 1:
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | (47) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 157.00/27.04 | | | | | | | | op(e2, e2) = e2)
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | REF_CLOSE: (2), (8), (10), (11), (15), (18), (22), (23), (28),
% 157.00/27.04 | | | | | | | | (29), (30), (36), (37), (42), (47) are inconsistent
% 157.00/27.04 | | | | | | | | by sub-proof #251.
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | Case 2:
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | (48) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 157.00/27.04 | | | | | | | | op(e2, e0) = e2)
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | BETA: splitting (48) gives:
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | Case 1:
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | (49) all_58_5 = e2 & op(e2, e1) = e2
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | REF_CLOSE: (30), (42), (49) are inconsistent by sub-proof
% 157.00/27.04 | | | | | | | | | #250.
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | Case 2:
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | (50) all_58_10 = e2 & op(e2, e0) = e2
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | ALPHA: (50) implies:
% 157.00/27.04 | | | | | | | | | (51) all_58_10 = e2
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | BETA: splitting (9) gives:
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | Case 1:
% 157.00/27.04 | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | (52) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 157.00/27.04 | | | | | | | | | | op(e1, e2) = e2)
% 157.00/27.04 | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | BETA: splitting (52) gives:
% 157.00/27.04 | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | Case 1:
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | | (53) all_58_6 = e2 & op(e1, e3) = e2
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | | ALPHA: (53) implies:
% 157.00/27.04 | | | | | | | | | | | (54) all_58_6 = e2
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | | COMBINE_EQS: (13), (54) imply:
% 157.00/27.04 | | | | | | | | | | | (55) e2 = e0
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | | COMBINE_EQS: (51), (55) imply:
% 157.00/27.04 | | | | | | | | | | | (56) all_58_10 = e0
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | | REF_CLOSE: (2), (15), (22), (23), (28), (29), (37), (42),
% 157.00/27.04 | | | | | | | | | | | (56) are inconsistent by sub-proof #252.
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | Case 2:
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | | (57) all_58_7 = e2 & op(e1, e2) = e2
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | | ALPHA: (57) implies:
% 157.00/27.04 | | | | | | | | | | | (58) all_58_7 = e2
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | | REF_CLOSE: (30), (46), (58) are inconsistent by sub-proof
% 157.00/27.04 | | | | | | | | | | | #1215.
% 157.00/27.04 | | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | End of split
% 157.00/27.04 | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | Case 2:
% 157.00/27.04 | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | (59) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2
% 157.00/27.04 | | | | | | | | | | & op(e1, e0) = e2)
% 157.00/27.04 | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | | REF_CLOSE: (1), (3), (14), (15), (17), (20), (21), (25),
% 157.00/27.04 | | | | | | | | | | (29), (51), (59) are inconsistent by sub-proof
% 157.00/27.04 | | | | | | | | | | #247.
% 157.00/27.04 | | | | | | | | | |
% 157.00/27.04 | | | | | | | | | End of split
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | End of split
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | End of split
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | End of split
% 157.00/27.04 | | | | | |
% 157.00/27.04 | | | | | Case 2:
% 157.00/27.04 | | | | | |
% 157.00/27.04 | | | | | | (60) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 157.00/27.04 | | | | | | e0) = e3)
% 157.00/27.04 | | | | | |
% 157.00/27.04 | | | | | | BETA: splitting (60) gives:
% 157.00/27.04 | | | | | |
% 157.00/27.04 | | | | | | Case 1:
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | (61) all_58_8 = e3 & op(e1, e1) = e3
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | REF_CLOSE: (3), (19), (29), (61) are inconsistent by sub-proof
% 157.00/27.04 | | | | | | | #1469.
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | Case 2:
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | (62) all_58_11 = e3 & op(e1, e0) = e3
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | ALPHA: (62) implies:
% 157.00/27.04 | | | | | | | (63) op(e1, e0) = e3
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | BETA: splitting (16) gives:
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | | Case 1:
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | (64) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 157.00/27.04 | | | | | | | | op(e2, e2) = e2)
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | REF_CLOSE: (2), (8), (10), (11), (15), (18), (22), (23), (28),
% 157.00/27.04 | | | | | | | | (29), (30), (36), (37), (42), (64) are inconsistent
% 157.00/27.04 | | | | | | | | by sub-proof #251.
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | Case 2:
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | (65) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 157.00/27.04 | | | | | | | | op(e2, e0) = e2)
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | BETA: splitting (65) gives:
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | | Case 1:
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | (66) all_58_5 = e2 & op(e2, e1) = e2
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | REF_CLOSE: (30), (42), (66) are inconsistent by sub-proof
% 157.00/27.04 | | | | | | | | | #250.
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | Case 2:
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | (67) all_58_10 = e2 & op(e2, e0) = e2
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | ALPHA: (67) implies:
% 157.00/27.04 | | | | | | | | | (68) all_58_10 = e2
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | | REF_CLOSE: (1), (14), (15), (17), (20), (21), (29), (63), (68)
% 157.00/27.04 | | | | | | | | | are inconsistent by sub-proof #246.
% 157.00/27.04 | | | | | | | | |
% 157.00/27.04 | | | | | | | | End of split
% 157.00/27.04 | | | | | | | |
% 157.00/27.04 | | | | | | | End of split
% 157.00/27.04 | | | | | | |
% 157.00/27.04 | | | | | | End of split
% 157.00/27.04 | | | | | |
% 157.00/27.04 | | | | | End of split
% 157.00/27.04 | | | | |
% 157.00/27.04 | | | | End of split
% 157.00/27.04 | | | |
% 157.00/27.04 | | | Case 2:
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | (69) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 157.00/27.04 | | | | = e3)
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | REF_CLOSE: (3), (5), (10), (19), (29), (69) are inconsistent by
% 157.00/27.04 | | | | sub-proof #245.
% 157.00/27.04 | | | |
% 157.00/27.04 | | | End of split
% 157.00/27.04 | | |
% 157.00/27.04 | | End of split
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (70) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 157.00/27.04 | | e3)
% 157.00/27.04 | |
% 157.00/27.04 | | BETA: splitting (70) gives:
% 157.00/27.04 | |
% 157.00/27.04 | | Case 1:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (71) all_58_6 = e3 & op(e1, e3) = e3
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (10), (13), (71) are inconsistent by sub-proof #749.
% 157.00/27.04 | | |
% 157.00/27.04 | | Case 2:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (72) all_58_12 = e3 & op(e0, e3) = e3
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (15), (31), (72) are inconsistent by sub-proof #1278.
% 157.00/27.04 | | |
% 157.00/27.04 | | End of split
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #245 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) op(e1, e1) = all_6_2
% 157.00/27.04 (2) all_58_14 = e0
% 157.00/27.04 (3) ~ (e3 = e0)
% 157.00/27.04 (4) ~ (all_6_2 = e3)
% 157.00/27.04 (5) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.00/27.04 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (5) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (7) all_58_8 = e3 & op(e1, e1) = e3
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #1469.
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (8) all_58_14 = e3 & op(e0, e1) = e3
% 157.00/27.04 | |
% 157.00/27.04 | | ALPHA: (8) implies:
% 157.00/27.04 | | (9) all_58_14 = e3
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #1444.
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #246 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.04 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.04 (2) all_58_10 = e2
% 157.00/27.04 (3) all_58_9 = e3
% 157.00/27.04 (4) ~ (e3 = e1)
% 157.00/27.04 (5) ~ (all_4_2 = e1)
% 157.00/27.04 (6) op(e0, e0) = all_4_2
% 157.00/27.04 (7) ~ (e2 = e1)
% 157.00/27.04 (8) op(e1, e0) = e3
% 157.00/27.04 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (1) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.00/27.04 | | e1)
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (2), (3), (4), (7), (10) are inconsistent by sub-proof #319.
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (11) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.00/27.04 | | e1)
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (4), (5), (6), (8), (9), (11) are inconsistent by sub-proof #318.
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #247 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.04 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.04 (2) op(e1, e1) = all_6_2
% 157.00/27.04 (3) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.00/27.04 (4) all_58_10 = e2
% 157.00/27.04 (5) all_58_9 = e3
% 157.00/27.04 (6) ~ (e3 = e1)
% 157.00/27.04 (7) ~ (all_4_2 = e1)
% 157.00/27.04 (8) op(e0, e0) = all_4_2
% 157.00/27.04 (9) ~ (e2 = e1)
% 157.00/27.04 (10) ~ (all_6_2 = e2)
% 157.00/27.04 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (3) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (12) all_58_8 = e2 & op(e1, e1) = e2
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (2), (10), (11), (12) are inconsistent by sub-proof #1440.
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (13) all_58_11 = e2 & op(e1, e0) = e2
% 157.00/27.04 | |
% 157.00/27.04 | | ALPHA: (13) implies:
% 157.00/27.04 | | (14) all_58_11 = e2
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (14) are inconsistent by
% 157.00/27.04 | | sub-proof #248.
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #248 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.04 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.04 (2) all_58_10 = e2
% 157.00/27.04 (3) all_58_9 = e3
% 157.00/27.04 (4) ~ (e3 = e1)
% 157.00/27.04 (5) ~ (all_4_2 = e1)
% 157.00/27.04 (6) op(e0, e0) = all_4_2
% 157.00/27.04 (7) all_58_11 = e2
% 157.00/27.04 (8) ~ (e2 = e1)
% 157.00/27.04 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (1) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.00/27.04 | | e1)
% 157.00/27.04 | |
% 157.00/27.04 | | BETA: splitting (10) gives:
% 157.00/27.04 | |
% 157.00/27.04 | | Case 1:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (11) all_58_9 = e1 & op(e3, e0) = e1
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #1078.
% 157.00/27.04 | | |
% 157.00/27.04 | | Case 2:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (12) all_58_10 = e1 & op(e2, e0) = e1
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (2), (8), (12) are inconsistent by sub-proof #1199.
% 157.00/27.04 | | |
% 157.00/27.04 | | End of split
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (13) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.00/27.04 | | e1)
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (5), (6), (7), (8), (9), (13) are inconsistent by sub-proof #249.
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #249 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) ~ (all_4_2 = e1)
% 157.00/27.04 (2) op(e0, e0) = all_4_2
% 157.00/27.04 (3) all_58_11 = e2
% 157.00/27.04 (4) ~ (e2 = e1)
% 157.00/27.04 (5) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.04 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (5) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (7) all_58_11 = e1 & op(e1, e0) = e1
% 157.00/27.04 | |
% 157.00/27.04 | | ALPHA: (7) implies:
% 157.00/27.04 | | (8) all_58_11 = e1
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1198.
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (9) all_58_15 = e1 & op(e0, e0) = e1
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #1418.
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #250 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) all_58_5 = e2 & op(e2, e1) = e2
% 157.00/27.04 (2) all_58_5 = e3
% 157.00/27.04 (3) ~ (e3 = e2)
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | ALPHA: (1) implies:
% 157.00/27.04 | (4) all_58_5 = e2
% 157.00/27.04 |
% 157.00/27.04 | COMBINE_EQS: (2), (4) imply:
% 157.00/27.04 | (5) e3 = e2
% 157.00/27.04 |
% 157.00/27.04 | REDUCE: (3), (5) imply:
% 157.00/27.04 | (6) $false
% 157.00/27.04 |
% 157.00/27.04 | CLOSE: (6) is inconsistent.
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #251 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.00/27.04 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.00/27.04 (2) op(e2, e3) = e3
% 157.00/27.04 (3) op(e2, e3) = all_52_1
% 157.00/27.04 (4) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 157.00/27.04 (5) ~ (e3 = e0)
% 157.00/27.04 (6) ~ (e2 = e0)
% 157.00/27.04 (7) all_58_5 = e3
% 157.00/27.04 (8) ~ (e3 = e1)
% 157.00/27.04 (9) all_58_2 = e3
% 157.00/27.04 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.00/27.04 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.00/27.04 (11) ~ (e1 = e0)
% 157.00/27.04 (12) ~ (all_8_2 = e1)
% 157.00/27.04 (13) op(e2, e2) = all_8_2
% 157.00/27.04 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04 (15) ~ (e3 = e2)
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (4) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (16) all_58_2 = e2 & op(e2, e3) = e2
% 157.00/27.04 | |
% 157.00/27.04 | | ALPHA: (16) implies:
% 157.00/27.04 | | (17) op(e2, e3) = e2
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (2), (3), (14), (15), (17) are inconsistent by sub-proof #1159.
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (18) all_58_3 = e2 & op(e2, e2) = e2
% 157.00/27.04 | |
% 157.00/27.04 | | ALPHA: (18) implies:
% 157.00/27.04 | | (19) all_58_3 = e2
% 157.00/27.04 | |
% 157.00/27.04 | | BETA: splitting (10) gives:
% 157.00/27.04 | |
% 157.00/27.04 | | Case 1:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 157.00/27.04 | | | e0)
% 157.00/27.04 | | |
% 157.00/27.04 | | | BETA: splitting (20) gives:
% 157.00/27.04 | | |
% 157.00/27.04 | | | Case 1:
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | (21) all_58_2 = e0 & op(e2, e3) = e0
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | ALPHA: (21) implies:
% 157.00/27.04 | | | | (22) all_58_2 = e0
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | COMBINE_EQS: (9), (22) imply:
% 157.00/27.04 | | | | (23) e3 = e0
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | REDUCE: (5), (23) imply:
% 157.00/27.04 | | | | (24) $false
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | CLOSE: (24) is inconsistent.
% 157.00/27.04 | | | |
% 157.00/27.04 | | | Case 2:
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | (25) all_58_3 = e0 & op(e2, e2) = e0
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | REF_CLOSE: (6), (19), (25) are inconsistent by sub-proof #1432.
% 157.00/27.04 | | | |
% 157.00/27.04 | | | End of split
% 157.00/27.04 | | |
% 157.00/27.04 | | Case 2:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (26) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 157.00/27.04 | | | e0)
% 157.00/27.04 | | |
% 157.00/27.04 | | | BETA: splitting (26) gives:
% 157.00/27.04 | | |
% 157.00/27.04 | | | Case 1:
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | (27) all_58_5 = e0 & op(e2, e1) = e0
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | REF_CLOSE: (5), (7), (27) are inconsistent by sub-proof #1446.
% 157.00/27.04 | | | |
% 157.00/27.04 | | | Case 2:
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | (28) all_58_10 = e0 & op(e2, e0) = e0
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | ALPHA: (28) implies:
% 157.00/27.04 | | | | (29) all_58_10 = e0
% 157.00/27.04 | | | |
% 157.00/27.04 | | | | REF_CLOSE: (1), (2), (7), (8), (11), (12), (13), (14), (29) are
% 157.00/27.04 | | | | inconsistent by sub-proof #252.
% 157.00/27.04 | | | |
% 157.00/27.04 | | | End of split
% 157.00/27.04 | | |
% 157.00/27.04 | | End of split
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #252 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.00/27.04 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.00/27.04 (2) op(e2, e3) = e3
% 157.00/27.04 (3) all_58_5 = e3
% 157.00/27.04 (4) ~ (e3 = e1)
% 157.00/27.04 (5) ~ (e1 = e0)
% 157.00/27.04 (6) ~ (all_8_2 = e1)
% 157.00/27.04 (7) all_58_10 = e0
% 157.00/27.04 (8) op(e2, e2) = all_8_2
% 157.00/27.04 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (1) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (10) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 157.00/27.04 | | e1)
% 157.00/27.04 | |
% 157.00/27.04 | | REF_CLOSE: (2), (4), (6), (8), (9), (10) are inconsistent by sub-proof
% 157.00/27.04 | | #1122.
% 157.00/27.04 | |
% 157.00/27.04 | Case 2:
% 157.00/27.04 | |
% 157.00/27.04 | | (11) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.00/27.04 | | e1)
% 157.00/27.04 | |
% 157.00/27.04 | | BETA: splitting (11) gives:
% 157.00/27.04 | |
% 157.00/27.04 | | Case 1:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (12) all_58_5 = e1 & op(e2, e1) = e1
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #1092.
% 157.00/27.04 | | |
% 157.00/27.04 | | Case 2:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (13) all_58_10 = e1 & op(e2, e0) = e1
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #1373.
% 157.00/27.04 | | |
% 157.00/27.04 | | End of split
% 157.00/27.04 | |
% 157.00/27.04 | End of split
% 157.00/27.04 |
% 157.00/27.04 End of proof
% 157.00/27.04
% 157.00/27.04 Sub-proof #253 shows that the following formulas are inconsistent:
% 157.00/27.04 ----------------------------------------------------------------
% 157.00/27.04 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.04 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.04 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.00/27.04 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.00/27.04 (3) ~ (all_4_2 = e2)
% 157.00/27.04 (4) ~ (e2 = e0)
% 157.00/27.04 (5) all_58_9 = e3
% 157.00/27.04 (6) op(e2, e0) = all_52_13
% 157.00/27.04 (7) ~ (e3 = e1)
% 157.00/27.04 (8) ~ (all_4_2 = e1)
% 157.00/27.04 (9) op(e0, e0) = all_4_2
% 157.00/27.04 (10) ~ (e2 = e1)
% 157.00/27.04 (11) ~ (e1 = e0)
% 157.00/27.04 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.04 (13) ~ (e3 = e2)
% 157.00/27.04 (14) all_58_10 = e0 & op(e2, e0) = e0
% 157.00/27.04
% 157.00/27.04 Begin of proof
% 157.00/27.04 |
% 157.00/27.04 | ALPHA: (14) implies:
% 157.00/27.04 | (15) all_58_10 = e0
% 157.00/27.04 | (16) op(e2, e0) = e0
% 157.00/27.04 |
% 157.00/27.04 | BETA: splitting (2) gives:
% 157.00/27.04 |
% 157.00/27.04 | Case 1:
% 157.00/27.04 | |
% 157.00/27.04 | | (17) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 157.00/27.04 | | e2)
% 157.00/27.04 | |
% 157.00/27.04 | | BETA: splitting (17) gives:
% 157.00/27.04 | |
% 157.00/27.04 | | Case 1:
% 157.00/27.04 | | |
% 157.00/27.04 | | | (18) all_58_9 = e2 & op(e3, e0) = e2
% 157.00/27.04 | | |
% 157.00/27.04 | | | ALPHA: (18) implies:
% 157.00/27.04 | | | (19) all_58_9 = e2
% 157.00/27.04 | | |
% 157.00/27.04 | | | REF_CLOSE: (5), (13), (19) are inconsistent by sub-proof #1245.
% 157.00/27.04 | | |
% 157.00/27.04 | | Case 2:
% 157.00/27.04 | | |
% 157.00/27.05 | | | (20) all_58_10 = e2 & op(e2, e0) = e2
% 157.00/27.05 | | |
% 157.00/27.05 | | | ALPHA: (20) implies:
% 157.00/27.05 | | | (21) op(e2, e0) = e2
% 157.00/27.05 | | |
% 157.00/27.05 | | | REF_CLOSE: (4), (6), (12), (16), (21) are inconsistent by sub-proof #1397.
% 157.00/27.05 | | |
% 157.00/27.05 | | End of split
% 157.00/27.05 | |
% 157.00/27.05 | Case 2:
% 157.00/27.05 | |
% 157.00/27.05 | | (22) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.00/27.05 | | e2)
% 157.00/27.05 | |
% 157.00/27.05 | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (15), (22) are
% 157.00/27.05 | | inconsistent by sub-proof #327.
% 157.00/27.05 | |
% 157.00/27.05 | End of split
% 157.00/27.05 |
% 157.00/27.05 End of proof
% 157.00/27.05
% 157.00/27.05 Sub-proof #254 shows that the following formulas are inconsistent:
% 157.00/27.05 ----------------------------------------------------------------
% 157.00/27.05 (1) all_54_13 = all_52_7
% 157.00/27.05 (2) ~ (all_52_7 = e2)
% 157.00/27.05 (3) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.00/27.05 (4) ~ (all_52_7 = e0)
% 157.00/27.05 (5) ~ (all_52_7 = e1)
% 157.00/27.05
% 157.00/27.05 Begin of proof
% 157.00/27.05 |
% 157.00/27.05 | BETA: splitting (3) gives:
% 157.00/27.05 |
% 157.00/27.05 | Case 1:
% 157.00/27.05 | |
% 157.00/27.05 | | (6) all_54_13 = e2
% 157.00/27.05 | |
% 157.00/27.05 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #1370.
% 157.00/27.05 | |
% 157.00/27.05 | Case 2:
% 157.00/27.05 | |
% 157.00/27.05 | | (7) all_54_13 = e1 | all_54_13 = e0
% 157.00/27.05 | |
% 157.00/27.05 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #875.
% 157.00/27.05 | |
% 157.00/27.05 | End of split
% 157.00/27.05 |
% 157.00/27.05 End of proof
% 157.00/27.05
% 157.00/27.05 Sub-proof #255 shows that the following formulas are inconsistent:
% 157.00/27.05 ----------------------------------------------------------------
% 157.00/27.05 (1) all_58_12 = e2
% 157.00/27.05 (2) all_58_14 = e3
% 157.00/27.05 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.00/27.05 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.05 (4) ~ (e3 = e1)
% 157.00/27.05 (5) all_58_13 = e3
% 157.00/27.05 (6) ~ (all_4_2 = e1)
% 157.00/27.05 (7) op(e0, e0) = all_4_2
% 157.00/27.05 (8) ~ (e2 = e1)
% 157.00/27.05 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.05
% 157.00/27.05 Begin of proof
% 157.00/27.05 |
% 157.00/27.05 | BETA: splitting (3) gives:
% 157.00/27.05 |
% 157.00/27.05 | Case 1:
% 157.00/27.05 | |
% 157.00/27.05 | | (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 157.00/27.05 | | e1)
% 157.00/27.05 | |
% 157.00/27.05 | | BETA: splitting (10) gives:
% 157.00/27.05 | |
% 157.00/27.05 | | Case 1:
% 157.00/27.05 | | |
% 157.00/27.05 | | | (11) all_58_12 = e1 & op(e0, e3) = e1
% 157.00/27.05 | | |
% 157.00/27.05 | | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #1492.
% 157.00/27.05 | | |
% 157.00/27.05 | | Case 2:
% 157.00/27.05 | | |
% 157.00/27.05 | | | (12) all_58_13 = e1 & op(e0, e2) = e1
% 157.00/27.05 | | |
% 157.00/27.05 | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #1165.
% 157.00/27.05 | | |
% 157.00/27.05 | | End of split
% 157.00/27.05 | |
% 157.00/27.05 | Case 2:
% 157.00/27.05 | |
% 157.00/27.05 | | (13) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.00/27.05 | | e1)
% 157.00/27.05 | |
% 157.00/27.05 | | REF_CLOSE: (2), (4), (6), (7), (9), (13) are inconsistent by sub-proof #256.
% 157.00/27.05 | |
% 157.00/27.05 | End of split
% 157.00/27.05 |
% 157.00/27.05 End of proof
% 157.00/27.05
% 157.00/27.05 Sub-proof #256 shows that the following formulas are inconsistent:
% 157.00/27.05 ----------------------------------------------------------------
% 157.00/27.05 (1) all_58_14 = e3
% 157.00/27.05 (2) ~ (e3 = e1)
% 157.00/27.05 (3) ~ (all_4_2 = e1)
% 157.00/27.05 (4) op(e0, e0) = all_4_2
% 157.00/27.05 (5) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.05 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.05
% 157.00/27.05 Begin of proof
% 157.00/27.05 |
% 157.00/27.05 | BETA: splitting (5) gives:
% 157.00/27.05 |
% 157.00/27.05 | Case 1:
% 157.00/27.05 | |
% 157.00/27.05 | | (7) all_58_14 = e1 & op(e0, e1) = e1
% 157.00/27.05 | |
% 157.00/27.05 | | ALPHA: (7) implies:
% 157.00/27.05 | | (8) all_58_14 = e1
% 157.00/27.05 | |
% 157.00/27.05 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #1147.
% 157.00/27.05 | |
% 157.00/27.05 | Case 2:
% 157.00/27.05 | |
% 157.00/27.05 | | (9) all_58_15 = e1 & op(e0, e0) = e1
% 157.00/27.05 | |
% 157.00/27.05 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1418.
% 157.00/27.05 | |
% 157.00/27.05 | End of split
% 157.00/27.05 |
% 157.00/27.05 End of proof
% 157.00/27.05
% 157.00/27.05 Sub-proof #257 shows that the following formulas are inconsistent:
% 157.00/27.05 ----------------------------------------------------------------
% 157.00/27.05 (1) op(e3, e0) = all_52_12
% 157.00/27.05 (2) ~ (e3 = e0)
% 157.00/27.05 (3) ~ (all_52_8 = e0)
% 157.00/27.05 (4) op(e3, e1) = all_52_8
% 157.00/27.05 (5) op(e3, e0) = e3
% 157.00/27.05 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.05 (7) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.00/27.05
% 157.00/27.05 Begin of proof
% 157.00/27.05 |
% 157.00/27.05 | BETA: splitting (7) gives:
% 157.00/27.05 |
% 157.00/27.05 | Case 1:
% 157.00/27.05 | |
% 157.00/27.05 | | (8) all_58_4 = e0 & op(e3, e1) = e0
% 157.00/27.05 | |
% 157.00/27.05 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #259.
% 157.00/27.05 | |
% 157.00/27.05 | Case 2:
% 157.00/27.05 | |
% 157.00/27.05 | | (9) all_58_9 = e0 & op(e3, e0) = e0
% 157.00/27.05 | |
% 157.00/27.05 | | ALPHA: (9) implies:
% 157.00/27.05 | | (10) op(e3, e0) = e0
% 157.00/27.05 | |
% 157.00/27.05 | | REF_CLOSE: (1), (2), (5), (6), (10) are inconsistent by sub-proof #258.
% 157.00/27.05 | |
% 157.00/27.05 | End of split
% 157.00/27.05 |
% 157.00/27.05 End of proof
% 157.00/27.05
% 157.00/27.05 Sub-proof #258 shows that the following formulas are inconsistent:
% 157.00/27.05 ----------------------------------------------------------------
% 157.00/27.05 (1) op(e3, e0) = all_52_12
% 157.00/27.05 (2) ~ (e3 = e0)
% 157.00/27.05 (3) op(e3, e0) = e0
% 157.00/27.05 (4) op(e3, e0) = e3
% 157.00/27.05 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.05
% 157.00/27.05 Begin of proof
% 157.00/27.05 |
% 157.00/27.05 | GROUND_INST: instantiating (5) with all_52_12, e0, e0, e3, simplifying with
% 157.00/27.05 | (1), (3) gives:
% 157.00/27.05 | (6) all_52_12 = e0
% 157.00/27.05 |
% 157.00/27.05 | GROUND_INST: instantiating (5) with all_52_12, e3, e0, e3, simplifying with
% 157.00/27.05 | (1), (4) gives:
% 157.00/27.05 | (7) all_52_12 = e3
% 157.00/27.05 |
% 157.00/27.05 | COMBINE_EQS: (6), (7) imply:
% 157.00/27.05 | (8) e3 = e0
% 157.00/27.05 |
% 157.00/27.05 | REDUCE: (2), (8) imply:
% 157.00/27.05 | (9) $false
% 157.00/27.05 |
% 157.00/27.05 | CLOSE: (9) is inconsistent.
% 157.00/27.05 |
% 157.00/27.05 End of proof
% 157.00/27.05
% 157.00/27.05 Sub-proof #259 shows that the following formulas are inconsistent:
% 157.00/27.05 ----------------------------------------------------------------
% 157.00/27.05 (1) all_58_4 = e0 & op(e3, e1) = e0
% 157.00/27.05 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.00/27.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.00/27.05 (3) op(e3, e1) = all_52_8
% 157.00/27.05 (4) ~ (all_52_8 = e0)
% 157.00/27.05
% 157.00/27.05 Begin of proof
% 157.00/27.05 |
% 157.00/27.05 | ALPHA: (1) implies:
% 157.00/27.05 | (5) op(e3, e1) = e0
% 157.00/27.05 |
% 157.00/27.05 | GROUND_INST: instantiating (2) with all_52_8, e0, e1, e3, simplifying with
% 157.00/27.05 | (3), (5) gives:
% 157.00/27.05 | (6) all_52_8 = e0
% 157.00/27.05 |
% 157.00/27.05 | REDUCE: (4), (6) imply:
% 157.00/27.05 | (7) $false
% 157.00/27.05 |
% 157.00/27.05 | CLOSE: (7) is inconsistent.
% 157.00/27.05 |
% 157.00/27.05 End of proof
% 157.00/27.05
% 157.00/27.05 Sub-proof #260 shows that the following formulas are inconsistent:
% 157.00/27.05 ----------------------------------------------------------------
% 157.00/27.05 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 157.00/27.05 (2) ~ (all_56_13 = e3) | (all_56_3 = e2 & op(e2, e3) = e2)
% 157.00/27.05 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.00/27.05 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.00/27.05 (5) op(e0, e3) = all_52_3
% 157.00/27.05 (6) op(e3, e0) = all_52_12
% 157.00/27.05 (7) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.00/27.05 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.00/27.05 (8) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.00/27.05 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.00/27.05 (9) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.00/27.05 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.00/27.05 (10) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.00/27.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.00/27.05 (11) op(e3, e3) = all_10_2
% 157.00/27.05 (12) op(e0, e0) = all_10_1
% 157.00/27.05 (13) all_54_13 = all_52_7
% 157.00/27.05 (14) op(e1, e1) = all_6_2
% 157.00/27.05 (15) ~ (all_52_7 = e3)
% 157.00/27.05 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.00/27.05 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.00/27.05 e1)
% 157.00/27.05 (17) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.00/27.05 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.00/27.05 (18) ~ (all_52_6 = all_52_14)
% 157.00/27.05 (19) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.00/27.05 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.00/27.05 (20) all_54_10 = all_6_2
% 157.00/27.05 (21) ~ (all_52_2 = all_52_3)
% 157.00/27.05 (22) ~ (all_52_4 = all_52_6)
% 157.00/27.05 (23) all_56_12 = all_10_2
% 157.00/27.05 (24) ~ (all_52_2 = all_10_2)
% 157.00/27.05 (25) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.00/27.05 (26) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.00/27.05 (27) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 157.00/27.05 op(e1, e1) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 157.00/27.05 e2) & op(e1, e1) = all_32_1 & $i(all_32_1))
% 157.00/27.05 (28) ~ (all_52_7 = all_52_11)
% 157.00/27.05 (29) ~ (all_4_2 = e3)
% 157.00/27.05 (30) ~ (all_52_12 = all_4_2)
% 157.00/27.05 (31) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.00/27.05 (32) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.00/27.05 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.00/27.05 (33) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.00/27.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.00/27.05 (34) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.00/27.05 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.00/27.05 (35) all_54_1 = all_52_4
% 157.00/27.05 (36) op(e3, e2) = all_52_4
% 157.00/27.05 (37) ~ (all_52_1 = all_52_13)
% 157.00/27.05 (38) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.00/27.05 (39) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 157.00/27.05 (40) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.00/27.05 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.00/27.05 (41) ~ (all_52_12 = all_52_13)
% 157.00/27.05 (42) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.00/27.05 (43) ~ (all_52_4 = all_52_12)
% 157.00/27.05 (44) all_54_0 = all_10_2
% 157.00/27.05 (45) op(e2, e1) = all_52_9
% 157.00/27.05 (46) op(e2, e3) = all_52_1
% 157.00/27.05 (47) ~ (all_52_13 = e3)
% 157.00/27.05 (48) ~ (all_52_1 = all_52_3)
% 157.00/27.05 (49) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 157.00/27.05 op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 157.00/27.05 e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 157.00/27.05 (50) all_54_2 = all_52_8
% 157.00/27.05 (51) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.00/27.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.00/27.05 (52) ~ (all_52_8 = all_52_9)
% 157.00/27.05 (53) ~ (all_52_2 = all_6_2)
% 157.00/27.05 (54) all_56_2 = e3
% 157.00/27.05 (55) all_56_12 = e0
% 157.00/27.05 (56) ~ (e3 = e0)
% 157.00/27.05 (57) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.00/27.05 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.00/27.05 (58) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.00/27.05 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.00/27.05 (59) ~ (all_52_9 = all_52_13)
% 157.00/27.05 (60) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.00/27.05 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.00/27.05 e2)
% 157.00/27.05 (61) ~ (e2 = e0)
% 157.00/27.05 (62) ~ (all_52_9 = e3)
% 157.00/27.05 (63) op(e3, e3) = e0
% 157.00/27.05 (64) ~ (all_52_11 = all_6_2)
% 157.00/27.05 (65) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.00/27.05 (66) ~ (all_52_2 = all_52_6)
% 157.00/27.05 (67) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.00/27.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.00/27.05 (68) all_58_9 = e3
% 157.00/27.05 (69) ~ (all_52_8 = e0)
% 157.00/27.05 (70) all_32_2 = all_10_2
% 157.00/27.05 (71) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 &
% 157.00/27.05 op(e3, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 157.00/27.05 e0) & op(e3, e3) = all_28_1 & $i(all_28_1))
% 157.00/27.05 (72) op(e1, e3) = all_52_2
% 157.00/27.05 (73) ~ (all_52_6 = all_6_2)
% 157.00/27.05 (74) op(e2, e0) = all_52_13
% 157.00/27.05 (75) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.00/27.05 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.00/27.05 (76) ~ (all_52_8 = all_52_12)
% 157.00/27.05 (77) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.00/27.05 (78) ~ (e3 = e1)
% 157.00/27.05 (79) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.00/27.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.00/27.05 (80) op(e1, e2) = all_52_6
% 157.00/27.05 (81) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.00/27.05 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.00/27.05 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.00/27.05 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.00/27.05 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.00/27.05 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.00/27.05 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.00/27.05 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.00/27.05 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.00/27.05 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.00/27.05 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.00/27.05 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.00/27.05 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.00/27.05 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.00/27.05 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.00/27.05 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.00/27.05 = e0)
% 157.00/27.05 (82) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.00/27.05 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.00/27.05 (83) ~ (all_4_2 = e1)
% 157.00/27.05 (84) ~ (all_52_4 = all_10_2)
% 157.00/27.05 (85) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.00/27.05 (86) ~ (all_52_4 = e0)
% 157.00/27.05 (87) ~ (all_52_3 = all_4_2)
% 157.00/27.05 (88) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.00/27.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.00/27.05 (89) ~ (all_52_3 = all_10_2)
% 157.00/27.05 (90) ~ (all_52_9 = all_6_2)
% 157.00/27.05 (91) op(e0, e0) = all_4_2
% 157.00/27.05 (92) all_54_8 = all_52_2
% 157.00/27.05 (93) all_54_7 = all_52_13
% 157.00/27.05 (94) ~ (all_52_8 = all_10_2)
% 157.00/27.05 (95) all_56_15 = all_4_2
% 157.00/27.05 (96) op(e0, e1) = all_52_11
% 157.00/27.05 (97) ~ (all_52_9 = all_52_11)
% 157.00/27.05 (98) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 157.00/27.05 (99) ~ (all_52_13 = all_4_2)
% 157.00/27.05 (100) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0
% 157.00/27.05 & op(e2, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 157.00/27.05 (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1))
% 157.00/27.05 (101) all_28_2 = all_6_2
% 157.00/27.05 (102) ~ (all_52_2 = all_52_14)
% 157.00/27.05 (103) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.00/27.05 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.00/27.05 (104) ~ (all_52_6 = all_52_7)
% 157.00/27.05 (105) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.00/27.05 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.00/27.05 (106) ~ (all_52_4 = e3)
% 157.00/27.05 (107) ~ (all_52_8 = all_6_2)
% 157.00/27.05 (108) all_54_6 = all_52_9
% 157.00/27.05 (109) ~ (e2 = e1)
% 157.00/27.05 (110) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.00/27.05 (111) all_54_3 = all_52_12
% 157.00/27.05 (112) ~ (all_52_4 = all_52_7)
% 157.00/27.05 (113) ~ (all_52_8 = all_52_11)
% 157.00/27.05 (114) ~ (all_52_12 = all_10_2)
% 157.00/27.05 (115) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.00/27.05 (116) ~ (e1 = e0)
% 157.00/27.05 (117) ~ (all_8_2 = e1)
% 157.00/27.05 (118) ~ (all_52_1 = e0)
% 157.00/27.05 (119) op(e3, e1) = all_52_8
% 157.00/27.05 (120) ~ (all_6_2 = e2)
% 157.00/27.05 (121) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.00/27.05 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.00/27.05 e3)
% 157.00/27.05 (122) all_56_14 = all_6_2
% 157.00/27.05 (123) all_56_13 = e3
% 157.00/27.05 (124) ~ (all_52_1 = all_10_2)
% 157.00/27.05 (125) ~ (all_52_12 = all_52_14)
% 157.00/27.05 (126) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.00/27.05 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.00/27.05 (127) all_22_2 = e3
% 157.00/27.05 (128) ~ (all_52_8 = e3)
% 157.00/27.05 (129) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.00/27.05 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.00/27.05 (130) all_54_14 = all_52_11
% 157.00/27.05 (131) ~ (all_52_7 = all_4_2)
% 157.00/27.05 (132) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.00/27.05 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.00/27.05 (133) op(e0, e2) = all_52_7
% 157.00/27.05 (134) op(e1, e0) = all_52_14
% 157.00/27.05 (135) ~ (all_52_1 = all_52_2)
% 157.00/27.05 (136) all_54_15 = all_4_2
% 157.00/27.05 (137) all_58_0 = e0
% 157.00/27.05 (138) all_20_2 = all_4_2
% 157.00/27.05 (139) op(e2, e2) = all_8_2
% 157.00/27.05 (140) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.00/27.05 (141) ~ (all_52_6 = e3)
% 157.00/27.05 (142) ~ (all_52_14 = all_6_2)
% 157.00/27.05 (143) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.00/27.05 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.05 (144) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.05 (145) ~ (all_52_3 = all_52_11)
% 157.04/27.05 (146) ~ (all_52_11 = all_4_2)
% 157.04/27.05 (147) all_54_11 = all_52_14
% 157.04/27.05 (148) ~ (all_52_13 = all_52_14)
% 157.04/27.05 (149) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.04/27.05 (150) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.04/27.05 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.05 (151) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.04/27.05 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.04/27.05 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.04/27.05 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.04/27.05 e0)))
% 157.04/27.05 (152) all_54_9 = all_52_6
% 157.04/27.05 (153) ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e3, e3) =
% 157.04/27.05 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e0) &
% 157.04/27.05 op(e3, e3) = all_14_1 & $i(all_14_1))
% 157.04/27.05 (154) ~ (all_52_4 = all_52_8)
% 157.04/27.05 (155) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.04/27.05 (156) all_54_12 = all_52_3
% 157.04/27.05 (157) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.04/27.05 (158) ~ (all_52_14 = all_4_2)
% 157.04/27.05 (159) ~ (all_52_1 = all_52_9)
% 157.04/27.05 (160) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.04/27.05 (161) ~ (all_52_1 = e3)
% 157.04/27.05 (162) ~ (all_52_3 = all_52_7)
% 157.04/27.05 (163) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.04/27.05 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.04/27.05
% 157.04/27.05 Begin of proof
% 157.04/27.05 |
% 157.04/27.05 | BETA: splitting (49) gives:
% 157.04/27.05 |
% 157.04/27.05 | Case 1:
% 157.04/27.05 | |
% 157.04/27.05 | | (164) ~ (all_22_2 = e3)
% 157.04/27.05 | |
% 157.04/27.05 | | REDUCE: (127), (164) imply:
% 157.04/27.05 | | (165) $false
% 157.04/27.05 | |
% 157.04/27.05 | | CLOSE: (165) is inconsistent.
% 157.04/27.05 | |
% 157.04/27.05 | Case 2:
% 157.04/27.05 | |
% 157.04/27.05 | | (166) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.04/27.05 | | all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) &
% 157.04/27.05 | | op(e3, e3) = all_22_1 & $i(all_22_1))
% 157.04/27.05 | |
% 157.04/27.05 | | BETA: splitting (153) gives:
% 157.04/27.05 | |
% 157.04/27.05 | | Case 1:
% 157.04/27.05 | | |
% 157.04/27.05 | | | (167) ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e3, e3) =
% 157.04/27.05 | | | all_14_1 & $i(all_14_0) & $i(all_14_1)
% 157.04/27.05 | | |
% 157.04/27.05 | | | ALPHA: (167) implies:
% 157.04/27.05 | | | (168) ~ (all_14_0 = e1)
% 157.04/27.05 | | | (169) op(e3, e3) = all_14_1
% 157.04/27.05 | | | (170) op(all_14_1, e2) = all_14_0
% 157.04/27.05 | | |
% 157.04/27.05 | | | BETA: splitting (103) gives:
% 157.04/27.05 | | |
% 157.04/27.05 | | | Case 1:
% 157.04/27.05 | | | |
% 157.04/27.05 | | | | (171) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2)
% 157.04/27.05 | | | | = e3)
% 157.04/27.05 | | | |
% 157.04/27.05 | | | | BETA: splitting (171) gives:
% 157.04/27.05 | | | |
% 157.04/27.05 | | | | Case 1:
% 157.04/27.05 | | | | |
% 157.04/27.05 | | | | | (172) all_58_2 = e3 & op(e2, e3) = e3
% 157.04/27.05 | | | | |
% 157.04/27.05 | | | | | ALPHA: (172) implies:
% 157.04/27.05 | | | | | (173) op(e2, e3) = e3
% 157.04/27.05 | | | | |
% 157.04/27.05 | | | | | REF_CLOSE: (46), (144), (161), (173) are inconsistent by sub-proof
% 157.04/27.05 | | | | | #1183.
% 157.04/27.05 | | | | |
% 157.04/27.05 | | | | Case 2:
% 157.04/27.05 | | | | |
% 157.04/27.05 | | | | | (174) all_58_3 = e3 & op(e2, e2) = e3
% 157.04/27.05 | | | | |
% 157.04/27.05 | | | | | ALPHA: (174) implies:
% 157.04/27.05 | | | | | (175) all_58_3 = e3
% 157.04/27.05 | | | | |
% 157.04/27.05 | | | | | BETA: splitting (2) gives:
% 157.04/27.05 | | | | |
% 157.04/27.05 | | | | | Case 1:
% 157.04/27.05 | | | | | |
% 157.04/27.05 | | | | | | (176) ~ (all_56_13 = e3)
% 157.04/27.05 | | | | | |
% 157.04/27.05 | | | | | | REDUCE: (123), (176) imply:
% 157.04/27.05 | | | | | | (177) $false
% 157.04/27.05 | | | | | |
% 157.04/27.05 | | | | | | CLOSE: (177) is inconsistent.
% 157.04/27.05 | | | | | |
% 157.04/27.05 | | | | | Case 2:
% 157.04/27.05 | | | | | |
% 157.04/27.05 | | | | | | (178) all_56_3 = e2 & op(e2, e3) = e2
% 157.04/27.05 | | | | | |
% 157.04/27.05 | | | | | | ALPHA: (178) implies:
% 157.04/27.05 | | | | | | (179) op(e2, e3) = e2
% 157.04/27.05 | | | | | |
% 157.04/27.06 | | | | | | GROUND_INST: instantiating (144) with all_52_1, e2, e3, e2,
% 157.04/27.06 | | | | | | simplifying with (46), (179) gives:
% 157.04/27.06 | | | | | | (180) all_52_1 = e2
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | GROUND_INST: instantiating (144) with e0, all_14_1, e3, e3,
% 157.04/27.06 | | | | | | simplifying with (63), (169) gives:
% 157.04/27.06 | | | | | | (181) all_14_1 = e0
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | REDUCE: (159), (180) imply:
% 157.04/27.06 | | | | | | (182) ~ (all_52_9 = e2)
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | SIMP: (182) implies:
% 157.04/27.06 | | | | | | (183) ~ (all_52_9 = e2)
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | REDUCE: (37), (180) imply:
% 157.04/27.06 | | | | | | (184) ~ (all_52_13 = e2)
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | SIMP: (184) implies:
% 157.04/27.06 | | | | | | (185) ~ (all_52_13 = e2)
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | REDUCE: (161), (180) imply:
% 157.04/27.06 | | | | | | (186) ~ (e3 = e2)
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | SIMP: (186) implies:
% 157.04/27.06 | | | | | | (187) ~ (e3 = e2)
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | REDUCE: (170), (181) imply:
% 157.04/27.06 | | | | | | (188) op(e0, e2) = all_14_0
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | BETA: splitting (166) gives:
% 157.04/27.06 | | | | | |
% 157.04/27.06 | | | | | | Case 1:
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | (189) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3,
% 157.04/27.06 | | | | | | | e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | ALPHA: (189) implies:
% 157.04/27.06 | | | | | | | (190) ~ (all_22_0 = e0)
% 157.04/27.06 | | | | | | | (191) op(e3, e3) = all_22_1
% 157.04/27.06 | | | | | | | (192) op(all_22_1, e2) = all_22_0
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | BETA: splitting (82) gives:
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | (193) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 157.04/27.06 | | | | | | | | op(e2, e2) = e2)
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | BETA: splitting (193) gives:
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | (194) all_58_2 = e2 & op(e2, e3) = e2
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | GROUND_INST: instantiating (144) with all_52_7, all_14_0, e2,
% 157.04/27.06 | | | | | | | | | e0, simplifying with (133), (188) gives:
% 157.04/27.06 | | | | | | | | | (195) all_52_7 = all_14_0
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | GROUND_INST: instantiating (144) with e0, all_22_1, e3, e3,
% 157.04/27.06 | | | | | | | | | simplifying with (63), (191) gives:
% 157.04/27.06 | | | | | | | | | (196) all_22_1 = e0
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | COMBINE_EQS: (13), (195) imply:
% 157.04/27.06 | | | | | | | | | (197) all_54_13 = all_14_0
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REDUCE: (112), (195) imply:
% 157.04/27.06 | | | | | | | | | (198) ~ (all_52_4 = all_14_0)
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REDUCE: (104), (195) imply:
% 157.04/27.06 | | | | | | | | | (199) ~ (all_52_6 = all_14_0)
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REDUCE: (15), (195) imply:
% 157.04/27.06 | | | | | | | | | (200) ~ (all_14_0 = e3)
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REDUCE: (192), (196) imply:
% 157.04/27.06 | | | | | | | | | (201) op(e0, e2) = all_22_0
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | GROUND_INST: instantiating (144) with all_14_0, all_22_0, e2,
% 157.04/27.06 | | | | | | | | | e0, simplifying with (188), (201) gives:
% 157.04/27.06 | | | | | | | | | (202) all_22_0 = all_14_0
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REDUCE: (190), (202) imply:
% 157.04/27.06 | | | | | | | | | (203) ~ (all_14_0 = e0)
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (14), (15), (16),
% 157.04/27.06 | | | | | | | | | (17), (18), (19), (20), (22), (25), (26), (29),
% 157.04/27.06 | | | | | | | | | (32), (33), (34), (35), (36), (38), (39), (40),
% 157.04/27.06 | | | | | | | | | (45), (46), (47), (50), (51), (52), (54), (56),
% 157.04/27.06 | | | | | | | | | (57), (58), (59), (60), (63), (64), (65), (67),
% 157.04/27.06 | | | | | | | | | (68), (72), (73), (74), (75), (79), (80), (81),
% 157.04/27.06 | | | | | | | | | (83), (85), (86), (88), (90), (91), (93), (95),
% 157.04/27.06 | | | | | | | | | (97), (99), (103), (105), (106), (108), (110),
% 157.04/27.06 | | | | | | | | | (113), (115), (117), (120), (121), (122), (126),
% 157.04/27.06 | | | | | | | | | (128), (129), (130), (132), (133), (134), (136),
% 157.04/27.06 | | | | | | | | | (137), (139), (140), (141), (143), (144), (147),
% 157.04/27.06 | | | | | | | | | (148), (149), (150), (151), (152), (154), (157),
% 157.04/27.06 | | | | | | | | | (158), (168), (175), (179), (183), (185), (188),
% 157.04/27.06 | | | | | | | | | (191), (197), (198), (199), (200), (203) are
% 157.04/27.06 | | | | | | | | | inconsistent by sub-proof #281.
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | (204) all_58_3 = e2 & op(e2, e2) = e2
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REF_CLOSE: (175), (187), (204) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | #719.
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | End of split
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | (205) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 157.04/27.06 | | | | | | | | op(e2, e0) = e2)
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | BETA: splitting (205) gives:
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | (206) all_58_5 = e2 & op(e2, e1) = e2
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | ALPHA: (206) implies:
% 157.04/27.06 | | | | | | | | | (207) all_58_5 = e2
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REF_CLOSE: (10), (56), (61), (78), (88), (109), (116), (144),
% 157.04/27.06 | | | | | | | | | (175), (179), (207) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | #898.
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | (208) all_58_10 = e2 & op(e2, e0) = e2
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | ALPHA: (208) implies:
% 157.04/27.06 | | | | | | | | | (209) all_58_10 = e2
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REF_CLOSE: (10), (46), (56), (61), (78), (88), (103), (109),
% 157.04/27.06 | | | | | | | | | (116), (117), (139), (144), (179), (187), (209) are
% 157.04/27.06 | | | | | | | | | inconsistent by sub-proof #905.
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | End of split
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | End of split
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | Case 2:
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | (210) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | ALPHA: (210) implies:
% 157.04/27.06 | | | | | | | (211) ~ (all_22_1 = e1)
% 157.04/27.06 | | | | | | | (212) op(e3, e3) = all_22_1
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | GROUND_INST: instantiating (144) with all_52_7, all_14_0, e2, e0,
% 157.04/27.06 | | | | | | | simplifying with (133), (188) gives:
% 157.04/27.06 | | | | | | | (213) all_52_7 = all_14_0
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | GROUND_INST: instantiating (144) with e0, all_22_1, e3, e3,
% 157.04/27.06 | | | | | | | simplifying with (63), (212) gives:
% 157.04/27.06 | | | | | | | (214) all_22_1 = e0
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | COMBINE_EQS: (13), (213) imply:
% 157.04/27.06 | | | | | | | (215) all_54_13 = all_14_0
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | REDUCE: (112), (213) imply:
% 157.04/27.06 | | | | | | | (216) ~ (all_52_4 = all_14_0)
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | REDUCE: (104), (213) imply:
% 157.04/27.06 | | | | | | | (217) ~ (all_52_6 = all_14_0)
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | REDUCE: (131), (213) imply:
% 157.04/27.06 | | | | | | | (218) ~ (all_14_0 = all_4_2)
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | REDUCE: (15), (213) imply:
% 157.04/27.06 | | | | | | | (219) ~ (all_14_0 = e3)
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | BETA: splitting (100) gives:
% 157.04/27.06 | | | | | | |
% 157.04/27.06 | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | (220) ~ (all_20_2 = e2)
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | REDUCE: (138), (220) imply:
% 157.04/27.06 | | | | | | | | (221) ~ (all_4_2 = e2)
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | BETA: splitting (149) gives:
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | (222) all_54_15 = e3
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REF_CLOSE: (29), (136), (222) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | #1543.
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | (223) ~ (all_54_15 = e3)
% 157.04/27.06 | | | | | | | | | (224) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | BETA: splitting (224) gives:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | (225) all_54_15 = e2
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | REF_CLOSE: (136), (221), (225) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | #1542.
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | (226) all_54_15 = e1 | all_54_15 = e0
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | BETA: splitting (226) gives:
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | (227) all_54_15 = e1
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | REF_CLOSE: (83), (136), (227) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | #1541.
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | (228) all_54_15 = e0
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | COMBINE_EQS: (136), (228) imply:
% 157.04/27.06 | | | | | | | | | | | (229) all_4_2 = e0
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | SIMP: (229) implies:
% 157.04/27.06 | | | | | | | | | | | (230) all_4_2 = e0
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | REDUCE: (218), (230) imply:
% 157.04/27.06 | | | | | | | | | | | (231) ~ (all_14_0 = e0)
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | REDUCE: (29), (230) imply:
% 157.04/27.06 | | | | | | | | | | | (232) ~ (e3 = e0)
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (14), (15), (16),
% 157.04/27.06 | | | | | | | | | | | (17), (18), (19), (20), (22), (25), (26), (29),
% 157.04/27.06 | | | | | | | | | | | (32), (33), (34), (35), (36), (38), (39), (40),
% 157.04/27.06 | | | | | | | | | | | (45), (46), (47), (50), (51), (52), (54), (56),
% 157.04/27.06 | | | | | | | | | | | (57), (58), (59), (60), (63), (64), (65), (67),
% 157.04/27.06 | | | | | | | | | | | (68), (72), (73), (74), (75), (79), (80), (81),
% 157.04/27.06 | | | | | | | | | | | (83), (85), (86), (88), (90), (91), (93), (95),
% 157.04/27.06 | | | | | | | | | | | (97), (99), (103), (105), (106), (108), (110),
% 157.04/27.06 | | | | | | | | | | | (113), (115), (117), (120), (121), (122), (126),
% 157.04/27.06 | | | | | | | | | | | (128), (129), (130), (132), (133), (134), (136),
% 157.04/27.06 | | | | | | | | | | | (137), (139), (140), (141), (143), (144), (147),
% 157.04/27.06 | | | | | | | | | | | (148), (149), (150), (151), (152), (154), (157),
% 157.04/27.06 | | | | | | | | | | | (158), (168), (175), (179), (183), (185), (188),
% 157.04/27.06 | | | | | | | | | | | (212), (215), (216), (217), (219), (231) are
% 157.04/27.06 | | | | | | | | | | | inconsistent by sub-proof #281.
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | End of split
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | End of split
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | End of split
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | (233) all_20_2 = e2
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | COMBINE_EQS: (138), (233) imply:
% 157.04/27.06 | | | | | | | | (234) all_4_2 = e2
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | COMBINE_EQS: (95), (234) imply:
% 157.04/27.06 | | | | | | | | (235) all_56_15 = e2
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | REDUCE: (218), (234) imply:
% 157.04/27.06 | | | | | | | | (236) ~ (all_14_0 = e2)
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | REDUCE: (91), (234) imply:
% 157.04/27.06 | | | | | | | | (237) op(e0, e0) = e2
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | BETA: splitting (140) gives:
% 157.04/27.06 | | | | | | | |
% 157.04/27.06 | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | (238) all_54_13 = e3
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | REF_CLOSE: (215), (219), (238) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | #288.
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | (239) ~ (all_54_13 = e3)
% 157.04/27.06 | | | | | | | | | (240) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | BETA: splitting (240) gives:
% 157.04/27.06 | | | | | | | | |
% 157.04/27.06 | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | (241) all_54_13 = e2
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | COMBINE_EQS: (215), (241) imply:
% 157.04/27.06 | | | | | | | | | | (242) all_14_0 = e2
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | SIMP: (242) implies:
% 157.04/27.06 | | | | | | | | | | (243) all_14_0 = e2
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | REDUCE: (236), (243) imply:
% 157.04/27.06 | | | | | | | | | | (244) $false
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | CLOSE: (244) is inconsistent.
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | (245) ~ (all_54_13 = e2)
% 157.04/27.06 | | | | | | | | | | (246) all_54_13 = e1 | all_54_13 = e0
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | BETA: splitting (160) gives:
% 157.04/27.06 | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | (247) all_56_12 = e3
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | REF_CLOSE: (55), (56), (247) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | #280.
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | (248) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | BETA: splitting (248) gives:
% 157.04/27.06 | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | (249) all_56_13 = e2
% 157.04/27.06 | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | REF_CLOSE: (123), (187), (249) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | #674.
% 157.04/27.06 | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | (250) ~ (all_56_13 = e2)
% 157.04/27.06 | | | | | | | | | | | | (251) all_56_14 = e1 | all_56_15 = e0
% 157.04/27.06 | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | BETA: splitting (246) gives:
% 157.04/27.06 | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | (252) all_54_13 = e1
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | REF_CLOSE: (168), (215), (252) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | | #283.
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | (253) all_54_13 = e0
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | COMBINE_EQS: (215), (253) imply:
% 157.04/27.06 | | | | | | | | | | | | | (254) all_14_0 = e0
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | SIMP: (254) implies:
% 157.04/27.06 | | | | | | | | | | | | | (255) all_14_0 = e0
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | REDUCE: (217), (255) imply:
% 157.04/27.06 | | | | | | | | | | | | | (256) ~ (all_52_6 = e0)
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | REDUCE: (219), (255) imply:
% 157.04/27.06 | | | | | | | | | | | | | (257) ~ (e3 = e0)
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | REDUCE: (236), (255) imply:
% 157.04/27.06 | | | | | | | | | | | | | (258) ~ (e2 = e0)
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | REDUCE: (168), (255) imply:
% 157.04/27.06 | | | | | | | | | | | | | (259) ~ (e1 = e0)
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | REDUCE: (188), (255) imply:
% 157.04/27.06 | | | | | | | | | | | | | (260) op(e0, e2) = e0
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | BETA: splitting (251) gives:
% 157.04/27.06 | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | (261) all_56_14 = e1
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | COMBINE_EQS: (122), (261) imply:
% 157.04/27.06 | | | | | | | | | | | | | | (262) all_6_2 = e1
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | SIMP: (262) implies:
% 157.04/27.06 | | | | | | | | | | | | | | (263) all_6_2 = e1
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | REDUCE: (53), (263) imply:
% 157.04/27.06 | | | | | | | | | | | | | | (264) ~ (all_52_2 = e1)
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | REDUCE: (73), (263) imply:
% 157.04/27.06 | | | | | | | | | | | | | | (265) ~ (all_52_6 = e1)
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | REDUCE: (107), (263) imply:
% 157.04/27.06 | | | | | | | | | | | | | | (266) ~ (all_52_8 = e1)
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | REDUCE: (90), (263) imply:
% 157.04/27.06 | | | | | | | | | | | | | | (267) ~ (all_52_9 = e1)
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | REDUCE: (120), (263) imply:
% 157.04/27.06 | | | | | | | | | | | | | | (268) ~ (e2 = e1)
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 157.04/27.06 | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | (269) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 157.04/27.06 | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 157.04/27.06 | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 157.04/27.06 | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | (270) all_58_0 = e1 & op(e3, e3) = e1
% 157.04/27.06 | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | (271) op(e3, e3) = e1
% 157.04/27.06 | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | REF_CLOSE: (144), (211), (212), (271) are inconsistent by
% 157.04/27.06 | | | | | | | | | | | | | | | | sub-proof #668.
% 157.04/27.06 | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | (272) all_58_1 = e1 & op(e3, e2) = e1
% 157.04/27.06 | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | (273) all_58_1 = e1
% 157.04/27.06 | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | (274) all_54_2 = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (128), (274) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | | | | | | #1210.
% 157.04/27.06 | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | (275) ~ (all_54_2 = e3)
% 157.04/27.06 | | | | | | | | | | | | | | | | | (276) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | (277) all_54_9 = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (152), (277) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | | | | | | | #1181.
% 157.04/27.06 | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | (278) ~ (all_54_9 = e3)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | (279) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | (280) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | (281) all_58_6 = e3 & op(e1, e3) = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | (282) all_58_6 = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | (283) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (284) all_58_9 = e2 & op(e3, e0) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (46), (56), (57), (61), (68), (78), (109),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (116), (143), (144), (179), (187), (282), (284)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #279.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (285) all_58_10 = e2 & op(e2, e0) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (286) all_58_10 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (46), (56), (61), (78), (88), (103), (109),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (116), (117), (139), (144), (179), (187), (286)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #905.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | (287) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (288) all_58_11 = e2 & op(e1, e0) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (289) all_58_11 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (15), (16), (17), (32), (40), (46),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (47), (56), (57), (58), (60), (61), (74), (75),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (78), (80), (88), (105), (109), (116), (121),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (129), (133), (141), (143), (144), (151), (175),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (179), (187), (237), (260), (289) are inconsistent
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #696.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (290) all_58_15 = e2 & op(e0, e0) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | (291) all_58_15 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | (292) all_54_6 = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (292) imply:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | (293) all_52_9 = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (293) imply:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | (294) $false
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | (295) ~ (all_54_6 = e3)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | (296) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | (297) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_58_9 = e1 & op(e3, e0) = e1
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_9 = e1
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (78), (299) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | #1461.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_10 = e1 & op(e2, e0) = e1
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_10 = e1
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (302) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (57), (72), (78), (109), (133), (144),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (211), (212), (264), (302) are inconsistent
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #277.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (303) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_14 = e3 & op(e0, e1) = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_58_14 = e3
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_58_0 = e2 & op(e3, e3) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (137), (307) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_1 = e2 & op(e3, e2) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (273), (308) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1213.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_4 = e2 & op(e3, e1) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_58_4 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (46), (56), (57), (61), (68), (78), (109),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (126), (137), (143), (144), (175), (179),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (282), (311), (312) are inconsistent by
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #275.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_58_7 = e2 & op(e1, e2) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_7 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) op(e1, e2) = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_54_6 = e2
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (183), (317) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1192.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_54_6 = e1 | all_54_6 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (15), (16), (17), (32), (36), (40),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (47), (56), (57), (58), (60), (61), (67),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (74), (75), (78), (79), (80), (88), (105), (106),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (116), (121), (126), (129), (132), (133),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (141), (143), (144), (151), (175), (179),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (237), (260), (291), (305), (311), (315),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) are inconsistent by sub-proof #274.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_58_7 = e0 & op(e1, e2) = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (144), (256), (321) are inconsistent by
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1301.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_58_13 = e0 & op(e0, e2) = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_58_13 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_12 = e1 & op(e0, e3) = e1
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_12 = e1
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) op(e0, e3) = e1
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_4 = e0 & op(e3, e1) = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_4 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (305),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) are inconsistent by sub-proof #854.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_58_5 = e0 & op(e2, e1) = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (331) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_58_5 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (14), (15), (16), (17), (26),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (32), (33), (36), (40), (45), (46), (47), (50),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (52), (54), (56), (57), (58), (59), (60),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (62), (67), (68), (69), (72), (74), (75), (78),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (88), (93), (105), (108), (116),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (119), (120), (121), (123), (128), (129),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (133), (139), (141), (143), (144), (151), (154),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (179), (185), (237), (256), (260), (261),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264), (266), (267), (273), (276), (282), (291),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301), (305), (311), (315), (316), (318), (323),
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326), (327), (332) are inconsistent by sub-proof
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #271.
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_8 = e0 & op(e1, e1) = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_58_8 = e0
% 157.04/27.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (14), (15), (16), (17), (32),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (40), (46), (47), (51), (56), (57), (58),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (61), (67), (68), (74), (75), (78), (80),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (88), (105), (109), (116), (117), (120), (121),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (129), (133), (139), (141), (143), (144), (151),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (179), (187), (237), (260), (273), (282),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (301), (305), (311), (315), (323), (326),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) are inconsistent by sub-proof #269.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_58_14 = e0 & op(e0, e1) = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_58_14 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (305), (337) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1444.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_58_13 = e1 & op(e0, e2) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) op(e0, e2) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (133), (144), (260), (339) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1396.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (40), (56), (61), (67), (68), (78),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (88), (105), (109), (116), (141), (144),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (179), (237), (282), (305), (311), (315),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323), (340) are inconsistent by sub-proof #268.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_58_13 = e2 & op(e0, e2) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) op(e0, e2) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (133), (144), (260), (342) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1040.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_58_9 = e2 & op(e3, e0) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (46), (56), (57), (61), (68), (78), (109),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (143), (144), (179), (187), (282), (343)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #279.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_58_15 = e3 & op(e0, e0) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_58_15 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) op(e0, e0) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (32), (34), (46), (56), (57), (61),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (78), (88), (109), (116), (137), (144),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (151), (175), (179), (187), (282), (345), (346)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #590.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | (347) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_58_11 = e1 & op(e1, e0) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_58_11 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (350) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (57), (72), (78), (109), (133), (144),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (211), (212), (264), (350) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #277.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (351) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_58_14 = e3 & op(e0, e1) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (352) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_14 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_0 = e2 & op(e3, e3) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (137), (355) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_58_1 = e2 & op(e3, e2) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (273), (356) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1213.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (357) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_4 = e2 & op(e3, e1) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (358) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_58_4 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (46), (56), (57), (61), (68), (78), (109),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (126), (137), (143), (144), (175), (179),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (282), (359), (360) are inconsistent by
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #275.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (361) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_7 = e2 & op(e1, e2) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (362) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_58_7 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_54_6 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (183), (364) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1192.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) ~ (all_54_6 = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_54_6 = e1 | all_54_6 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (15), (16), (17), (32), (36), (40),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (47), (56), (57), (58), (60), (61), (67),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (74), (75), (78), (79), (80), (88), (105), (106),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (116), (121), (126), (129), (132), (133),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (141), (143), (144), (151), (175), (179),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (237), (260), (291), (353), (359), (363),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) are inconsistent by sub-proof #274.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_58_7 = e0 & op(e1, e2) = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (369) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_58_7 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (32), (46), (51), (56), (57), (61), (78),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (116), (120), (143), (144), (179), (187),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349), (370) are inconsistent by sub-proof #743.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_58_13 = e0 & op(e0, e2) = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_58_13 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_58_12 = e1 & op(e0, e3) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_12 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (117), (139), (144), (179), (376) are
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1074.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (377) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_58_5 = e1 & op(e2, e1) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (378) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) op(e2, e1) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (366) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_54_6 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (267), (380) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #562.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_54_6 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (381) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_52_9 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (382) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_52_9 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (383) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) op(e2, e1) = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_58_15 = e0 & op(e0, e0) = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (291),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353), (359), (385) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #629.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_54_9 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (388) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_52_6 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (389) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_52_6 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (390) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) ~ (all_52_4 = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_54_1 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (392) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_52_4 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (393) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) $false
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (394) is inconsistent.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) ~ (all_54_1 = e3)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (396) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_54_1 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (397) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_52_4 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (398) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) $false
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (399) is inconsistent.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) ~ (all_54_1 = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_54_1 = e1 | all_54_1 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_54_1 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (402) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_52_4 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (403) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) ~ (e3 = e1)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (144) with e0, e1, e1, e2,
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (379), (384) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) e1 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (405) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_58_1 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (14), (32), (33), (46), (56), (57),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (78), (88), (109), (116), (120), (129),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (133), (143), (144), (175), (179), (187), (282),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353), (359), (375), (387), (406) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #817.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_54_1 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (407) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_52_4 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (408) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) $false
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (409) is inconsistent.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_54_9 = e1 | all_54_9 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (152), (256), (265), (410) are inconsistent by
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1169.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_58_10 = e1 & op(e2, e0) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (411) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_58_10 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (61), (144), (175), (179), (413) are
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #909.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_58_5 = e0 & op(e2, e1) = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (415) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_58_5 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10), (14), (32), (33), (40), (46),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (56), (57), (60), (61), (67), (68), (75),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (80), (88), (105), (109), (116), (120),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141), (143), (144), (151), (175), (179), (187),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (273), (282), (349), (353), (359), (363),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (375), (412), (416) are inconsistent by
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #273.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_58_10 = e0 & op(e2, e0) = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (78), (109), (116), (175), (273), (363),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (412), (417) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #270.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_58_13 = e1 & op(e0, e2) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (418) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) op(e0, e2) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (133), (144), (260), (419) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1396.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (40), (56), (61), (67), (68), (78),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (88), (105), (109), (116), (141), (144),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (179), (237), (282), (353), (359), (363),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (420) are inconsistent by sub-proof #268.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_58_13 = e2 & op(e0, e2) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (421) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) op(e0, e2) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (133), (144), (260), (422) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1040.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_58_9 = e2 & op(e3, e0) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (46), (56), (57), (61), (68), (78), (109),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (143), (144), (179), (187), (282), (423)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #279.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_58_15 = e3 & op(e0, e0) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (424) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_58_15 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) op(e0, e0) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (32), (34), (46), (56), (57), (61),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (78), (88), (109), (116), (137), (144),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (151), (175), (179), (187), (282), (425), (426)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #590.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_58_15 = e1 & op(e0, e0) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | (428) op(e0, e0) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (144), (237), (428) are inconsistent by
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1386.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | (429) all_58_7 = e3 & op(e1, e2) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (141), (144), (429) are inconsistent by
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | sub-proof #1184.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | (430) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | (431) all_58_8 = e3 & op(e1, e1) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (15), (33), (56), (57), (61), (72),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | (78), (79), (88), (105), (109), (116), (120),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | (121), (133), (144), (175), (179), (187), (211),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | (212), (237), (264), (431) are inconsistent by
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | sub-proof #267.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | (432) all_58_11 = e3 & op(e1, e0) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | ALPHA: (432) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | (433) all_58_11 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | (434) op(e1, e0) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | (435) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (436) all_58_9 = e2 & op(e3, e0) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (437) all_58_9 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (437) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (438) e3 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | SIMP: (438) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (439) e3 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (433), (439) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (440) all_58_11 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (15), (16), (17), (32), (40), (46),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (47), (56), (57), (58), (60), (61), (74), (75),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (78), (80), (88), (105), (109), (116), (121),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (129), (133), (141), (143), (144), (151), (175),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (179), (187), (237), (260), (440) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #696.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (441) all_58_10 = e2 & op(e2, e0) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (442) all_58_10 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (46), (56), (61), (78), (88), (103), (109),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (116), (117), (139), (144), (179), (187), (442)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #905.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | (443) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (443) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (444) all_58_11 = e2 & op(e1, e0) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (444) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (445) all_58_11 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (15), (16), (17), (32), (40), (46),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (47), (56), (57), (58), (60), (61), (74), (75),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (78), (80), (88), (105), (109), (116), (121),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (129), (133), (141), (143), (144), (151), (175),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (179), (187), (237), (260), (445) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #696.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (446) all_58_15 = e2 & op(e0, e0) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (446) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | (447) all_58_15 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | (448) all_54_6 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (448) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | (449) all_52_9 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (449) imply:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | (450) $false
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (450) is inconsistent.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | (451) ~ (all_54_6 = e3)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | (452) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | (453) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_58_9 = e1 & op(e3, e0) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (454) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_58_9 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (78), (455) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | #1461.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_58_10 = e1 & op(e2, e0) = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | (457) all_58_10 = e1
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (458) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (57), (72), (78), (109), (133), (144),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (211), (212), (264), (458) are inconsistent
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #277.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (459) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (459) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_58_14 = e3 & op(e0, e1) = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_58_14 = e3
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_58_0 = e2 & op(e3, e3) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (137), (463) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_58_1 = e2 & op(e3, e2) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (273), (464) are inconsistent by sub-proof
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1213.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (465) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_58_4 = e2 & op(e3, e1) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (466) implies:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_58_4 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) op(e3, e1) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (469) gives:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_58_1 = e2 & op(e3, e2) = e2
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (78), (109), (116), (126), (137), (467),
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) are inconsistent by sub-proof #276.
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_58_3 = e2 & op(e2, e2) = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (471) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) all_58_3 = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (472) imply:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) e3 = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (473) imply:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_58_9 = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (475) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_58_4 = e1 & op(e3, e1) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (476) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_58_4 = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (461),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) are inconsistent by sub-proof #850.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_58_5 = e1 & op(e2, e1) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (478) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_58_5 = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_58_9 = e1 & op(e3, e0) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (461),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467), (474), (480) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #849.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (56), (61), (78), (88), (109), (116), (144),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (179), (457), (479) are inconsistent by
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #754.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (109), (144), (237), (434), (481) are
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #788.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (482) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_58_8 = e1 & op(e1, e1) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_58_8 = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (485) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) all_58_4 = e0 & op(e3, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (486) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_58_4 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (461),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) are inconsistent by sub-proof #854.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_58_5 = e0 & op(e2, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_58_5 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) all_58_15 = e0 & op(e0, e0) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (447),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (467), (490) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #629.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (56), (61), (78), (109), (116), (144),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (179), (433), (474), (489), (492) are
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #837.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (493) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_58_8 = e0 & op(e1, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (484), (494) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1271.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_58_14 = e0 & op(e0, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (461), (495) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #882.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_58_14 = e1 & op(e0, e1) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_58_14 = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (461), (497) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1147.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (498) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_58_7 = e2 & op(e1, e2) = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_58_7 = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) op(e1, e2) = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (452) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_54_6 = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (183), (502) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1192.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_54_6 = e1 | all_54_6 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (15), (16), (17), (32), (36), (40),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (47), (56), (57), (58), (60), (61), (67),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (74), (75), (78), (79), (80), (88), (105), (106),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (116), (121), (126), (129), (132), (133),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (141), (143), (144), (151), (175), (179),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (237), (260), (447), (461), (467), (500),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) are inconsistent by sub-proof #274.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (505) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_58_7 = e0 & op(e1, e2) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (506) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_58_7 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (15), (16), (32), (33), (46), (51),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (61), (78), (88), (109), (116), (120),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (133), (143), (144), (151), (175), (179),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (237), (433), (447), (461), (507) are
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_58_13 = e0 & op(e0, e2) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (508) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_58_13 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (510) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_58_12 = e1 & op(e0, e3) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (511) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_58_12 = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) op(e0, e3) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (514) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_58_4 = e0 & op(e3, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (515) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_58_4 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (461),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) are inconsistent by sub-proof #854.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_58_5 = e0 & op(e2, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (517) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_58_5 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (61), (68), (116), (144), (150),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (187), (273), (467), (519) are inconsistent
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #284.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (520) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) all_58_6 = e3 & op(e1, e3) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (521) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_58_6 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (14), (15), (16), (17), (26),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (32), (33), (36), (40), (45), (46), (47), (50),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (52), (54), (56), (57), (58), (59), (60),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (62), (67), (68), (69), (72), (74), (75), (78),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (88), (93), (105), (108), (116),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (119), (120), (121), (123), (128), (129),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (133), (139), (141), (143), (144), (151), (154),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (179), (185), (237), (256), (260), (261),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264), (266), (267), (273), (276), (447), (457),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (467), (500), (501), (503), (509), (512),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513), (518), (522) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #271.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_58_12 = e3 & op(e0, e3) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (523) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_58_12 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (15), (16), (32), (33), (46), (56),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (57), (60), (61), (78), (88), (109), (116), (120),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (133), (137), (144), (151), (175), (179),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (461), (467), (524) are inconsistent by
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #774.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (525) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_58_8 = e0 & op(e1, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (526) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_58_8 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) op(e1, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_0 = e3 & op(e3, e3) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (530) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_58_0 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (16), (56), (61), (78), (109), (116),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (144), (175), (179), (237), (273), (434),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (500), (509), (527), (531) are inconsistent
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #433.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_58_2 = e3 & op(e2, e3) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) op(e2, e3) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (144), (179), (187), (533) are inconsistent
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1159.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (534) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_58_6 = e3 & op(e1, e3) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (535) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_58_6 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (14), (15), (16), (17), (32),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (40), (46), (47), (51), (56), (57), (58),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (61), (67), (68), (74), (75), (78), (80),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (88), (105), (109), (116), (117), (120), (121),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (129), (133), (139), (141), (143), (144), (151),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (179), (187), (237), (260), (273), (447),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457), (461), (467), (500), (509), (512), (527),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) are inconsistent by sub-proof #269.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_58_12 = e3 & op(e0, e3) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (537) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_58_12 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (62), (144), (187), (468), (539) are
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #293.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (540) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) all_58_8 = e3 & op(e1, e1) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (541) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) op(e1, e1) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (144), (528), (542) are inconsistent by
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1466.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (15), (16), (32), (33), (46), (56),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (57), (60), (61), (78), (88), (109), (116), (120),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (133), (137), (144), (151), (175), (179),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (461), (538) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #773.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_58_14 = e0 & op(e0, e1) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (543) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) all_58_14 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (461), (544) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1444.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_58_13 = e1 & op(e0, e2) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (545) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) op(e0, e2) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (133), (144), (260), (546) are inconsistent
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1396.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (109), (144), (237), (461), (547) are
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #435.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_58_13 = e2 & op(e0, e2) = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) op(e0, e2) = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (550) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_58_1 = e0 & op(e3, e2) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (273), (551) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1327.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) all_58_3 = e0 & op(e2, e2) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (175), (552) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #910.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (553) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_58_7 = e0 & op(e1, e2) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_58_7 = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (15), (16), (32), (33), (46), (51),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (61), (78), (88), (109), (116), (120),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (133), (143), (144), (151), (175), (179),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187), (237), (433), (447), (461), (555) are
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_58_13 = e0 & op(e0, e2) = e0
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (133), (144), (260), (549) are inconsistent
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1040.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) all_58_9 = e2 & op(e3, e0) = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (557) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_58_9 = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (558) imply:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) e3 = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (433), (559) imply:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_58_11 = e2
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (56), (61), (68), (78), (109), (116), (151),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447), (560) are inconsistent by sub-proof #1453.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_58_15 = e3 & op(e0, e0) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (34), (56), (61), (74), (78), (83),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (91), (109), (116), (144), (151), (187), (433),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (434), (561) are inconsistent by sub-proof #262.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | (562) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (109), (144), (237), (434), (562) are
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #788.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | (563) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 157.04/27.08 | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 157.04/27.08 | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | BETA: splitting (563) gives:
% 157.04/27.08 | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | (564) all_58_4 = e1 & op(e3, e1) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | ALPHA: (564) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | (565) all_58_4 = e1
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | (566) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | BETA: splitting (566) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (567) all_58_6 = e3 & op(e1, e3) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | ALPHA: (567) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (568) all_58_6 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | (569) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (57), (72), (78), (109), (133), (144),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | (179), (211), (212), (264), (569) are inconsistent
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | by sub-proof #277.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | (570) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (570) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (571) all_58_14 = e3 & op(e0, e1) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | ALPHA: (571) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (572) all_58_14 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (565),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (572) are inconsistent by sub-proof #850.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (573) all_58_15 = e3 & op(e0, e0) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | ALPHA: (573) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (574) all_58_15 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (575) op(e0, e0) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (32), (34), (46), (56), (57), (61),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (68), (78), (88), (109), (116), (137), (144),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (151), (175), (179), (187), (568), (574), (575)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #590.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (576) all_58_7 = e3 & op(e1, e2) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (141), (144), (576) are inconsistent by
% 157.04/27.08 | | | | | | | | | | | | | | | | | | sub-proof #1184.
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | (577) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | BETA: splitting (577) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (578) all_58_8 = e3 & op(e1, e1) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (15), (33), (56), (57), (61), (72),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (78), (79), (88), (105), (109), (116), (120),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (121), (133), (144), (175), (179), (187), (211),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (212), (237), (264), (578) are inconsistent by
% 157.04/27.08 | | | | | | | | | | | | | | | | | | sub-proof #267.
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (579) all_58_11 = e3 & op(e1, e0) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | ALPHA: (579) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (580) all_58_11 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | (581) op(e1, e0) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | (582) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (57), (72), (78), (109), (133), (144),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | (179), (211), (212), (264), (582) are inconsistent
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | by sub-proof #277.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | (583) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (584) all_58_14 = e3 & op(e0, e1) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | ALPHA: (584) implies:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (585) all_58_14 = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (33), (56), (61), (78), (88), (109),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (116), (120), (144), (175), (179), (187), (565),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (585) are inconsistent by sub-proof #850.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (586) all_58_15 = e3 & op(e0, e0) = e3
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (34), (56), (61), (74), (78), (83),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (91), (109), (116), (144), (151), (187), (580),
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | | (581), (586) are inconsistent by sub-proof #262.
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | (587) all_58_9 = e1 & op(e3, e0) = e1
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | | REF_CLOSE: (68), (78), (587) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | | | #1078.
% 157.04/27.08 | | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | Case 2:
% 157.04/27.08 | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | (588) all_56_15 = e0
% 157.04/27.08 | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | | REF_CLOSE: (61), (235), (588) are inconsistent by sub-proof
% 157.04/27.08 | | | | | | | | | | | | | | #871.
% 157.04/27.08 | | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | | End of split
% 157.04/27.08 | | | | | | | | | | | | |
% 157.04/27.08 | | | | | | | | | | | | End of split
% 157.04/27.09 | | | | | | | | | | | |
% 157.04/27.09 | | | | | | | | | | | End of split
% 157.04/27.09 | | | | | | | | | | |
% 157.04/27.09 | | | | | | | | | | End of split
% 157.04/27.09 | | | | | | | | | |
% 157.04/27.09 | | | | | | | | | End of split
% 157.04/27.09 | | | | | | | | |
% 157.04/27.09 | | | | | | | | End of split
% 157.04/27.09 | | | | | | | |
% 157.04/27.09 | | | | | | | End of split
% 157.04/27.09 | | | | | | |
% 157.04/27.09 | | | | | | End of split
% 157.04/27.09 | | | | | |
% 157.04/27.09 | | | | | End of split
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | End of split
% 157.04/27.09 | | | |
% 157.04/27.09 | | | Case 2:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | (589) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2,
% 157.04/27.09 | | | | e0) = e3)
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | REF_CLOSE: (45), (47), (62), (74), (144), (589) are inconsistent by
% 157.04/27.09 | | | | sub-proof #261.
% 157.04/27.09 | | | |
% 157.04/27.09 | | | End of split
% 157.04/27.09 | | |
% 157.04/27.09 | | Case 2:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (590) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 & $i(all_14_1)
% 157.04/27.09 | | |
% 157.04/27.09 | | | ALPHA: (590) implies:
% 157.04/27.09 | | | (591) ~ (all_14_1 = e0)
% 157.04/27.09 | | | (592) op(e3, e3) = all_14_1
% 157.04/27.09 | | |
% 157.04/27.09 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 157.04/27.09 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.04/27.09 | | | (24), (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 157.04/27.09 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 157.04/27.09 | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (56),
% 157.04/27.09 | | | (57), (58), (59), (60), (61), (62), (64), (65), (66), (67),
% 157.04/27.09 | | | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 157.04/27.09 | | | (80), (81), (83), (84), (85), (87), (88), (89), (90), (91),
% 157.04/27.09 | | | (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 157.04/27.09 | | | (102), (104), (105), (106), (107), (108), (109), (110), (111),
% 157.04/27.09 | | | (112), (113), (114), (115), (116), (119), (120), (121), (122),
% 157.04/27.09 | | | (123), (124), (125), (126), (127), (129), (130), (131), (132),
% 157.04/27.09 | | | (133), (134), (135), (136), (138), (140), (141), (142), (143),
% 157.04/27.09 | | | (144), (145), (146), (147), (148), (149), (150), (151), (152),
% 157.04/27.09 | | | (154), (155), (156), (157), (158), (159), (160), (161), (162),
% 157.04/27.09 | | | (163), (591), (592) are inconsistent by sub-proof #354.
% 157.04/27.09 | | |
% 157.04/27.09 | | End of split
% 157.04/27.09 | |
% 157.04/27.09 | End of split
% 157.04/27.09 |
% 157.04/27.09 End of proof
% 157.04/27.09
% 157.04/27.09 Sub-proof #261 shows that the following formulas are inconsistent:
% 157.04/27.09 ----------------------------------------------------------------
% 157.04/27.09 (1) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.04/27.09 (2) op(e2, e1) = all_52_9
% 157.04/27.09 (3) ~ (all_52_13 = e3)
% 157.04/27.09 (4) ~ (all_52_9 = e3)
% 157.04/27.09 (5) op(e2, e0) = all_52_13
% 157.04/27.09 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.09
% 157.04/27.09 Begin of proof
% 157.04/27.09 |
% 157.04/27.09 | BETA: splitting (1) gives:
% 157.04/27.09 |
% 157.04/27.09 | Case 1:
% 157.04/27.09 | |
% 157.04/27.09 | | (7) all_58_5 = e3 & op(e2, e1) = e3
% 157.04/27.09 | |
% 157.04/27.09 | | ALPHA: (7) implies:
% 157.04/27.09 | | (8) op(e2, e1) = e3
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1196.
% 157.04/27.09 | |
% 157.04/27.09 | Case 2:
% 157.04/27.09 | |
% 157.04/27.09 | | (9) all_58_10 = e3 & op(e2, e0) = e3
% 157.04/27.09 | |
% 157.04/27.09 | | ALPHA: (9) implies:
% 157.04/27.09 | | (10) op(e2, e0) = e3
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1364.
% 157.04/27.09 | |
% 157.04/27.09 | End of split
% 157.04/27.09 |
% 157.04/27.09 End of proof
% 157.04/27.09
% 157.04/27.09 Sub-proof #262 shows that the following formulas are inconsistent:
% 157.04/27.09 ----------------------------------------------------------------
% 157.04/27.09 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.09 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.09 (2) op(e0, e0) = all_10_1
% 157.04/27.09 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.04/27.09 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.04/27.09 (4) all_58_15 = e3 & op(e0, e0) = e3
% 157.04/27.09 (5) ~ (e3 = e0)
% 157.04/27.09 (6) ~ (e2 = e0)
% 157.04/27.09 (7) op(e2, e0) = all_52_13
% 157.04/27.09 (8) ~ (e3 = e1)
% 157.04/27.09 (9) ~ (all_4_2 = e1)
% 157.04/27.09 (10) op(e0, e0) = all_4_2
% 157.04/27.09 (11) ~ (e2 = e1)
% 157.04/27.09 (12) ~ (e1 = e0)
% 157.04/27.09 (13) op(e1, e0) = e3
% 157.04/27.09 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.09 (15) ~ (e3 = e2)
% 157.04/27.09 (16) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.09 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.04/27.09 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.04/27.09 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.04/27.09 (17) all_58_11 = e3
% 157.04/27.09
% 157.04/27.09 Begin of proof
% 157.04/27.09 |
% 157.04/27.09 | ALPHA: (4) implies:
% 157.04/27.09 | (18) op(e0, e0) = e3
% 157.04/27.09 |
% 157.04/27.09 | BETA: splitting (16) gives:
% 157.04/27.09 |
% 157.04/27.09 | Case 1:
% 157.04/27.09 | |
% 157.04/27.09 | | (19) all_58_15 = e0 & op(e0, e0) = e0
% 157.04/27.09 | |
% 157.04/27.09 | | ALPHA: (19) implies:
% 157.04/27.09 | | (20) op(e0, e0) = e0
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (2), (5), (14), (18), (20) are inconsistent by sub-proof #313.
% 157.04/27.09 | |
% 157.04/27.09 | Case 2:
% 157.04/27.09 | |
% 157.04/27.09 | | (21) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 157.04/27.09 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 157.04/27.09 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 157.04/27.09 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.04/27.09 | |
% 157.04/27.09 | | ALPHA: (21) implies:
% 157.04/27.09 | | (22) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 157.04/27.09 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 157.04/27.09 | | (15), (17), (18), (22) are inconsistent by sub-proof #263.
% 157.04/27.09 | |
% 157.04/27.09 | End of split
% 157.04/27.09 |
% 157.04/27.09 End of proof
% 157.04/27.09
% 157.04/27.09 Sub-proof #263 shows that the following formulas are inconsistent:
% 157.04/27.09 ----------------------------------------------------------------
% 157.04/27.09 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.09 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.09 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.04/27.09 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.04/27.09 (3) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 157.04/27.09 (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.09 (4) ~ (e3 = e0)
% 157.04/27.09 (5) ~ (e2 = e0)
% 157.04/27.09 (6) op(e2, e0) = all_52_13
% 157.04/27.09 (7) ~ (e3 = e1)
% 157.04/27.09 (8) ~ (all_4_2 = e1)
% 157.04/27.09 (9) op(e0, e0) = all_4_2
% 157.04/27.09 (10) ~ (e2 = e1)
% 157.04/27.09 (11) ~ (e1 = e0)
% 157.04/27.09 (12) op(e1, e0) = e3
% 157.04/27.09 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.09 (14) ~ (e3 = e2)
% 157.04/27.09 (15) all_58_11 = e3
% 157.04/27.09 (16) op(e0, e0) = e3
% 157.04/27.09
% 157.04/27.09 Begin of proof
% 157.04/27.09 |
% 157.04/27.09 | BETA: splitting (3) gives:
% 157.04/27.09 |
% 157.04/27.09 | Case 1:
% 157.04/27.09 | |
% 157.04/27.09 | | (17) all_58_9 = e0 & op(e3, e0) = e0
% 157.04/27.09 | |
% 157.04/27.09 | | ALPHA: (17) implies:
% 157.04/27.09 | | (18) op(e3, e0) = e0
% 157.04/27.09 | |
% 157.04/27.09 | | BETA: splitting (2) gives:
% 157.04/27.09 | |
% 157.04/27.09 | | Case 1:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 157.04/27.09 | | | e2)
% 157.04/27.09 | | |
% 157.04/27.09 | | | BETA: splitting (19) gives:
% 157.04/27.09 | | |
% 157.04/27.09 | | | Case 1:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | (20) all_58_9 = e2 & op(e3, e0) = e2
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | ALPHA: (20) implies:
% 157.04/27.09 | | | | (21) op(e3, e0) = e2
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | REF_CLOSE: (5), (13), (18), (21) are inconsistent by sub-proof #1500.
% 157.04/27.09 | | | |
% 157.04/27.09 | | | Case 2:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | (22) all_58_10 = e2 & op(e2, e0) = e2
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | ALPHA: (22) implies:
% 157.04/27.09 | | | | (23) all_58_10 = e2
% 157.04/27.09 | | | | (24) op(e2, e0) = e2
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.04/27.09 | | | | (13), (15), (23), (24) are inconsistent by sub-proof #266.
% 157.04/27.09 | | | |
% 157.04/27.09 | | | End of split
% 157.04/27.09 | | |
% 157.04/27.09 | | Case 2:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (25) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0)
% 157.04/27.09 | | | = e2)
% 157.04/27.09 | | |
% 157.04/27.09 | | | REF_CLOSE: (13), (14), (15), (16), (25) are inconsistent by sub-proof
% 157.04/27.09 | | | #265.
% 157.04/27.09 | | |
% 157.04/27.09 | | End of split
% 157.04/27.09 | |
% 157.04/27.09 | Case 2:
% 157.04/27.09 | |
% 157.04/27.09 | | (26) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 157.04/27.09 | | e0)
% 157.04/27.09 | |
% 157.04/27.09 | | BETA: splitting (26) gives:
% 157.04/27.09 | |
% 157.04/27.09 | | Case 1:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (27) all_58_10 = e0 & op(e2, e0) = e0
% 157.04/27.09 | | |
% 157.04/27.09 | | | ALPHA: (27) implies:
% 157.04/27.09 | | | (28) all_58_10 = e0
% 157.04/27.09 | | |
% 157.04/27.09 | | | BETA: splitting (2) gives:
% 157.04/27.09 | | |
% 157.04/27.09 | | | Case 1:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | (29) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 157.04/27.09 | | | | = e2)
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | BETA: splitting (29) gives:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | Case 1:
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | (30) all_58_9 = e2 & op(e3, e0) = e2
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | ALPHA: (30) implies:
% 157.04/27.09 | | | | | (31) all_58_9 = e2
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | REF_CLOSE: (1), (7), (8), (9), (10), (11), (12), (13), (28), (31) are
% 157.04/27.09 | | | | | inconsistent by sub-proof #264.
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | Case 2:
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | (32) all_58_10 = e2 & op(e2, e0) = e2
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | ALPHA: (32) implies:
% 157.04/27.09 | | | | | (33) all_58_10 = e2
% 157.04/27.09 | | | | | (34) op(e2, e0) = e2
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.04/27.09 | | | | | (13), (15), (33), (34) are inconsistent by sub-proof #266.
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | End of split
% 157.04/27.09 | | | |
% 157.04/27.09 | | | Case 2:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | (35) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 157.04/27.09 | | | | e0) = e2)
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | REF_CLOSE: (13), (14), (15), (16), (35) are inconsistent by sub-proof
% 157.04/27.09 | | | | #265.
% 157.04/27.09 | | | |
% 157.04/27.09 | | | End of split
% 157.04/27.09 | | |
% 157.04/27.09 | | Case 2:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (36) all_58_11 = e0 & op(e1, e0) = e0
% 157.04/27.09 | | |
% 157.04/27.09 | | | REF_CLOSE: (4), (15), (36) are inconsistent by sub-proof #1083.
% 157.04/27.09 | | |
% 157.04/27.09 | | End of split
% 157.04/27.09 | |
% 157.04/27.09 | End of split
% 157.04/27.09 |
% 157.04/27.09 End of proof
% 157.04/27.09
% 157.04/27.09 Sub-proof #264 shows that the following formulas are inconsistent:
% 157.04/27.09 ----------------------------------------------------------------
% 157.04/27.09 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.09 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.09 (2) ~ (e3 = e1)
% 157.04/27.09 (3) ~ (all_4_2 = e1)
% 157.04/27.09 (4) op(e0, e0) = all_4_2
% 157.04/27.09 (5) ~ (e2 = e1)
% 157.04/27.09 (6) ~ (e1 = e0)
% 157.04/27.09 (7) op(e1, e0) = e3
% 157.04/27.09 (8) all_58_10 = e0
% 157.04/27.09 (9) all_58_9 = e2
% 157.04/27.09 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.09
% 157.04/27.09 Begin of proof
% 157.04/27.09 |
% 157.04/27.09 | BETA: splitting (1) gives:
% 157.04/27.09 |
% 157.04/27.09 | Case 1:
% 157.04/27.09 | |
% 157.04/27.09 | | (11) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.04/27.09 | | e1)
% 157.04/27.09 | |
% 157.04/27.09 | | BETA: splitting (11) gives:
% 157.04/27.09 | |
% 157.04/27.09 | | Case 1:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (12) all_58_9 = e1 & op(e3, e0) = e1
% 157.04/27.09 | | |
% 157.04/27.09 | | | REF_CLOSE: (5), (9), (12) are inconsistent by sub-proof #1325.
% 157.04/27.09 | | |
% 157.04/27.09 | | Case 2:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (13) all_58_10 = e1 & op(e2, e0) = e1
% 157.04/27.09 | | |
% 157.04/27.09 | | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #1373.
% 157.04/27.09 | | |
% 157.04/27.09 | | End of split
% 157.04/27.09 | |
% 157.04/27.09 | Case 2:
% 157.04/27.09 | |
% 157.04/27.09 | | (14) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.04/27.09 | | e1)
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (2), (3), (4), (7), (10), (14) are inconsistent by sub-proof
% 157.04/27.09 | | #318.
% 157.04/27.09 | |
% 157.04/27.09 | End of split
% 157.04/27.09 |
% 157.04/27.09 End of proof
% 157.04/27.09
% 157.04/27.09 Sub-proof #265 shows that the following formulas are inconsistent:
% 157.04/27.09 ----------------------------------------------------------------
% 157.04/27.09 (1) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.04/27.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.09 (3) ~ (e3 = e2)
% 157.04/27.09 (4) all_58_11 = e3
% 157.04/27.09 (5) op(e0, e0) = e3
% 157.04/27.09
% 157.04/27.09 Begin of proof
% 157.04/27.09 |
% 157.04/27.09 | BETA: splitting (1) gives:
% 157.04/27.09 |
% 157.04/27.09 | Case 1:
% 157.04/27.09 | |
% 157.04/27.09 | | (6) all_58_11 = e2 & op(e1, e0) = e2
% 157.04/27.09 | |
% 157.04/27.09 | | ALPHA: (6) implies:
% 157.04/27.09 | | (7) all_58_11 = e2
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1049.
% 157.04/27.09 | |
% 157.04/27.09 | Case 2:
% 157.04/27.09 | |
% 157.04/27.09 | | (8) all_58_15 = e2 & op(e0, e0) = e2
% 157.04/27.09 | |
% 157.04/27.09 | | ALPHA: (8) implies:
% 157.04/27.09 | | (9) op(e0, e0) = e2
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1382.
% 157.04/27.09 | |
% 157.04/27.09 | End of split
% 157.04/27.09 |
% 157.04/27.09 End of proof
% 157.04/27.09
% 157.04/27.09 Sub-proof #266 shows that the following formulas are inconsistent:
% 157.04/27.09 ----------------------------------------------------------------
% 157.04/27.09 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.09 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.09 (2) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 157.04/27.09 (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.09 (3) all_58_10 = e2
% 157.04/27.09 (4) op(e2, e0) = e2
% 157.04/27.09 (5) ~ (e3 = e0)
% 157.04/27.09 (6) ~ (e2 = e0)
% 157.04/27.09 (7) op(e2, e0) = all_52_13
% 157.04/27.09 (8) ~ (e3 = e1)
% 157.04/27.09 (9) ~ (all_4_2 = e1)
% 157.04/27.09 (10) op(e0, e0) = all_4_2
% 157.04/27.09 (11) ~ (e2 = e1)
% 157.04/27.09 (12) ~ (e1 = e0)
% 157.04/27.09 (13) op(e1, e0) = e3
% 157.04/27.09 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.09 (15) all_58_11 = e3
% 157.04/27.09
% 157.04/27.09 Begin of proof
% 157.04/27.09 |
% 157.04/27.09 | BETA: splitting (1) gives:
% 157.04/27.09 |
% 157.04/27.09 | Case 1:
% 157.04/27.09 | |
% 157.04/27.09 | | (16) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.04/27.09 | | e1)
% 157.04/27.09 | |
% 157.04/27.09 | | BETA: splitting (16) gives:
% 157.04/27.09 | |
% 157.04/27.09 | | Case 1:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (17) all_58_9 = e1 & op(e3, e0) = e1
% 157.04/27.09 | | |
% 157.04/27.09 | | | ALPHA: (17) implies:
% 157.04/27.09 | | | (18) all_58_9 = e1
% 157.04/27.09 | | |
% 157.04/27.09 | | | BETA: splitting (2) gives:
% 157.04/27.09 | | |
% 157.04/27.09 | | | Case 1:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | (19) all_58_9 = e0 & op(e3, e0) = e0
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | REF_CLOSE: (12), (18), (19) are inconsistent by sub-proof #1202.
% 157.04/27.09 | | | |
% 157.04/27.09 | | | Case 2:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | (20) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 157.04/27.09 | | | | e0) = e0)
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | BETA: splitting (20) gives:
% 157.04/27.09 | | | |
% 157.04/27.09 | | | | Case 1:
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | (21) all_58_10 = e0 & op(e2, e0) = e0
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | ALPHA: (21) implies:
% 157.04/27.09 | | | | | (22) op(e2, e0) = e0
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | REF_CLOSE: (4), (6), (7), (14), (22) are inconsistent by sub-proof
% 157.04/27.09 | | | | | #1397.
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | Case 2:
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | (23) all_58_11 = e0 & op(e1, e0) = e0
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | | REF_CLOSE: (5), (15), (23) are inconsistent by sub-proof #1083.
% 157.04/27.09 | | | | |
% 157.04/27.09 | | | | End of split
% 157.04/27.09 | | | |
% 157.04/27.09 | | | End of split
% 157.04/27.09 | | |
% 157.04/27.09 | | Case 2:
% 157.04/27.09 | | |
% 157.04/27.09 | | | (24) all_58_10 = e1 & op(e2, e0) = e1
% 157.04/27.09 | | |
% 157.04/27.09 | | | ALPHA: (24) implies:
% 157.04/27.09 | | | (25) all_58_10 = e1
% 157.04/27.09 | | |
% 157.04/27.09 | | | REF_CLOSE: (3), (11), (25) are inconsistent by sub-proof #1091.
% 157.04/27.09 | | |
% 157.04/27.09 | | End of split
% 157.04/27.09 | |
% 157.04/27.09 | Case 2:
% 157.04/27.09 | |
% 157.04/27.09 | | (26) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.04/27.09 | | e1)
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (8), (9), (10), (13), (14), (26) are inconsistent by sub-proof
% 157.04/27.09 | | #318.
% 157.04/27.09 | |
% 157.04/27.09 | End of split
% 157.04/27.09 |
% 157.04/27.09 End of proof
% 157.04/27.09
% 157.04/27.09 Sub-proof #267 shows that the following formulas are inconsistent:
% 157.04/27.09 ----------------------------------------------------------------
% 157.04/27.09 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.09 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.04/27.09 (2) op(e1, e1) = all_6_2
% 157.04/27.09 (3) ~ (all_52_7 = e3)
% 157.04/27.09 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.04/27.09 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.04/27.09 (5) ~ (e3 = e0)
% 157.04/27.09 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.09 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.09 (7) ~ (e2 = e0)
% 157.04/27.09 (8) op(e1, e3) = all_52_2
% 157.04/27.09 (9) op(e2, e3) = e2
% 157.04/27.09 (10) ~ (e3 = e1)
% 157.04/27.09 (11) all_58_8 = e3 & op(e1, e1) = e3
% 157.04/27.09 (12) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.04/27.09 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.04/27.09 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.09 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.04/27.09 (14) op(e0, e0) = e2
% 157.04/27.09 (15) ~ (all_52_2 = e1)
% 157.04/27.09 (16) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.04/27.09 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.04/27.09 (17) ~ (e2 = e1)
% 157.04/27.09 (18) ~ (all_22_1 = e1)
% 157.04/27.09 (19) ~ (e1 = e0)
% 157.04/27.09 (20) all_58_3 = e3
% 157.04/27.09 (21) ~ (all_6_2 = e2)
% 157.04/27.09 (22) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.04/27.09 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.04/27.09 e3)
% 157.04/27.09 (23) op(e0, e2) = all_52_7
% 157.04/27.09 (24) op(e3, e3) = all_22_1
% 157.04/27.09 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.09 (26) ~ (e3 = e2)
% 157.04/27.09
% 157.04/27.09 Begin of proof
% 157.04/27.09 |
% 157.04/27.09 | ALPHA: (11) implies:
% 157.04/27.09 | (27) all_58_8 = e3
% 157.04/27.09 |
% 157.04/27.09 | BETA: splitting (22) gives:
% 157.04/27.09 |
% 157.04/27.09 | Case 1:
% 157.04/27.09 | |
% 157.04/27.09 | | (28) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 157.04/27.09 | | e3)
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (3), (6), (8), (9), (10), (15), (17), (18), (23), (24), (25),
% 157.04/27.09 | | (28) are inconsistent by sub-proof #277.
% 157.04/27.09 | |
% 157.04/27.09 | Case 2:
% 157.04/27.09 | |
% 157.04/27.09 | | (29) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.04/27.09 | | e3)
% 157.04/27.09 | |
% 157.04/27.09 | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (12), (13), (14), (16), (17),
% 157.04/27.09 | | (19), (20), (21), (25), (26), (27), (29) are inconsistent by
% 157.04/27.09 | | sub-proof #505.
% 157.04/27.09 | |
% 157.04/27.09 | End of split
% 157.04/27.09 |
% 157.04/27.09 End of proof
% 157.04/27.09
% 157.04/27.09 Sub-proof #268 shows that the following formulas are inconsistent:
% 157.04/27.09 ----------------------------------------------------------------
% 157.04/27.09 (1) all_58_13 = e0
% 157.04/27.09 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.09 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.09 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.09 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.09 (4) all_58_14 = e3
% 157.04/27.09 (5) all_58_7 = e2
% 157.04/27.09 (6) all_58_6 = e3
% 157.04/27.09 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.04/27.09 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.04/27.09 (8) ~ (e3 = e0)
% 157.04/27.09 (9) ~ (e2 = e0)
% 157.04/27.09 (10) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.04/27.09 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.09 (11) all_58_9 = e3
% 157.04/27.09 (12) op(e2, e3) = e2
% 157.04/27.09 (13) ~ (e3 = e1)
% 157.04/27.09 (14) op(e1, e2) = all_52_6
% 157.04/27.09 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.09 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.04/27.09 (16) op(e0, e0) = e2
% 157.04/27.09 (17) all_58_4 = e2
% 157.04/27.09 (18) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.09 (19) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.04/27.09 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.04/27.09 (20) ~ (e2 = e1)
% 157.04/27.09 (21) ~ (e1 = e0)
% 157.04/27.09 (22) all_58_3 = e3
% 157.04/27.09 (23) ~ (all_52_6 = e3)
% 157.04/27.10 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.10
% 157.04/27.10 Begin of proof
% 157.04/27.10 |
% 157.04/27.10 | BETA: splitting (18) gives:
% 157.04/27.10 |
% 157.04/27.10 | Case 1:
% 157.04/27.10 | |
% 157.04/27.10 | | (25) all_58_14 = e1 & op(e0, e1) = e1
% 157.04/27.10 | |
% 157.04/27.10 | | ALPHA: (25) implies:
% 157.04/27.10 | | (26) all_58_14 = e1
% 157.04/27.10 | |
% 157.04/27.10 | | COMBINE_EQS: (4), (26) imply:
% 157.04/27.10 | | (27) e3 = e1
% 157.04/27.10 | |
% 157.04/27.10 | | COMBINE_EQS: (6), (27) imply:
% 157.04/27.10 | | (28) all_58_6 = e1
% 157.04/27.10 | |
% 157.04/27.10 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 157.04/27.10 | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (28)
% 157.04/27.10 | | are inconsistent by sub-proof #409.
% 157.04/27.10 | |
% 157.04/27.10 | Case 2:
% 157.04/27.10 | |
% 157.04/27.10 | | (29) all_58_15 = e1 & op(e0, e0) = e1
% 157.04/27.10 | |
% 157.04/27.10 | | ALPHA: (29) implies:
% 157.04/27.10 | | (30) op(e0, e0) = e1
% 157.04/27.10 | |
% 157.04/27.10 | | REF_CLOSE: (16), (20), (24), (30) are inconsistent by sub-proof #1386.
% 157.04/27.10 | |
% 157.04/27.10 | End of split
% 157.04/27.10 |
% 157.04/27.10 End of proof
% 157.04/27.10
% 157.04/27.10 Sub-proof #269 shows that the following formulas are inconsistent:
% 157.04/27.10 ----------------------------------------------------------------
% 157.04/27.10 (1) all_58_13 = e0
% 157.04/27.10 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.04/27.10 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.04/27.10 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.10 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.10 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.10 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.10 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.10 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.04/27.10 (6) all_58_14 = e3
% 157.04/27.10 (7) op(e1, e1) = all_6_2
% 157.04/27.10 (8) ~ (all_52_7 = e3)
% 157.04/27.10 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.04/27.10 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.10 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.04/27.10 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.04/27.10 (11) all_58_7 = e2
% 157.04/27.10 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.04/27.10 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.04/27.10 (13) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.04/27.10 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.04/27.10 (14) all_58_6 = e3
% 157.04/27.10 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.04/27.10 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.04/27.10 (16) op(e2, e3) = all_52_1
% 157.04/27.10 (17) ~ (all_52_13 = e3)
% 157.04/27.10 (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.04/27.10 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.04/27.10 (19) ~ (e3 = e0)
% 157.04/27.10 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.10 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.10 (21) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.04/27.10 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.04/27.10 (22) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.10 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.04/27.10 e2)
% 157.04/27.10 (23) ~ (e2 = e0)
% 157.04/27.10 (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.04/27.10 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.10 (25) all_58_9 = e3
% 157.04/27.10 (26) op(e2, e0) = all_52_13
% 157.04/27.10 (27) op(e2, e3) = e2
% 157.04/27.10 (28) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.10 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.04/27.11 (29) ~ (e3 = e1)
% 157.04/27.11 (30) op(e1, e2) = all_52_6
% 157.04/27.11 (31) all_58_1 = e1
% 157.04/27.11 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.11 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.04/27.11 (33) all_58_10 = e1
% 157.04/27.11 (34) op(e0, e0) = e2
% 157.04/27.11 (35) all_58_4 = e2
% 157.04/27.11 (36) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.04/27.11 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.04/27.11 (37) op(e0, e2) = e0
% 157.04/27.11 (38) all_58_15 = e2
% 157.04/27.11 (39) ~ (e2 = e1)
% 157.04/27.11 (40) ~ (e1 = e0)
% 157.04/27.11 (41) ~ (all_8_2 = e1)
% 157.04/27.11 (42) all_58_3 = e3
% 157.04/27.11 (43) ~ (all_6_2 = e2)
% 157.04/27.11 (44) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.04/27.11 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.04/27.11 e3)
% 157.04/27.11 (45) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.04/27.11 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.11 (46) op(e0, e2) = all_52_7
% 157.04/27.11 (47) op(e2, e2) = all_8_2
% 157.04/27.11 (48) ~ (all_52_6 = e3)
% 157.04/27.11 (49) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.04/27.11 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.11 (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.11 (51) all_58_8 = e0
% 157.04/27.11 (52) ~ (e3 = e2)
% 157.04/27.11 (53) all_58_12 = e1
% 157.04/27.11 (54) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.11 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.04/27.11 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.04/27.11 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.04/27.11
% 157.04/27.11 Begin of proof
% 157.04/27.11 |
% 157.04/27.11 | BETA: splitting (32) gives:
% 157.04/27.11 |
% 157.04/27.11 | Case 1:
% 157.04/27.11 | |
% 157.04/27.11 | | (55) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 157.04/27.11 | | e0)
% 157.04/27.11 | |
% 157.04/27.11 | | REF_CLOSE: (19), (23), (27), (42), (50), (55) are inconsistent by sub-proof
% 157.04/27.11 | | #909.
% 157.04/27.11 | |
% 157.04/27.11 | Case 2:
% 157.04/27.11 | |
% 157.04/27.11 | | (56) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 157.04/27.11 | | e0)
% 157.04/27.11 | |
% 157.04/27.11 | | BETA: splitting (56) gives:
% 157.04/27.11 | |
% 157.04/27.11 | | Case 1:
% 157.04/27.11 | | |
% 157.04/27.11 | | | (57) all_58_5 = e0 & op(e2, e1) = e0
% 157.04/27.11 | | |
% 157.04/27.11 | | | ALPHA: (57) implies:
% 157.04/27.11 | | | (58) all_58_5 = e0
% 157.04/27.11 | | |
% 157.04/27.11 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.04/27.11 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.04/27.11 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 157.04/27.11 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 157.04/27.11 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 157.04/27.11 | | | (53), (54), (58) are inconsistent by sub-proof #272.
% 157.04/27.11 | | |
% 157.04/27.11 | | Case 2:
% 157.04/27.11 | | |
% 157.04/27.11 | | | (59) all_58_10 = e0 & op(e2, e0) = e0
% 157.04/27.11 | | |
% 157.04/27.11 | | | REF_CLOSE: (1), (3), (11), (29), (31), (33), (39), (40), (42), (59) are
% 157.04/27.11 | | | inconsistent by sub-proof #270.
% 157.04/27.11 | | |
% 157.04/27.11 | | End of split
% 157.04/27.11 | |
% 157.04/27.11 | End of split
% 157.04/27.11 |
% 157.04/27.11 End of proof
% 157.04/27.11
% 157.04/27.11 Sub-proof #270 shows that the following formulas are inconsistent:
% 157.04/27.11 ----------------------------------------------------------------
% 157.04/27.11 (1) all_58_13 = e0
% 157.04/27.11 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.11 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.11 (3) all_58_7 = e2
% 157.04/27.11 (4) ~ (e3 = e1)
% 157.04/27.11 (5) all_58_1 = e1
% 157.04/27.11 (6) all_58_10 = e1
% 157.04/27.11 (7) ~ (e2 = e1)
% 157.04/27.11 (8) ~ (e1 = e0)
% 157.04/27.11 (9) all_58_3 = e3
% 157.04/27.11 (10) all_58_10 = e0 & op(e2, e0) = e0
% 157.04/27.11
% 157.04/27.11 Begin of proof
% 157.04/27.11 |
% 157.04/27.11 | ALPHA: (10) implies:
% 157.04/27.11 | (11) all_58_10 = e0
% 157.04/27.11 |
% 157.04/27.11 | COMBINE_EQS: (6), (11) imply:
% 157.04/27.11 | (12) e1 = e0
% 157.04/27.11 |
% 157.04/27.11 | COMBINE_EQS: (5), (12) imply:
% 157.04/27.11 | (13) all_58_1 = e0
% 157.04/27.11 |
% 157.04/27.11 | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (13) are inconsistent by
% 157.04/27.11 | sub-proof #857.
% 157.04/27.11 |
% 157.04/27.11 End of proof
% 157.04/27.11
% 157.04/27.11 Sub-proof #271 shows that the following formulas are inconsistent:
% 157.04/27.11 ----------------------------------------------------------------
% 157.04/27.11 (1) op(e0, e3) = e1
% 157.04/27.11 (2) all_58_13 = e0
% 157.04/27.11 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.04/27.11 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.04/27.11 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.11 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.11 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.11 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.11 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.11 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.04/27.11 (7) all_58_14 = e3
% 157.04/27.11 (8) op(e1, e1) = all_6_2
% 157.04/27.11 (9) ~ (all_52_7 = e3)
% 157.04/27.11 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.11 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.04/27.11 e1)
% 157.04/27.11 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.04/27.11 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.04/27.11 (12) all_56_14 = e1
% 157.04/27.11 (13) all_58_7 = e2
% 157.04/27.11 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.04/27.11 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.04/27.11 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.04/27.11 (16) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.04/27.11 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.04/27.11 (17) all_58_6 = e3
% 157.04/27.11 (18) op(e3, e2) = all_52_4
% 157.04/27.11 (19) op(e1, e2) = e2
% 157.04/27.11 (20) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.04/27.11 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.04/27.11 (21) op(e2, e1) = all_52_9
% 157.04/27.11 (22) op(e2, e3) = all_52_1
% 157.04/27.11 (23) ~ (all_52_13 = e3)
% 157.04/27.11 (24) all_54_2 = all_52_8
% 157.04/27.11 (25) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.04/27.11 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.04/27.11 (26) ~ (all_52_8 = all_52_9)
% 157.04/27.11 (27) all_56_2 = e3
% 157.04/27.11 (28) ~ (e3 = e0)
% 157.04/27.11 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.11 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.11 (30) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.04/27.11 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.04/27.11 (31) ~ (all_52_9 = all_52_13)
% 157.04/27.11 (32) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.11 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.04/27.11 e2)
% 157.04/27.11 (33) ~ (all_52_9 = e3)
% 157.04/27.11 (34) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.04/27.11 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.11 (35) all_58_9 = e3
% 157.04/27.11 (36) ~ (all_52_8 = e0)
% 157.04/27.11 (37) op(e1, e3) = all_52_2
% 157.04/27.11 (38) op(e2, e0) = all_52_13
% 157.04/27.11 (39) op(e2, e3) = e2
% 157.04/27.11 (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.11 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.04/27.11 (41) ~ (e3 = e1)
% 157.04/27.11 (42) op(e1, e2) = all_52_6
% 157.04/27.11 (43) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.04/27.11 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.04/27.11 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.04/27.11 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.04/27.11 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.04/27.11 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.04/27.11 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.04/27.11 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.04/27.11 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.04/27.11 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.04/27.11 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.04/27.11 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.04/27.11 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.04/27.11 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.04/27.11 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.04/27.11 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.04/27.11 = e0)
% 157.04/27.11 (44) all_58_1 = e1
% 157.04/27.11 (45) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.11 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.04/27.11 (46) all_58_10 = e1
% 157.04/27.11 (47) all_54_7 = all_52_13
% 157.04/27.11 (48) ~ (all_52_13 = e2)
% 157.04/27.11 (49) all_58_5 = e0
% 157.04/27.11 (50) op(e0, e0) = e2
% 157.04/27.11 (51) ~ (all_52_6 = e0)
% 157.04/27.11 (52) ~ (all_52_2 = e1)
% 157.04/27.11 (53) all_58_4 = e2
% 157.04/27.11 (54) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.04/27.11 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.04/27.11 (55) all_54_6 = all_52_9
% 157.04/27.11 (56) op(e0, e2) = e0
% 157.04/27.11 (57) all_58_15 = e2
% 157.04/27.11 (58) ~ (e1 = e0)
% 157.04/27.11 (59) ~ (all_8_2 = e1)
% 157.04/27.11 (60) all_58_3 = e3
% 157.04/27.11 (61) op(e3, e1) = all_52_8
% 157.04/27.11 (62) ~ (all_6_2 = e2)
% 157.04/27.11 (63) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.04/27.11 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.04/27.11 e3)
% 157.04/27.11 (64) all_56_13 = e3
% 157.04/27.11 (65) ~ (all_52_8 = e3)
% 157.04/27.11 (66) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.04/27.11 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.11 (67) op(e0, e2) = all_52_7
% 157.04/27.11 (68) ~ (all_52_8 = e1)
% 157.04/27.11 (69) op(e2, e2) = all_8_2
% 157.04/27.11 (70) ~ (all_52_6 = e3)
% 157.04/27.11 (71) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.04/27.11 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.11 (72) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.11 (73) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.04/27.11 (74) ~ (all_52_9 = e1)
% 157.04/27.11 (75) all_58_12 = e1
% 157.04/27.11 (76) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.11 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.04/27.11 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.04/27.11 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.04/27.11 (77) all_54_6 = e1 | all_54_6 = e0
% 157.04/27.11 (78) ~ (all_52_4 = all_52_8)
% 157.04/27.11
% 157.04/27.11 Begin of proof
% 157.04/27.11 |
% 157.04/27.11 | BETA: splitting (73) gives:
% 157.04/27.11 |
% 157.04/27.11 | Case 1:
% 157.04/27.11 | |
% 157.04/27.11 | | (79) all_54_2 = e2
% 157.04/27.11 | |
% 157.04/27.11 | | COMBINE_EQS: (24), (79) imply:
% 157.04/27.11 | | (80) all_52_8 = e2
% 157.04/27.11 | |
% 157.04/27.11 | | SIMP: (80) implies:
% 157.04/27.11 | | (81) all_52_8 = e2
% 157.04/27.11 | |
% 157.04/27.11 | | REDUCE: (78), (81) imply:
% 157.04/27.11 | | (82) ~ (all_52_4 = e2)
% 157.04/27.11 | |
% 157.04/27.11 | | REDUCE: (26), (81) imply:
% 157.04/27.11 | | (83) ~ (all_52_9 = e2)
% 157.04/27.11 | |
% 157.04/27.11 | | SIMP: (83) implies:
% 157.04/27.11 | | (84) ~ (all_52_9 = e2)
% 157.04/27.11 | |
% 157.04/27.11 | | REDUCE: (65), (81) imply:
% 157.04/27.11 | | (85) ~ (e3 = e2)
% 157.04/27.11 | |
% 157.04/27.11 | | SIMP: (85) implies:
% 157.04/27.11 | | (86) ~ (e3 = e2)
% 157.04/27.11 | |
% 157.04/27.11 | | REDUCE: (68), (81) imply:
% 157.04/27.11 | | (87) ~ (e2 = e1)
% 157.04/27.11 | |
% 157.04/27.11 | | REDUCE: (36), (81) imply:
% 157.04/27.11 | | (88) ~ (e2 = e0)
% 157.04/27.11 | |
% 157.04/27.11 | | REDUCE: (61), (81) imply:
% 157.04/27.11 | | (89) op(e3, e1) = e2
% 157.04/27.11 | |
% 157.04/27.11 | | BETA: splitting (34) gives:
% 157.04/27.11 | |
% 157.04/27.11 | | Case 1:
% 157.04/27.11 | | |
% 157.04/27.11 | | | (90) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 157.04/27.11 | | | e0)
% 157.04/27.11 | | |
% 157.04/27.11 | | | BETA: splitting (90) gives:
% 157.04/27.11 | | |
% 157.04/27.11 | | | Case 1:
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | (91) all_58_6 = e0 & op(e1, e3) = e0
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | ALPHA: (91) implies:
% 157.04/27.11 | | | | (92) all_58_6 = e0
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | REF_CLOSE: (17), (28), (92) are inconsistent by sub-proof #1321.
% 157.04/27.11 | | | |
% 157.04/27.11 | | | Case 2:
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | (93) all_58_7 = e0 & op(e1, e2) = e0
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | REF_CLOSE: (42), (51), (72), (93) are inconsistent by sub-proof #1301.
% 157.04/27.11 | | | |
% 157.04/27.11 | | | End of split
% 157.04/27.11 | | |
% 157.04/27.11 | | Case 2:
% 157.04/27.11 | | |
% 157.04/27.11 | | | (94) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 157.04/27.11 | | | e0)
% 157.04/27.11 | | |
% 157.04/27.11 | | | BETA: splitting (94) gives:
% 157.04/27.11 | | |
% 157.04/27.11 | | | Case 1:
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | (95) all_58_8 = e0 & op(e1, e1) = e0
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | ALPHA: (95) implies:
% 157.04/27.11 | | | | (96) all_58_8 = e0
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 157.04/27.11 | | | | (15), (16), (17), (20), (22), (23), (25), (28), (29), (30),
% 157.04/27.11 | | | | (32), (34), (35), (38), (39), (40), (41), (42), (44), (45),
% 157.04/27.11 | | | | (46), (49), (50), (53), (54), (56), (57), (58), (59), (60),
% 157.04/27.11 | | | | (62), (63), (66), (67), (69), (70), (71), (72), (75), (76),
% 157.04/27.11 | | | | (86), (87), (88), (96) are inconsistent by sub-proof #272.
% 157.04/27.11 | | | |
% 157.04/27.11 | | | Case 2:
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | (97) all_58_11 = e0 & op(e1, e0) = e0
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | ALPHA: (97) implies:
% 157.04/27.11 | | | | (98) all_58_11 = e0
% 157.04/27.11 | | | | (99) op(e1, e0) = e0
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | BETA: splitting (76) gives:
% 157.04/27.11 | | | |
% 157.04/27.11 | | | | Case 1:
% 157.04/27.11 | | | | |
% 157.04/27.11 | | | | | (100) all_58_15 = e0 & op(e0, e0) = e0
% 157.04/27.11 | | | | |
% 157.04/27.11 | | | | | REF_CLOSE: (6), (7), (8), (16), (28), (39), (41), (45), (53), (57),
% 157.04/27.11 | | | | | (58), (60), (62), (72), (86), (87), (88), (100) are
% 157.04/27.11 | | | | | inconsistent by sub-proof #629.
% 157.04/27.11 | | | | |
% 157.04/27.11 | | | | Case 2:
% 157.04/27.11 | | | | |
% 157.04/27.11 | | | | | (101) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 157.04/27.11 | | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 157.04/27.11 | | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.04/27.11 | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.04/27.11 | | | | |
% 157.04/27.11 | | | | | ALPHA: (101) implies:
% 157.04/27.11 | | | | | (102) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 157.04/27.11 | | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.04/27.11 | | | | |
% 157.04/27.11 | | | | | BETA: splitting (43) gives:
% 157.04/27.11 | | | | |
% 157.04/27.11 | | | | | Case 1:
% 157.04/27.11 | | | | | |
% 157.04/27.11 | | | | | | (103) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) &
% 157.04/27.11 | | | | | | op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 &
% 157.04/27.11 | | | | | | all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 &
% 157.04/27.11 | | | | | | op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~
% 157.04/27.11 | | | | | | (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.04/27.11 | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) &
% 157.04/27.11 | | | | | | op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_2 = e3 &
% 157.04/27.11 | | | | | | all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 &
% 157.04/27.11 | | | | | | op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 157.04/27.11 | | | | | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.04/27.11 | | | | | |
% 157.04/27.11 | | | | | | BETA: splitting (103) gives:
% 157.04/27.11 | | | | | |
% 157.04/27.11 | | | | | | Case 1:
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | (104) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) &
% 157.04/27.11 | | | | | | | op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 &
% 157.04/27.11 | | | | | | | all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 &
% 157.04/27.11 | | | | | | | op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~
% 157.04/27.11 | | | | | | | (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | REF_CLOSE: (18), (22), (39), (72), (82), (86), (89), (104) are
% 157.04/27.11 | | | | | | | inconsistent by sub-proof #286.
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | Case 2:
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | (105) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) &
% 157.04/27.11 | | | | | | | op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_2 = e3 &
% 157.04/27.11 | | | | | | | all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 &
% 157.04/27.11 | | | | | | | op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~
% 157.04/27.11 | | | | | | | (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | BETA: splitting (105) gives:
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | (106) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) &
% 157.04/27.11 | | | | | | | | op(e3, e1) = e1 & op(e1, e3) = e1
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | ALPHA: (106) implies:
% 157.04/27.11 | | | | | | | | (107) op(e1, e3) = e1
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | REF_CLOSE: (37), (52), (72), (107) are inconsistent by sub-proof
% 157.04/27.11 | | | | | | | | #1412.
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | (108) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) &
% 157.04/27.11 | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 &
% 157.04/27.11 | | | | | | | | all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0
% 157.04/27.11 | | | | | | | | & op(e0, e3) = e0)
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | BETA: splitting (108) gives:
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | (109) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) &
% 157.04/27.11 | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = e3
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | ALPHA: (109) implies:
% 157.04/27.11 | | | | | | | | | (110) op(e0, e3) = e3
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | BETA: splitting (77) gives:
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | (111) all_54_6 = e1
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | REF_CLOSE: (55), (74), (111) are inconsistent by sub-proof
% 157.04/27.11 | | | | | | | | | | #562.
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | (112) all_54_6 = e0
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | COMBINE_EQS: (55), (112) imply:
% 157.04/27.11 | | | | | | | | | | (113) all_52_9 = e0
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | SIMP: (113) implies:
% 157.04/27.11 | | | | | | | | | | (114) all_52_9 = e0
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | REDUCE: (31), (114) imply:
% 157.04/27.11 | | | | | | | | | | (115) ~ (all_52_13 = e0)
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | SIMP: (115) implies:
% 157.04/27.11 | | | | | | | | | | (116) ~ (all_52_13 = e0)
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | REDUCE: (33), (114) imply:
% 157.04/27.11 | | | | | | | | | | (117) ~ (e3 = e0)
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | REDUCE: (84), (114) imply:
% 157.04/27.11 | | | | | | | | | | (118) ~ (e2 = e0)
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | BETA: splitting (14) gives:
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | (119) all_54_7 = e3
% 157.04/27.11 | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | REF_CLOSE: (23), (47), (119) are inconsistent by sub-proof
% 157.04/27.11 | | | | | | | | | | | #1428.
% 157.04/27.11 | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | (120) ~ (all_54_7 = e3)
% 157.04/27.11 | | | | | | | | | | | (121) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.04/27.11 | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | BETA: splitting (121) gives:
% 157.04/27.11 | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | (122) all_54_7 = e2
% 157.04/27.11 | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | REF_CLOSE: (47), (48), (122) are inconsistent by sub-proof
% 157.04/27.11 | | | | | | | | | | | | #1427.
% 157.04/27.11 | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | (123) ~ (all_54_7 = e2)
% 157.04/27.11 | | | | | | | | | | | | (124) all_54_7 = e1 | all_54_7 = e0
% 157.04/27.11 | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | BETA: splitting (124) gives:
% 157.04/27.11 | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | (125) all_54_7 = e1
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | COMBINE_EQS: (47), (125) imply:
% 157.04/27.11 | | | | | | | | | | | | | (126) all_52_13 = e1
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | SIMP: (126) implies:
% 157.04/27.11 | | | | | | | | | | | | | (127) all_52_13 = e1
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | REDUCE: (23), (127) imply:
% 157.04/27.11 | | | | | | | | | | | | | (128) ~ (e3 = e1)
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | REDUCE: (48), (127) imply:
% 157.04/27.11 | | | | | | | | | | | | | (129) ~ (e2 = e1)
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | GROUND_INST: instantiating (72) with e1, e3, e3, e0,
% 157.04/27.11 | | | | | | | | | | | | | simplifying with (1), (110) gives:
% 157.04/27.11 | | | | | | | | | | | | | (130) e3 = e1
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | COMBINE_EQS: (17), (130) imply:
% 157.04/27.11 | | | | | | | | | | | | | (131) all_58_6 = e1
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (13), (20), (28), (35), (39),
% 157.04/27.11 | | | | | | | | | | | | | (41), (42), (44), (45), (50), (53), (54), (58),
% 157.04/27.11 | | | | | | | | | | | | | (60), (70), (72), (87), (88), (98), (131) are
% 157.04/27.11 | | | | | | | | | | | | | inconsistent by sub-proof #410.
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | (132) all_54_7 = e0
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | | REF_CLOSE: (47), (116), (132) are inconsistent by sub-proof
% 157.04/27.11 | | | | | | | | | | | | | #1112.
% 157.04/27.11 | | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | | End of split
% 157.04/27.11 | | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | | End of split
% 157.04/27.11 | | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | | End of split
% 157.04/27.11 | | | | | | | | | |
% 157.04/27.11 | | | | | | | | | End of split
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | (133) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) &
% 157.04/27.11 | | | | | | | | | op(e3, e0) = e0 & op(e0, e3) = e0
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | REF_CLOSE: (27), (28), (133) are inconsistent by sub-proof
% 157.04/27.11 | | | | | | | | | #310.
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | End of split
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | End of split
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | End of split
% 157.04/27.11 | | | | | |
% 157.04/27.11 | | | | | Case 2:
% 157.04/27.11 | | | | | |
% 157.04/27.11 | | | | | | (134) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) &
% 157.04/27.11 | | | | | | op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 &
% 157.04/27.11 | | | | | | all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 &
% 157.04/27.11 | | | | | | op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 157.04/27.11 | | | | | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 157.04/27.11 | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) &
% 157.04/27.11 | | | | | | op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 &
% 157.04/27.11 | | | | | | all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) = e1 &
% 157.04/27.11 | | | | | | op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~
% 157.04/27.11 | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.04/27.11 | | | | | |
% 157.04/27.11 | | | | | | BETA: splitting (134) gives:
% 157.04/27.11 | | | | | |
% 157.04/27.11 | | | | | | Case 1:
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | (135) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) &
% 157.04/27.11 | | | | | | | op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 &
% 157.04/27.11 | | | | | | | all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 &
% 157.04/27.11 | | | | | | | op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 157.04/27.11 | | | | | | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | BETA: splitting (135) gives:
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | (136) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) &
% 157.04/27.11 | | | | | | | | op(e2, e1) = e2 & op(e1, e2) = e2
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | ALPHA: (136) implies:
% 157.04/27.11 | | | | | | | | (137) op(e2, e1) = e2
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | REF_CLOSE: (21), (72), (84), (137) are inconsistent by sub-proof
% 157.04/27.11 | | | | | | | | #1441.
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | (138) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) &
% 157.04/27.11 | | | | | | | | op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.04/27.11 | | | | | | | | all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) =
% 157.04/27.11 | | | | | | | | e2 & op(e0, e2) = e2)
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | BETA: splitting (138) gives:
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | (139) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) &
% 157.04/27.11 | | | | | | | | | op(e2, e1) = e1 & op(e1, e2) = e1
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | ALPHA: (139) implies:
% 157.04/27.11 | | | | | | | | | (140) op(e1, e2) = e1
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | REF_CLOSE: (19), (72), (87), (140) are inconsistent by
% 157.04/27.11 | | | | | | | | | sub-proof #1088.
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | (141) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0)
% 157.04/27.11 | | | | | | | | | & op(e2, e0) = e2 & op(e0, e2) = e2
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | ALPHA: (141) implies:
% 157.04/27.11 | | | | | | | | | (142) op(e2, e0) = e2
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | REF_CLOSE: (38), (48), (72), (142) are inconsistent by
% 157.04/27.11 | | | | | | | | | sub-proof #1535.
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | End of split
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | End of split
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | Case 2:
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | (143) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) &
% 157.04/27.11 | | | | | | | op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 &
% 157.04/27.11 | | | | | | | all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) = e1
% 157.04/27.11 | | | | | | | & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 &
% 157.04/27.11 | | | | | | | ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | BETA: splitting (143) gives:
% 157.04/27.11 | | | | | | |
% 157.04/27.11 | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | (144) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) &
% 157.04/27.11 | | | | | | | | op(e2, e0) = e0 & op(e0, e2) = e0
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | ALPHA: (144) implies:
% 157.04/27.11 | | | | | | | | (145) ~ (all_56_13 = e2)
% 157.04/27.11 | | | | | | | | (146) op(e2, e0) = e0
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | BETA: splitting (77) gives:
% 157.04/27.11 | | | | | | | |
% 157.04/27.11 | | | | | | | | Case 1:
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | (147) all_54_6 = e1
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | REF_CLOSE: (55), (74), (147) are inconsistent by sub-proof
% 157.04/27.11 | | | | | | | | | #562.
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | Case 2:
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | (148) all_54_6 = e0
% 157.04/27.11 | | | | | | | | |
% 157.04/27.11 | | | | | | | | | COMBINE_EQS: (55), (148) imply:
% 157.04/27.12 | | | | | | | | | (149) all_52_9 = e0
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | SIMP: (149) implies:
% 157.04/27.12 | | | | | | | | | (150) all_52_9 = e0
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | REDUCE: (31), (150) imply:
% 157.04/27.12 | | | | | | | | | (151) ~ (all_52_13 = e0)
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | SIMP: (151) implies:
% 157.04/27.12 | | | | | | | | | (152) ~ (all_52_13 = e0)
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | REDUCE: (33), (150) imply:
% 157.04/27.12 | | | | | | | | | (153) ~ (e3 = e0)
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | REDUCE: (84), (150) imply:
% 157.04/27.12 | | | | | | | | | (154) ~ (e2 = e0)
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | BETA: splitting (14) gives:
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | Case 1:
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | (155) all_54_7 = e3
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | REF_CLOSE: (23), (47), (155) are inconsistent by sub-proof
% 157.04/27.12 | | | | | | | | | | #1428.
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | (156) ~ (all_54_7 = e3)
% 157.04/27.12 | | | | | | | | | | (157) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | BETA: splitting (157) gives:
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | Case 1:
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | (158) all_54_7 = e2
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | REF_CLOSE: (47), (48), (158) are inconsistent by sub-proof
% 157.04/27.12 | | | | | | | | | | | #1427.
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | (159) ~ (all_54_7 = e2)
% 157.04/27.12 | | | | | | | | | | | (160) all_54_7 = e1 | all_54_7 = e0
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | BETA: splitting (160) gives:
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | Case 1:
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | (161) all_54_7 = e1
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | COMBINE_EQS: (47), (161) imply:
% 157.04/27.12 | | | | | | | | | | | | (162) all_52_13 = e1
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | SIMP: (162) implies:
% 157.04/27.12 | | | | | | | | | | | | (163) all_52_13 = e1
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | REDUCE: (23), (163) imply:
% 157.04/27.12 | | | | | | | | | | | | (164) ~ (e3 = e1)
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | REDUCE: (48), (163) imply:
% 157.04/27.12 | | | | | | | | | | | | (165) ~ (e2 = e1)
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | REDUCE: (38), (163) imply:
% 157.04/27.12 | | | | | | | | | | | | (166) op(e2, e0) = e1
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | GROUND_INST: instantiating (72) with e0, e1, e0, e2,
% 157.04/27.12 | | | | | | | | | | | | simplifying with (146), (166) gives:
% 157.04/27.12 | | | | | | | | | | | | (167) e1 = e0
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | COMBINE_EQS: (44), (167) imply:
% 157.04/27.12 | | | | | | | | | | | | (168) all_58_1 = e0
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (15), (16), (17), (22), (28),
% 157.04/27.12 | | | | | | | | | | | | (29), (39), (41), (45), (53), (58), (60), (62),
% 157.04/27.12 | | | | | | | | | | | | (66), (67), (71), (72), (75), (86), (87), (88),
% 157.04/27.12 | | | | | | | | | | | | (102), (168) are inconsistent by sub-proof #817.
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | (169) all_54_7 = e0
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | REF_CLOSE: (47), (152), (169) are inconsistent by sub-proof
% 157.04/27.12 | | | | | | | | | | | | #1112.
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | End of split
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | End of split
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | End of split
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | End of split
% 157.04/27.12 | | | | | | | |
% 157.04/27.12 | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | |
% 157.04/27.12 | | | | | | | | (170) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) &
% 157.04/27.12 | | | | | | | | op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 &
% 157.04/27.12 | | | | | | | | all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) =
% 157.04/27.12 | | | | | | | | e0 & op(e0, e1) = e0)
% 157.04/27.12 | | | | | | | |
% 157.04/27.12 | | | | | | | | BETA: splitting (170) gives:
% 157.04/27.12 | | | | | | | |
% 157.04/27.12 | | | | | | | | Case 1:
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | (171) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0)
% 157.04/27.12 | | | | | | | | | & op(e1, e0) = e1 & op(e0, e1) = e1
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | ALPHA: (171) implies:
% 157.04/27.12 | | | | | | | | | (172) op(e1, e0) = e1
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | BETA: splitting (77) gives:
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | Case 1:
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | (173) all_54_6 = e1
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | REF_CLOSE: (55), (74), (173) are inconsistent by sub-proof
% 157.04/27.12 | | | | | | | | | | #562.
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | (174) all_54_6 = e0
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | COMBINE_EQS: (55), (174) imply:
% 157.04/27.12 | | | | | | | | | | (175) all_52_9 = e0
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | SIMP: (175) implies:
% 157.04/27.12 | | | | | | | | | | (176) all_52_9 = e0
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | REDUCE: (31), (176) imply:
% 157.04/27.12 | | | | | | | | | | (177) ~ (all_52_13 = e0)
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | SIMP: (177) implies:
% 157.04/27.12 | | | | | | | | | | (178) ~ (all_52_13 = e0)
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | REDUCE: (33), (176) imply:
% 157.04/27.12 | | | | | | | | | | (179) ~ (e3 = e0)
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | REDUCE: (84), (176) imply:
% 157.04/27.12 | | | | | | | | | | (180) ~ (e2 = e0)
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | BETA: splitting (14) gives:
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | Case 1:
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | (181) all_54_7 = e3
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | REF_CLOSE: (23), (47), (181) are inconsistent by sub-proof
% 157.04/27.12 | | | | | | | | | | | #1428.
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | (182) ~ (all_54_7 = e3)
% 157.04/27.12 | | | | | | | | | | | (183) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | BETA: splitting (183) gives:
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | Case 1:
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | (184) all_54_7 = e2
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | REF_CLOSE: (47), (48), (184) are inconsistent by sub-proof
% 157.04/27.12 | | | | | | | | | | | | #1427.
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | (185) ~ (all_54_7 = e2)
% 157.04/27.12 | | | | | | | | | | | | (186) all_54_7 = e1 | all_54_7 = e0
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | BETA: splitting (186) gives:
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | Case 1:
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | (187) all_54_7 = e1
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | COMBINE_EQS: (47), (187) imply:
% 157.04/27.12 | | | | | | | | | | | | | (188) all_52_13 = e1
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | SIMP: (188) implies:
% 157.04/27.12 | | | | | | | | | | | | | (189) all_52_13 = e1
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | REDUCE: (23), (189) imply:
% 157.04/27.12 | | | | | | | | | | | | | (190) ~ (e3 = e1)
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | REDUCE: (48), (189) imply:
% 157.04/27.12 | | | | | | | | | | | | | (191) ~ (e2 = e1)
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | GROUND_INST: instantiating (72) with e0, e1, e0, e1,
% 157.04/27.12 | | | | | | | | | | | | | simplifying with (99), (172) gives:
% 157.04/27.12 | | | | | | | | | | | | | (192) e1 = e0
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | COMBINE_EQS: (44), (192) imply:
% 157.04/27.12 | | | | | | | | | | | | | (193) all_58_1 = e0
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (15), (16), (17), (22), (28),
% 157.04/27.12 | | | | | | | | | | | | | (29), (39), (41), (45), (53), (58), (60), (62),
% 157.04/27.12 | | | | | | | | | | | | | (66), (67), (71), (72), (75), (86), (87), (88),
% 157.04/27.12 | | | | | | | | | | | | | (102), (193) are inconsistent by sub-proof #817.
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | (194) all_54_7 = e0
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | | REF_CLOSE: (47), (178), (194) are inconsistent by sub-proof
% 157.04/27.12 | | | | | | | | | | | | | #1112.
% 157.04/27.12 | | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | | End of split
% 157.04/27.12 | | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | | End of split
% 157.04/27.12 | | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | | End of split
% 157.04/27.12 | | | | | | | | | |
% 157.04/27.12 | | | | | | | | | End of split
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | Case 2:
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | (195) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1)
% 157.04/27.12 | | | | | | | | | & op(e1, e0) = e0 & op(e0, e1) = e0
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | ALPHA: (195) implies:
% 157.04/27.12 | | | | | | | | | (196) ~ (all_56_14 = e1)
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | REDUCE: (12), (196) imply:
% 157.04/27.12 | | | | | | | | | (197) $false
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | | CLOSE: (197) is inconsistent.
% 157.04/27.12 | | | | | | | | |
% 157.04/27.12 | | | | | | | | End of split
% 157.04/27.12 | | | | | | | |
% 157.04/27.12 | | | | | | | End of split
% 157.04/27.12 | | | | | | |
% 157.04/27.12 | | | | | | End of split
% 157.04/27.12 | | | | | |
% 157.04/27.12 | | | | | End of split
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | End of split
% 157.04/27.12 | | | |
% 157.04/27.12 | | | End of split
% 157.04/27.12 | | |
% 157.04/27.12 | | End of split
% 157.04/27.12 | |
% 157.04/27.12 | Case 2:
% 157.04/27.12 | |
% 157.04/27.12 | | (198) all_54_2 = e1 | all_54_2 = e0
% 157.04/27.12 | |
% 157.04/27.12 | | REF_CLOSE: (24), (36), (68), (198) are inconsistent by sub-proof #561.
% 157.04/27.12 | |
% 157.04/27.12 | End of split
% 157.04/27.12 |
% 157.04/27.12 End of proof
% 157.04/27.12
% 157.04/27.12 Sub-proof #272 shows that the following formulas are inconsistent:
% 157.04/27.12 ----------------------------------------------------------------
% 157.04/27.12 (1) all_58_13 = e0
% 157.04/27.12 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.04/27.12 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.04/27.12 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.12 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.12 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.12 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.12 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.12 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.04/27.12 (6) all_58_14 = e3
% 157.04/27.12 (7) op(e1, e1) = all_6_2
% 157.04/27.12 (8) ~ (all_52_7 = e3)
% 157.04/27.12 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.04/27.12 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.12 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.04/27.12 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.04/27.12 (11) all_58_7 = e2
% 157.04/27.12 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.04/27.12 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.04/27.12 (13) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.04/27.12 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.04/27.12 (14) all_58_6 = e3
% 157.04/27.12 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.04/27.12 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.04/27.12 (16) op(e2, e3) = all_52_1
% 157.04/27.12 (17) ~ (all_52_13 = e3)
% 157.04/27.12 (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.04/27.12 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.04/27.12 (19) ~ (e3 = e0)
% 157.04/27.12 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.12 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.12 (21) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.04/27.12 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.04/27.12 (22) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.12 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.04/27.12 e2)
% 157.04/27.12 (23) ~ (e2 = e0)
% 157.04/27.12 (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.04/27.12 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.12 (25) all_58_9 = e3
% 157.04/27.12 (26) op(e2, e0) = all_52_13
% 157.04/27.12 (27) op(e2, e3) = e2
% 157.04/27.12 (28) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.12 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.04/27.12 (29) ~ (e3 = e1)
% 157.04/27.12 (30) op(e1, e2) = all_52_6
% 157.04/27.12 (31) all_58_1 = e1
% 157.04/27.12 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.12 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.04/27.12 (33) all_58_10 = e1
% 157.04/27.12 (34) all_58_5 = e0
% 157.04/27.12 (35) op(e0, e0) = e2
% 157.04/27.12 (36) all_58_4 = e2
% 157.04/27.12 (37) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.04/27.12 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.04/27.12 (38) op(e0, e2) = e0
% 157.04/27.12 (39) all_58_15 = e2
% 157.04/27.12 (40) ~ (e2 = e1)
% 157.04/27.12 (41) ~ (e1 = e0)
% 157.04/27.12 (42) ~ (all_8_2 = e1)
% 157.04/27.12 (43) all_58_3 = e3
% 157.04/27.12 (44) ~ (all_6_2 = e2)
% 157.04/27.12 (45) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.04/27.12 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.04/27.12 e3)
% 157.04/27.12 (46) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.04/27.12 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.12 (47) op(e0, e2) = all_52_7
% 157.04/27.12 (48) op(e2, e2) = all_8_2
% 157.04/27.12 (49) ~ (all_52_6 = e3)
% 157.04/27.12 (50) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.04/27.12 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.12 (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.12 (52) all_58_8 = e0
% 157.04/27.12 (53) ~ (e3 = e2)
% 157.04/27.12 (54) all_58_12 = e1
% 157.04/27.12 (55) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.12 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.04/27.12 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.04/27.12 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.04/27.12
% 157.04/27.12 Begin of proof
% 157.04/27.12 |
% 157.04/27.12 | BETA: splitting (2) gives:
% 157.04/27.12 |
% 157.04/27.12 | Case 1:
% 157.04/27.12 | |
% 157.04/27.12 | | (56) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 157.04/27.12 | | e1)
% 157.04/27.12 | |
% 157.04/27.12 | | BETA: splitting (56) gives:
% 157.04/27.12 | |
% 157.04/27.12 | | Case 1:
% 157.04/27.12 | | |
% 157.04/27.12 | | | (57) all_58_6 = e1 & op(e1, e3) = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | ALPHA: (57) implies:
% 157.04/27.12 | | | (58) all_58_6 = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | REF_CLOSE: (1), (3), (4), (6), (11), (15), (19), (23), (25), (27), (29),
% 157.04/27.12 | | | (30), (31), (32), (35), (36), (37), (40), (41), (43), (49),
% 157.04/27.12 | | | (51), (52), (58) are inconsistent by sub-proof #411.
% 157.04/27.12 | | |
% 157.04/27.12 | | Case 2:
% 157.04/27.12 | | |
% 157.04/27.12 | | | (59) all_58_7 = e1 & op(e1, e2) = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (15),
% 157.04/27.12 | | | (16), (17), (18), (19), (20), (21), (22), (23), (26), (27),
% 157.04/27.12 | | | (28), (29), (30), (32), (35), (37), (38), (39), (40), (41),
% 157.04/27.12 | | | (43), (44), (45), (46), (47), (49), (50), (51), (53), (55),
% 157.04/27.12 | | | (59) are inconsistent by sub-proof #637.
% 157.04/27.12 | | |
% 157.04/27.12 | | End of split
% 157.04/27.12 | |
% 157.04/27.12 | Case 2:
% 157.04/27.12 | |
% 157.04/27.12 | | (60) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 157.04/27.12 | | e1)
% 157.04/27.12 | |
% 157.04/27.12 | | BETA: splitting (60) gives:
% 157.04/27.12 | |
% 157.04/27.12 | | Case 1:
% 157.04/27.12 | | |
% 157.04/27.12 | | | (61) all_58_8 = e1 & op(e1, e1) = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | ALPHA: (61) implies:
% 157.04/27.12 | | | (62) all_58_8 = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | COMBINE_EQS: (52), (62) imply:
% 157.04/27.12 | | | (63) e1 = e0
% 157.04/27.12 | | |
% 157.04/27.12 | | | SIMP: (63) implies:
% 157.04/27.12 | | | (64) e1 = e0
% 157.04/27.12 | | |
% 157.04/27.12 | | | COMBINE_EQS: (31), (64) imply:
% 157.04/27.12 | | | (65) all_58_1 = e0
% 157.04/27.12 | | |
% 157.04/27.12 | | | REF_CLOSE: (3), (5), (6), (7), (11), (12), (13), (16), (19), (20), (22),
% 157.04/27.12 | | | (23), (27), (28), (29), (32), (33), (34), (36), (40), (41),
% 157.04/27.12 | | | (43), (44), (50), (51), (53), (54), (55), (65) are inconsistent
% 157.04/27.12 | | | by sub-proof #646.
% 157.04/27.12 | | |
% 157.04/27.12 | | Case 2:
% 157.04/27.12 | | |
% 157.04/27.12 | | | (66) all_58_11 = e1 & op(e1, e0) = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | ALPHA: (66) implies:
% 157.04/27.12 | | | (67) all_58_11 = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | BETA: splitting (5) gives:
% 157.04/27.12 | | |
% 157.04/27.12 | | | Case 1:
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | (68) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 157.04/27.12 | | | | = e1)
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | REF_CLOSE: (27), (40), (42), (48), (51), (68) are inconsistent by
% 157.04/27.12 | | | | sub-proof #1074.
% 157.04/27.12 | | | |
% 157.04/27.12 | | | Case 2:
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | (69) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 157.04/27.12 | | | | = e1)
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | BETA: splitting (69) gives:
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | Case 1:
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | (70) all_58_5 = e1 & op(e2, e1) = e1
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | ALPHA: (70) implies:
% 157.04/27.12 | | | | | (71) all_58_5 = e1
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | COMBINE_EQS: (34), (71) imply:
% 157.04/27.12 | | | | | (72) e1 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | COMBINE_EQS: (31), (72) imply:
% 157.04/27.12 | | | | | (73) all_58_1 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | REF_CLOSE: (1), (3), (11), (29), (40), (41), (43), (73) are
% 157.04/27.12 | | | | | inconsistent by sub-proof #857.
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | Case 2:
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | (74) all_58_10 = e1 & op(e2, e0) = e1
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (12), (13), (14), (15),
% 157.04/27.12 | | | | | (16), (18), (19), (20), (22), (23), (24), (25), (27), (28),
% 157.04/27.12 | | | | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (40),
% 157.04/27.12 | | | | | (41), (43), (44), (49), (50), (51), (53), (54), (55), (67)
% 157.04/27.12 | | | | | are inconsistent by sub-proof #273.
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | End of split
% 157.04/27.12 | | | |
% 157.04/27.12 | | | End of split
% 157.04/27.12 | | |
% 157.04/27.12 | | End of split
% 157.04/27.12 | |
% 157.04/27.12 | End of split
% 157.04/27.12 |
% 157.04/27.12 End of proof
% 157.04/27.12
% 157.04/27.12 Sub-proof #273 shows that the following formulas are inconsistent:
% 157.04/27.12 ----------------------------------------------------------------
% 157.04/27.12 (1) all_58_13 = e0
% 157.04/27.12 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.12 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.12 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.12 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.12 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.12 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.04/27.12 (5) all_58_14 = e3
% 157.04/27.12 (6) all_58_11 = e1
% 157.04/27.12 (7) op(e1, e1) = all_6_2
% 157.04/27.12 (8) all_58_7 = e2
% 157.04/27.12 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.04/27.12 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.04/27.12 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.04/27.12 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.04/27.12 (11) all_58_6 = e3
% 157.04/27.12 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.04/27.12 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.04/27.12 (13) op(e2, e3) = all_52_1
% 157.04/27.12 (14) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.04/27.12 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.04/27.12 (15) ~ (e3 = e0)
% 157.04/27.12 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.12 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.12 (17) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.12 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.04/27.12 e2)
% 157.04/27.12 (18) ~ (e2 = e0)
% 157.04/27.12 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.04/27.12 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.12 (20) all_58_9 = e3
% 157.04/27.12 (21) op(e2, e3) = e2
% 157.04/27.12 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.12 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.04/27.12 (23) ~ (e3 = e1)
% 157.04/27.12 (24) op(e1, e2) = all_52_6
% 157.04/27.12 (25) all_58_1 = e1
% 157.04/27.12 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.12 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.04/27.12 (27) all_58_10 = e1
% 157.04/27.12 (28) all_58_5 = e0
% 157.04/27.12 (29) op(e0, e0) = e2
% 157.04/27.12 (30) all_58_4 = e2
% 157.04/27.12 (31) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.04/27.12 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.04/27.12 (32) ~ (e2 = e1)
% 157.04/27.12 (33) ~ (e1 = e0)
% 157.04/27.12 (34) all_58_3 = e3
% 157.04/27.12 (35) ~ (all_6_2 = e2)
% 157.04/27.12 (36) ~ (all_52_6 = e3)
% 157.04/27.12 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.04/27.12 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.12 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.12 (39) ~ (e3 = e2)
% 157.04/27.12 (40) all_58_12 = e1
% 157.04/27.12 (41) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.12 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.04/27.12 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.04/27.12 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.04/27.12
% 157.04/27.12 Begin of proof
% 157.04/27.12 |
% 157.04/27.12 | BETA: splitting (31) gives:
% 157.04/27.12 |
% 157.04/27.12 | Case 1:
% 157.04/27.12 | |
% 157.04/27.12 | | (42) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 157.04/27.12 | | e1)
% 157.04/27.12 | |
% 157.04/27.12 | | REF_CLOSE: (4), (5), (7), (10), (15), (18), (21), (23), (26), (27), (32),
% 157.04/27.12 | | (33), (34), (35), (38), (39), (42) are inconsistent by sub-proof
% 157.04/27.12 | | #356.
% 157.04/27.12 | |
% 157.04/27.12 | Case 2:
% 157.04/27.12 | |
% 157.04/27.12 | | (43) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 157.04/27.12 | | e1)
% 157.04/27.12 | |
% 157.04/27.12 | | BETA: splitting (43) gives:
% 157.04/27.12 | |
% 157.04/27.12 | | Case 1:
% 157.04/27.12 | | |
% 157.04/27.12 | | | (44) all_58_8 = e1 & op(e1, e1) = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | ALPHA: (44) implies:
% 157.04/27.12 | | | (45) all_58_8 = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | BETA: splitting (19) gives:
% 157.04/27.12 | | |
% 157.04/27.12 | | | Case 1:
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | (46) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 157.04/27.12 | | | | = e0)
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | BETA: splitting (46) gives:
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | Case 1:
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | (47) all_58_6 = e0 & op(e1, e3) = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | ALPHA: (47) implies:
% 157.04/27.12 | | | | | (48) all_58_6 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | REF_CLOSE: (11), (15), (48) are inconsistent by sub-proof #1321.
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | Case 2:
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | (49) all_58_7 = e0 & op(e1, e2) = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | ALPHA: (49) implies:
% 157.04/27.12 | | | | | (50) all_58_7 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | REF_CLOSE: (6), (7), (9), (13), (14), (15), (16), (18), (21), (23),
% 157.04/27.12 | | | | | (32), (33), (35), (37), (38), (39), (50) are inconsistent
% 157.04/27.12 | | | | | by sub-proof #743.
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | End of split
% 157.04/27.12 | | | |
% 157.04/27.12 | | | Case 2:
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | (51) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.04/27.12 | | | | = e0)
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | BETA: splitting (51) gives:
% 157.04/27.12 | | | |
% 157.04/27.12 | | | | Case 1:
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | (52) all_58_8 = e0 & op(e1, e1) = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | ALPHA: (52) implies:
% 157.04/27.12 | | | | | (53) all_58_8 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | COMBINE_EQS: (45), (53) imply:
% 157.04/27.12 | | | | | (54) e1 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | COMBINE_EQS: (25), (54) imply:
% 157.04/27.12 | | | | | (55) all_58_1 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (13), (15), (16), (17),
% 157.04/27.12 | | | | | (18), (21), (22), (23), (26), (27), (28), (30), (32), (33),
% 157.04/27.12 | | | | | (34), (35), (37), (38), (39), (40), (41), (55) are
% 157.04/27.12 | | | | | inconsistent by sub-proof #646.
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | Case 2:
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | (56) all_58_11 = e0 & op(e1, e0) = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | ALPHA: (56) implies:
% 157.04/27.12 | | | | | (57) all_58_11 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | COMBINE_EQS: (6), (57) imply:
% 157.04/27.12 | | | | | (58) e1 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | COMBINE_EQS: (25), (58) imply:
% 157.04/27.12 | | | | | (59) all_58_1 = e0
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (13), (15), (16), (17),
% 157.04/27.12 | | | | | (18), (21), (22), (23), (26), (27), (28), (30), (32), (33),
% 157.04/27.12 | | | | | (34), (35), (37), (38), (39), (40), (41), (59) are
% 157.04/27.12 | | | | | inconsistent by sub-proof #646.
% 157.04/27.12 | | | | |
% 157.04/27.12 | | | | End of split
% 157.04/27.12 | | | |
% 157.04/27.12 | | | End of split
% 157.04/27.12 | | |
% 157.04/27.12 | | Case 2:
% 157.04/27.12 | | |
% 157.04/27.12 | | | (60) all_58_14 = e1 & op(e0, e1) = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | ALPHA: (60) implies:
% 157.04/27.12 | | | (61) all_58_14 = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | COMBINE_EQS: (5), (61) imply:
% 157.04/27.12 | | | (62) e3 = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | SIMP: (62) implies:
% 157.04/27.12 | | | (63) e3 = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | COMBINE_EQS: (11), (63) imply:
% 157.04/27.12 | | | (64) all_58_6 = e1
% 157.04/27.12 | | |
% 157.04/27.12 | | | REF_CLOSE: (1), (2), (3), (5), (8), (12), (15), (18), (19), (20), (21),
% 157.04/27.12 | | | (23), (24), (26), (29), (30), (31), (32), (33), (34), (36),
% 157.04/27.12 | | | (38), (64) are inconsistent by sub-proof #409.
% 157.04/27.12 | | |
% 157.04/27.12 | | End of split
% 157.04/27.12 | |
% 157.04/27.12 | End of split
% 157.04/27.12 |
% 157.04/27.12 End of proof
% 157.04/27.12
% 157.04/27.12 Sub-proof #274 shows that the following formulas are inconsistent:
% 157.04/27.12 ----------------------------------------------------------------
% 157.04/27.12 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.04/27.12 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.04/27.12 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.12 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.12 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.12 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.12 (4) all_58_14 = e3
% 157.04/27.12 (5) ~ (all_52_7 = e3)
% 157.04/27.12 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.04/27.12 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.12 (7) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.04/27.12 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.04/27.12 (8) all_58_7 = e2
% 157.04/27.12 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.04/27.12 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.04/27.12 (10) op(e3, e2) = all_52_4
% 157.04/27.12 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.04/27.12 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.04/27.12 (12) op(e2, e3) = all_52_1
% 157.04/27.12 (13) ~ (all_52_13 = e3)
% 157.04/27.13 (14) ~ (e3 = e0)
% 157.04/27.13 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.13 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.13 (16) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.04/27.13 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.04/27.13 (17) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.13 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.04/27.13 e2)
% 157.04/27.13 (18) ~ (e2 = e0)
% 157.04/27.13 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.04/27.13 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.13 (20) op(e2, e0) = all_52_13
% 157.04/27.13 (21) op(e2, e3) = e2
% 157.04/27.13 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.13 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.04/27.13 (23) ~ (e3 = e1)
% 157.04/27.13 (24) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.04/27.13 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.04/27.13 (25) op(e1, e2) = all_52_6
% 157.04/27.13 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.13 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.04/27.13 (27) op(e0, e0) = e2
% 157.04/27.13 (28) all_58_4 = e2
% 157.04/27.13 (29) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.04/27.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.04/27.13 (30) ~ (all_52_4 = e3)
% 157.04/27.13 (31) op(e0, e2) = e0
% 157.04/27.13 (32) all_58_15 = e2
% 157.04/27.13 (33) ~ (e2 = e1)
% 157.04/27.13 (34) ~ (e1 = e0)
% 157.04/27.13 (35) all_58_3 = e3
% 157.04/27.13 (36) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.04/27.13 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.04/27.13 e3)
% 157.04/27.13 (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.04/27.13 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.04/27.13 (38) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.04/27.13 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.13 (39) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 157.04/27.13 (40) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.04/27.13 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.04/27.13 (41) op(e0, e2) = all_52_7
% 157.04/27.13 (42) all_58_0 = e0
% 157.04/27.13 (43) ~ (all_52_6 = e3)
% 157.04/27.13 (44) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.04/27.13 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.13 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.13 (46) ~ (e3 = e2)
% 157.04/27.13 (47) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.13 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.04/27.13 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.04/27.13 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.04/27.13
% 157.04/27.13 Begin of proof
% 157.04/27.13 |
% 157.04/27.13 | BETA: splitting (39) gives:
% 157.04/27.13 |
% 157.04/27.13 | Case 1:
% 157.04/27.13 | |
% 157.04/27.13 | | (48) all_58_1 = e0 & op(e3, e2) = e0
% 157.04/27.13 | |
% 157.04/27.13 | | ALPHA: (48) implies:
% 157.04/27.13 | | (49) all_58_1 = e0
% 157.04/27.13 | |
% 157.04/27.13 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.04/27.13 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.04/27.13 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 157.04/27.13 | | (35), (36), (37), (38), (40), (41), (42), (43), (44), (45), (46),
% 157.04/27.13 | | (47), (49) are inconsistent by sub-proof #391.
% 157.04/27.13 | |
% 157.04/27.13 | Case 2:
% 157.04/27.13 | |
% 157.04/27.13 | | (50) all_58_3 = e0 & op(e2, e2) = e0
% 157.04/27.13 | |
% 157.04/27.13 | | REF_CLOSE: (14), (35), (50) are inconsistent by sub-proof #910.
% 157.04/27.13 | |
% 157.04/27.13 | End of split
% 157.04/27.13 |
% 157.04/27.13 End of proof
% 157.04/27.13
% 157.04/27.13 Sub-proof #275 shows that the following formulas are inconsistent:
% 157.04/27.13 ----------------------------------------------------------------
% 157.04/27.13 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.04/27.13 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.04/27.13 (2) all_58_6 = e3
% 157.04/27.13 (3) op(e2, e3) = all_52_1
% 157.04/27.13 (4) ~ (e3 = e0)
% 157.04/27.13 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.13 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.13 (6) ~ (e2 = e0)
% 157.04/27.13 (7) all_58_9 = e3
% 157.04/27.13 (8) op(e2, e3) = e2
% 157.04/27.13 (9) ~ (e3 = e1)
% 157.04/27.13 (10) all_58_4 = e2
% 157.04/27.13 (11) ~ (e2 = e1)
% 157.04/27.13 (12) ~ (e1 = e0)
% 157.04/27.13 (13) all_58_3 = e3
% 157.04/27.13 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.04/27.13 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.04/27.13 (15) all_58_0 = e0
% 157.04/27.13 (16) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.04/27.13 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.13 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.13 (18) ~ (e3 = e2)
% 157.04/27.13 (19) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 157.04/27.13
% 157.04/27.13 Begin of proof
% 157.04/27.13 |
% 157.04/27.13 | BETA: splitting (19) gives:
% 157.04/27.13 |
% 157.04/27.13 | Case 1:
% 157.04/27.13 | |
% 157.04/27.13 | | (20) all_58_1 = e2 & op(e3, e2) = e2
% 157.04/27.13 | |
% 157.04/27.13 | | REF_CLOSE: (7), (9), (10), (11), (12), (14), (15), (20) are inconsistent by
% 157.04/27.13 | | sub-proof #276.
% 157.04/27.13 | |
% 157.04/27.13 | Case 2:
% 157.04/27.13 | |
% 157.04/27.13 | | (21) all_58_3 = e2 & op(e2, e2) = e2
% 157.04/27.13 | |
% 157.04/27.13 | | ALPHA: (21) implies:
% 157.04/27.13 | | (22) all_58_3 = e2
% 157.04/27.13 | |
% 157.04/27.13 | | COMBINE_EQS: (13), (22) imply:
% 157.04/27.13 | | (23) e3 = e2
% 157.04/27.13 | |
% 157.04/27.13 | | COMBINE_EQS: (2), (23) imply:
% 157.04/27.13 | | (24) all_58_6 = e2
% 157.04/27.13 | |
% 157.04/27.13 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11), (12), (16), (17), (18),
% 157.04/27.13 | | (24) are inconsistent by sub-proof #1152.
% 157.04/27.13 | |
% 157.04/27.13 | End of split
% 157.04/27.13 |
% 157.04/27.13 End of proof
% 157.04/27.13
% 157.04/27.13 Sub-proof #276 shows that the following formulas are inconsistent:
% 157.04/27.13 ----------------------------------------------------------------
% 157.04/27.13 (1) all_58_9 = e3
% 157.04/27.13 (2) ~ (e3 = e1)
% 157.04/27.13 (3) all_58_4 = e2
% 157.04/27.13 (4) ~ (e2 = e1)
% 157.04/27.13 (5) ~ (e1 = e0)
% 157.04/27.13 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.04/27.13 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.04/27.13 (7) all_58_1 = e2 & op(e3, e2) = e2
% 157.04/27.13 (8) all_58_0 = e0
% 157.04/27.13
% 157.04/27.13 Begin of proof
% 157.04/27.13 |
% 157.04/27.13 | ALPHA: (7) implies:
% 157.04/27.13 | (9) all_58_1 = e2
% 157.04/27.13 |
% 157.04/27.13 | BETA: splitting (6) gives:
% 157.04/27.13 |
% 157.04/27.13 | Case 1:
% 157.04/27.13 | |
% 157.04/27.13 | | (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 157.04/27.13 | | e1)
% 157.04/27.13 | |
% 157.04/27.13 | | BETA: splitting (10) gives:
% 157.04/27.13 | |
% 157.04/27.13 | | Case 1:
% 157.04/27.13 | | |
% 157.04/27.13 | | | (11) all_58_0 = e1 & op(e3, e3) = e1
% 157.04/27.13 | | |
% 157.04/27.13 | | | REF_CLOSE: (5), (8), (11) are inconsistent by sub-proof #1495.
% 157.04/27.13 | | |
% 157.04/27.13 | | Case 2:
% 157.04/27.13 | | |
% 157.04/27.13 | | | (12) all_58_1 = e1 & op(e3, e2) = e1
% 157.04/27.13 | | |
% 157.04/27.13 | | | REF_CLOSE: (4), (9), (12) are inconsistent by sub-proof #1219.
% 157.04/27.13 | | |
% 157.04/27.13 | | End of split
% 157.04/27.13 | |
% 157.04/27.13 | Case 2:
% 157.04/27.13 | |
% 157.04/27.13 | | (13) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 157.04/27.13 | | e1)
% 157.04/27.13 | |
% 157.04/27.13 | | REF_CLOSE: (1), (2), (3), (4), (13) are inconsistent by sub-proof #642.
% 157.04/27.13 | |
% 157.04/27.13 | End of split
% 157.04/27.13 |
% 157.04/27.13 End of proof
% 157.04/27.13
% 157.04/27.13 Sub-proof #277 shows that the following formulas are inconsistent:
% 157.04/27.13 ----------------------------------------------------------------
% 157.04/27.13 (1) ~ (all_52_7 = e3)
% 157.04/27.13 (2) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.13 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.13 (3) op(e1, e3) = all_52_2
% 157.04/27.13 (4) op(e2, e3) = e2
% 157.04/27.13 (5) ~ (e3 = e1)
% 157.04/27.13 (6) ~ (all_52_2 = e1)
% 157.04/27.13 (7) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.04/27.13 (8) ~ (e2 = e1)
% 157.04/27.13 (9) ~ (all_22_1 = e1)
% 157.04/27.13 (10) op(e0, e2) = all_52_7
% 157.04/27.13 (11) op(e3, e3) = all_22_1
% 157.04/27.13 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.13
% 157.04/27.13 Begin of proof
% 157.04/27.13 |
% 157.04/27.13 | BETA: splitting (7) gives:
% 157.04/27.13 |
% 157.04/27.13 | Case 1:
% 157.04/27.13 | |
% 157.04/27.13 | | (13) all_58_12 = e3 & op(e0, e3) = e3
% 157.04/27.13 | |
% 157.04/27.13 | | ALPHA: (13) implies:
% 157.04/27.13 | | (14) all_58_12 = e3
% 157.04/27.13 | |
% 157.04/27.13 | | BETA: splitting (2) gives:
% 157.04/27.13 | |
% 157.04/27.13 | | Case 1:
% 157.04/27.13 | | |
% 157.04/27.13 | | | (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 157.04/27.13 | | | e1)
% 157.04/27.13 | | |
% 157.04/27.13 | | | REF_CLOSE: (4), (8), (9), (11), (12), (15) are inconsistent by sub-proof
% 157.04/27.13 | | | #278.
% 157.04/27.13 | | |
% 157.04/27.13 | | Case 2:
% 157.04/27.13 | | |
% 157.04/27.13 | | | (16) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 157.04/27.13 | | | e1)
% 157.04/27.13 | | |
% 157.04/27.13 | | | BETA: splitting (16) gives:
% 157.04/27.13 | | |
% 157.04/27.13 | | | Case 1:
% 157.04/27.13 | | | |
% 157.04/27.13 | | | | (17) all_58_6 = e1 & op(e1, e3) = e1
% 157.04/27.13 | | | |
% 157.04/27.13 | | | | ALPHA: (17) implies:
% 157.04/27.13 | | | | (18) op(e1, e3) = e1
% 157.04/27.13 | | | |
% 157.04/27.13 | | | | REF_CLOSE: (3), (6), (12), (18) are inconsistent by sub-proof #1412.
% 157.04/27.13 | | | |
% 157.04/27.13 | | | Case 2:
% 157.04/27.13 | | | |
% 157.04/27.13 | | | | (19) all_58_12 = e1 & op(e0, e3) = e1
% 157.04/27.13 | | | |
% 157.04/27.13 | | | | REF_CLOSE: (5), (14), (19) are inconsistent by sub-proof #1388.
% 157.04/27.13 | | | |
% 157.04/27.13 | | | End of split
% 157.04/27.13 | | |
% 157.04/27.13 | | End of split
% 157.04/27.13 | |
% 157.04/27.13 | Case 2:
% 157.04/27.13 | |
% 157.04/27.13 | | (20) all_58_13 = e3 & op(e0, e2) = e3
% 157.04/27.13 | |
% 157.04/27.13 | | REF_CLOSE: (1), (10), (12), (20) are inconsistent by sub-proof #1449.
% 157.04/27.13 | |
% 157.04/27.13 | End of split
% 157.04/27.13 |
% 157.04/27.13 End of proof
% 157.04/27.13
% 157.04/27.13 Sub-proof #278 shows that the following formulas are inconsistent:
% 157.04/27.13 ----------------------------------------------------------------
% 157.04/27.13 (1) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 157.04/27.13 (2) op(e2, e3) = e2
% 157.04/27.13 (3) ~ (e2 = e1)
% 157.04/27.13 (4) ~ (all_22_1 = e1)
% 157.04/27.13 (5) op(e3, e3) = all_22_1
% 157.04/27.13 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.13
% 157.04/27.13 Begin of proof
% 157.04/27.13 |
% 157.04/27.13 | BETA: splitting (1) gives:
% 157.04/27.13 |
% 157.04/27.13 | Case 1:
% 157.04/27.13 | |
% 157.04/27.13 | | (7) all_58_0 = e1 & op(e3, e3) = e1
% 157.04/27.13 | |
% 157.04/27.13 | | ALPHA: (7) implies:
% 157.04/27.13 | | (8) op(e3, e3) = e1
% 157.04/27.13 | |
% 157.04/27.13 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #668.
% 157.04/27.13 | |
% 157.04/27.13 | Case 2:
% 157.04/27.13 | |
% 157.04/27.13 | | (9) all_58_2 = e1 & op(e2, e3) = e1
% 157.04/27.13 | |
% 157.04/27.13 | | ALPHA: (9) implies:
% 157.04/27.13 | | (10) op(e2, e3) = e1
% 157.04/27.13 | |
% 157.04/27.13 | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #1430.
% 157.04/27.13 | |
% 157.04/27.13 | End of split
% 157.04/27.13 |
% 157.04/27.13 End of proof
% 157.04/27.13
% 157.04/27.13 Sub-proof #279 shows that the following formulas are inconsistent:
% 157.04/27.13 ----------------------------------------------------------------
% 157.04/27.13 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.04/27.13 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.04/27.13 (2) all_58_6 = e3
% 157.04/27.13 (3) all_58_9 = e2 & op(e3, e0) = e2
% 157.04/27.13 (4) op(e2, e3) = all_52_1
% 157.04/27.13 (5) ~ (e3 = e0)
% 157.04/27.13 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.13 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.13 (7) ~ (e2 = e0)
% 157.04/27.13 (8) all_58_9 = e3
% 157.04/27.13 (9) op(e2, e3) = e2
% 157.04/27.13 (10) ~ (e3 = e1)
% 157.04/27.13 (11) ~ (e2 = e1)
% 157.04/27.13 (12) ~ (e1 = e0)
% 157.04/27.13 (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.04/27.13 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.13 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.13 (15) ~ (e3 = e2)
% 157.04/27.13
% 157.04/27.13 Begin of proof
% 157.04/27.13 |
% 157.04/27.13 | ALPHA: (3) implies:
% 157.04/27.13 | (16) all_58_9 = e2
% 157.04/27.13 |
% 157.04/27.13 | COMBINE_EQS: (8), (16) imply:
% 157.04/27.13 | (17) e3 = e2
% 157.04/27.13 |
% 157.04/27.13 | SIMP: (17) implies:
% 157.04/27.13 | (18) e3 = e2
% 157.04/27.13 |
% 157.04/27.13 | COMBINE_EQS: (2), (18) imply:
% 157.04/27.13 | (19) all_58_6 = e2
% 157.04/27.13 |
% 157.04/27.13 | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 157.04/27.13 | (19) are inconsistent by sub-proof #1152.
% 157.04/27.13 |
% 157.04/27.13 End of proof
% 157.04/27.13
% 157.04/27.13 Sub-proof #280 shows that the following formulas are inconsistent:
% 157.04/27.13 ----------------------------------------------------------------
% 157.04/27.13 (1) all_56_12 = e3
% 157.04/27.13 (2) all_56_12 = e0
% 157.04/27.13 (3) ~ (e3 = e0)
% 157.04/27.13
% 157.04/27.13 Begin of proof
% 157.04/27.13 |
% 157.04/27.13 | COMBINE_EQS: (1), (2) imply:
% 157.04/27.13 | (4) e3 = e0
% 157.04/27.13 |
% 157.04/27.13 | SIMP: (4) implies:
% 157.04/27.13 | (5) e3 = e0
% 157.04/27.13 |
% 157.04/27.13 | REDUCE: (3), (5) imply:
% 157.04/27.13 | (6) $false
% 157.04/27.13 |
% 157.04/27.13 | CLOSE: (6) is inconsistent.
% 157.04/27.13 |
% 157.04/27.13 End of proof
% 157.04/27.13
% 157.04/27.13 Sub-proof #281 shows that the following formulas are inconsistent:
% 157.04/27.13 ----------------------------------------------------------------
% 157.04/27.13 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.04/27.13 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.04/27.13 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.04/27.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.04/27.13 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.13 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.04/27.13 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.04/27.13 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.13 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.04/27.13 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.04/27.13 (7) op(e1, e1) = all_6_2
% 157.04/27.13 (8) ~ (all_52_7 = e3)
% 157.04/27.13 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.04/27.13 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.04/27.13 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.04/27.13 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.04/27.13 (11) ~ (all_52_6 = all_52_14)
% 157.04/27.13 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.04/27.13 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.04/27.13 (13) ~ (all_14_0 = e0)
% 157.04/27.13 (14) all_54_10 = all_6_2
% 157.04/27.13 (15) ~ (all_52_4 = all_52_6)
% 157.04/27.13 (16) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.04/27.13 (17) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.04/27.13 (18) ~ (all_4_2 = e3)
% 157.04/27.13 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.04/27.13 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.04/27.13 (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.04/27.13 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.04/27.13 (21) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.04/27.13 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.04/27.13 (22) all_54_1 = all_52_4
% 157.04/27.13 (23) op(e3, e2) = all_52_4
% 157.04/27.13 (24) ~ (all_14_0 = e3)
% 157.04/27.13 (25) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.04/27.13 (26) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 157.04/27.13 (27) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.04/27.13 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.04/27.13 (28) op(e2, e1) = all_52_9
% 157.04/27.13 (29) op(e2, e3) = all_52_1
% 157.04/27.13 (30) ~ (all_52_13 = e3)
% 157.04/27.13 (31) ~ (all_14_0 = e1)
% 157.04/27.13 (32) all_54_2 = all_52_8
% 157.04/27.13 (33) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.04/27.13 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.04/27.13 (34) ~ (all_52_8 = all_52_9)
% 157.04/27.13 (35) all_56_2 = e3
% 157.04/27.13 (36) ~ (e3 = e0)
% 157.04/27.13 (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.04/27.13 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.04/27.13 (38) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.04/27.13 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.04/27.13 (39) ~ (all_52_9 = all_52_13)
% 157.04/27.13 (40) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.13 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.04/27.13 e2)
% 157.04/27.13 (41) op(e3, e3) = e0
% 157.04/27.13 (42) ~ (all_52_11 = all_6_2)
% 157.04/27.13 (43) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.04/27.13 (44) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.04/27.13 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.04/27.13 (45) all_58_9 = e3
% 157.04/27.13 (46) op(e1, e3) = all_52_2
% 157.04/27.13 (47) ~ (all_52_6 = all_6_2)
% 157.04/27.13 (48) op(e2, e0) = all_52_13
% 157.04/27.13 (49) op(e2, e3) = e2
% 157.04/27.13 (50) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.13 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.04/27.13 (51) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.04/27.13 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.04/27.13 (52) op(e1, e2) = all_52_6
% 157.04/27.13 (53) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.04/27.13 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.04/27.13 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.04/27.13 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.04/27.13 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.04/27.13 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.04/27.13 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.04/27.13 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.04/27.13 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.04/27.13 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.04/27.13 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.04/27.13 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.04/27.13 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.04/27.13 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.04/27.13 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.04/27.13 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.04/27.13 = e0)
% 157.04/27.13 (54) ~ (all_4_2 = e1)
% 157.04/27.13 (55) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.04/27.13 (56) ~ (all_52_4 = e0)
% 157.04/27.13 (57) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.04/27.13 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.04/27.13 (58) ~ (all_52_9 = all_6_2)
% 157.04/27.13 (59) op(e0, e2) = all_14_0
% 157.04/27.13 (60) op(e0, e0) = all_4_2
% 157.04/27.13 (61) all_54_7 = all_52_13
% 157.04/27.13 (62) ~ (all_52_13 = e2)
% 157.04/27.13 (63) all_56_15 = all_4_2
% 157.04/27.13 (64) ~ (all_52_9 = all_52_11)
% 157.04/27.13 (65) ~ (all_52_13 = all_4_2)
% 157.04/27.13 (66) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.04/27.13 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.04/27.13 (67) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.04/27.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.04/27.13 (68) ~ (all_52_4 = e3)
% 157.04/27.13 (69) all_54_6 = all_52_9
% 157.04/27.13 (70) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.04/27.13 (71) ~ (all_52_8 = all_52_11)
% 157.04/27.13 (72) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.04/27.13 (73) all_54_13 = all_14_0
% 157.04/27.13 (74) ~ (all_8_2 = e1)
% 157.04/27.13 (75) all_58_3 = e3
% 157.04/27.13 (76) ~ (all_6_2 = e2)
% 157.04/27.13 (77) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.04/27.13 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.04/27.13 e3)
% 157.04/27.13 (78) all_56_14 = all_6_2
% 157.04/27.13 (79) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.04/27.13 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.04/27.13 (80) ~ (all_52_9 = e2)
% 157.04/27.13 (81) ~ (all_52_8 = e3)
% 157.04/27.13 (82) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.04/27.13 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.04/27.13 (83) all_54_14 = all_52_11
% 157.04/27.13 (84) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.04/27.13 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.04/27.13 (85) op(e0, e2) = all_52_7
% 157.04/27.13 (86) op(e1, e0) = all_52_14
% 157.04/27.13 (87) op(e3, e3) = all_22_1
% 157.04/27.13 (88) all_54_15 = all_4_2
% 157.04/27.13 (89) all_58_0 = e0
% 157.04/27.13 (90) op(e2, e2) = all_8_2
% 157.04/27.13 (91) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.04/27.13 (92) ~ (all_52_6 = e3)
% 157.04/27.13 (93) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.04/27.13 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.04/27.13 (94) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.04/27.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.04/27.13 (95) all_54_11 = all_52_14
% 157.04/27.13 (96) ~ (all_52_13 = all_52_14)
% 157.04/27.13 (97) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.04/27.13 (98) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.04/27.13 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.13 (99) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.04/27.13 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.04/27.13 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.04/27.13 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.04/27.13 (100) all_54_9 = all_52_6
% 157.04/27.13 (101) ~ (all_52_4 = all_52_8)
% 157.04/27.13 (102) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.04/27.13 (103) ~ (all_52_4 = all_14_0)
% 157.04/27.13 (104) ~ (all_52_14 = all_4_2)
% 157.04/27.13 (105) ~ (all_52_6 = all_14_0)
% 157.04/27.13
% 157.04/27.13 Begin of proof
% 157.04/27.13 |
% 157.04/27.13 | BETA: splitting (50) gives:
% 157.04/27.13 |
% 157.04/27.13 | Case 1:
% 157.04/27.13 | |
% 157.04/27.13 | | (106) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 157.04/27.13 | | e0)
% 157.04/27.13 | |
% 157.04/27.13 | | BETA: splitting (106) gives:
% 157.04/27.13 | |
% 157.04/27.13 | | Case 1:
% 157.04/27.13 | | |
% 157.04/27.13 | | | (107) all_58_1 = e0 & op(e3, e2) = e0
% 157.04/27.13 | | |
% 157.04/27.13 | | | REF_CLOSE: (23), (56), (94), (107) are inconsistent by sub-proof #1221.
% 157.04/27.13 | | |
% 157.04/27.13 | | Case 2:
% 157.04/27.13 | | |
% 157.04/27.14 | | | (108) all_58_3 = e0 & op(e2, e2) = e0
% 157.04/27.14 | | |
% 157.04/27.14 | | | REF_CLOSE: (36), (75), (108) are inconsistent by sub-proof #756.
% 157.04/27.14 | | |
% 157.04/27.14 | | End of split
% 157.04/27.14 | |
% 157.04/27.14 | Case 2:
% 157.04/27.14 | |
% 157.04/27.14 | | (109) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 157.04/27.14 | | e0)
% 157.04/27.14 | |
% 157.04/27.14 | | BETA: splitting (109) gives:
% 157.04/27.14 | |
% 157.04/27.14 | | Case 1:
% 157.04/27.14 | | |
% 157.04/27.14 | | | (110) all_58_7 = e0 & op(e1, e2) = e0
% 157.04/27.14 | | |
% 157.04/27.14 | | | ALPHA: (110) implies:
% 157.04/27.14 | | | (111) all_58_7 = e0
% 157.04/27.14 | | |
% 157.04/27.14 | | | BETA: splitting (97) gives:
% 157.04/27.14 | | |
% 157.04/27.14 | | | Case 1:
% 157.04/27.14 | | | |
% 157.04/27.14 | | | | (112) all_54_15 = e3
% 157.04/27.14 | | | |
% 157.04/27.14 | | | | REF_CLOSE: (18), (88), (112) are inconsistent by sub-proof #1543.
% 157.04/27.14 | | | |
% 157.04/27.14 | | | Case 2:
% 157.04/27.14 | | | |
% 157.04/27.14 | | | | (113) ~ (all_54_15 = e3)
% 157.04/27.14 | | | | (114) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.04/27.14 | | | |
% 157.04/27.14 | | | | BETA: splitting (91) gives:
% 157.04/27.14 | | | |
% 157.04/27.14 | | | | Case 1:
% 157.04/27.14 | | | | |
% 157.04/27.14 | | | | | (115) all_54_13 = e3
% 157.04/27.14 | | | | |
% 157.04/27.14 | | | | | REF_CLOSE: (24), (73), (115) are inconsistent by sub-proof #288.
% 157.04/27.14 | | | | |
% 157.04/27.14 | | | | Case 2:
% 157.04/27.14 | | | | |
% 157.04/27.14 | | | | | (116) ~ (all_54_13 = e3)
% 157.04/27.14 | | | | | (117) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.04/27.14 | | | | |
% 157.04/27.14 | | | | | BETA: splitting (117) gives:
% 157.04/27.14 | | | | |
% 157.04/27.14 | | | | | Case 1:
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | (118) all_54_13 = e2
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | COMBINE_EQS: (73), (118) imply:
% 157.04/27.14 | | | | | | (119) all_14_0 = e2
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | SIMP: (119) implies:
% 157.04/27.14 | | | | | | (120) all_14_0 = e2
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | REDUCE: (103), (120) imply:
% 157.04/27.14 | | | | | | (121) ~ (all_52_4 = e2)
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | REDUCE: (105), (120) imply:
% 157.04/27.14 | | | | | | (122) ~ (all_52_6 = e2)
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | REDUCE: (24), (120) imply:
% 157.04/27.14 | | | | | | (123) ~ (e3 = e2)
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | SIMP: (123) implies:
% 157.04/27.14 | | | | | | (124) ~ (e3 = e2)
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | REDUCE: (13), (120) imply:
% 157.04/27.14 | | | | | | (125) ~ (e2 = e0)
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | REDUCE: (59), (120) imply:
% 157.04/27.14 | | | | | | (126) op(e0, e2) = e2
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | BETA: splitting (25) gives:
% 157.04/27.14 | | | | | |
% 157.04/27.14 | | | | | | Case 1:
% 157.04/27.14 | | | | | | |
% 157.04/27.14 | | | | | | | (127) all_54_1 = e3
% 157.04/27.14 | | | | | | |
% 157.04/27.14 | | | | | | | REF_CLOSE: (22), (68), (127) are inconsistent by sub-proof #1305.
% 157.04/27.14 | | | | | | |
% 157.04/27.14 | | | | | | Case 2:
% 157.04/27.14 | | | | | | |
% 157.04/27.14 | | | | | | | (128) ~ (all_54_1 = e3)
% 157.04/27.14 | | | | | | | (129) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.04/27.14 | | | | | | |
% 157.04/27.14 | | | | | | | BETA: splitting (129) gives:
% 157.04/27.14 | | | | | | |
% 157.04/27.14 | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | |
% 157.04/27.14 | | | | | | | | (130) all_54_1 = e2
% 157.04/27.14 | | | | | | | |
% 157.04/27.14 | | | | | | | | REF_CLOSE: (22), (121), (130) are inconsistent by sub-proof
% 157.04/27.14 | | | | | | | | #1304.
% 157.04/27.14 | | | | | | | |
% 157.04/27.14 | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | |
% 157.04/27.14 | | | | | | | | (131) ~ (all_54_1 = e2)
% 157.04/27.14 | | | | | | | | (132) all_54_1 = e1 | all_54_1 = e0
% 157.04/27.14 | | | | | | | |
% 157.04/27.14 | | | | | | | | BETA: splitting (38) gives:
% 157.04/27.14 | | | | | | | |
% 157.04/27.14 | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | |
% 157.04/27.14 | | | | | | | | | (133) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 157.04/27.14 | | | | | | | | | op(e3, e2) = e2)
% 157.04/27.14 | | | | | | | | |
% 157.04/27.14 | | | | | | | | | BETA: splitting (133) gives:
% 157.04/27.14 | | | | | | | | |
% 157.04/27.14 | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | (134) all_58_0 = e2 & op(e3, e3) = e2
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | REF_CLOSE: (89), (125), (134) are inconsistent by sub-proof
% 157.04/27.14 | | | | | | | | | | #702.
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | (135) all_58_1 = e2 & op(e3, e2) = e2
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | ALPHA: (135) implies:
% 157.04/27.14 | | | | | | | | | | (136) op(e3, e2) = e2
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | REF_CLOSE: (23), (94), (121), (136) are inconsistent by
% 157.04/27.14 | | | | | | | | | | sub-proof #1539.
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | End of split
% 157.04/27.14 | | | | | | | | |
% 157.04/27.14 | | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | | |
% 157.04/27.14 | | | | | | | | | (137) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 157.04/27.14 | | | | | | | | | op(e3, e0) = e2)
% 157.04/27.14 | | | | | | | | |
% 157.04/27.14 | | | | | | | | | BETA: splitting (137) gives:
% 157.04/27.14 | | | | | | | | |
% 157.04/27.14 | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | (138) all_58_4 = e2 & op(e3, e1) = e2
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | ALPHA: (138) implies:
% 157.04/27.14 | | | | | | | | | | (139) all_58_4 = e2
% 157.04/27.14 | | | | | | | | | | (140) op(e3, e1) = e2
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | BETA: splitting (132) gives:
% 157.04/27.14 | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | (141) all_54_1 = e1
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | COMBINE_EQS: (22), (141) imply:
% 157.04/27.14 | | | | | | | | | | | (142) all_52_4 = e1
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | SIMP: (142) implies:
% 157.04/27.14 | | | | | | | | | | | (143) all_52_4 = e1
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | REDUCE: (15), (143) imply:
% 157.04/27.14 | | | | | | | | | | | (144) ~ (all_52_6 = e1)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | SIMP: (144) implies:
% 157.04/27.14 | | | | | | | | | | | (145) ~ (all_52_6 = e1)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | REDUCE: (101), (143) imply:
% 157.04/27.14 | | | | | | | | | | | (146) ~ (all_52_8 = e1)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | SIMP: (146) implies:
% 157.04/27.14 | | | | | | | | | | | (147) ~ (all_52_8 = e1)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | REDUCE: (68), (143) imply:
% 157.04/27.14 | | | | | | | | | | | (148) ~ (e3 = e1)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | SIMP: (148) implies:
% 157.04/27.14 | | | | | | | | | | | (149) ~ (e3 = e1)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | REDUCE: (121), (143) imply:
% 157.04/27.14 | | | | | | | | | | | (150) ~ (e2 = e1)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | SIMP: (150) implies:
% 157.04/27.14 | | | | | | | | | | | (151) ~ (e2 = e1)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | REDUCE: (56), (143) imply:
% 157.04/27.14 | | | | | | | | | | | (152) ~ (e1 = e0)
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | BETA: splitting (79) gives:
% 157.04/27.14 | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | (153) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 157.04/27.14 | | | | | | | | | | | | & op(e3, e2) = e1)
% 157.04/27.14 | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | BETA: splitting (153) gives:
% 157.04/27.14 | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | (154) all_58_0 = e1 & op(e3, e3) = e1
% 157.04/27.14 | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | ALPHA: (154) implies:
% 157.04/27.14 | | | | | | | | | | | | | (155) op(e3, e3) = e1
% 157.04/27.14 | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | REF_CLOSE: (41), (87), (94), (152), (155) are inconsistent by
% 157.04/27.14 | | | | | | | | | | | | | sub-proof #767.
% 157.04/27.14 | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | (156) all_58_1 = e1 & op(e3, e2) = e1
% 157.04/27.14 | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | ALPHA: (156) implies:
% 157.04/27.14 | | | | | | | | | | | | | (157) all_58_1 = e1
% 157.04/27.14 | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | BETA: splitting (114) gives:
% 157.04/27.14 | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | (158) all_54_15 = e2
% 157.04/27.14 | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | REF_CLOSE: (26), (63), (85), (88), (94), (125), (126), (158)
% 157.04/27.14 | | | | | | | | | | | | | | are inconsistent by sub-proof #287.
% 157.04/27.14 | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | (159) ~ (all_54_15 = e2)
% 157.04/27.14 | | | | | | | | | | | | | | (160) all_54_15 = e1 | all_54_15 = e0
% 157.04/27.14 | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | REDUCE: (88), (159) imply:
% 157.04/27.14 | | | | | | | | | | | | | | (161) ~ (all_4_2 = e2)
% 157.04/27.14 | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 157.04/27.14 | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | (162) all_54_15 = e1
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | REF_CLOSE: (54), (88), (162) are inconsistent by sub-proof
% 157.04/27.14 | | | | | | | | | | | | | | | #1541.
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | (163) all_54_15 = e0
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | COMBINE_EQS: (88), (163) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | (164) all_4_2 = e0
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | SIMP: (164) implies:
% 157.04/27.14 | | | | | | | | | | | | | | | (165) all_4_2 = e0
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | COMBINE_EQS: (63), (165) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | (166) all_56_15 = e0
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | REDUCE: (65), (165) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | (167) ~ (all_52_13 = e0)
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | REDUCE: (18), (165) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | (168) ~ (e3 = e0)
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | REDUCE: (161), (165) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | (169) ~ (e2 = e0)
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 157.04/27.14 | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | (170) all_54_9 = e3
% 157.04/27.14 | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (170) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | (171) all_52_6 = e3
% 157.04/27.14 | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | REDUCE: (92), (171) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | (172) $false
% 157.04/27.14 | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 157.04/27.14 | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | (173) ~ (all_54_9 = e3)
% 157.04/27.14 | | | | | | | | | | | | | | | | (174) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.04/27.14 | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 157.04/27.14 | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | (175) all_54_7 = e3
% 157.04/27.14 | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (175) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | | (176) all_52_13 = e3
% 157.04/27.14 | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | REDUCE: (30), (176) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | | (177) $false
% 157.04/27.14 | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 157.04/27.14 | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | (178) ~ (all_54_7 = e3)
% 157.04/27.14 | | | | | | | | | | | | | | | | | (179) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.04/27.14 | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 157.04/27.14 | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | (180) all_54_7 = e2
% 157.04/27.14 | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (180) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | (181) all_52_13 = e2
% 157.04/27.14 | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | REDUCE: (62), (181) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | (182) $false
% 157.04/27.14 | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 157.04/27.14 | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | Case 2:
% 157.04/27.14 | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | (183) ~ (all_54_7 = e2)
% 157.04/27.14 | | | | | | | | | | | | | | | | | | (184) all_54_7 = e1 | all_54_7 = e0
% 157.04/27.14 | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 157.04/27.14 | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | (185) all_54_7 = e1
% 157.04/27.14 | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (185) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | (186) all_52_13 = e1
% 157.04/27.14 | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | REDUCE: (39), (186) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | (187) ~ (all_52_9 = e1)
% 157.04/27.14 | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | REDUCE: (96), (186) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | (188) ~ (all_52_14 = e1)
% 157.04/27.14 | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | SIMP: (188) implies:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | (189) ~ (all_52_14 = e1)
% 157.04/27.14 | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | (190) ~ (all_56_14 = e0)
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (190) imply:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | (191) ~ (all_6_2 = e0)
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | (192) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | |
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.04/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (193) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (29), (49), (94), (121), (124), (140), (193)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #286.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (194) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | (195) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | (196) op(e3, e1) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (197) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (29), (36), (45), (49), (57), (66), (74),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (90), (94), (124), (125), (149), (151), (152),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (197) are inconsistent by sub-proof #285.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (198) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_58_11 = e2 & op(e1, e0) = e2
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_58_11 = e2
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_54_9 = e2
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (201) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_52_6 = e2
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (202) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (203) $false
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (204) ~ (all_54_9 = e2)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_54_9 = e1 | all_54_9 = e0
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_54_9 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (206) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_52_6 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (207) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) $false
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (208) is inconsistent.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_9 = e0
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (209) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_52_6 = e0
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (210) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) ~ (e1 = e0)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with e1, e2, e1, e3,
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (140), (196) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) e2 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (200), (212) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_58_11 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19), (29), (33), (36), (37), (49), (76),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (93), (94), (111), (124), (125), (149), (151),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (152), (213) are inconsistent by sub-proof #743.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_58_15 = e2 & op(e0, e0) = e2
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (94), (161), (214) are inconsistent by
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1452.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | (215) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (36), (166), (215) are inconsistent by
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #309.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | (216) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (217) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (52), (62), (94), (122), (145), (217) are
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1128.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (218) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | (219) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | (220) op(e0, e2) = e0
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (94), (125), (126), (220) are inconsistent
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1040.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | (221) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (222) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (223) ~ (all_56_15 = e0)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (223) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (224) $false
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (225) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (226) ~ (all_56_14 = e1)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (227) op(e0, e1) = e0
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (226) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_6_2 = e1)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | (229) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_9 = e1 & op(e3, e0) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (149), (230) are inconsistent by sub-proof
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | #1078.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_58_10 = e1 & op(e2, e0) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_58_10 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (29), (36), (45), (49), (57), (66), (74),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (94), (124), (125), (149), (151), (152),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) are inconsistent by sub-proof #285.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_58_11 = e2 & op(e1, e0) = e2
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_58_11 = e2
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_4 = e1 & op(e3, e1) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_4 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (239) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) e2 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (236), (240) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_58_11 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19), (29), (33), (36), (37), (49), (76),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (93), (94), (111), (124), (125), (149), (151),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (152), (241) are inconsistent by sub-proof #743.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_58_5 = e1 & op(e2, e1) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_58_5 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (49), (57), (75), (94), (125), (149),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (151), (152), (232), (243) are inconsistent by
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #754.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_58_8 = e1 & op(e1, e1) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (245) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_58_8 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_54_10 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (247) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_6_2 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (248) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_6_2 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (249) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_56_14 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (249) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_52_9 = e3)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) ~ (all_56_14 = e3)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (252) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) $false
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_56_6 = e1 & op(e1, e3) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) op(e1, e3) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (94), (124), (140), (251), (256) are
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #293.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_58_8 = e3 & op(e1, e1) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_58_8 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (259) imply:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) e3 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (27), (36), (44), (45), (52), (92),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (94), (99), (124), (125), (149), (151), (152),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (236), (259), (260) are inconsistent by
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #297.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_58_14 = e3 & op(e0, e1) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_58_14 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_58_0 = e3 & op(e3, e3) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_58_0 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) op(e3, e3) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (19),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (23), (27), (29), (30), (33), (36),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (40), (48), (49), (50), (51), (52),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (57), (60), (67), (68), (75), (76), (77), (79),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (82), (84), (85), (87), (92), (93), (94), (98),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (124), (125), (149), (151), (152), (161),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (265), (266) are inconsistent by sub-proof
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #779.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_2 = e3 & op(e2, e3) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) op(e2, e3) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (49), (94), (124), (268) are inconsistent by
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1159.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_6 = e3 & op(e1, e3) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) op(e1, e3) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (94), (149), (255), (271) are inconsistent
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1164.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_58_12 = e3 & op(e0, e3) = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_12 = e3
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (85), (94), (99), (125), (126), (149),
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (151), (152), (262), (273) are inconsistent by
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #778.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (76), (191), (228), (274) are inconsistent
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1527.
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_58_14 = e1 & op(e0, e1) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_58_14 = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) op(e0, e1) = e1
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_54_10 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (278) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_6_2 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_6_2 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (280) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_56_14 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (280) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) ~ (all_52_9 = e3)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (280) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_52_11 = e3)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) ~ (all_56_14 = e3)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (281), (284) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) $false
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_56_6 = e1 & op(e1, e3) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) op(e1, e3) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (94), (124), (140), (282), (288) are
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #293.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_8 = e3 & op(e1, e1) = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_58_8 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_54_6 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (292) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_52_9 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (282), (293) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) $false
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) ~ (all_54_6 = e3)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (36), (45), (49), (94), (98), (124), (125),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (152), (157), (297) are inconsistent by
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #284.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_6 = e3 & op(e1, e3) = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) op(e1, e3) = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (94), (149), (287), (300) are inconsistent
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1164.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_12 = e3 & op(e0, e3) = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_12 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_0 = e1 & op(e3, e3) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_58_0 = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (32), (34), (36), (37), (39), (49), (55),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (64), (69), (71), (80), (81), (83), (93),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (94), (102), (125), (147), (152), (167), (184),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282), (283), (287), (302), (305) are inconsistent
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #533.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_58_2 = e1 & op(e2, e3) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) op(e2, e3) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (94), (151), (307) are inconsistent by
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1430.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_58_6 = e1 & op(e1, e3) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_6 = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_54_6 = e2
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (80), (311) are inconsistent by sub-proof
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1192.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_54_6 = e1 | all_54_6 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_54_6 = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (187), (313) are inconsistent by sub-proof
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #562.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_54_6 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (314) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_52_9 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (315) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_52_9 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (316) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) ~ (e1 = e0)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with e0, e1, e1, e0,
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (227), (277) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) e1 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (318) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_58_1 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (45), (49), (79), (89), (94), (139), (149),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (151), (152), (302), (310), (319) are inconsistent
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #502.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_12 = e1 & op(e0, e3) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_58_12 = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (321) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) e3 = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (27), (36), (44), (45), (52), (92),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (94), (99), (124), (125), (149), (151), (152),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (236), (291), (322) are inconsistent by
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #297.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_58_14 = e3 & op(e0, e1) = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_58_14 = e3
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (276), (324) are inconsistent by sub-proof
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1147.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (76), (191), (228), (325) are inconsistent
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1527.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_15 = e2 & op(e0, e0) = e2
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (94), (161), (326) are inconsistent by
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1452.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | (327) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_11 = e1 & op(e1, e0) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_11 = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19), (29), (33), (36), (37), (49), (76),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (93), (94), (111), (124), (125), (149), (151),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (152), (329) are inconsistent by sub-proof #743.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_15 = e1 & op(e0, e0) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (60), (94), (330) are inconsistent by
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1418.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | (331) all_56_14 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | (332) all_56_8 = e1 & op(e1, e0) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | (333) op(e1, e0) = e1
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (331) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | (334) all_6_2 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | SIMP: (334) implies:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | (335) all_6_2 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (335) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | (336) ~ (all_52_6 = e0)
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (54), (72), (86), (88), (94), (95), (100),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | (104), (114), (145), (161), (174), (189), (333),
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | | (336) are inconsistent by sub-proof #1168.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | (337) all_54_7 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (337) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | (338) all_52_13 = e0
% 157.20/27.15 | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | REDUCE: (167), (338) imply:
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | (339) $false
% 157.20/27.15 | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | | CLOSE: (339) is inconsistent.
% 157.20/27.15 | | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | (340) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 157.20/27.15 | | | | | | | | | | | | & op(e3, e0) = e1)
% 157.20/27.15 | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | | REF_CLOSE: (45), (139), (149), (151), (340) are inconsistent
% 157.20/27.15 | | | | | | | | | | | | by sub-proof #642.
% 157.20/27.15 | | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | (341) all_54_1 = e0
% 157.20/27.15 | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | | REF_CLOSE: (22), (56), (341) are inconsistent by sub-proof
% 157.20/27.15 | | | | | | | | | | | #1115.
% 157.20/27.15 | | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | Case 2:
% 157.20/27.15 | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | (342) all_58_9 = e2 & op(e3, e0) = e2
% 157.20/27.15 | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | | REF_CLOSE: (45), (124), (342) are inconsistent by sub-proof
% 157.20/27.15 | | | | | | | | | | #1353.
% 157.20/27.15 | | | | | | | | | |
% 157.20/27.15 | | | | | | | | | End of split
% 157.20/27.15 | | | | | | | | |
% 157.20/27.15 | | | | | | | | End of split
% 157.20/27.15 | | | | | | | |
% 157.20/27.15 | | | | | | | End of split
% 157.20/27.15 | | | | | | |
% 157.20/27.15 | | | | | | End of split
% 157.20/27.15 | | | | | |
% 157.20/27.15 | | | | | Case 2:
% 157.20/27.15 | | | | | |
% 157.20/27.15 | | | | | | (343) all_54_13 = e1 | all_54_13 = e0
% 157.20/27.15 | | | | | |
% 157.20/27.15 | | | | | | REF_CLOSE: (13), (31), (73), (343) are inconsistent by sub-proof
% 157.20/27.15 | | | | | | #282.
% 157.20/27.15 | | | | | |
% 157.20/27.15 | | | | | End of split
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | End of split
% 157.20/27.15 | | | |
% 157.20/27.15 | | | End of split
% 157.20/27.15 | | |
% 157.20/27.15 | | Case 2:
% 157.20/27.15 | | |
% 157.20/27.15 | | | (344) all_58_13 = e0 & op(e0, e2) = e0
% 157.20/27.15 | | |
% 157.20/27.15 | | | ALPHA: (344) implies:
% 157.20/27.15 | | | (345) op(e0, e2) = e0
% 157.20/27.15 | | |
% 157.20/27.15 | | | BETA: splitting (91) gives:
% 157.20/27.15 | | |
% 157.20/27.15 | | | Case 1:
% 157.20/27.15 | | | |
% 157.20/27.15 | | | | (346) all_54_13 = e3
% 157.20/27.15 | | | |
% 157.20/27.15 | | | | REF_CLOSE: (24), (73), (346) are inconsistent by sub-proof #288.
% 157.20/27.15 | | | |
% 157.20/27.15 | | | Case 2:
% 157.20/27.15 | | | |
% 157.20/27.15 | | | | (347) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.20/27.15 | | | |
% 157.20/27.15 | | | | BETA: splitting (347) gives:
% 157.20/27.15 | | | |
% 157.20/27.15 | | | | Case 1:
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | | (348) all_54_13 = e2
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | | COMBINE_EQS: (73), (348) imply:
% 157.20/27.15 | | | | | (349) all_14_0 = e2
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | | SIMP: (349) implies:
% 157.20/27.15 | | | | | (350) all_14_0 = e2
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | | REDUCE: (13), (350) imply:
% 157.20/27.15 | | | | | (351) ~ (e2 = e0)
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | | REDUCE: (59), (350) imply:
% 157.20/27.15 | | | | | (352) op(e0, e2) = e2
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | | REF_CLOSE: (85), (94), (345), (351), (352) are inconsistent by
% 157.20/27.15 | | | | | sub-proof #1040.
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | Case 2:
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | | (353) all_54_13 = e1 | all_54_13 = e0
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | | REF_CLOSE: (13), (31), (73), (353) are inconsistent by sub-proof #282.
% 157.20/27.15 | | | | |
% 157.20/27.15 | | | | End of split
% 157.20/27.15 | | | |
% 157.20/27.15 | | | End of split
% 157.20/27.15 | | |
% 157.20/27.15 | | End of split
% 157.20/27.15 | |
% 157.20/27.15 | End of split
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #282 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) all_54_13 = e1 | all_54_13 = e0
% 157.20/27.15 (2) all_54_13 = all_14_0
% 157.20/27.15 (3) ~ (all_14_0 = e1)
% 157.20/27.15 (4) ~ (all_14_0 = e0)
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | BETA: splitting (1) gives:
% 157.20/27.15 |
% 157.20/27.15 | Case 1:
% 157.20/27.15 | |
% 157.20/27.15 | | (5) all_54_13 = e1
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #283.
% 157.20/27.15 | |
% 157.20/27.15 | Case 2:
% 157.20/27.15 | |
% 157.20/27.15 | | (6) all_54_13 = e0
% 157.20/27.15 | |
% 157.20/27.15 | | COMBINE_EQS: (2), (6) imply:
% 157.20/27.15 | | (7) all_14_0 = e0
% 157.20/27.15 | |
% 157.20/27.15 | | SIMP: (7) implies:
% 157.20/27.15 | | (8) all_14_0 = e0
% 157.20/27.15 | |
% 157.20/27.15 | | REDUCE: (4), (8) imply:
% 157.20/27.15 | | (9) $false
% 157.20/27.15 | |
% 157.20/27.15 | | CLOSE: (9) is inconsistent.
% 157.20/27.15 | |
% 157.20/27.15 | End of split
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #283 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) all_54_13 = all_14_0
% 157.20/27.15 (2) all_54_13 = e1
% 157.20/27.15 (3) ~ (all_14_0 = e1)
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | COMBINE_EQS: (1), (2) imply:
% 157.20/27.15 | (4) all_14_0 = e1
% 157.20/27.15 |
% 157.20/27.15 | SIMP: (4) implies:
% 157.20/27.15 | (5) all_14_0 = e1
% 157.20/27.15 |
% 157.20/27.15 | REDUCE: (3), (5) imply:
% 157.20/27.15 | (6) $false
% 157.20/27.15 |
% 157.20/27.15 | CLOSE: (6) is inconsistent.
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #284 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 157.20/27.15 (2) op(e2, e3) = all_52_1
% 157.20/27.15 (3) ~ (e3 = e0)
% 157.20/27.15 (4) ~ (e2 = e0)
% 157.20/27.15 (5) all_58_9 = e3
% 157.20/27.15 (6) op(e2, e3) = e2
% 157.20/27.15 (7) all_58_1 = e1
% 157.20/27.15 (8) all_58_4 = e2
% 157.20/27.15 (9) ~ (e1 = e0)
% 157.20/27.15 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.15 (11) ~ (e3 = e2)
% 157.20/27.15 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.20/27.15 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | BETA: splitting (1) gives:
% 157.20/27.15 |
% 157.20/27.15 | Case 1:
% 157.20/27.15 | |
% 157.20/27.15 | | (13) all_58_0 = e3 & op(e3, e3) = e3
% 157.20/27.15 | |
% 157.20/27.15 | | ALPHA: (13) implies:
% 157.20/27.15 | | (14) op(e3, e3) = e3
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (12), (14) are inconsistent
% 157.20/27.15 | | by sub-proof #1312.
% 157.20/27.15 | |
% 157.20/27.15 | Case 2:
% 157.20/27.15 | |
% 157.20/27.15 | | (15) all_58_2 = e3 & op(e2, e3) = e3
% 157.20/27.15 | |
% 157.20/27.15 | | ALPHA: (15) implies:
% 157.20/27.15 | | (16) op(e2, e3) = e3
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (2), (6), (10), (11), (16) are inconsistent by sub-proof #1159.
% 157.20/27.15 | |
% 157.20/27.15 | End of split
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #285 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.20/27.15 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.20/27.15 (2) op(e2, e3) = all_52_1
% 157.20/27.15 (3) ~ (e3 = e0)
% 157.20/27.15 (4) ~ (e2 = e0)
% 157.20/27.15 (5) all_58_9 = e3
% 157.20/27.15 (6) op(e2, e3) = e2
% 157.20/27.15 (7) ~ (e3 = e1)
% 157.20/27.15 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.20/27.15 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.20/27.15 (9) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.20/27.15 (10) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.20/27.15 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.20/27.15 (11) ~ (e2 = e1)
% 157.20/27.15 (12) ~ (e1 = e0)
% 157.20/27.15 (13) ~ (all_8_2 = e1)
% 157.20/27.15 (14) op(e2, e2) = all_8_2
% 157.20/27.15 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.15 (16) ~ (e3 = e2)
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | BETA: splitting (9) gives:
% 157.20/27.15 |
% 157.20/27.15 | Case 1:
% 157.20/27.15 | |
% 157.20/27.15 | | (17) all_58_9 = e2 & op(e3, e0) = e2
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (5), (16), (17) are inconsistent by sub-proof #1353.
% 157.20/27.15 | |
% 157.20/27.15 | Case 2:
% 157.20/27.15 | |
% 157.20/27.15 | | (18) all_58_10 = e2 & op(e2, e0) = e2
% 157.20/27.15 | |
% 157.20/27.15 | | ALPHA: (18) implies:
% 157.20/27.15 | | (19) all_58_10 = e2
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (14),
% 157.20/27.15 | | (15), (16), (19) are inconsistent by sub-proof #905.
% 157.20/27.15 | |
% 157.20/27.15 | End of split
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #286 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) op(e3, e2) = all_52_4
% 157.20/27.15 (2) ~ (all_52_4 = e2)
% 157.20/27.15 (3) op(e3, e1) = e2
% 157.20/27.15 (4) op(e2, e3) = all_52_1
% 157.20/27.15 (5) op(e2, e3) = e2
% 157.20/27.15 (6) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.20/27.15 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3)
% 157.20/27.15 & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 &
% 157.20/27.15 ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.20/27.15 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.15 (8) ~ (e3 = e2)
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | BETA: splitting (6) gives:
% 157.20/27.15 |
% 157.20/27.15 | Case 1:
% 157.20/27.15 | |
% 157.20/27.15 | | (9) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3
% 157.20/27.15 | | & op(e2, e3) = e3
% 157.20/27.15 | |
% 157.20/27.15 | | ALPHA: (9) implies:
% 157.20/27.15 | | (10) op(e2, e3) = e3
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (4), (5), (7), (8), (10) are inconsistent by sub-proof #1159.
% 157.20/27.15 | |
% 157.20/27.15 | Case 2:
% 157.20/27.15 | |
% 157.20/27.15 | | (11) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) =
% 157.20/27.15 | | e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~
% 157.20/27.15 | | (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (1), (2), (3), (7), (8), (11) are inconsistent by sub-proof #292.
% 157.20/27.15 | |
% 157.20/27.15 | End of split
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #287 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 157.20/27.15 (2) ~ (e2 = e0)
% 157.20/27.15 (3) all_54_15 = e2
% 157.20/27.15 (4) all_56_15 = all_4_2
% 157.20/27.15 (5) op(e0, e2) = e2
% 157.20/27.15 (6) op(e0, e2) = all_52_7
% 157.20/27.15 (7) all_54_15 = all_4_2
% 157.20/27.15 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | COMBINE_EQS: (3), (7) imply:
% 157.20/27.15 | (9) all_4_2 = e2
% 157.20/27.15 |
% 157.20/27.15 | SIMP: (9) implies:
% 157.20/27.15 | (10) all_4_2 = e2
% 157.20/27.15 |
% 157.20/27.15 | COMBINE_EQS: (4), (10) imply:
% 157.20/27.15 | (11) all_56_15 = e2
% 157.20/27.15 |
% 157.20/27.15 | REF_CLOSE: (1), (2), (5), (6), (8), (11) are inconsistent by sub-proof #892.
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #288 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) all_54_13 = all_14_0
% 157.20/27.15 (2) all_54_13 = e3
% 157.20/27.15 (3) ~ (all_14_0 = e3)
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | COMBINE_EQS: (1), (2) imply:
% 157.20/27.15 | (4) all_14_0 = e3
% 157.20/27.15 |
% 157.20/27.15 | SIMP: (4) implies:
% 157.20/27.15 | (5) all_14_0 = e3
% 157.20/27.15 |
% 157.20/27.15 | REDUCE: (3), (5) imply:
% 157.20/27.15 | (6) $false
% 157.20/27.15 |
% 157.20/27.15 | CLOSE: (6) is inconsistent.
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #289 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) op(e3, e1) = e2
% 157.20/27.15 (2) all_58_9 = e3
% 157.20/27.15 (3) ~ (e3 = e1)
% 157.20/27.15 (4) ~ (e2 = e1)
% 157.20/27.15 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.15 (6) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | BETA: splitting (6) gives:
% 157.20/27.15 |
% 157.20/27.15 | Case 1:
% 157.20/27.15 | |
% 157.20/27.15 | | (7) all_58_4 = e1 & op(e3, e1) = e1
% 157.20/27.15 | |
% 157.20/27.15 | | ALPHA: (7) implies:
% 157.20/27.15 | | (8) op(e3, e1) = e1
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #338.
% 157.20/27.15 | |
% 157.20/27.15 | Case 2:
% 157.20/27.15 | |
% 157.20/27.15 | | (9) all_58_9 = e1 & op(e3, e0) = e1
% 157.20/27.15 | |
% 157.20/27.15 | | ALPHA: (9) implies:
% 157.20/27.15 | | (10) all_58_9 = e1
% 157.20/27.15 | |
% 157.20/27.15 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #1461.
% 157.20/27.15 | |
% 157.20/27.15 | End of split
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #290 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.20/27.15 (2) all_56_14 = e3
% 157.20/27.15 (3) ~ (all_52_4 = all_52_6)
% 157.20/27.15 (4) all_54_1 = all_52_4
% 157.20/27.15 (5) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.20/27.15 (6) ~ (all_52_4 = e2)
% 157.20/27.15 (7) ~ (all_52_6 = e2)
% 157.20/27.15 (8) ~ (all_52_6 = all_6_2)
% 157.20/27.15 (9) ~ (all_52_4 = e0)
% 157.20/27.15 (10) ~ (all_52_6 = e0)
% 157.20/27.15 (11) ~ (all_52_4 = e3)
% 157.20/27.15 (12) all_56_14 = all_6_2
% 157.20/27.15 (13) all_54_9 = all_52_6
% 157.20/27.15
% 157.20/27.15 Begin of proof
% 157.20/27.15 |
% 157.20/27.15 | COMBINE_EQS: (2), (12) imply:
% 157.20/27.15 | (14) all_6_2 = e3
% 157.20/27.15 |
% 157.20/27.15 | SIMP: (14) implies:
% 157.20/27.15 | (15) all_6_2 = e3
% 157.20/27.15 |
% 157.20/27.15 | REDUCE: (8), (15) imply:
% 157.20/27.15 | (16) ~ (all_52_6 = e3)
% 157.20/27.15 |
% 157.20/27.15 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (13), (16) are
% 157.20/27.15 | inconsistent by sub-proof #1099.
% 157.20/27.15 |
% 157.20/27.15 End of proof
% 157.20/27.15
% 157.20/27.15 Sub-proof #291 shows that the following formulas are inconsistent:
% 157.20/27.15 ----------------------------------------------------------------
% 157.20/27.15 (1) op(e0, e3) = all_52_3
% 157.20/27.15 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.20/27.15 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.20/27.15 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.20/27.15 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.20/27.15 (4) op(e1, e1) = all_6_2
% 157.20/27.15 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.20/27.15 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.20/27.15 (6) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.20/27.15 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.20/27.15 (7) all_54_10 = all_6_2
% 157.20/27.15 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.20/27.15 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.20/27.15 (9) op(e2, e3) = e3
% 157.20/27.15 (10) op(e3, e2) = all_52_4
% 157.20/27.15 (11) ~ (all_52_3 = e0)
% 157.20/27.15 (12) ~ (all_52_4 = e2)
% 157.20/27.15 (13) op(e3, e1) = e2
% 157.20/27.15 (14) op(e2, e1) = all_52_9
% 157.20/27.15 (15) all_58_6 = e2
% 157.20/27.15 (16) ~ (all_52_3 = e3)
% 157.20/27.15 (17) all_56_2 = e3
% 157.20/27.15 (18) ~ (e3 = e0)
% 157.20/27.15 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.20/27.15 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.20/27.15 (20) ~ (e2 = e0)
% 157.20/27.15 (21) ~ (all_52_9 = e3)
% 157.20/27.15 (22) ~ (all_8_2 = e3)
% 157.20/27.15 (23) ~ (all_52_11 = all_6_2)
% 157.20/27.15 (24) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.20/27.15 (25) ~ (all_52_6 = e2)
% 157.20/27.15 (26) ~ (all_52_3 = e2)
% 157.20/27.15 (27) all_58_9 = e3
% 157.20/27.15 (28) op(e2, e0) = all_52_13
% 157.20/27.15 (29) ~ (e3 = e1)
% 157.20/27.15 (30) all_56_13 = e2
% 157.20/27.15 (31) op(e1, e2) = all_52_6
% 157.20/27.15 (32) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.20/27.15 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.20/27.15 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.20/27.15 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.20/27.15 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.20/27.15 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.20/27.15 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.20/27.15 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.20/27.15 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.20/27.15 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.20/27.15 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.20/27.15 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.20/27.15 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.20/27.15 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.20/27.15 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.20/27.15 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.20/27.15 = e0)
% 157.20/27.15 (33) all_58_1 = e1
% 157.20/27.16 (34) ~ (all_52_11 = e2)
% 157.20/27.16 (35) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.20/27.16 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.20/27.16 (36) ~ (all_6_2 = e3)
% 157.20/27.16 (37) ~ (all_52_13 = e2)
% 157.20/27.16 (38) op(e0, e0) = e2
% 157.20/27.16 (39) op(e0, e1) = all_52_11
% 157.20/27.16 (40) ~ (all_52_9 = all_52_11)
% 157.20/27.16 (41) all_58_4 = e2
% 157.20/27.16 (42) ~ (all_52_6 = e1)
% 157.20/27.16 (43) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.20/27.16 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.20/27.16 (44) op(e0, e2) = e0
% 157.20/27.16 (45) ~ (e2 = e1)
% 157.20/27.16 (46) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.20/27.16 (47) ~ (e1 = e0)
% 157.20/27.16 (48) ~ (all_8_2 = e1)
% 157.20/27.16 (49) ~ (all_6_2 = e2)
% 157.20/27.16 (50) all_56_14 = all_6_2
% 157.20/27.16 (51) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.20/27.16 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.20/27.16 (52) all_54_14 = all_52_11
% 157.20/27.16 (53) op(e0, e2) = all_52_7
% 157.20/27.16 (54) all_58_0 = e0
% 157.20/27.16 (55) op(e2, e2) = all_8_2
% 157.20/27.16 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.16 (57) ~ (all_52_3 = all_52_11)
% 157.20/27.16 (58) ~ (e3 = e2)
% 157.20/27.16 (59) ~ (all_52_11 = e0)
% 157.20/27.16 (60) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.20/27.16 (61) all_54_12 = all_52_3
% 157.20/27.16 (62) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.20/27.16 (63) all_58_3 = e2
% 157.20/27.16
% 157.20/27.16 Begin of proof
% 157.20/27.16 |
% 157.20/27.16 | BETA: splitting (6) gives:
% 157.20/27.16 |
% 157.20/27.16 | Case 1:
% 157.20/27.16 | |
% 157.20/27.16 | | (64) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 157.20/27.16 | | e3)
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (13), (14), (21), (56), (58), (64) are inconsistent by sub-proof
% 157.20/27.16 | | #293.
% 157.20/27.16 | |
% 157.20/27.16 | Case 2:
% 157.20/27.16 | |
% 157.20/27.16 | | (65) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 157.20/27.16 | | e3)
% 157.20/27.16 | |
% 157.20/27.16 | | BETA: splitting (65) gives:
% 157.20/27.16 | |
% 157.20/27.16 | | Case 1:
% 157.20/27.16 | | |
% 157.20/27.16 | | | (66) all_58_8 = e3 & op(e1, e1) = e3
% 157.20/27.16 | | |
% 157.20/27.16 | | | REF_CLOSE: (4), (36), (56), (66) are inconsistent by sub-proof #1469.
% 157.20/27.16 | | |
% 157.20/27.16 | | Case 2:
% 157.20/27.16 | | |
% 157.20/27.16 | | | (67) all_58_14 = e3 & op(e0, e1) = e3
% 157.20/27.16 | | |
% 157.20/27.16 | | | ALPHA: (67) implies:
% 157.20/27.16 | | | (68) all_58_14 = e3
% 157.20/27.16 | | |
% 157.20/27.16 | | | BETA: splitting (60) gives:
% 157.20/27.16 | | |
% 157.20/27.16 | | | Case 1:
% 157.20/27.16 | | | |
% 157.20/27.16 | | | | (69) all_54_12 = e3
% 157.20/27.16 | | | |
% 157.20/27.16 | | | | REF_CLOSE: (16), (61), (69) are inconsistent by sub-proof #1234.
% 157.20/27.16 | | | |
% 157.20/27.16 | | | Case 2:
% 157.20/27.16 | | | |
% 157.20/27.16 | | | | (70) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.20/27.16 | | | |
% 157.20/27.16 | | | | BETA: splitting (43) gives:
% 157.20/27.16 | | | |
% 157.20/27.16 | | | | Case 1:
% 157.20/27.16 | | | | |
% 157.20/27.16 | | | | | (71) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2,
% 157.20/27.16 | | | | | e2) = e3)
% 157.20/27.16 | | | | |
% 157.20/27.16 | | | | | BETA: splitting (71) gives:
% 157.20/27.16 | | | | |
% 157.20/27.16 | | | | | Case 1:
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | (72) all_58_2 = e3 & op(e2, e3) = e3
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | ALPHA: (72) implies:
% 157.20/27.16 | | | | | | (73) all_58_2 = e3
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | BETA: splitting (5) gives:
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | Case 1:
% 157.20/27.16 | | | | | | |
% 157.20/27.16 | | | | | | | (74) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 157.20/27.16 | | | | | | | op(e0, e2) = e1)
% 157.20/27.16 | | | | | | |
% 157.20/27.16 | | | | | | | BETA: splitting (74) gives:
% 157.20/27.16 | | | | | | |
% 157.20/27.16 | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | | (75) all_58_12 = e1 & op(e0, e3) = e1
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | | ALPHA: (75) implies:
% 157.20/27.16 | | | | | | | | (76) all_58_12 = e1
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | | BETA: splitting (32) gives:
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | |
% 157.20/27.16 | | | | | | | | | (77) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) &
% 157.20/27.16 | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2
% 157.20/27.16 | | | | | | | | | & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) =
% 157.20/27.16 | | | | | | | | | e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 =
% 157.20/27.16 | | | | | | | | | e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1,
% 157.20/27.16 | | | | | | | | | e3) = e3) | (all_56_1 = e1 & all_56_6 = e1 & ~
% 157.20/27.16 | | | | | | | | | (all_56_12 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 157.20/27.16 | | | | | | | | | e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15
% 157.20/27.16 | | | | | | | | | = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.20/27.16 | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) &
% 157.20/27.16 | | | | | | | | | op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.20/27.16 | | | | | | | | |
% 157.20/27.16 | | | | | | | | | BETA: splitting (77) gives:
% 157.20/27.16 | | | | | | | | |
% 157.20/27.16 | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | (78) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2)
% 157.20/27.16 | | | | | | | | | | & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_0 =
% 157.20/27.16 | | | | | | | | | | e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3,
% 157.20/27.16 | | | | | | | | | | e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 &
% 157.20/27.16 | | | | | | | | | | all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) =
% 157.20/27.16 | | | | | | | | | | e3 & op(e1, e3) = e3)
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | BETA: splitting (78) gives:
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | (79) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.20/27.16 | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | ALPHA: (79) implies:
% 157.20/27.16 | | | | | | | | | | | (80) op(e3, e2) = e3
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | REF_CLOSE: (27), (29), (41), (45), (47), (51), (54), (56),
% 157.20/27.16 | | | | | | | | | | | (80) are inconsistent by sub-proof #1126.
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | (81) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.20/27.16 | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.20/27.16 | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.20/27.16 | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | REF_CLOSE: (10), (12), (13), (56), (58), (81) are
% 157.20/27.16 | | | | | | | | | | | inconsistent by sub-proof #292.
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | (82) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3)
% 157.20/27.16 | | | | | | | | | | & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_2 =
% 157.20/27.16 | | | | | | | | | | e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3,
% 157.20/27.16 | | | | | | | | | | e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 &
% 157.20/27.16 | | | | | | | | | | all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) =
% 157.20/27.16 | | | | | | | | | | e0 & op(e0, e3) = e0)
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | BETA: splitting (82) gives:
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | (83) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.20/27.16 | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | ALPHA: (83) implies:
% 157.20/27.16 | | | | | | | | | | | (84) op(e3, e1) = e1
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | REF_CLOSE: (13), (45), (56), (84) are inconsistent by
% 157.20/27.16 | | | | | | | | | | | sub-proof #338.
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | (85) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.20/27.16 | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.20/27.16 | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.20/27.16 | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | BETA: splitting (85) gives:
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | (86) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.20/27.16 | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | ALPHA: (86) implies:
% 157.20/27.16 | | | | | | | | | | | | (87) op(e0, e3) = e3
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | BETA: splitting (70) gives:
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | (88) all_54_12 = e2
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | REF_CLOSE: (26), (61), (88) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | | | | | | | | #1189.
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | (89) ~ (all_54_12 = e2)
% 157.20/27.16 | | | | | | | | | | | | | (90) all_54_12 = e1 | all_54_12 = e0
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | BETA: splitting (90) gives:
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | (91) all_54_12 = e1
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | COMBINE_EQS: (61), (91) imply:
% 157.20/27.16 | | | | | | | | | | | | | | (92) all_52_3 = e1
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | SIMP: (92) implies:
% 157.20/27.16 | | | | | | | | | | | | | | (93) all_52_3 = e1
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | REDUCE: (57), (93) imply:
% 157.20/27.16 | | | | | | | | | | | | | | (94) ~ (all_52_11 = e1)
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | SIMP: (94) implies:
% 157.20/27.16 | | | | | | | | | | | | | | (95) ~ (all_52_11 = e1)
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | REDUCE: (1), (93) imply:
% 157.20/27.16 | | | | | | | | | | | | | | (96) op(e0, e3) = e1
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | (97) all_54_14 = e3
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | COMBINE_EQS: (52), (97) imply:
% 157.20/27.16 | | | | | | | | | | | | | | | (98) all_52_11 = e3
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | SIMP: (98) implies:
% 157.20/27.16 | | | | | | | | | | | | | | | (99) all_52_11 = e3
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | REDUCE: (23), (99) imply:
% 157.20/27.16 | | | | | | | | | | | | | | | (100) ~ (all_6_2 = e3)
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with e1, e3, e3, e0,
% 157.20/27.16 | | | | | | | | | | | | | | | simplifying with (87), (96) gives:
% 157.20/27.16 | | | | | | | | | | | | | | | (101) e3 = e1
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | COMBINE_EQS: (68), (101) imply:
% 157.20/27.16 | | | | | | | | | | | | | | | (102) all_58_14 = e1
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (14), (26), (29), (34), (36),
% 157.20/27.16 | | | | | | | | | | | | | | | (40), (41), (52), (56), (57), (58), (59), (61),
% 157.20/27.16 | | | | | | | | | | | | | | | (62), (70), (102) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | | | | | | | | | | #1145.
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | (103) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (59), (95), (103) are inconsistent by
% 157.20/27.16 | | | | | | | | | | | | | | | sub-proof #1149.
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | (104) all_54_12 = e0
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | REF_CLOSE: (11), (61), (104) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | | | | | | | | | #1223.
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | (105) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.20/27.16 | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | ALPHA: (105) implies:
% 157.20/27.16 | | | | | | | | | | | | (106) all_56_2 = e0
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | COMBINE_EQS: (17), (106) imply:
% 157.20/27.16 | | | | | | | | | | | | (107) e3 = e0
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | COMBINE_EQS: (73), (107) imply:
% 157.20/27.16 | | | | | | | | | | | | (108) all_58_2 = e0
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | REF_CLOSE: (8), (15), (18), (29), (54), (58), (76), (108) are
% 157.20/27.16 | | | | | | | | | | | | inconsistent by sub-proof #1248.
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | |
% 157.20/27.16 | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | |
% 157.20/27.16 | | | | | | | | | (109) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1)
% 157.20/27.16 | | | | | | | | | & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_4 =
% 157.20/27.16 | | | | | | | | | e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2,
% 157.20/27.16 | | | | | | | | | e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.20/27.16 | | | | | | | | | all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) =
% 157.20/27.16 | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_5 = e0 & all_56_10
% 157.20/27.16 | | | | | | | | | = e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 &
% 157.20/27.16 | | | | | | | | | op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1
% 157.20/27.16 | | | | | | | | | & ~ (all_56_15 = e0) & op(e1, e0) = e1 & op(e0,
% 157.20/27.16 | | | | | | | | | e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~
% 157.20/27.16 | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 157.20/27.16 | | | | | | | | | e0)
% 157.20/27.16 | | | | | | | | |
% 157.20/27.16 | | | | | | | | | BETA: splitting (109) gives:
% 157.20/27.16 | | | | | | | | |
% 157.20/27.16 | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | (110) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.20/27.16 | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.20/27.16 | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.20/27.16 | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.20/27.16 | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.20/27.16 | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | REF_CLOSE: (25), (28), (31), (37), (42), (56), (110) are
% 157.20/27.16 | | | | | | | | | | inconsistent by sub-proof #1128.
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | (111) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.20/27.16 | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.20/27.16 | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.20/27.16 | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.20/27.16 | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.20/27.16 | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | BETA: splitting (111) gives:
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | (112) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.20/27.16 | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | ALPHA: (112) implies:
% 157.20/27.16 | | | | | | | | | | | (113) ~ (all_56_13 = e2)
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | REDUCE: (30), (113) imply:
% 157.20/27.16 | | | | | | | | | | | (114) $false
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | CLOSE: (114) is inconsistent.
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | (115) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.20/27.16 | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.20/27.16 | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.20/27.16 | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | BETA: splitting (115) gives:
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | (116) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.20/27.16 | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | ALPHA: (116) implies:
% 157.20/27.16 | | | | | | | | | | | | (117) op(e0, e1) = e1
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | BETA: splitting (70) gives:
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | (118) all_54_12 = e2
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | REF_CLOSE: (26), (61), (118) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | | | | | | | | #1189.
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | (119) ~ (all_54_12 = e2)
% 157.20/27.16 | | | | | | | | | | | | | (120) all_54_12 = e1 | all_54_12 = e0
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | BETA: splitting (120) gives:
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | (121) all_54_12 = e1
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | COMBINE_EQS: (61), (121) imply:
% 157.20/27.16 | | | | | | | | | | | | | | (122) all_52_3 = e1
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | SIMP: (122) implies:
% 157.20/27.16 | | | | | | | | | | | | | | (123) all_52_3 = e1
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | REDUCE: (57), (123) imply:
% 157.20/27.16 | | | | | | | | | | | | | | (124) ~ (all_52_11 = e1)
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | SIMP: (124) implies:
% 157.20/27.16 | | | | | | | | | | | | | | (125) ~ (all_52_11 = e1)
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | Case 1:
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | (126) all_54_14 = e3
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | COMBINE_EQS: (52), (126) imply:
% 157.20/27.16 | | | | | | | | | | | | | | | (127) all_52_11 = e3
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | SIMP: (127) implies:
% 157.20/27.16 | | | | | | | | | | | | | | | (128) all_52_11 = e3
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | REDUCE: (23), (128) imply:
% 157.20/27.16 | | | | | | | | | | | | | | | (129) ~ (all_6_2 = e3)
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | REDUCE: (39), (128) imply:
% 157.20/27.16 | | | | | | | | | | | | | | | (130) op(e0, e1) = e3
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with e1, e3, e1, e0,
% 157.20/27.16 | | | | | | | | | | | | | | | simplifying with (117), (130) gives:
% 157.20/27.16 | | | | | | | | | | | | | | | (131) e3 = e1
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | COMBINE_EQS: (68), (131) imply:
% 157.20/27.16 | | | | | | | | | | | | | | | (132) all_58_14 = e1
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (14), (26), (29), (34), (36),
% 157.20/27.16 | | | | | | | | | | | | | | | (40), (41), (52), (56), (57), (58), (59), (61),
% 157.20/27.16 | | | | | | | | | | | | | | | (62), (70), (132) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | | | | | | | | | | #1145.
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | (133) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (59), (125), (133) are inconsistent by
% 157.20/27.16 | | | | | | | | | | | | | | | sub-proof #1149.
% 157.20/27.16 | | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | (134) all_54_12 = e0
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | | REF_CLOSE: (11), (61), (134) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | | | | | | | | | #1223.
% 157.20/27.16 | | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | (135) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.20/27.16 | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | | REF_CLOSE: (2), (7), (24), (31), (33), (36), (42), (44),
% 157.20/27.16 | | | | | | | | | | | | (46), (47), (48), (49), (50), (53), (55), (56),
% 157.20/27.16 | | | | | | | | | | | | (135) are inconsistent by sub-proof #1102.
% 157.20/27.16 | | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | | |
% 157.20/27.16 | | | | | | | | | End of split
% 157.20/27.16 | | | | | | | | |
% 157.20/27.16 | | | | | | | | End of split
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | Case 2:
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | | (136) all_58_13 = e1 & op(e0, e2) = e1
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | | ALPHA: (136) implies:
% 157.20/27.16 | | | | | | | | (137) op(e0, e2) = e1
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | | REF_CLOSE: (44), (47), (53), (56), (137) are inconsistent by
% 157.20/27.16 | | | | | | | | sub-proof #1396.
% 157.20/27.16 | | | | | | | |
% 157.20/27.16 | | | | | | | End of split
% 157.20/27.16 | | | | | | |
% 157.20/27.16 | | | | | | Case 2:
% 157.20/27.16 | | | | | | |
% 157.20/27.16 | | | | | | | (138) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 157.20/27.16 | | | | | | | op(e0, e0) = e1)
% 157.20/27.16 | | | | | | |
% 157.20/27.16 | | | | | | | REF_CLOSE: (4), (6), (11), (14), (26), (29), (34), (36), (38),
% 157.20/27.16 | | | | | | | (40), (41), (45), (52), (56), (57), (58), (59), (61),
% 157.20/27.16 | | | | | | | (62), (70), (138) are inconsistent by sub-proof #1144.
% 157.20/27.16 | | | | | | |
% 157.20/27.16 | | | | | | End of split
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | Case 2:
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | (139) all_58_3 = e3 & op(e2, e2) = e3
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | REF_CLOSE: (22), (55), (56), (139) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | #1437.
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | End of split
% 157.20/27.16 | | | | |
% 157.20/27.16 | | | | Case 2:
% 157.20/27.16 | | | | |
% 157.20/27.16 | | | | | (140) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2,
% 157.20/27.16 | | | | | e0) = e3)
% 157.20/27.16 | | | | |
% 157.20/27.16 | | | | | BETA: splitting (140) gives:
% 157.20/27.16 | | | | |
% 157.20/27.16 | | | | | Case 1:
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | (141) all_58_5 = e3 & op(e2, e1) = e3
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | REF_CLOSE: (11), (14), (26), (34), (40), (52), (56), (57), (59),
% 157.20/27.16 | | | | | | (61), (62), (70), (141) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | #1148.
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | Case 2:
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | (142) all_58_10 = e3 & op(e2, e0) = e3
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (11), (14), (15),
% 157.20/27.16 | | | | | | (18), (19), (20), (26), (29), (31), (33), (34), (35),
% 157.20/27.16 | | | | | | (36), (38), (40), (41), (42), (44), (45), (47), (48),
% 157.20/27.16 | | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (61),
% 157.20/27.16 | | | | | | (62), (63), (70), (142) are inconsistent by sub-proof
% 157.20/27.16 | | | | | | #1117.
% 157.20/27.16 | | | | | |
% 157.20/27.16 | | | | | End of split
% 157.20/27.16 | | | | |
% 157.20/27.16 | | | | End of split
% 157.20/27.16 | | | |
% 157.20/27.16 | | | End of split
% 157.20/27.16 | | |
% 157.20/27.16 | | End of split
% 157.20/27.16 | |
% 157.20/27.16 | End of split
% 157.20/27.16 |
% 157.20/27.16 End of proof
% 157.20/27.16
% 157.20/27.16 Sub-proof #292 shows that the following formulas are inconsistent:
% 157.20/27.16 ----------------------------------------------------------------
% 157.20/27.16 (1) op(e3, e2) = all_52_4
% 157.20/27.16 (2) ~ (all_52_4 = e2)
% 157.20/27.16 (3) op(e3, e1) = e2
% 157.20/27.16 (4) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 &
% 157.20/27.16 op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1)
% 157.20/27.16 & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.20/27.16 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.16 (6) ~ (e3 = e2)
% 157.20/27.16
% 157.20/27.16 Begin of proof
% 157.20/27.16 |
% 157.20/27.16 | BETA: splitting (4) gives:
% 157.20/27.16 |
% 157.20/27.16 | Case 1:
% 157.20/27.16 | |
% 157.20/27.16 | | (7) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2
% 157.20/27.16 | | & op(e2, e3) = e2
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (7) implies:
% 157.20/27.16 | | (8) op(e3, e2) = e2
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1539.
% 157.20/27.16 | |
% 157.20/27.16 | Case 2:
% 157.20/27.16 | |
% 157.20/27.16 | | (9) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3
% 157.20/27.16 | | & op(e1, e3) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (9) implies:
% 157.20/27.16 | | (10) op(e3, e1) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1502.
% 157.20/27.16 | |
% 157.20/27.16 | End of split
% 157.20/27.16 |
% 157.20/27.16 End of proof
% 157.20/27.16
% 157.20/27.16 Sub-proof #293 shows that the following formulas are inconsistent:
% 157.20/27.16 ----------------------------------------------------------------
% 157.20/27.16 (1) op(e3, e1) = e2
% 157.20/27.16 (2) op(e2, e1) = all_52_9
% 157.20/27.16 (3) ~ (all_52_9 = e3)
% 157.20/27.16 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 157.20/27.16 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.16 (6) ~ (e3 = e2)
% 157.20/27.16
% 157.20/27.16 Begin of proof
% 157.20/27.16 |
% 157.20/27.16 | BETA: splitting (4) gives:
% 157.20/27.16 |
% 157.20/27.16 | Case 1:
% 157.20/27.16 | |
% 157.20/27.16 | | (7) all_58_4 = e3 & op(e3, e1) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (7) implies:
% 157.20/27.16 | | (8) op(e3, e1) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1502.
% 157.20/27.16 | |
% 157.20/27.16 | Case 2:
% 157.20/27.16 | |
% 157.20/27.16 | | (9) all_58_5 = e3 & op(e2, e1) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (9) implies:
% 157.20/27.16 | | (10) op(e2, e1) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #1196.
% 157.20/27.16 | |
% 157.20/27.16 | End of split
% 157.20/27.16 |
% 157.20/27.16 End of proof
% 157.20/27.16
% 157.20/27.16 Sub-proof #294 shows that the following formulas are inconsistent:
% 157.20/27.16 ----------------------------------------------------------------
% 157.20/27.16 (1) all_58_9 = e3
% 157.20/27.16 (2) op(e2, e0) = all_52_13
% 157.20/27.16 (3) ~ (all_52_13 = e2)
% 157.20/27.16 (4) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.20/27.16 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.16 (6) ~ (e3 = e2)
% 157.20/27.16
% 157.20/27.16 Begin of proof
% 157.20/27.16 |
% 157.20/27.16 | BETA: splitting (4) gives:
% 157.20/27.16 |
% 157.20/27.16 | Case 1:
% 157.20/27.16 | |
% 157.20/27.16 | | (7) all_58_9 = e2 & op(e3, e0) = e2
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (7) implies:
% 157.20/27.16 | | (8) all_58_9 = e2
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #1245.
% 157.20/27.16 | |
% 157.20/27.16 | Case 2:
% 157.20/27.16 | |
% 157.20/27.16 | | (9) all_58_10 = e2 & op(e2, e0) = e2
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (9) implies:
% 157.20/27.16 | | (10) op(e2, e0) = e2
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #1535.
% 157.20/27.16 | |
% 157.20/27.16 | End of split
% 157.20/27.16 |
% 157.20/27.16 End of proof
% 157.20/27.16
% 157.20/27.16 Sub-proof #295 shows that the following formulas are inconsistent:
% 157.20/27.16 ----------------------------------------------------------------
% 157.20/27.16 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.20/27.16 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.20/27.16 (2) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.20/27.16 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.20/27.16 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.20/27.16 (4) ~ (all_4_2 = e2)
% 157.20/27.16 (5) op(e2, e1) = all_52_9
% 157.20/27.16 (6) ~ (all_52_9 = e3)
% 157.20/27.16 (7) all_58_9 = e3
% 157.20/27.16 (8) ~ (e3 = e1)
% 157.20/27.16 (9) ~ (all_4_2 = e1)
% 157.20/27.16 (10) op(e0, e0) = all_4_2
% 157.20/27.16 (11) ~ (e2 = e1)
% 157.20/27.16 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.16 (13) ~ (e3 = e2)
% 157.20/27.16
% 157.20/27.16 Begin of proof
% 157.20/27.16 |
% 157.20/27.16 | BETA: splitting (2) gives:
% 157.20/27.16 |
% 157.20/27.16 | Case 1:
% 157.20/27.16 | |
% 157.20/27.16 | | (14) all_58_5 = e3 & op(e2, e1) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (14) implies:
% 157.20/27.16 | | (15) op(e2, e1) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (5), (6), (12), (15) are inconsistent by sub-proof #1196.
% 157.20/27.16 | |
% 157.20/27.16 | Case 2:
% 157.20/27.16 | |
% 157.20/27.16 | | (16) all_58_10 = e3 & op(e2, e0) = e3
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (16) are
% 157.20/27.16 | | inconsistent by sub-proof #331.
% 157.20/27.16 | |
% 157.20/27.16 | End of split
% 157.20/27.16 |
% 157.20/27.16 End of proof
% 157.20/27.16
% 157.20/27.16 Sub-proof #296 shows that the following formulas are inconsistent:
% 157.20/27.16 ----------------------------------------------------------------
% 157.20/27.16 (1) op(e1, e1) = e3
% 157.20/27.16 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.20/27.16 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.20/27.16 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.20/27.16 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.20/27.16 (4) ~ (e3 = e0)
% 157.20/27.16 (5) ~ (e2 = e0)
% 157.20/27.16 (6) all_58_9 = e3
% 157.20/27.16 (7) ~ (e3 = e1)
% 157.20/27.16 (8) ~ (all_4_2 = e1)
% 157.20/27.16 (9) ~ (all_24_1 = e2)
% 157.20/27.16 (10) op(e0, e0) = all_4_2
% 157.20/27.16 (11) ~ (e2 = e1)
% 157.20/27.16 (12) ~ (e1 = e0)
% 157.20/27.16 (13) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.20/27.16 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.16 (15) ~ (e3 = e2)
% 157.20/27.16 (16) op(e0, e0) = all_24_1
% 157.20/27.16
% 157.20/27.16 Begin of proof
% 157.20/27.16 |
% 157.20/27.16 | BETA: splitting (13) gives:
% 157.20/27.16 |
% 157.20/27.16 | Case 1:
% 157.20/27.16 | |
% 157.20/27.16 | | (17) all_58_8 = e0 & op(e1, e1) = e0
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (17) implies:
% 157.20/27.16 | | (18) op(e1, e1) = e0
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (1), (4), (14), (18) are inconsistent by sub-proof #1466.
% 157.20/27.16 | |
% 157.20/27.16 | Case 2:
% 157.20/27.16 | |
% 157.20/27.16 | | (19) all_58_11 = e0 & op(e1, e0) = e0
% 157.20/27.16 | |
% 157.20/27.16 | | ALPHA: (19) implies:
% 157.20/27.16 | | (20) all_58_11 = e0
% 157.20/27.16 | |
% 157.20/27.16 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 157.20/27.16 | | (16), (20) are inconsistent by sub-proof #305.
% 157.20/27.16 | |
% 157.20/27.16 | End of split
% 157.20/27.16 |
% 157.20/27.16 End of proof
% 157.20/27.16
% 157.20/27.16 Sub-proof #297 shows that the following formulas are inconsistent:
% 157.20/27.16 ----------------------------------------------------------------
% 157.20/27.16 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.20/27.16 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.20/27.16 (2) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.20/27.16 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.20/27.16 (3) all_58_8 = e3
% 157.20/27.17 (4) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.20/27.17 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.20/27.17 (5) ~ (e3 = e0)
% 157.20/27.17 (6) ~ (e2 = e0)
% 157.20/27.17 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.20/27.17 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.20/27.17 (8) all_58_9 = e3
% 157.20/27.17 (9) ~ (e3 = e1)
% 157.20/27.17 (10) op(e1, e2) = all_52_6
% 157.20/27.17 (11) all_58_10 = e1
% 157.20/27.17 (12) e3 = e1
% 157.20/27.17 (13) all_58_11 = e2
% 157.20/27.17 (14) ~ (e2 = e1)
% 157.20/27.17 (15) ~ (e1 = e0)
% 157.20/27.17 (16) ~ (all_52_6 = e3)
% 157.20/27.17 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (18) ~ (e3 = e2)
% 157.20/27.17 (19) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.20/27.17 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.20/27.17 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.20/27.17 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | SIMP: (12) implies:
% 157.20/27.17 | (20) e3 = e1
% 157.20/27.17 |
% 157.20/27.17 | COMBINE_EQS: (8), (20) imply:
% 157.20/27.17 | (21) all_58_9 = e1
% 157.20/27.17 |
% 157.20/27.17 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 157.20/27.17 | (15), (16), (17), (18), (19), (21) are inconsistent by sub-proof
% 157.20/27.17 | #932.
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #298 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.20/27.17 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.20/27.17 (2) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.20/27.17 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.20/27.17 (3) all_58_8 = e3
% 157.20/27.17 (4) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.20/27.17 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.20/27.17 (5) op(e3, e1) = e2
% 157.20/27.17 (6) ~ (e3 = e0)
% 157.20/27.17 (7) ~ (e2 = e0)
% 157.20/27.17 (8) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.20/27.17 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.20/27.17 (9) all_58_9 = e3
% 157.20/27.17 (10) ~ (e3 = e1)
% 157.20/27.17 (11) op(e1, e2) = all_52_6
% 157.20/27.17 (12) all_58_10 = e1
% 157.20/27.17 (13) all_58_5 = e0
% 157.20/27.17 (14) op(e0, e1) = e2
% 157.20/27.17 (15) op(e0, e1) = all_52_11
% 157.20/27.17 (16) all_58_11 = e2
% 157.20/27.17 (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.20/27.17 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.20/27.17 (18) ~ (e2 = e1)
% 157.20/27.17 (19) ~ (e1 = e0)
% 157.20/27.17 (20) ~ (all_52_6 = e3)
% 157.20/27.17 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (22) ~ (e3 = e2)
% 157.20/27.17 (23) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.20/27.17 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.20/27.17 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.20/27.17 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (17) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (24) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 157.20/27.17 | | e1)
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (5), (13), (18), (19), (21), (24) are inconsistent by sub-proof
% 157.20/27.17 | | #299.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (25) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 157.20/27.17 | | e1)
% 157.20/27.17 | |
% 157.20/27.17 | | BETA: splitting (25) gives:
% 157.20/27.17 | |
% 157.20/27.17 | | Case 1:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (26) all_58_8 = e1 & op(e1, e1) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | ALPHA: (26) implies:
% 157.20/27.17 | | | (27) all_58_8 = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | COMBINE_EQS: (3), (27) imply:
% 157.20/27.17 | | | (28) e3 = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | COMBINE_EQS: (9), (28) imply:
% 157.20/27.17 | | | (29) all_58_9 = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (16),
% 157.20/27.17 | | | (18), (19), (20), (21), (22), (23), (29) are inconsistent by
% 157.20/27.17 | | | sub-proof #932.
% 157.20/27.17 | | |
% 157.20/27.17 | | Case 2:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (30) all_58_14 = e1 & op(e0, e1) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | ALPHA: (30) implies:
% 157.20/27.17 | | | (31) op(e0, e1) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (14), (15), (18), (21), (31) are inconsistent by sub-proof
% 157.20/27.17 | | | #1473.
% 157.20/27.17 | | |
% 157.20/27.17 | | End of split
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #299 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) op(e3, e1) = e2
% 157.20/27.17 (2) all_58_5 = e0
% 157.20/27.17 (3) ~ (e2 = e1)
% 157.20/27.17 (4) ~ (e1 = e0)
% 157.20/27.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (6) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (6) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (7) all_58_4 = e1 & op(e3, e1) = e1
% 157.20/27.17 | |
% 157.20/27.17 | | ALPHA: (7) implies:
% 157.20/27.17 | | (8) op(e3, e1) = e1
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #338.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (9) all_58_5 = e1 & op(e2, e1) = e1
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1121.
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #300 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) op(e1, e3) = all_52_2
% 157.20/27.17 (2) ~ (e3 = e1)
% 157.20/27.17 (3) op(e1, e2) = all_52_6
% 157.20/27.17 (4) op(e1, e3) = e1
% 157.20/27.17 (5) ~ (all_52_6 = e3)
% 157.20/27.17 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (7) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (8) all_58_6 = e3 & op(e1, e3) = e3
% 157.20/27.17 | |
% 157.20/27.17 | | ALPHA: (8) implies:
% 157.20/27.17 | | (9) op(e1, e3) = e3
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (1), (2), (4), (6), (9) are inconsistent by sub-proof #1164.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (10) all_58_7 = e3 & op(e1, e2) = e3
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1184.
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #301 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) all_58_9 = e3
% 157.20/27.17 (2) all_58_10 = e1
% 157.20/27.17 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.20/27.17 (4) ~ (e2 = e1)
% 157.20/27.17 (5) ~ (e3 = e2)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (3) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (6) all_58_9 = e2 & op(e3, e0) = e2
% 157.20/27.17 | |
% 157.20/27.17 | | ALPHA: (6) implies:
% 157.20/27.17 | | (7) all_58_9 = e2
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #1245.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (8) all_58_10 = e2 & op(e2, e0) = e2
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #307.
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #302 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) op(e0, e3) = all_10_0
% 157.20/27.17 (2) op(e2, e3) = e3
% 157.20/27.17 (3) ~ (all_10_0 = e2)
% 157.20/27.17 (4) op(e2, e3) = all_52_1
% 157.20/27.17 (5) all_58_6 = e2
% 157.20/27.17 (6) ~ (e2 = e0)
% 157.20/27.17 (7) e2 = e0
% 157.20/27.17 (8) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 157.20/27.17 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 157.20/27.17 (9) all_58_0 = e0
% 157.20/27.17 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (11) ~ (e3 = e2)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | SIMP: (7) implies:
% 157.20/27.17 | (12) e2 = e0
% 157.20/27.17 |
% 157.20/27.17 | COMBINE_EQS: (5), (12) imply:
% 157.20/27.17 | (13) all_58_6 = e0
% 157.20/27.17 |
% 157.20/27.17 | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (13) are
% 157.20/27.17 | inconsistent by sub-proof #303.
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #303 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) op(e0, e3) = all_10_0
% 157.20/27.17 (2) op(e2, e3) = e3
% 157.20/27.17 (3) ~ (all_10_0 = e2)
% 157.20/27.17 (4) op(e2, e3) = all_52_1
% 157.20/27.17 (5) ~ (e2 = e0)
% 157.20/27.17 (6) all_58_6 = e0
% 157.20/27.17 (7) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 157.20/27.17 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 157.20/27.17 (8) all_58_0 = e0
% 157.20/27.17 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (10) ~ (e3 = e2)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (7) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (11) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 157.20/27.17 | | e2)
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11) are inconsistent by sub-proof
% 157.20/27.17 | | #304.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (12) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 157.20/27.17 | | e2)
% 157.20/27.17 | |
% 157.20/27.17 | | BETA: splitting (12) gives:
% 157.20/27.17 | |
% 157.20/27.17 | | Case 1:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (13) all_58_6 = e2 & op(e1, e3) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (5), (6), (13) are inconsistent by sub-proof #345.
% 157.20/27.17 | | |
% 157.20/27.17 | | Case 2:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (14) all_58_12 = e2 & op(e0, e3) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (1), (3), (9), (14) are inconsistent by sub-proof #344.
% 157.20/27.17 | | |
% 157.20/27.17 | | End of split
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #304 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 157.20/27.17 (2) op(e2, e3) = e3
% 157.20/27.17 (3) op(e2, e3) = all_52_1
% 157.20/27.17 (4) ~ (e2 = e0)
% 157.20/27.17 (5) all_58_0 = e0
% 157.20/27.17 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (7) ~ (e3 = e2)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (1) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (8) all_58_0 = e2 & op(e3, e3) = e2
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #702.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (9) all_58_2 = e2 & op(e2, e3) = e2
% 157.20/27.17 | |
% 157.20/27.17 | | ALPHA: (9) implies:
% 157.20/27.17 | | (10) op(e2, e3) = e2
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (2), (3), (6), (7), (10) are inconsistent by sub-proof #1159.
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #305 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.20/27.17 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.20/27.17 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.20/27.17 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.20/27.17 (3) ~ (e2 = e0)
% 157.20/27.17 (4) all_58_9 = e3
% 157.20/27.17 (5) ~ (e3 = e1)
% 157.20/27.17 (6) ~ (all_4_2 = e1)
% 157.20/27.17 (7) ~ (all_24_1 = e2)
% 157.20/27.17 (8) op(e0, e0) = all_4_2
% 157.20/27.17 (9) ~ (e2 = e1)
% 157.20/27.17 (10) ~ (e1 = e0)
% 157.20/27.17 (11) all_58_11 = e0
% 157.20/27.17 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (13) ~ (e3 = e2)
% 157.20/27.17 (14) op(e0, e0) = all_24_1
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (1) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (15) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.20/27.17 | | e1)
% 157.20/27.17 | |
% 157.20/27.17 | | BETA: splitting (15) gives:
% 157.20/27.17 | |
% 157.20/27.17 | | Case 1:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (16) all_58_9 = e1 & op(e3, e0) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (4), (5), (16) are inconsistent by sub-proof #1078.
% 157.20/27.17 | | |
% 157.20/27.17 | | Case 2:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (17) all_58_10 = e1 & op(e2, e0) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | ALPHA: (17) implies:
% 157.20/27.17 | | | (18) all_58_10 = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (2), (3), (4), (7), (9), (11), (12), (13), (14), (18) are
% 157.20/27.17 | | | inconsistent by sub-proof #306.
% 157.20/27.17 | | |
% 157.20/27.17 | | End of split
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (19) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.20/27.17 | | e1)
% 157.20/27.17 | |
% 157.20/27.17 | | BETA: splitting (19) gives:
% 157.20/27.17 | |
% 157.20/27.17 | | Case 1:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (20) all_58_11 = e1 & op(e1, e0) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (10), (11), (20) are inconsistent by sub-proof #459.
% 157.20/27.17 | | |
% 157.20/27.17 | | Case 2:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (21) all_58_15 = e1 & op(e0, e0) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (6), (8), (12), (21) are inconsistent by sub-proof #1418.
% 157.20/27.17 | | |
% 157.20/27.17 | | End of split
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #306 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.20/27.17 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.20/27.17 (2) ~ (e2 = e0)
% 157.20/27.17 (3) all_58_9 = e3
% 157.20/27.17 (4) ~ (all_24_1 = e2)
% 157.20/27.17 (5) all_58_10 = e1
% 157.20/27.17 (6) ~ (e2 = e1)
% 157.20/27.17 (7) all_58_11 = e0
% 157.20/27.17 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (9) ~ (e3 = e2)
% 157.20/27.17 (10) op(e0, e0) = all_24_1
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (1) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 157.20/27.17 | | e2)
% 157.20/27.17 | |
% 157.20/27.17 | | BETA: splitting (11) gives:
% 157.20/27.17 | |
% 157.20/27.17 | | Case 1:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (12) all_58_9 = e2 & op(e3, e0) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (3), (9), (12) are inconsistent by sub-proof #1353.
% 157.20/27.17 | | |
% 157.20/27.17 | | Case 2:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (13) all_58_10 = e2 & op(e2, e0) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (5), (6), (13) are inconsistent by sub-proof #307.
% 157.20/27.17 | | |
% 157.20/27.17 | | End of split
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (14) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.20/27.17 | | e2)
% 157.20/27.17 | |
% 157.20/27.17 | | BETA: splitting (14) gives:
% 157.20/27.17 | |
% 157.20/27.17 | | Case 1:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (15) all_58_11 = e2 & op(e1, e0) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (2), (7), (15) are inconsistent by sub-proof #507.
% 157.20/27.17 | | |
% 157.20/27.17 | | Case 2:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (16) all_58_15 = e2 & op(e0, e0) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | ALPHA: (16) implies:
% 157.20/27.17 | | | (17) op(e0, e0) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (4), (8), (10), (17) are inconsistent by sub-proof #317.
% 157.20/27.17 | | |
% 157.20/27.17 | | End of split
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #307 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) all_58_10 = e2 & op(e2, e0) = e2
% 157.20/27.17 (2) all_58_10 = e1
% 157.20/27.17 (3) ~ (e2 = e1)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | ALPHA: (1) implies:
% 157.20/27.17 | (4) all_58_10 = e2
% 157.20/27.17 |
% 157.20/27.17 | COMBINE_EQS: (2), (4) imply:
% 157.20/27.17 | (5) e2 = e1
% 157.20/27.17 |
% 157.20/27.17 | REDUCE: (3), (5) imply:
% 157.20/27.17 | (6) $false
% 157.20/27.17 |
% 157.20/27.17 | CLOSE: (6) is inconsistent.
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #308 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) op(e2, e1) = all_52_9
% 157.20/27.17 (2) all_56_15 = e0
% 157.20/27.17 (3) op(e1, e2) = all_52_6
% 157.20/27.17 (4) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.20/27.17 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2)
% 157.20/27.17 & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2
% 157.20/27.17 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.20/27.17 (5) ~ (all_52_6 = e1)
% 157.20/27.17 (6) ~ (all_52_9 = e2)
% 157.20/27.17 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (4) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (8) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2
% 157.20/27.17 | | & op(e1, e2) = e2
% 157.20/27.17 | |
% 157.20/27.17 | | ALPHA: (8) implies:
% 157.20/27.17 | | (9) op(e2, e1) = e2
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (1), (6), (7), (9) are inconsistent by sub-proof #1441.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (10) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) =
% 157.20/27.17 | | e1 & op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~
% 157.20/27.17 | | (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.20/27.17 | |
% 157.20/27.17 | | BETA: splitting (10) gives:
% 157.20/27.17 | |
% 157.20/27.17 | | Case 1:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (11) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) =
% 157.20/27.17 | | | e1 & op(e1, e2) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | ALPHA: (11) implies:
% 157.20/27.17 | | | (12) op(e1, e2) = e1
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (3), (5), (7), (12) are inconsistent by sub-proof #1166.
% 157.20/27.17 | | |
% 157.20/27.17 | | Case 2:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (13) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0)
% 157.20/27.17 | | | = e2 & op(e0, e2) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | ALPHA: (13) implies:
% 157.20/27.17 | | | (14) ~ (all_56_15 = e0)
% 157.20/27.17 | | |
% 157.20/27.17 | | | REDUCE: (2), (14) imply:
% 157.20/27.17 | | | (15) $false
% 157.20/27.17 | | |
% 157.20/27.17 | | | CLOSE: (15) is inconsistent.
% 157.20/27.17 | | |
% 157.20/27.17 | | End of split
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #309 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 &
% 157.20/27.17 op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3)
% 157.20/27.17 & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.20/27.17 (2) all_56_15 = e0
% 157.20/27.17 (3) all_56_2 = e3
% 157.20/27.17 (4) ~ (e3 = e0)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (1) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (5) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3
% 157.20/27.17 | | & op(e0, e3) = e3
% 157.20/27.17 | |
% 157.20/27.17 | | ALPHA: (5) implies:
% 157.20/27.17 | | (6) ~ (all_56_15 = e0)
% 157.20/27.17 | |
% 157.20/27.17 | | REDUCE: (2), (6) imply:
% 157.20/27.17 | | (7) $false
% 157.20/27.17 | |
% 157.20/27.17 | | CLOSE: (7) is inconsistent.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (8) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0
% 157.20/27.17 | | & op(e0, e3) = e0
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #310.
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #310 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 &
% 157.20/27.17 op(e0, e3) = e0
% 157.20/27.17 (2) all_56_2 = e3
% 157.20/27.17 (3) ~ (e3 = e0)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | ALPHA: (1) implies:
% 157.20/27.17 | (4) all_56_2 = e0
% 157.20/27.17 |
% 157.20/27.17 | COMBINE_EQS: (2), (4) imply:
% 157.20/27.17 | (5) e3 = e0
% 157.20/27.17 |
% 157.20/27.17 | REDUCE: (3), (5) imply:
% 157.20/27.17 | (6) $false
% 157.20/27.17 |
% 157.20/27.17 | CLOSE: (6) is inconsistent.
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #311 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.20/27.17 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.20/27.17 (2) op(e3, e2) = all_52_4
% 157.20/27.17 (3) op(e2, e3) = all_52_1
% 157.20/27.17 (4) all_58_10 = e2
% 157.20/27.17 (5) ~ (e3 = e0)
% 157.20/27.17 (6) ~ (e2 = e0)
% 157.20/27.17 (7) ~ (e3 = e1)
% 157.20/27.17 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.20/27.17 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.20/27.17 (9) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.20/27.17 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.20/27.17 (10) ~ (all_52_4 = e3)
% 157.20/27.17 (11) ~ (e2 = e1)
% 157.20/27.17 (12) ~ (e1 = e0)
% 157.20/27.17 (13) ~ (all_8_2 = e1)
% 157.20/27.17 (14) op(e3, e1) = all_52_8
% 157.20/27.17 (15) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.20/27.17 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.20/27.17 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.20/27.17 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.20/27.17 (16) ~ (all_52_8 = e3)
% 157.20/27.17 (17) op(e2, e2) = all_8_2
% 157.20/27.17 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (19) ~ (e3 = e2)
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (15) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (20) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) =
% 157.20/27.17 | | e3 & op(e2, e3) = e3
% 157.20/27.17 | |
% 157.20/27.17 | | ALPHA: (20) implies:
% 157.20/27.17 | | (21) op(e3, e2) = e3
% 157.20/27.17 | |
% 157.20/27.17 | | REF_CLOSE: (2), (10), (18), (21) are inconsistent by sub-proof #1540.
% 157.20/27.17 | |
% 157.20/27.17 | Case 2:
% 157.20/27.17 | |
% 157.20/27.17 | | (22) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) =
% 157.20/27.17 | | e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6 = e3 & ~
% 157.20/27.17 | | (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.20/27.17 | |
% 157.20/27.17 | | BETA: splitting (22) gives:
% 157.20/27.17 | |
% 157.20/27.17 | | Case 1:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (23) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) & op(e3, e2) =
% 157.20/27.17 | | | e2 & op(e2, e3) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | ALPHA: (23) implies:
% 157.20/27.17 | | | (24) op(e2, e3) = e2
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (17),
% 157.20/27.17 | | | (18), (19), (24) are inconsistent by sub-proof #905.
% 157.20/27.17 | | |
% 157.20/27.17 | | Case 2:
% 157.20/27.17 | | |
% 157.20/27.17 | | | (25) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) =
% 157.20/27.17 | | | e3 & op(e1, e3) = e3
% 157.20/27.17 | | |
% 157.20/27.17 | | | ALPHA: (25) implies:
% 157.20/27.17 | | | (26) op(e3, e1) = e3
% 157.20/27.17 | | |
% 157.20/27.17 | | | REF_CLOSE: (14), (16), (18), (26) are inconsistent by sub-proof #1538.
% 157.20/27.17 | | |
% 157.20/27.17 | | End of split
% 157.20/27.17 | |
% 157.20/27.17 | End of split
% 157.20/27.17 |
% 157.20/27.17 End of proof
% 157.20/27.17
% 157.20/27.17 Sub-proof #312 shows that the following formulas are inconsistent:
% 157.20/27.17 ----------------------------------------------------------------
% 157.20/27.17 (1) ~ (e2 = e0)
% 157.20/27.17 (2) ~ (all_24_1 = e2)
% 157.20/27.17 (3) op(e0, e1) = all_52_11
% 157.20/27.17 (4) op(e0, e1) = e0
% 157.20/27.17 (5) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.20/27.17 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.17 (7) op(e0, e0) = all_24_1
% 157.20/27.17
% 157.20/27.17 Begin of proof
% 157.20/27.17 |
% 157.20/27.17 | BETA: splitting (5) gives:
% 157.20/27.17 |
% 157.20/27.17 | Case 1:
% 157.20/27.17 | |
% 157.20/27.17 | | (8) all_58_14 = e2 & op(e0, e1) = e2
% 157.20/27.17 | |
% 157.20/27.17 | | ALPHA: (8) implies:
% 157.20/27.18 | | (9) op(e0, e1) = e2
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (1), (3), (4), (6), (9) are inconsistent by sub-proof #1372.
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (10) all_58_15 = e2 & op(e0, e0) = e2
% 157.20/27.18 | |
% 157.20/27.18 | | ALPHA: (10) implies:
% 157.20/27.18 | | (11) op(e0, e0) = e2
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (2), (6), (7), (11) are inconsistent by sub-proof #317.
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #313 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) op(e0, e0) = all_10_1
% 157.20/27.18 (2) ~ (e3 = e0)
% 157.20/27.18 (3) op(e0, e0) = e0
% 157.20/27.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18 (5) op(e0, e0) = e3
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | GROUND_INST: instantiating (4) with e3, all_10_1, e0, e0, simplifying with
% 157.20/27.18 | (1), (5) gives:
% 157.20/27.18 | (6) all_10_1 = e3
% 157.20/27.18 |
% 157.20/27.18 | GROUND_INST: instantiating (4) with e0, all_10_1, e0, e0, simplifying with
% 157.20/27.18 | (1), (3) gives:
% 157.20/27.18 | (7) all_10_1 = e0
% 157.20/27.18 |
% 157.20/27.18 | COMBINE_EQS: (6), (7) imply:
% 157.20/27.18 | (8) e3 = e0
% 157.20/27.18 |
% 157.20/27.18 | SIMP: (8) implies:
% 157.20/27.18 | (9) e3 = e0
% 157.20/27.18 |
% 157.20/27.18 | REDUCE: (2), (9) imply:
% 157.20/27.18 | (10) $false
% 157.20/27.18 |
% 157.20/27.18 | CLOSE: (10) is inconsistent.
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #314 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) all_58_14 = e3 & op(e0, e1) = e3
% 157.20/27.18 (2) all_58_14 = e0
% 157.20/27.18 (3) ~ (e3 = e0)
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | ALPHA: (1) implies:
% 157.20/27.18 | (4) all_58_14 = e3
% 157.20/27.18 |
% 157.20/27.18 | COMBINE_EQS: (2), (4) imply:
% 157.20/27.18 | (5) e3 = e0
% 157.20/27.18 |
% 157.20/27.18 | REDUCE: (3), (5) imply:
% 157.20/27.18 | (6) $false
% 157.20/27.18 |
% 157.20/27.18 | CLOSE: (6) is inconsistent.
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #315 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) op(e2, e1) = all_52_9
% 157.20/27.18 (2) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.20/27.18 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.20/27.18 (3) ~ (e2 = e0)
% 157.20/27.18 (4) all_58_9 = e3
% 157.20/27.18 (5) ~ (e3 = e1)
% 157.20/27.18 (6) ~ (e2 = e1)
% 157.20/27.18 (7) ~ (all_52_9 = e0)
% 157.20/27.18 (8) ~ (e1 = e0)
% 157.20/27.18 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.20/27.18 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.20/27.18 (10) all_58_0 = e0
% 157.20/27.18 (11) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 157.20/27.18 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18 (13) ~ (e3 = e2)
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (11) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (14) all_58_4 = e0 & op(e3, e1) = e0
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14) are
% 157.20/27.18 | | inconsistent by sub-proof #348.
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (15) all_58_5 = e0 & op(e2, e1) = e0
% 157.20/27.18 | |
% 157.20/27.18 | | ALPHA: (15) implies:
% 157.20/27.18 | | (16) op(e2, e1) = e0
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (1), (7), (12), (16) are inconsistent by sub-proof #1300.
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #316 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.20/27.18 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.20/27.18 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.20/27.18 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.20/27.18 (3) all_58_11 = e3 & op(e1, e0) = e3
% 157.20/27.18 (4) all_58_9 = e3
% 157.20/27.18 (5) ~ (e3 = e1)
% 157.20/27.18 (6) ~ (all_4_2 = e1)
% 157.20/27.18 (7) ~ (all_24_1 = e2)
% 157.20/27.18 (8) op(e0, e0) = all_4_2
% 157.20/27.18 (9) ~ (e2 = e1)
% 157.20/27.18 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18 (11) ~ (e3 = e2)
% 157.20/27.18 (12) op(e0, e0) = all_24_1
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | ALPHA: (3) implies:
% 157.20/27.18 | (13) all_58_11 = e3
% 157.20/27.18 | (14) op(e1, e0) = e3
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (2) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 157.20/27.18 | | e2)
% 157.20/27.18 | |
% 157.20/27.18 | | BETA: splitting (15) gives:
% 157.20/27.18 | |
% 157.20/27.18 | | Case 1:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (16) all_58_9 = e2 & op(e3, e0) = e2
% 157.20/27.18 | | |
% 157.20/27.18 | | | ALPHA: (16) implies:
% 157.20/27.18 | | | (17) all_58_9 = e2
% 157.20/27.18 | | |
% 157.20/27.18 | | | REF_CLOSE: (4), (11), (17) are inconsistent by sub-proof #1245.
% 157.20/27.18 | | |
% 157.20/27.18 | | Case 2:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (18) all_58_10 = e2 & op(e2, e0) = e2
% 157.20/27.18 | | |
% 157.20/27.18 | | | ALPHA: (18) implies:
% 157.20/27.18 | | | (19) all_58_10 = e2
% 157.20/27.18 | | |
% 157.20/27.18 | | | BETA: splitting (1) gives:
% 157.20/27.18 | | |
% 157.20/27.18 | | | Case 1:
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | (20) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 157.20/27.18 | | | | = e1)
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | REF_CLOSE: (4), (5), (9), (19), (20) are inconsistent by sub-proof #319.
% 157.20/27.18 | | | |
% 157.20/27.18 | | | Case 2:
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | (21) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 157.20/27.18 | | | | e0) = e1)
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | REF_CLOSE: (5), (6), (8), (10), (14), (21) are inconsistent by sub-proof
% 157.20/27.18 | | | | #318.
% 157.20/27.18 | | | |
% 157.20/27.18 | | | End of split
% 157.20/27.18 | | |
% 157.20/27.18 | | End of split
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (22) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.20/27.18 | | e2)
% 157.20/27.18 | |
% 157.20/27.18 | | BETA: splitting (22) gives:
% 157.20/27.18 | |
% 157.20/27.18 | | Case 1:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (23) all_58_11 = e2 & op(e1, e0) = e2
% 157.20/27.18 | | |
% 157.20/27.18 | | | REF_CLOSE: (11), (13), (23) are inconsistent by sub-proof #852.
% 157.20/27.18 | | |
% 157.20/27.18 | | Case 2:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (24) all_58_15 = e2 & op(e0, e0) = e2
% 157.20/27.18 | | |
% 157.20/27.18 | | | ALPHA: (24) implies:
% 157.20/27.18 | | | (25) op(e0, e0) = e2
% 157.20/27.18 | | |
% 157.20/27.18 | | | REF_CLOSE: (7), (10), (12), (25) are inconsistent by sub-proof #317.
% 157.20/27.18 | | |
% 157.20/27.18 | | End of split
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #317 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18 (2) op(e0, e0) = all_24_1
% 157.20/27.18 (3) op(e0, e0) = e2
% 157.20/27.18 (4) ~ (all_24_1 = e2)
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | GROUND_INST: instantiating (1) with e2, all_24_1, e0, e0, simplifying with
% 157.20/27.18 | (2), (3) gives:
% 157.20/27.18 | (5) all_24_1 = e2
% 157.20/27.18 |
% 157.20/27.18 | REDUCE: (4), (5) imply:
% 157.20/27.18 | (6) $false
% 157.20/27.18 |
% 157.20/27.18 | CLOSE: (6) is inconsistent.
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #318 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) ~ (e3 = e1)
% 157.20/27.18 (2) ~ (all_4_2 = e1)
% 157.20/27.18 (3) op(e0, e0) = all_4_2
% 157.20/27.18 (4) op(e1, e0) = e3
% 157.20/27.18 (5) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.20/27.18 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (5) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (7) all_58_11 = e1 & op(e1, e0) = e1
% 157.20/27.18 | |
% 157.20/27.18 | | ALPHA: (7) implies:
% 157.20/27.18 | | (8) op(e1, e0) = e1
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1275.
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (9) all_58_15 = e1 & op(e0, e0) = e1
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #1418.
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #319 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.20/27.18 (2) all_58_10 = e2
% 157.20/27.18 (3) all_58_9 = e3
% 157.20/27.18 (4) ~ (e3 = e1)
% 157.20/27.18 (5) ~ (e2 = e1)
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (1) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (6) all_58_9 = e1 & op(e3, e0) = e1
% 157.20/27.18 | |
% 157.20/27.18 | | ALPHA: (6) implies:
% 157.20/27.18 | | (7) all_58_9 = e1
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1461.
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (8) all_58_10 = e1 & op(e2, e0) = e1
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #1199.
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #320 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) all_58_13 = e3
% 157.20/27.18 (2) all_58_13 = e2
% 157.20/27.18 (3) ~ (e3 = e2)
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | COMBINE_EQS: (1), (2) imply:
% 157.20/27.18 | (4) e3 = e2
% 157.20/27.18 |
% 157.20/27.18 | SIMP: (4) implies:
% 157.20/27.18 | (5) e3 = e2
% 157.20/27.18 |
% 157.20/27.18 | REDUCE: (3), (5) imply:
% 157.20/27.18 | (6) $false
% 157.20/27.18 |
% 157.20/27.18 | CLOSE: (6) is inconsistent.
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #321 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) ~ (all_52_1 = all_8_2)
% 157.20/27.18 (2) op(e2, e3) = all_52_1
% 157.20/27.18 (3) ~ (all_8_2 = e0)
% 157.20/27.18 (4) op(e2, e3) = e2
% 157.20/27.18 (5) ~ (all_8_2 = e1)
% 157.20/27.18 (6) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 157.20/27.18 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18 (8) all_54_5 = all_8_2
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (6) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (9) all_54_5 = e2
% 157.20/27.18 | |
% 157.20/27.18 | | COMBINE_EQS: (8), (9) imply:
% 157.20/27.18 | | (10) all_8_2 = e2
% 157.20/27.18 | |
% 157.20/27.18 | | SIMP: (10) implies:
% 157.20/27.18 | | (11) all_8_2 = e2
% 157.20/27.18 | |
% 157.20/27.18 | | REDUCE: (1), (11) imply:
% 157.20/27.18 | | (12) ~ (all_52_1 = e2)
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (2), (4), (7), (12) are inconsistent by sub-proof #1544.
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (13) all_54_5 = e1 | all_54_5 = e0
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (3), (5), (8), (13) are inconsistent by sub-proof #1239.
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #322 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.20/27.18 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.20/27.18 (2) all_58_7 = e0
% 157.20/27.18 (3) ~ (e3 = e1)
% 157.20/27.18 (4) all_58_13 = e3
% 157.20/27.18 (5) ~ (e2 = e1)
% 157.20/27.18 (6) ~ (e1 = e0)
% 157.20/27.18 (7) ~ (all_8_2 = e1)
% 157.20/27.18 (8) all_58_1 = e2
% 157.20/27.18 (9) op(e2, e2) = all_8_2
% 157.20/27.18 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (1) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (11) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 157.20/27.18 | | e1)
% 157.20/27.18 | |
% 157.20/27.18 | | BETA: splitting (11) gives:
% 157.20/27.18 | |
% 157.20/27.18 | | Case 1:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (12) all_58_1 = e1 & op(e3, e2) = e1
% 157.20/27.18 | | |
% 157.20/27.18 | | | REF_CLOSE: (5), (8), (12) are inconsistent by sub-proof #1219.
% 157.20/27.18 | | |
% 157.20/27.18 | | Case 2:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (13) all_58_3 = e1 & op(e2, e2) = e1
% 157.20/27.18 | | |
% 157.20/27.18 | | | REF_CLOSE: (7), (9), (10), (13) are inconsistent by sub-proof #1423.
% 157.20/27.18 | | |
% 157.20/27.18 | | End of split
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (14) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 157.20/27.18 | | e1)
% 157.20/27.18 | |
% 157.20/27.18 | | BETA: splitting (14) gives:
% 157.20/27.18 | |
% 157.20/27.18 | | Case 1:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (15) all_58_7 = e1 & op(e1, e2) = e1
% 157.20/27.18 | | |
% 157.20/27.18 | | | REF_CLOSE: (2), (6), (15) are inconsistent by sub-proof #1250.
% 157.20/27.18 | | |
% 157.20/27.18 | | Case 2:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (16) all_58_13 = e1 & op(e0, e2) = e1
% 157.20/27.18 | | |
% 157.20/27.18 | | | ALPHA: (16) implies:
% 157.20/27.18 | | | (17) all_58_13 = e1
% 157.20/27.18 | | |
% 157.20/27.18 | | | REF_CLOSE: (3), (4), (17) are inconsistent by sub-proof #1264.
% 157.20/27.18 | | |
% 157.20/27.18 | | End of split
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #323 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) ~ (all_52_1 = all_8_2)
% 157.20/27.18 (2) op(e2, e1) = all_52_9
% 157.20/27.18 (3) op(e2, e3) = all_52_1
% 157.20/27.18 (4) ~ (all_8_2 = e3)
% 157.20/27.18 (5) ~ (all_8_2 = e0)
% 157.20/27.18 (6) op(e2, e0) = all_52_13
% 157.20/27.18 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 157.20/27.18 (8) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.20/27.18 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.20/27.18 (9) all_58_3 = e0 & op(e2, e2) = e0
% 157.20/27.18 (10) ~ (all_8_2 = e1)
% 157.20/27.18 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18 (12) all_54_5 = all_8_2
% 157.20/27.18 (13) ~ (all_52_9 = all_8_2)
% 157.20/27.18 (14) ~ (all_52_13 = all_8_2)
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | ALPHA: (9) implies:
% 157.20/27.18 | (15) all_58_3 = e0
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (7) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (16) all_54_5 = e3
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (4), (12), (16) are inconsistent by sub-proof #1161.
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (17) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (11), (12), (13), (14), (15),
% 157.20/27.18 | | (17) are inconsistent by sub-proof #324.
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #324 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) ~ (all_52_1 = all_8_2)
% 157.20/27.18 (2) op(e2, e1) = all_52_9
% 157.20/27.18 (3) op(e2, e3) = all_52_1
% 157.20/27.18 (4) ~ (all_8_2 = e0)
% 157.20/27.18 (5) op(e2, e0) = all_52_13
% 157.20/27.18 (6) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.20/27.18 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.20/27.18 (7) all_58_3 = e0
% 157.20/27.18 (8) ~ (all_8_2 = e1)
% 157.20/27.18 (9) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 157.20/27.18 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18 (11) all_54_5 = all_8_2
% 157.20/27.18 (12) ~ (all_52_9 = all_8_2)
% 157.20/27.18 (13) ~ (all_52_13 = all_8_2)
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (9) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (14) all_54_5 = e2
% 157.20/27.18 | |
% 157.20/27.18 | | COMBINE_EQS: (11), (14) imply:
% 157.20/27.18 | | (15) all_8_2 = e2
% 157.20/27.18 | |
% 157.20/27.18 | | SIMP: (15) implies:
% 157.20/27.18 | | (16) all_8_2 = e2
% 157.20/27.18 | |
% 157.20/27.18 | | REDUCE: (1), (16) imply:
% 157.20/27.18 | | (17) ~ (all_52_1 = e2)
% 157.20/27.18 | |
% 157.20/27.18 | | REDUCE: (13), (16) imply:
% 157.20/27.18 | | (18) ~ (all_52_13 = e2)
% 157.20/27.18 | |
% 157.20/27.18 | | REDUCE: (4), (16) imply:
% 157.20/27.18 | | (19) ~ (e2 = e0)
% 157.20/27.18 | |
% 157.20/27.18 | | BETA: splitting (6) gives:
% 157.20/27.18 | |
% 157.20/27.18 | | Case 1:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (20) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 157.20/27.18 | | | e2)
% 157.20/27.18 | | |
% 157.20/27.18 | | | BETA: splitting (20) gives:
% 157.20/27.18 | | |
% 157.20/27.18 | | | Case 1:
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | (21) all_58_2 = e2 & op(e2, e3) = e2
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | ALPHA: (21) implies:
% 157.20/27.18 | | | | (22) op(e2, e3) = e2
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | REF_CLOSE: (3), (10), (17), (22) are inconsistent by sub-proof #1544.
% 157.20/27.18 | | | |
% 157.20/27.18 | | | Case 2:
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | (23) all_58_3 = e2 & op(e2, e2) = e2
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | ALPHA: (23) implies:
% 157.20/27.18 | | | | (24) all_58_3 = e2
% 157.20/27.18 | | | |
% 157.20/27.18 | | | | REF_CLOSE: (7), (19), (24) are inconsistent by sub-proof #1377.
% 157.20/27.18 | | | |
% 157.20/27.18 | | | End of split
% 157.20/27.18 | | |
% 157.20/27.18 | | Case 2:
% 157.20/27.18 | | |
% 157.20/27.18 | | | (25) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 157.20/27.18 | | | e2)
% 157.20/27.18 | | |
% 157.20/27.18 | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (12), (18), (25) are
% 157.20/27.18 | | | inconsistent by sub-proof #325.
% 157.20/27.18 | | |
% 157.20/27.18 | | End of split
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.20/27.18 | | (26) all_54_5 = e1 | all_54_5 = e0
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (4), (8), (11), (26) are inconsistent by sub-proof #1239.
% 157.20/27.18 | |
% 157.20/27.18 | End of split
% 157.20/27.18 |
% 157.20/27.18 End of proof
% 157.20/27.18
% 157.20/27.18 Sub-proof #325 shows that the following formulas are inconsistent:
% 157.20/27.18 ----------------------------------------------------------------
% 157.20/27.18 (1) op(e2, e1) = all_52_9
% 157.20/27.18 (2) ~ (all_8_2 = e0)
% 157.20/27.18 (3) op(e2, e0) = all_52_13
% 157.20/27.18 (4) ~ (all_52_13 = e2)
% 157.20/27.18 (5) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.20/27.18 (6) ~ (all_8_2 = e1)
% 157.20/27.18 (7) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 157.20/27.18 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.20/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.20/27.18 (9) all_54_5 = all_8_2
% 157.20/27.18 (10) ~ (all_52_9 = all_8_2)
% 157.20/27.18
% 157.20/27.18 Begin of proof
% 157.20/27.18 |
% 157.20/27.18 | BETA: splitting (5) gives:
% 157.20/27.18 |
% 157.20/27.18 | Case 1:
% 157.20/27.18 | |
% 157.20/27.18 | | (11) all_58_5 = e2 & op(e2, e1) = e2
% 157.20/27.18 | |
% 157.20/27.18 | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11) are inconsistent by
% 157.20/27.18 | | sub-proof #915.
% 157.20/27.18 | |
% 157.20/27.18 | Case 2:
% 157.20/27.18 | |
% 157.26/27.18 | | (12) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.18 | |
% 157.26/27.18 | | ALPHA: (12) implies:
% 157.26/27.18 | | (13) op(e2, e0) = e2
% 157.26/27.18 | |
% 157.26/27.18 | | REF_CLOSE: (3), (4), (8), (13) are inconsistent by sub-proof #1535.
% 157.26/27.18 | |
% 157.26/27.18 | End of split
% 157.26/27.18 |
% 157.26/27.18 End of proof
% 157.26/27.18
% 157.26/27.18 Sub-proof #326 shows that the following formulas are inconsistent:
% 157.26/27.18 ----------------------------------------------------------------
% 157.26/27.18 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.18 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.18 (2) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.18 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.18 (3) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 157.26/27.18 (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.18 (4) ~ (all_4_2 = e2)
% 157.26/27.18 (5) ~ (e3 = e0)
% 157.26/27.18 (6) ~ (e2 = e0)
% 157.26/27.18 (7) all_58_9 = e3
% 157.26/27.18 (8) ~ (e3 = e1)
% 157.26/27.18 (9) ~ (all_4_2 = e1)
% 157.26/27.18 (10) op(e0, e0) = all_4_2
% 157.26/27.18 (11) ~ (e2 = e1)
% 157.26/27.18 (12) ~ (e1 = e0)
% 157.26/27.18 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.18 (14) ~ (e3 = e2)
% 157.26/27.18
% 157.26/27.18 Begin of proof
% 157.26/27.18 |
% 157.26/27.18 | BETA: splitting (3) gives:
% 157.26/27.18 |
% 157.26/27.18 | Case 1:
% 157.26/27.18 | |
% 157.26/27.18 | | (15) all_58_9 = e0 & op(e3, e0) = e0
% 157.26/27.18 | |
% 157.26/27.18 | | REF_CLOSE: (5), (7), (15) are inconsistent by sub-proof #1460.
% 157.26/27.18 | |
% 157.26/27.18 | Case 2:
% 157.26/27.18 | |
% 157.26/27.18 | | (16) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 157.26/27.18 | | e0)
% 157.26/27.18 | |
% 157.26/27.18 | | BETA: splitting (16) gives:
% 157.26/27.18 | |
% 157.26/27.18 | | Case 1:
% 157.26/27.18 | | |
% 157.26/27.18 | | | (17) all_58_10 = e0 & op(e2, e0) = e0
% 157.26/27.18 | | |
% 157.26/27.18 | | | ALPHA: (17) implies:
% 157.26/27.18 | | | (18) all_58_10 = e0
% 157.26/27.18 | | |
% 157.26/27.18 | | | BETA: splitting (2) gives:
% 157.26/27.18 | | |
% 157.26/27.18 | | | Case 1:
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 157.26/27.18 | | | | = e2)
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | BETA: splitting (19) gives:
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | Case 1:
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | (20) all_58_9 = e2 & op(e3, e0) = e2
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | REF_CLOSE: (7), (14), (20) are inconsistent by sub-proof #1353.
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | Case 2:
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | (21) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | ALPHA: (21) implies:
% 157.26/27.18 | | | | | (22) all_58_10 = e2
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 157.26/27.18 | | | | | (22) are inconsistent by sub-proof #328.
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | End of split
% 157.26/27.18 | | | |
% 157.26/27.18 | | | Case 2:
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | (23) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 157.26/27.18 | | | | e0) = e2)
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (11), (12), (13), (18), (23)
% 157.26/27.18 | | | | are inconsistent by sub-proof #327.
% 157.26/27.18 | | | |
% 157.26/27.18 | | | End of split
% 157.26/27.18 | | |
% 157.26/27.18 | | Case 2:
% 157.26/27.18 | | |
% 157.26/27.18 | | | (24) all_58_11 = e0 & op(e1, e0) = e0
% 157.26/27.18 | | |
% 157.26/27.18 | | | ALPHA: (24) implies:
% 157.26/27.18 | | | (25) all_58_11 = e0
% 157.26/27.18 | | |
% 157.26/27.18 | | | BETA: splitting (2) gives:
% 157.26/27.18 | | |
% 157.26/27.18 | | | Case 1:
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | (26) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 157.26/27.18 | | | | = e2)
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | BETA: splitting (26) gives:
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | Case 1:
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | (27) all_58_9 = e2 & op(e3, e0) = e2
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | REF_CLOSE: (7), (14), (27) are inconsistent by sub-proof #1353.
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | Case 2:
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | (28) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | ALPHA: (28) implies:
% 157.26/27.18 | | | | | (29) all_58_10 = e2
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 157.26/27.18 | | | | | (29) are inconsistent by sub-proof #328.
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | End of split
% 157.26/27.18 | | | |
% 157.26/27.18 | | | Case 2:
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | (30) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 157.26/27.18 | | | | e0) = e2)
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | BETA: splitting (30) gives:
% 157.26/27.18 | | | |
% 157.26/27.18 | | | | Case 1:
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | (31) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | REF_CLOSE: (6), (25), (31) are inconsistent by sub-proof #507.
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | Case 2:
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | (32) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | | REF_CLOSE: (4), (10), (13), (32) are inconsistent by sub-proof #1452.
% 157.26/27.18 | | | | |
% 157.26/27.18 | | | | End of split
% 157.26/27.18 | | | |
% 157.26/27.18 | | | End of split
% 157.26/27.18 | | |
% 157.26/27.18 | | End of split
% 157.26/27.18 | |
% 157.26/27.18 | End of split
% 157.26/27.18 |
% 157.26/27.18 End of proof
% 157.26/27.18
% 157.26/27.18 Sub-proof #327 shows that the following formulas are inconsistent:
% 157.26/27.18 ----------------------------------------------------------------
% 157.26/27.18 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.18 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.18 (2) ~ (all_4_2 = e2)
% 157.26/27.18 (3) all_58_9 = e3
% 157.26/27.18 (4) ~ (e3 = e1)
% 157.26/27.18 (5) ~ (all_4_2 = e1)
% 157.26/27.18 (6) op(e0, e0) = all_4_2
% 157.26/27.18 (7) ~ (e2 = e1)
% 157.26/27.19 (8) ~ (e1 = e0)
% 157.26/27.19 (9) all_58_10 = e0
% 157.26/27.19 (10) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.19 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.19
% 157.26/27.19 Begin of proof
% 157.26/27.19 |
% 157.26/27.19 | BETA: splitting (10) gives:
% 157.26/27.19 |
% 157.26/27.19 | Case 1:
% 157.26/27.19 | |
% 157.26/27.19 | | (12) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.19 | |
% 157.26/27.19 | | ALPHA: (12) implies:
% 157.26/27.19 | | (13) all_58_11 = e2
% 157.26/27.19 | |
% 157.26/27.19 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (13) are
% 157.26/27.19 | | inconsistent by sub-proof #350.
% 157.26/27.19 | |
% 157.26/27.19 | Case 2:
% 157.26/27.19 | |
% 157.26/27.19 | | (14) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.19 | |
% 157.26/27.19 | | REF_CLOSE: (2), (6), (11), (14) are inconsistent by sub-proof #1452.
% 157.26/27.19 | |
% 157.26/27.19 | End of split
% 157.26/27.19 |
% 157.26/27.19 End of proof
% 157.26/27.19
% 157.26/27.19 Sub-proof #328 shows that the following formulas are inconsistent:
% 157.26/27.19 ----------------------------------------------------------------
% 157.26/27.19 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.19 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.19 (2) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 157.26/27.19 (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.19 (3) all_58_10 = e2
% 157.26/27.19 (4) ~ (e3 = e0)
% 157.26/27.19 (5) ~ (e2 = e0)
% 157.26/27.19 (6) all_58_9 = e3
% 157.26/27.19 (7) ~ (e3 = e1)
% 157.26/27.19 (8) ~ (all_4_2 = e1)
% 157.26/27.19 (9) op(e0, e0) = all_4_2
% 157.26/27.19 (10) ~ (e2 = e1)
% 157.26/27.19 (11) ~ (e1 = e0)
% 157.26/27.19 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.19
% 157.26/27.19 Begin of proof
% 157.26/27.19 |
% 157.26/27.19 | BETA: splitting (1) gives:
% 157.26/27.19 |
% 157.26/27.19 | Case 1:
% 157.26/27.19 | |
% 157.26/27.19 | | (13) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.26/27.19 | | e1)
% 157.26/27.19 | |
% 157.26/27.19 | | REF_CLOSE: (3), (6), (7), (10), (13) are inconsistent by sub-proof #329.
% 157.26/27.19 | |
% 157.26/27.19 | Case 2:
% 157.26/27.19 | |
% 157.26/27.19 | | (14) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.19 | | e1)
% 157.26/27.19 | |
% 157.26/27.19 | | BETA: splitting (14) gives:
% 157.26/27.19 | |
% 157.26/27.19 | | Case 1:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (15) all_58_11 = e1 & op(e1, e0) = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | ALPHA: (15) implies:
% 157.26/27.19 | | | (16) all_58_11 = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | BETA: splitting (2) gives:
% 157.26/27.19 | | |
% 157.26/27.19 | | | Case 1:
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | (17) all_58_9 = e0 & op(e3, e0) = e0
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | REF_CLOSE: (4), (6), (17) are inconsistent by sub-proof #1460.
% 157.26/27.19 | | | |
% 157.26/27.19 | | | Case 2:
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | (18) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 157.26/27.19 | | | | e0) = e0)
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | BETA: splitting (18) gives:
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | Case 1:
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | (19) all_58_10 = e0 & op(e2, e0) = e0
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REF_CLOSE: (3), (5), (19) are inconsistent by sub-proof #908.
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | Case 2:
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | (20) all_58_11 = e0 & op(e1, e0) = e0
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REF_CLOSE: (11), (16), (20) are inconsistent by sub-proof #577.
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | End of split
% 157.26/27.19 | | | |
% 157.26/27.19 | | | End of split
% 157.26/27.19 | | |
% 157.26/27.19 | | Case 2:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (21) all_58_15 = e1 & op(e0, e0) = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | REF_CLOSE: (8), (9), (12), (21) are inconsistent by sub-proof #1418.
% 157.26/27.19 | | |
% 157.26/27.19 | | End of split
% 157.26/27.19 | |
% 157.26/27.19 | End of split
% 157.26/27.19 |
% 157.26/27.19 End of proof
% 157.26/27.19
% 157.26/27.19 Sub-proof #329 shows that the following formulas are inconsistent:
% 157.26/27.19 ----------------------------------------------------------------
% 157.26/27.19 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.19 (2) all_58_10 = e2
% 157.26/27.19 (3) all_58_9 = e3
% 157.26/27.19 (4) ~ (e3 = e1)
% 157.26/27.19 (5) ~ (e2 = e1)
% 157.26/27.19
% 157.26/27.19 Begin of proof
% 157.26/27.19 |
% 157.26/27.19 | BETA: splitting (1) gives:
% 157.26/27.19 |
% 157.26/27.19 | Case 1:
% 157.26/27.19 | |
% 157.26/27.19 | | (6) all_58_9 = e1 & op(e3, e0) = e1
% 157.26/27.19 | |
% 157.26/27.19 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #1078.
% 157.26/27.19 | |
% 157.26/27.19 | Case 2:
% 157.26/27.19 | |
% 157.26/27.19 | | (7) all_58_10 = e1 & op(e2, e0) = e1
% 157.26/27.19 | |
% 157.26/27.19 | | ALPHA: (7) implies:
% 157.26/27.19 | | (8) all_58_10 = e1
% 157.26/27.19 | |
% 157.26/27.19 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #1091.
% 157.26/27.19 | |
% 157.26/27.19 | End of split
% 157.26/27.19 |
% 157.26/27.19 End of proof
% 157.26/27.19
% 157.26/27.19 Sub-proof #330 shows that the following formulas are inconsistent:
% 157.26/27.19 ----------------------------------------------------------------
% 157.26/27.19 (1) ~ (all_4_2 = e2)
% 157.26/27.19 (2) ~ (e2 = e0)
% 157.26/27.19 (3) op(e0, e0) = all_4_2
% 157.26/27.19 (4) all_58_11 = e0
% 157.26/27.19 (5) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.19 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.19
% 157.26/27.19 Begin of proof
% 157.26/27.19 |
% 157.26/27.19 | BETA: splitting (5) gives:
% 157.26/27.19 |
% 157.26/27.19 | Case 1:
% 157.26/27.19 | |
% 157.26/27.19 | | (7) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.19 | |
% 157.26/27.19 | | ALPHA: (7) implies:
% 157.26/27.19 | | (8) all_58_11 = e2
% 157.26/27.19 | |
% 157.26/27.19 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #1458.
% 157.26/27.19 | |
% 157.26/27.19 | Case 2:
% 157.26/27.19 | |
% 157.26/27.19 | | (9) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.19 | |
% 157.26/27.19 | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #1452.
% 157.26/27.19 | |
% 157.26/27.19 | End of split
% 157.26/27.19 |
% 157.26/27.19 End of proof
% 157.26/27.19
% 157.26/27.19 Sub-proof #331 shows that the following formulas are inconsistent:
% 157.26/27.19 ----------------------------------------------------------------
% 157.26/27.19 (1) all_58_10 = e3 & op(e2, e0) = e3
% 157.26/27.19 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.19 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.19 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.19 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.19 (4) ~ (all_4_2 = e2)
% 157.26/27.19 (5) all_58_9 = e3
% 157.26/27.19 (6) ~ (e3 = e1)
% 157.26/27.19 (7) ~ (all_4_2 = e1)
% 157.26/27.19 (8) op(e0, e0) = all_4_2
% 157.26/27.19 (9) ~ (e2 = e1)
% 157.26/27.19 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.19 (11) ~ (e3 = e2)
% 157.26/27.19
% 157.26/27.19 Begin of proof
% 157.26/27.19 |
% 157.26/27.19 | ALPHA: (1) implies:
% 157.26/27.19 | (12) all_58_10 = e3
% 157.26/27.19 |
% 157.26/27.19 | BETA: splitting (2) gives:
% 157.26/27.19 |
% 157.26/27.19 | Case 1:
% 157.26/27.19 | |
% 157.26/27.19 | | (13) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.26/27.19 | | e1)
% 157.26/27.19 | |
% 157.26/27.19 | | BETA: splitting (13) gives:
% 157.26/27.19 | |
% 157.26/27.19 | | Case 1:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (14) all_58_9 = e1 & op(e3, e0) = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | ALPHA: (14) implies:
% 157.26/27.19 | | | (15) all_58_9 = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | REF_CLOSE: (5), (6), (15) are inconsistent by sub-proof #1461.
% 157.26/27.19 | | |
% 157.26/27.19 | | Case 2:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (16) all_58_10 = e1 & op(e2, e0) = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | REF_CLOSE: (6), (12), (16) are inconsistent by sub-proof #1178.
% 157.26/27.19 | | |
% 157.26/27.19 | | End of split
% 157.26/27.19 | |
% 157.26/27.19 | Case 2:
% 157.26/27.19 | |
% 157.26/27.19 | | (17) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.19 | | e1)
% 157.26/27.19 | |
% 157.26/27.19 | | BETA: splitting (17) gives:
% 157.26/27.19 | |
% 157.26/27.19 | | Case 1:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (18) all_58_11 = e1 & op(e1, e0) = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | ALPHA: (18) implies:
% 157.26/27.19 | | | (19) all_58_11 = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | BETA: splitting (3) gives:
% 157.26/27.19 | | |
% 157.26/27.19 | | | Case 1:
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 157.26/27.19 | | | | = e2)
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | BETA: splitting (20) gives:
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | Case 1:
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | (21) all_58_9 = e2 & op(e3, e0) = e2
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | ALPHA: (21) implies:
% 157.26/27.19 | | | | | (22) all_58_9 = e2
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REF_CLOSE: (5), (11), (22) are inconsistent by sub-proof #1245.
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | Case 2:
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | (23) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REF_CLOSE: (11), (12), (23) are inconsistent by sub-proof #1050.
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | End of split
% 157.26/27.19 | | | |
% 157.26/27.19 | | | Case 2:
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | (24) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 157.26/27.19 | | | | e0) = e2)
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | REF_CLOSE: (4), (8), (9), (10), (19), (24) are inconsistent by sub-proof
% 157.26/27.19 | | | | #942.
% 157.26/27.19 | | | |
% 157.26/27.19 | | | End of split
% 157.26/27.19 | | |
% 157.26/27.19 | | Case 2:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (25) all_58_15 = e1 & op(e0, e0) = e1
% 157.26/27.19 | | |
% 157.26/27.19 | | | REF_CLOSE: (7), (8), (10), (25) are inconsistent by sub-proof #1418.
% 157.26/27.19 | | |
% 157.26/27.19 | | End of split
% 157.26/27.19 | |
% 157.26/27.19 | End of split
% 157.26/27.19 |
% 157.26/27.19 End of proof
% 157.26/27.19
% 157.26/27.19 Sub-proof #332 shows that the following formulas are inconsistent:
% 157.26/27.19 ----------------------------------------------------------------
% 157.26/27.19 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.19 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.19 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.19 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.19 (3) op(e1, e1) = all_6_2
% 157.26/27.19 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.26/27.19 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.19 (5) ~ (all_52_6 = all_52_14)
% 157.26/27.19 (6) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.26/27.19 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.26/27.19 (7) all_58_12 = e3
% 157.26/27.19 (8) op(e1, e2) = e3
% 157.26/27.19 (9) op(e0, e3) = all_10_0
% 157.26/27.19 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.19 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.19 (11) ~ (all_52_1 = all_8_2)
% 157.26/27.19 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.19 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.19 (13) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 157.26/27.19 (14) ~ (all_4_2 = e2)
% 157.26/27.19 (15) ~ (all_52_1 = all_52_13)
% 157.26/27.19 (16) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.19 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.19 (17) ~ (all_10_0 = e2)
% 157.26/27.19 (18) all_56_13 = all_8_2
% 157.26/27.19 (19) op(e2, e1) = all_52_9
% 157.26/27.19 (20) op(e2, e3) = all_52_1
% 157.26/27.19 (21) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.19 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.19 (22) ~ (all_52_8 = all_52_9)
% 157.26/27.19 (23) all_56_2 = e3
% 157.26/27.19 (24) ~ (e3 = e0)
% 157.26/27.19 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.19 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.19 (26) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.19 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.19 (27) ~ (all_52_9 = all_52_13)
% 157.26/27.19 (28) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.19 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.19 e2)
% 157.26/27.19 (29) ~ (e2 = e0)
% 157.26/27.19 (30) ~ (all_8_2 = e3)
% 157.26/27.19 (31) all_58_5 = e3
% 157.26/27.19 (32) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.26/27.19 (33) all_58_9 = e3
% 157.26/27.19 (34) op(e1, e3) = all_52_2
% 157.26/27.19 (35) op(e2, e0) = all_52_13
% 157.26/27.19 (36) all_56_15 = e0
% 157.26/27.19 (37) all_58_7 = e3
% 157.26/27.19 (38) ~ (e3 = e1)
% 157.26/27.19 (39) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.19 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.19 (40) op(e1, e2) = all_52_6
% 157.26/27.19 (41) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.26/27.19 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.19 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.26/27.19 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.26/27.19 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.26/27.19 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.19 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.26/27.19 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.26/27.19 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.26/27.19 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.19 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.26/27.19 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.26/27.19 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.26/27.19 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.26/27.19 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.26/27.19 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.26/27.19 = e0)
% 157.26/27.19 (42) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.19 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.26/27.19 (43) ~ (all_4_2 = e1)
% 157.26/27.19 (44) all_54_4 = all_52_1
% 157.26/27.19 (45) op(e0, e0) = all_4_2
% 157.26/27.19 (46) op(e0, e1) = all_52_11
% 157.26/27.19 (47) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 157.26/27.19 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 157.26/27.19 (48) ~ (all_52_2 = all_52_14)
% 157.26/27.19 (49) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.26/27.19 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.26/27.19 (50) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.19 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.19 (51) all_58_3 = e0
% 157.26/27.19 (52) ~ (e2 = e1)
% 157.26/27.19 (53) ~ (e1 = e0)
% 157.26/27.19 (54) ~ (all_8_2 = e1)
% 157.26/27.19 (55) ~ (all_52_7 = all_8_2)
% 157.26/27.19 (56) ~ (all_56_13 = e0) | (all_56_5 = e2 & op(e2, e0) = e2)
% 157.26/27.19 (57) op(e3, e1) = all_52_8
% 157.26/27.19 (58) ~ (all_6_2 = e2)
% 157.26/27.19 (59) all_56_14 = all_6_2
% 157.26/27.19 (60) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.19 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.19 (61) ~ (all_52_8 = e3)
% 157.26/27.19 (62) op(e2, e2) = e0
% 157.26/27.19 (63) op(e0, e2) = all_52_7
% 157.26/27.19 (64) op(e1, e0) = all_52_14
% 157.26/27.19 (65) all_58_0 = e0
% 157.26/27.19 (66) op(e2, e2) = all_8_2
% 157.26/27.19 (67) ~ (all_52_14 = all_6_2)
% 157.26/27.19 (68) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.19 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.19 (69) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.19 (70) ~ (all_52_13 = all_52_14)
% 157.26/27.19 (71) ~ (e3 = e2)
% 157.26/27.19 (72) ~ (all_52_13 = all_8_2)
% 157.26/27.19 (73) ~ (all_52_1 = all_52_9)
% 157.26/27.19
% 157.26/27.19 Begin of proof
% 157.26/27.19 |
% 157.26/27.19 | BETA: splitting (39) gives:
% 157.26/27.19 |
% 157.26/27.19 | Case 1:
% 157.26/27.19 | |
% 157.26/27.19 | | (74) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 157.26/27.19 | | e0)
% 157.26/27.19 | |
% 157.26/27.19 | | BETA: splitting (74) gives:
% 157.26/27.19 | |
% 157.26/27.19 | | Case 1:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (75) all_58_4 = e0 & op(e3, e1) = e0
% 157.26/27.19 | | |
% 157.26/27.19 | | | REF_CLOSE: (26), (29), (33), (38), (52), (53), (60), (65), (69), (71),
% 157.26/27.19 | | | (75) are inconsistent by sub-proof #348.
% 157.26/27.19 | | |
% 157.26/27.19 | | Case 2:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (76) all_58_5 = e0 & op(e2, e1) = e0
% 157.26/27.19 | | |
% 157.26/27.19 | | | ALPHA: (76) implies:
% 157.26/27.19 | | | (77) all_58_5 = e0
% 157.26/27.19 | | |
% 157.26/27.19 | | | REF_CLOSE: (24), (31), (77) are inconsistent by sub-proof #1392.
% 157.26/27.19 | | |
% 157.26/27.19 | | End of split
% 157.26/27.19 | |
% 157.26/27.19 | Case 2:
% 157.26/27.19 | |
% 157.26/27.19 | | (78) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.26/27.19 | | e0)
% 157.26/27.19 | |
% 157.26/27.19 | | BETA: splitting (78) gives:
% 157.26/27.19 | |
% 157.26/27.19 | | Case 1:
% 157.26/27.19 | | |
% 157.26/27.19 | | | (79) all_58_8 = e0 & op(e1, e1) = e0
% 157.26/27.19 | | |
% 157.26/27.19 | | | ALPHA: (79) implies:
% 157.26/27.19 | | | (80) all_58_8 = e0
% 157.26/27.19 | | | (81) op(e1, e1) = e0
% 157.26/27.19 | | |
% 157.26/27.19 | | | BETA: splitting (6) gives:
% 157.26/27.19 | | |
% 157.26/27.19 | | | Case 1:
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | (82) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 157.26/27.19 | | | | = e3)
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | BETA: splitting (82) gives:
% 157.26/27.19 | | | |
% 157.26/27.19 | | | | Case 1:
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | (83) all_58_4 = e3 & op(e3, e1) = e3
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | ALPHA: (83) implies:
% 157.26/27.19 | | | | | (84) op(e3, e1) = e3
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REF_CLOSE: (57), (61), (69), (84) are inconsistent by sub-proof #1538.
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | Case 2:
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | (85) all_58_5 = e3 & op(e2, e1) = e3
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | ALPHA: (85) implies:
% 157.26/27.19 | | | | | (86) op(e2, e1) = e3
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | GROUND_INST: instantiating (69) with all_6_2, e0, e1, e1, simplifying
% 157.26/27.19 | | | | | with (3), (81) gives:
% 157.26/27.19 | | | | | (87) all_6_2 = e0
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | GROUND_INST: instantiating (69) with all_52_6, e3, e2, e1, simplifying
% 157.26/27.19 | | | | | with (8), (40) gives:
% 157.26/27.19 | | | | | (88) all_52_6 = e3
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | GROUND_INST: instantiating (69) with all_52_9, e3, e1, e2, simplifying
% 157.26/27.19 | | | | | with (19), (86) gives:
% 157.26/27.19 | | | | | (89) all_52_9 = e3
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | GROUND_INST: instantiating (69) with all_8_2, e0, e2, e2, simplifying
% 157.26/27.19 | | | | | with (62), (66) gives:
% 157.26/27.19 | | | | | (90) all_8_2 = e0
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | COMBINE_EQS: (59), (87) imply:
% 157.26/27.19 | | | | | (91) all_56_14 = e0
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | COMBINE_EQS: (18), (90) imply:
% 157.26/27.19 | | | | | (92) all_56_13 = e0
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REDUCE: (73), (89) imply:
% 157.26/27.19 | | | | | (93) ~ (all_52_1 = e3)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REDUCE: (11), (90) imply:
% 157.26/27.19 | | | | | (94) ~ (all_52_1 = e0)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REDUCE: (5), (88) imply:
% 157.26/27.19 | | | | | (95) ~ (all_52_14 = e3)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | SIMP: (95) implies:
% 157.26/27.19 | | | | | (96) ~ (all_52_14 = e3)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REDUCE: (55), (90) imply:
% 157.26/27.19 | | | | | (97) ~ (all_52_7 = e0)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REDUCE: (27), (89) imply:
% 157.26/27.19 | | | | | (98) ~ (all_52_13 = e3)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | SIMP: (98) implies:
% 157.26/27.19 | | | | | (99) ~ (all_52_13 = e3)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REDUCE: (72), (90) imply:
% 157.26/27.19 | | | | | (100) ~ (all_52_13 = e0)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REDUCE: (67), (87) imply:
% 157.26/27.19 | | | | | (101) ~ (all_52_14 = e0)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | REDUCE: (30), (90) imply:
% 157.26/27.19 | | | | | (102) ~ (e3 = e0)
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | BETA: splitting (56) gives:
% 157.26/27.19 | | | | |
% 157.26/27.19 | | | | | Case 1:
% 157.26/27.19 | | | | | |
% 157.26/27.19 | | | | | | (103) ~ (all_56_13 = e0)
% 157.26/27.19 | | | | | |
% 157.26/27.19 | | | | | | REDUCE: (92), (103) imply:
% 157.26/27.19 | | | | | | (104) $false
% 157.26/27.19 | | | | | |
% 157.26/27.19 | | | | | | CLOSE: (104) is inconsistent.
% 157.26/27.19 | | | | | |
% 157.26/27.19 | | | | | Case 2:
% 157.26/27.19 | | | | | |
% 157.26/27.19 | | | | | | (105) all_56_5 = e2 & op(e2, e0) = e2
% 157.26/27.19 | | | | | |
% 157.26/27.19 | | | | | | ALPHA: (105) implies:
% 157.26/27.19 | | | | | | (106) op(e2, e0) = e2
% 157.26/27.19 | | | | | |
% 157.26/27.19 | | | | | | BETA: splitting (32) gives:
% 157.26/27.19 | | | | | |
% 157.26/27.19 | | | | | | Case 1:
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | (107) ~ (all_56_14 = e0)
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | REDUCE: (91), (107) imply:
% 157.26/27.19 | | | | | | | (108) $false
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | CLOSE: (108) is inconsistent.
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | Case 2:
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | (109) all_56_8 = e1 & op(e1, e0) = e1
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | ALPHA: (109) implies:
% 157.26/27.19 | | | | | | | (110) all_56_8 = e1
% 157.26/27.19 | | | | | | | (111) op(e1, e0) = e1
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | GROUND_INST: instantiating (69) with all_52_14, e1, e0, e1,
% 157.26/27.19 | | | | | | | simplifying with (64), (111) gives:
% 157.26/27.19 | | | | | | | (112) all_52_14 = e1
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | GROUND_INST: instantiating (69) with all_52_13, e2, e0, e2,
% 157.26/27.19 | | | | | | | simplifying with (35), (106) gives:
% 157.26/27.19 | | | | | | | (113) all_52_13 = e2
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | REDUCE: (15), (113) imply:
% 157.26/27.19 | | | | | | | (114) ~ (all_52_1 = e2)
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | REDUCE: (48), (112) imply:
% 157.26/27.19 | | | | | | | (115) ~ (all_52_2 = e1)
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | REDUCE: (99), (113) imply:
% 157.26/27.19 | | | | | | | (116) ~ (e3 = e2)
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | REDUCE: (96), (112) imply:
% 157.26/27.19 | | | | | | | (117) ~ (e3 = e1)
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | BETA: splitting (1) gives:
% 157.26/27.19 | | | | | | |
% 157.26/27.19 | | | | | | | Case 1:
% 157.26/27.19 | | | | | | | |
% 157.26/27.19 | | | | | | | | (118) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 157.26/27.19 | | | | | | | | op(e1, e2) = e1)
% 157.26/27.19 | | | | | | | |
% 157.26/27.19 | | | | | | | | REF_CLOSE: (34), (37), (38), (69), (115), (118) are inconsistent
% 157.26/27.19 | | | | | | | | by sub-proof #1298.
% 157.26/27.19 | | | | | | | |
% 157.26/27.19 | | | | | | | Case 2:
% 157.26/27.19 | | | | | | | |
% 157.26/27.19 | | | | | | | | (119) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 157.26/27.19 | | | | | | | | op(e1, e0) = e1)
% 157.26/27.19 | | | | | | | |
% 157.26/27.19 | | | | | | | | BETA: splitting (119) gives:
% 157.26/27.19 | | | | | | | |
% 157.26/27.19 | | | | | | | | Case 1:
% 157.26/27.19 | | | | | | | | |
% 157.26/27.19 | | | | | | | | | (120) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.19 | | | | | | | | |
% 157.26/27.19 | | | | | | | | | ALPHA: (120) implies:
% 157.26/27.19 | | | | | | | | | (121) all_58_8 = e1
% 157.26/27.19 | | | | | | | | |
% 157.26/27.19 | | | | | | | | | REF_CLOSE: (53), (80), (121) are inconsistent by sub-proof
% 157.26/27.19 | | | | | | | | | #1445.
% 157.26/27.19 | | | | | | | | |
% 157.26/27.19 | | | | | | | | Case 2:
% 157.26/27.19 | | | | | | | | |
% 157.26/27.19 | | | | | | | | | (122) all_58_11 = e1 & op(e1, e0) = e1
% 157.26/27.19 | | | | | | | | |
% 157.26/27.19 | | | | | | | | | ALPHA: (122) implies:
% 157.26/27.19 | | | | | | | | | (123) all_58_11 = e1
% 157.26/27.19 | | | | | | | | |
% 157.26/27.19 | | | | | | | | | BETA: splitting (2) gives:
% 157.26/27.19 | | | | | | | | |
% 157.26/27.19 | | | | | | | | | Case 1:
% 157.26/27.19 | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | (124) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 157.26/27.19 | | | | | | | | | | & op(e2, e2) = e1)
% 157.26/27.19 | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | BETA: splitting (124) gives:
% 157.26/27.19 | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | Case 1:
% 157.26/27.19 | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | (125) all_58_2 = e1 & op(e2, e3) = e1
% 157.26/27.19 | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | ALPHA: (125) implies:
% 157.26/27.19 | | | | | | | | | | | (126) op(e2, e3) = e1
% 157.26/27.19 | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | BETA: splitting (13) gives:
% 157.26/27.19 | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | Case 1:
% 157.26/27.19 | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | (127) all_54_4 = e3
% 157.26/27.19 | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | COMBINE_EQS: (44), (127) imply:
% 157.26/27.19 | | | | | | | | | | | | (128) all_52_1 = e3
% 157.26/27.19 | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | REDUCE: (93), (128) imply:
% 157.26/27.19 | | | | | | | | | | | | (129) $false
% 157.26/27.19 | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 157.26/27.19 | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | Case 2:
% 157.26/27.19 | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | (130) ~ (all_54_4 = e3)
% 157.26/27.19 | | | | | | | | | | | | (131) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 157.26/27.19 | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | BETA: splitting (47) gives:
% 157.26/27.19 | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | Case 1:
% 157.26/27.19 | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | (132) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 157.26/27.19 | | | | | | | | | | | | | & op(e2, e3) = e2)
% 157.26/27.19 | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | REF_CLOSE: (29), (52), (65), (69), (126), (132) are
% 157.26/27.19 | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 157.26/27.19 | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | Case 2:
% 157.26/27.19 | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | (133) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 157.26/27.19 | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 157.26/27.19 | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | BETA: splitting (133) gives:
% 157.26/27.19 | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | Case 1:
% 157.26/27.19 | | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | | (134) all_58_6 = e2 & op(e1, e3) = e2
% 157.26/27.19 | | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | | ALPHA: (134) implies:
% 157.26/27.19 | | | | | | | | | | | | | | (135) all_58_6 = e2
% 157.26/27.19 | | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 157.26/27.19 | | | | | | | | | | | | | |
% 157.26/27.19 | | | | | | | | | | | | | | Case 1:
% 157.26/27.19 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | (136) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 157.26/27.20 | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | (137) all_58_2 = e2 & op(e2, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | (138) op(e2, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | REF_CLOSE: (52), (69), (126), (138) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | | sub-proof #1430.
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | (139) all_58_3 = e2 & op(e2, e2) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (9), (10), (17), (20), (21), (24), (25),
% 157.26/27.20 | | | | | | | | | | | | | | | | (29), (37), (38), (47), (51), (52), (53), (58),
% 157.26/27.20 | | | | | | | | | | | | | | | | (65), (69), (71), (80), (135), (139) are
% 157.26/27.20 | | | | | | | | | | | | | | | | inconsistent by sub-proof #342.
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | (140) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 157.26/27.20 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | (141) all_58_5 = e2 & op(e2, e1) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (24), (25), (29), (31), (38), (52),
% 157.26/27.20 | | | | | | | | | | | | | | | | (53), (68), (69), (71), (135), (141) are
% 157.26/27.20 | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | (142) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | (143) all_58_10 = e2
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | (144) all_54_4 = e2
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (144) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | (145) all_52_1 = e2
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | REDUCE: (114), (145) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | (146) $false
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | (147) ~ (all_54_4 = e2)
% 157.26/27.20 | | | | | | | | | | | | | | | | | (148) all_54_4 = e1 | all_54_4 = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (149) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.26/27.20 | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (150) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (151) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (152) op(e2, e3) = e3
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (44), (69), (93), (94), (148), (152) are
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1236.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (153) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (154) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (155) op(e2, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (69), (126), (155) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #1430.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (156) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (157) op(e3, e1) = e3
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (61), (69), (157) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #1538.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (158) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (159) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (160) op(e1, e3) = e1
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (69), (115), (160) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | sub-proof #1412.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (161) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (162) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (163) ~ (all_56_15 = e0)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (163) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (164) $false
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (165) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (166) all_56_2 = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (166) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (167) e3 = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (167) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (168) all_58_7 = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (24), (38), (69), (71), (81), (111), (135),
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (168) are inconsistent by sub-proof #1269.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (169) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.26/27.20 | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (170) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (171) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (172) op(e2, e1) = e2
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (173) all_54_4 = e1
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (173) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (174) all_52_1 = e1
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (174) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (175) ~ (e2 = e1)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (69) with e3, e2, e1, e2,
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | simplifying with (86), (172) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (176) e3 = e2
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (176) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (177) all_58_5 = e2
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (30), (38), (49), (52), (54), (66), (69),
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (71), (143), (172), (177) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #889.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (178) all_54_4 = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (178) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (179) all_52_1 = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (179) imply:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | (180) $false
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (181) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (38), (69), (86), (181) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | sub-proof #340.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (182) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (183) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (184) op(e0, e2) = e0
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (69), (97), (184) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | sub-proof #1532.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (185) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (34), (36), (37), (38), (53), (69), (80),
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | (110), (115), (123), (185) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | | sub-proof #339.
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | (186) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | REF_CLOSE: (9), (17), (69), (186) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | sub-proof #344.
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (187) all_58_3 = e1 & op(e2, e2) = e1
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | REF_CLOSE: (54), (66), (69), (187) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | sub-proof #1423.
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | (188) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1
% 157.26/27.20 | | | | | | | | | | & op(e2, e0) = e1)
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | BETA: splitting (188) gives:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (189) all_58_5 = e1 & op(e2, e1) = e1
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | ALPHA: (189) implies:
% 157.26/27.20 | | | | | | | | | | | (190) op(e2, e1) = e1
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | REF_CLOSE: (38), (69), (86), (190) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | sub-proof #352.
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (191) all_58_10 = e1 & op(e2, e0) = e1
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | ALPHA: (191) implies:
% 157.26/27.20 | | | | | | | | | | | (192) all_58_10 = e1
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | BETA: splitting (47) gives:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | (193) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 157.26/27.20 | | | | | | | | | | | | & op(e2, e3) = e2)
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | BETA: splitting (193) gives:
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | (194) all_58_0 = e2 & op(e3, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | REF_CLOSE: (29), (65), (194) are inconsistent by sub-proof
% 157.26/27.20 | | | | | | | | | | | | | #702.
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | (195) all_58_2 = e2 & op(e2, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | ALPHA: (195) implies:
% 157.26/27.20 | | | | | | | | | | | | | (196) op(e2, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | REF_CLOSE: (20), (69), (114), (196) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | sub-proof #1544.
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | (197) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 157.26/27.20 | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | BETA: splitting (197) gives:
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | (198) all_58_6 = e2 & op(e1, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | ALPHA: (198) implies:
% 157.26/27.20 | | | | | | | | | | | | | (199) all_58_6 = e2
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | BETA: splitting (42) gives:
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | (200) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 157.26/27.20 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | (201) all_58_2 = e2 & op(e2, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | (202) op(e2, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | REF_CLOSE: (20), (69), (114), (202) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | | | sub-proof #1544.
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | (203) all_58_3 = e2 & op(e2, e2) = e2
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (9), (10), (17), (20), (21), (24), (25),
% 157.26/27.20 | | | | | | | | | | | | | | | (29), (37), (38), (47), (51), (52), (53), (58),
% 157.26/27.20 | | | | | | | | | | | | | | | (65), (69), (71), (80), (199), (203) are
% 157.26/27.20 | | | | | | | | | | | | | | | inconsistent by sub-proof #342.
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | (204) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 157.26/27.20 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | (205) all_58_5 = e2 & op(e2, e1) = e2
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (24), (25), (29), (31), (38), (52),
% 157.26/27.20 | | | | | | | | | | | | | | | (53), (68), (69), (71), (199), (205) are
% 157.26/27.20 | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | (206) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 157.26/27.20 | | | | | | | | | | | | | | | (207) all_58_10 = e2
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | | REF_CLOSE: (52), (192), (207) are inconsistent by sub-proof
% 157.26/27.20 | | | | | | | | | | | | | | | #1091.
% 157.26/27.20 | | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | (208) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | | REF_CLOSE: (9), (17), (69), (208) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | | | sub-proof #344.
% 157.26/27.20 | | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | End of split
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | End of split
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | End of split
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | End of split
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | End of split
% 157.26/27.20 | | | |
% 157.26/27.20 | | | Case 2:
% 157.26/27.20 | | | |
% 157.26/27.20 | | | | (209) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 157.26/27.20 | | | | e1) = e3)
% 157.26/27.20 | | | |
% 157.26/27.20 | | | | BETA: splitting (209) gives:
% 157.26/27.20 | | | |
% 157.26/27.20 | | | | Case 1:
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | (210) all_58_8 = e3 & op(e1, e1) = e3
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | ALPHA: (210) implies:
% 157.26/27.20 | | | | | (211) op(e1, e1) = e3
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | REF_CLOSE: (24), (69), (81), (211) are inconsistent by sub-proof
% 157.26/27.20 | | | | | #1466.
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | Case 2:
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | (212) all_58_14 = e3 & op(e0, e1) = e3
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | ALPHA: (212) implies:
% 157.26/27.20 | | | | | (213) all_58_14 = e3
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | BETA: splitting (4) gives:
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | Case 1:
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | (214) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 157.26/27.20 | | | | | | op(e0, e2) = e1)
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | BETA: splitting (214) gives:
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | Case 1:
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | (215) all_58_12 = e1 & op(e0, e3) = e1
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | ALPHA: (215) implies:
% 157.26/27.20 | | | | | | | (216) all_58_12 = e1
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | REF_CLOSE: (7), (38), (216) are inconsistent by sub-proof #1516.
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | Case 2:
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | (217) all_58_13 = e1 & op(e0, e2) = e1
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | ALPHA: (217) implies:
% 157.26/27.20 | | | | | | | (218) op(e0, e2) = e1
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | BETA: splitting (12) gives:
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | (219) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 157.26/27.20 | | | | | | | | op(e2, e1) = e2)
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | BETA: splitting (219) gives:
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | (220) all_58_4 = e2 & op(e3, e1) = e2
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | ALPHA: (220) implies:
% 157.26/27.20 | | | | | | | | | (221) all_58_4 = e2
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | BETA: splitting (28) gives:
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | (222) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 157.26/27.20 | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | BETA: splitting (222) gives:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (223) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | REF_CLOSE: (9), (17), (69), (223) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | sub-proof #344.
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (224) all_58_13 = e2 & op(e0, e2) = e2
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | ALPHA: (224) implies:
% 157.26/27.20 | | | | | | | | | | | (225) op(e0, e2) = e2
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | REF_CLOSE: (52), (63), (69), (218), (225) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | sub-proof #1319.
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | (226) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 157.26/27.20 | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | BETA: splitting (226) gives:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (227) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | ALPHA: (227) implies:
% 157.26/27.20 | | | | | | | | | | | (228) op(e0, e1) = e2
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | REF_CLOSE: (31), (38), (46), (50), (52), (53), (69), (80),
% 157.26/27.20 | | | | | | | | | | | (221), (228) are inconsistent by sub-proof #1471.
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (229) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | REF_CLOSE: (14), (45), (69), (229) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | sub-proof #1452.
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | (230) all_58_5 = e2 & op(e2, e1) = e2
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | ALPHA: (230) implies:
% 157.26/27.20 | | | | | | | | | (231) all_58_5 = e2
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | REF_CLOSE: (31), (71), (231) are inconsistent by sub-proof
% 157.26/27.20 | | | | | | | | | #897.
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | End of split
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | (232) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 157.26/27.20 | | | | | | | | op(e0, e1) = e2)
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | BETA: splitting (232) gives:
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | (233) all_58_8 = e2 & op(e1, e1) = e2
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | REF_CLOSE: (3), (58), (69), (233) are inconsistent by
% 157.26/27.20 | | | | | | | | | sub-proof #1440.
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | (234) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | REF_CLOSE: (71), (213), (234) are inconsistent by sub-proof
% 157.26/27.20 | | | | | | | | | #1439.
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | End of split
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | End of split
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | End of split
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | Case 2:
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | (235) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 157.26/27.20 | | | | | | op(e0, e0) = e1)
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | BETA: splitting (235) gives:
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | Case 1:
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | (236) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | REF_CLOSE: (38), (213), (236) are inconsistent by sub-proof #844.
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | Case 2:
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | (237) all_58_15 = e1 & op(e0, e0) = e1
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | REF_CLOSE: (43), (45), (69), (237) are inconsistent by sub-proof
% 157.26/27.20 | | | | | | | #1418.
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | End of split
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | End of split
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | End of split
% 157.26/27.20 | | | |
% 157.26/27.20 | | | End of split
% 157.26/27.20 | | |
% 157.26/27.20 | | Case 2:
% 157.26/27.20 | | |
% 157.26/27.20 | | | (238) all_58_14 = e0 & op(e0, e1) = e0
% 157.26/27.20 | | |
% 157.26/27.20 | | | ALPHA: (238) implies:
% 157.26/27.20 | | | (239) all_58_14 = e0
% 157.26/27.20 | | | (240) op(e0, e1) = e0
% 157.26/27.20 | | |
% 157.26/27.20 | | | BETA: splitting (12) gives:
% 157.26/27.20 | | |
% 157.26/27.20 | | | Case 1:
% 157.26/27.20 | | | |
% 157.26/27.20 | | | | (241) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 157.26/27.20 | | | | = e2)
% 157.26/27.20 | | | |
% 157.26/27.20 | | | | BETA: splitting (241) gives:
% 157.26/27.20 | | | |
% 157.26/27.20 | | | | Case 1:
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | (242) all_58_4 = e2 & op(e3, e1) = e2
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | ALPHA: (242) implies:
% 157.26/27.20 | | | | | (243) op(e3, e1) = e2
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | BETA: splitting (28) gives:
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | Case 1:
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | (244) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 157.26/27.20 | | | | | | op(e0, e2) = e2)
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | BETA: splitting (244) gives:
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | Case 1:
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | (245) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | REF_CLOSE: (9), (17), (69), (245) are inconsistent by sub-proof
% 157.26/27.20 | | | | | | | #344.
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | Case 2:
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | (246) all_58_13 = e2 & op(e0, e2) = e2
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | ALPHA: (246) implies:
% 157.26/27.20 | | | | | | | (247) op(e0, e2) = e2
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | BETA: splitting (50) gives:
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | (248) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 &
% 157.26/27.20 | | | | | | | | op(e2, e1) = e1)
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | REF_CLOSE: (31), (38), (52), (69), (243), (248) are inconsistent
% 157.26/27.20 | | | | | | | | by sub-proof #337.
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | (249) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 157.26/27.20 | | | | | | | | op(e0, e1) = e1)
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | BETA: splitting (249) gives:
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | (250) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | ALPHA: (250) implies:
% 157.26/27.20 | | | | | | | | | (251) all_58_8 = e1
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | BETA: splitting (4) gives:
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | (252) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 157.26/27.20 | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | REF_CLOSE: (7), (38), (52), (63), (69), (247), (252) are
% 157.26/27.20 | | | | | | | | | | inconsistent by sub-proof #336.
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | (253) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 157.26/27.20 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | BETA: splitting (253) gives:
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 1:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (254) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | ALPHA: (254) implies:
% 157.26/27.20 | | | | | | | | | | | (255) all_58_14 = e1
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | COMBINE_EQS: (239), (255) imply:
% 157.26/27.20 | | | | | | | | | | | (256) e1 = e0
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | COMBINE_EQS: (251), (256) imply:
% 157.26/27.20 | | | | | | | | | | | (257) all_58_8 = e0
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | REF_CLOSE: (31), (38), (50), (52), (53), (69), (239), (243),
% 157.26/27.20 | | | | | | | | | | | (257) are inconsistent by sub-proof #335.
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | (258) all_58_15 = e1 & op(e0, e0) = e1
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | | REF_CLOSE: (43), (45), (69), (258) are inconsistent by
% 157.26/27.20 | | | | | | | | | | | sub-proof #1418.
% 157.26/27.20 | | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | | |
% 157.26/27.20 | | | | | | | | | End of split
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | Case 2:
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | (259) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | ALPHA: (259) implies:
% 157.26/27.20 | | | | | | | | | (260) all_58_14 = e1
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | | REF_CLOSE: (53), (239), (260) are inconsistent by sub-proof
% 157.26/27.20 | | | | | | | | | #614.
% 157.26/27.20 | | | | | | | | |
% 157.26/27.20 | | | | | | | | End of split
% 157.26/27.20 | | | | | | | |
% 157.26/27.20 | | | | | | | End of split
% 157.26/27.20 | | | | | | |
% 157.26/27.20 | | | | | | End of split
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | Case 2:
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | (261) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 157.26/27.20 | | | | | | op(e0, e0) = e2)
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | | REF_CLOSE: (14), (29), (45), (46), (69), (240), (261) are
% 157.26/27.20 | | | | | | inconsistent by sub-proof #334.
% 157.26/27.20 | | | | | |
% 157.26/27.20 | | | | | End of split
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | Case 2:
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | (262) all_58_5 = e2 & op(e2, e1) = e2
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | ALPHA: (262) implies:
% 157.26/27.20 | | | | | (263) all_58_5 = e2
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | | REF_CLOSE: (31), (71), (263) are inconsistent by sub-proof #897.
% 157.26/27.20 | | | | |
% 157.26/27.20 | | | | End of split
% 157.26/27.20 | | | |
% 157.26/27.20 | | | Case 2:
% 157.26/27.20 | | | |
% 157.26/27.20 | | | | (264) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 157.26/27.20 | | | | e1) = e2)
% 157.26/27.20 | | | |
% 157.26/27.20 | | | | REF_CLOSE: (3), (29), (46), (58), (69), (240), (264) are inconsistent by
% 157.26/27.20 | | | | sub-proof #333.
% 157.26/27.20 | | | |
% 157.26/27.20 | | | End of split
% 157.26/27.20 | | |
% 157.26/27.20 | | End of split
% 157.26/27.20 | |
% 157.26/27.20 | End of split
% 157.26/27.20 |
% 157.26/27.20 End of proof
% 157.26/27.20
% 157.26/27.20 Sub-proof #333 shows that the following formulas are inconsistent:
% 157.26/27.20 ----------------------------------------------------------------
% 157.26/27.20 (1) op(e1, e1) = all_6_2
% 157.26/27.20 (2) ~ (e2 = e0)
% 157.26/27.20 (3) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.20 (4) op(e0, e1) = all_52_11
% 157.26/27.20 (5) op(e0, e1) = e0
% 157.26/27.20 (6) ~ (all_6_2 = e2)
% 157.26/27.20 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.20
% 157.26/27.20 Begin of proof
% 157.26/27.20 |
% 157.26/27.20 | BETA: splitting (3) gives:
% 157.26/27.20 |
% 157.26/27.20 | Case 1:
% 157.26/27.20 | |
% 157.26/27.20 | | (8) all_58_8 = e2 & op(e1, e1) = e2
% 157.26/27.20 | |
% 157.26/27.20 | | REF_CLOSE: (1), (6), (7), (8) are inconsistent by sub-proof #1440.
% 157.26/27.20 | |
% 157.26/27.20 | Case 2:
% 157.26/27.20 | |
% 157.26/27.20 | | (9) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.20 | |
% 157.26/27.20 | | ALPHA: (9) implies:
% 157.26/27.20 | | (10) op(e0, e1) = e2
% 157.26/27.20 | |
% 157.26/27.20 | | REF_CLOSE: (2), (4), (5), (7), (10) are inconsistent by sub-proof #1372.
% 157.26/27.20 | |
% 157.26/27.20 | End of split
% 157.26/27.20 |
% 157.26/27.20 End of proof
% 157.26/27.20
% 157.26/27.20 Sub-proof #334 shows that the following formulas are inconsistent:
% 157.26/27.20 ----------------------------------------------------------------
% 157.26/27.20 (1) ~ (all_4_2 = e2)
% 157.26/27.20 (2) ~ (e2 = e0)
% 157.26/27.20 (3) op(e0, e0) = all_4_2
% 157.26/27.20 (4) op(e0, e1) = all_52_11
% 157.26/27.21 (5) op(e0, e1) = e0
% 157.26/27.21 (6) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.21 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (6) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (8) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.21 | |
% 157.26/27.21 | | ALPHA: (8) implies:
% 157.26/27.21 | | (9) op(e0, e1) = e2
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (2), (4), (5), (7), (9) are inconsistent by sub-proof #1372.
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (10) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (1), (3), (7), (10) are inconsistent by sub-proof #1452.
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #335 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) all_58_14 = e0
% 157.26/27.21 (2) op(e3, e1) = e2
% 157.26/27.21 (3) all_58_5 = e3
% 157.26/27.21 (4) ~ (e3 = e1)
% 157.26/27.21 (5) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.21 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.21 (6) ~ (e2 = e1)
% 157.26/27.21 (7) ~ (e1 = e0)
% 157.26/27.21 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (9) all_58_8 = e0
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (5) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (10) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 157.26/27.21 | | e1)
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (2), (3), (4), (6), (8), (10) are inconsistent by sub-proof #337.
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (11) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 157.26/27.21 | | e1)
% 157.26/27.21 | |
% 157.26/27.21 | | BETA: splitting (11) gives:
% 157.26/27.21 | |
% 157.26/27.21 | | Case 1:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (12) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.21 | | |
% 157.26/27.21 | | | REF_CLOSE: (7), (9), (12) are inconsistent by sub-proof #1474.
% 157.26/27.21 | | |
% 157.26/27.21 | | Case 2:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (13) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.21 | | |
% 157.26/27.21 | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #482.
% 157.26/27.21 | | |
% 157.26/27.21 | | End of split
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #336 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) all_58_12 = e3
% 157.26/27.21 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.21 (3) ~ (e3 = e1)
% 157.26/27.21 (4) ~ (e2 = e1)
% 157.26/27.21 (5) op(e0, e2) = e2
% 157.26/27.21 (6) op(e0, e2) = all_52_7
% 157.26/27.21 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (2) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (8) all_58_12 = e1 & op(e0, e3) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1388.
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (9) all_58_13 = e1 & op(e0, e2) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | ALPHA: (9) implies:
% 157.26/27.21 | | (10) op(e0, e2) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (4), (5), (6), (7), (10) are inconsistent by sub-proof #1319.
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #337 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) op(e3, e1) = e2
% 157.26/27.21 (2) all_58_5 = e3
% 157.26/27.21 (3) ~ (e3 = e1)
% 157.26/27.21 (4) ~ (e2 = e1)
% 157.26/27.21 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (6) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (6) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (7) all_58_4 = e1 & op(e3, e1) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | ALPHA: (7) implies:
% 157.26/27.21 | | (8) op(e3, e1) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #338.
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (9) all_58_5 = e1 & op(e2, e1) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #1092.
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #338 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (2) op(e3, e1) = e2
% 157.26/27.21 (3) op(e3, e1) = e1
% 157.26/27.21 (4) ~ (e2 = e1)
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | GROUND_INST: instantiating (1) with e2, e1, e1, e3, simplifying with (2), (3)
% 157.26/27.21 | gives:
% 157.26/27.21 | (5) e2 = e1
% 157.26/27.21 |
% 157.26/27.21 | REDUCE: (4), (5) imply:
% 157.26/27.21 | (6) $false
% 157.26/27.21 |
% 157.26/27.21 | CLOSE: (6) is inconsistent.
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #339 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.21 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.21 (2) all_58_11 = e1
% 157.26/27.21 (3) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) = e1 &
% 157.26/27.21 op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.26/27.21 e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.26/27.21 (4) op(e1, e3) = all_52_2
% 157.26/27.21 (5) all_56_15 = e0
% 157.26/27.21 (6) all_58_7 = e3
% 157.26/27.21 (7) ~ (e3 = e1)
% 157.26/27.21 (8) ~ (all_52_2 = e1)
% 157.26/27.21 (9) ~ (e1 = e0)
% 157.26/27.21 (10) all_56_8 = e1
% 157.26/27.21 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (12) all_58_8 = e0
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (3) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (13) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) =
% 157.26/27.21 | | e1 & op(e0, e1) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | ALPHA: (13) implies:
% 157.26/27.21 | | (14) ~ (all_56_15 = e0)
% 157.26/27.21 | |
% 157.26/27.21 | | REDUCE: (5), (14) imply:
% 157.26/27.21 | | (15) $false
% 157.26/27.21 | |
% 157.26/27.21 | | CLOSE: (15) is inconsistent.
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (16) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) =
% 157.26/27.21 | | e0 & op(e0, e1) = e0
% 157.26/27.21 | |
% 157.26/27.21 | | ALPHA: (16) implies:
% 157.26/27.21 | | (17) all_56_8 = e0
% 157.26/27.21 | |
% 157.26/27.21 | | COMBINE_EQS: (10), (17) imply:
% 157.26/27.21 | | (18) e1 = e0
% 157.26/27.21 | |
% 157.26/27.21 | | SIMP: (18) implies:
% 157.26/27.21 | | (19) e1 = e0
% 157.26/27.21 | |
% 157.26/27.21 | | COMBINE_EQS: (2), (19) imply:
% 157.26/27.21 | | (20) all_58_11 = e0
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (11), (12), (20) are inconsistent
% 157.26/27.21 | | by sub-proof #1296.
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #340 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) op(e2, e1) = e3
% 157.26/27.21 (2) all_56_15 = e0
% 157.26/27.21 (3) ~ (e3 = e1)
% 157.26/27.21 (4) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 &
% 157.26/27.21 op(e1, e2) = e1) | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.26/27.21 e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.26/27.21 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (4) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (6) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1
% 157.26/27.21 | | & op(e1, e2) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | ALPHA: (6) implies:
% 157.26/27.21 | | (7) op(e2, e1) = e1
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #352.
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (8) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) =
% 157.26/27.21 | | e2 & op(e0, e2) = e2
% 157.26/27.21 | |
% 157.26/27.21 | | ALPHA: (8) implies:
% 157.26/27.21 | | (9) ~ (all_56_15 = e0)
% 157.26/27.21 | |
% 157.26/27.21 | | REDUCE: (2), (9) imply:
% 157.26/27.21 | | (10) $false
% 157.26/27.21 | |
% 157.26/27.21 | | CLOSE: (10) is inconsistent.
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #341 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) all_58_5 = e2 & op(e2, e1) = e2
% 157.26/27.21 (2) all_58_12 = e3
% 157.26/27.21 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.21 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.21 (4) all_58_6 = e2
% 157.26/27.21 (5) ~ (e3 = e0)
% 157.26/27.21 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.21 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.21 (7) ~ (e2 = e0)
% 157.26/27.21 (8) all_58_5 = e3
% 157.26/27.21 (9) ~ (e3 = e1)
% 157.26/27.21 (10) ~ (e2 = e1)
% 157.26/27.21 (11) ~ (e1 = e0)
% 157.26/27.21 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.21 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.21 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (14) ~ (e3 = e2)
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | ALPHA: (1) implies:
% 157.26/27.21 | (15) all_58_5 = e2
% 157.26/27.21 |
% 157.26/27.21 | COMBINE_EQS: (8), (15) imply:
% 157.26/27.21 | (16) e3 = e2
% 157.26/27.21 |
% 157.26/27.21 | COMBINE_EQS: (2), (16) imply:
% 157.26/27.21 | (17) all_58_12 = e2
% 157.26/27.21 |
% 157.26/27.21 | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14), (17)
% 157.26/27.21 | are inconsistent by sub-proof #1481.
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #342 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.21 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.21 (2) op(e1, e1) = all_6_2
% 157.26/27.21 (3) op(e0, e3) = all_10_0
% 157.26/27.21 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.21 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.21 (5) ~ (all_10_0 = e2)
% 157.26/27.21 (6) op(e2, e3) = all_52_1
% 157.26/27.21 (7) all_58_6 = e2
% 157.26/27.21 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.21 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.21 (9) ~ (e3 = e0)
% 157.26/27.21 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.21 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.21 (11) all_58_3 = e2 & op(e2, e2) = e2
% 157.26/27.21 (12) ~ (e2 = e0)
% 157.26/27.21 (13) all_58_7 = e3
% 157.26/27.21 (14) ~ (e3 = e1)
% 157.26/27.21 (15) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 157.26/27.21 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 157.26/27.21 (16) all_58_3 = e0
% 157.26/27.21 (17) ~ (e2 = e1)
% 157.26/27.21 (18) ~ (e1 = e0)
% 157.26/27.21 (19) ~ (all_6_2 = e2)
% 157.26/27.21 (20) all_58_0 = e0
% 157.26/27.21 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (22) all_58_8 = e0
% 157.26/27.21 (23) ~ (e3 = e2)
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | ALPHA: (11) implies:
% 157.26/27.21 | (24) all_58_3 = e2
% 157.26/27.21 |
% 157.26/27.21 | COMBINE_EQS: (16), (24) imply:
% 157.26/27.21 | (25) e2 = e0
% 157.26/27.21 |
% 157.26/27.21 | SIMP: (25) implies:
% 157.26/27.21 | (26) e2 = e0
% 157.26/27.21 |
% 157.26/27.21 | COMBINE_EQS: (7), (26) imply:
% 157.26/27.21 | (27) all_58_6 = e0
% 157.26/27.21 |
% 157.26/27.21 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14),
% 157.26/27.21 | (15), (17), (18), (19), (20), (21), (22), (23), (27) are
% 157.26/27.21 | inconsistent by sub-proof #343.
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #343 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.21 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.21 (2) op(e1, e1) = all_6_2
% 157.26/27.21 (3) op(e0, e3) = all_10_0
% 157.26/27.21 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.21 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.21 (5) ~ (all_10_0 = e2)
% 157.26/27.21 (6) op(e2, e3) = all_52_1
% 157.26/27.21 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.21 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.21 (8) ~ (e3 = e0)
% 157.26/27.21 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.21 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.21 (10) ~ (e2 = e0)
% 157.26/27.21 (11) all_58_6 = e0
% 157.26/27.21 (12) all_58_7 = e3
% 157.26/27.21 (13) ~ (e3 = e1)
% 157.26/27.21 (14) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 157.26/27.21 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 157.26/27.21 (15) ~ (e2 = e1)
% 157.26/27.21 (16) ~ (e1 = e0)
% 157.26/27.21 (17) ~ (all_6_2 = e2)
% 157.26/27.21 (18) all_58_0 = e0
% 157.26/27.21 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (20) all_58_8 = e0
% 157.26/27.21 (21) ~ (e3 = e2)
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (14) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (22) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 157.26/27.21 | | e2)
% 157.26/27.21 | |
% 157.26/27.21 | | BETA: splitting (22) gives:
% 157.26/27.21 | |
% 157.26/27.21 | | Case 1:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (23) all_58_0 = e2 & op(e3, e3) = e2
% 157.26/27.21 | | |
% 157.26/27.21 | | | REF_CLOSE: (10), (18), (23) are inconsistent by sub-proof #702.
% 157.26/27.21 | | |
% 157.26/27.21 | | Case 2:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (24) all_58_2 = e2 & op(e2, e3) = e2
% 157.26/27.21 | | |
% 157.26/27.21 | | | ALPHA: (24) implies:
% 157.26/27.21 | | | (25) op(e2, e3) = e2
% 157.26/27.21 | | |
% 157.26/27.21 | | | BETA: splitting (9) gives:
% 157.26/27.21 | | |
% 157.26/27.21 | | | Case 1:
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 157.26/27.21 | | | | = e1)
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | REF_CLOSE: (15), (16), (18), (19), (25), (26) are inconsistent by
% 157.26/27.21 | | | | sub-proof #1160.
% 157.26/27.21 | | | |
% 157.26/27.21 | | | Case 2:
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | (27) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 157.26/27.21 | | | | = e1)
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | BETA: splitting (27) gives:
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | Case 1:
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | (28) all_58_6 = e1 & op(e1, e3) = e1
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | REF_CLOSE: (11), (16), (28) are inconsistent by sub-proof #1064.
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | Case 2:
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | (29) all_58_12 = e1 & op(e0, e3) = e1
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | ALPHA: (29) implies:
% 157.26/27.21 | | | | | (30) all_58_12 = e1
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (11), (12), (13), (15), (16),
% 157.26/27.21 | | | | | (17), (18), (19), (20), (21), (25), (30) are inconsistent
% 157.26/27.21 | | | | | by sub-proof #346.
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | End of split
% 157.26/27.21 | | | |
% 157.26/27.21 | | | End of split
% 157.26/27.21 | | |
% 157.26/27.21 | | End of split
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (31) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 157.26/27.21 | | e2)
% 157.26/27.21 | |
% 157.26/27.21 | | BETA: splitting (31) gives:
% 157.26/27.21 | |
% 157.26/27.21 | | Case 1:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (32) all_58_6 = e2 & op(e1, e3) = e2
% 157.26/27.21 | | |
% 157.26/27.21 | | | REF_CLOSE: (10), (11), (32) are inconsistent by sub-proof #345.
% 157.26/27.21 | | |
% 157.26/27.21 | | Case 2:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (33) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.21 | | |
% 157.26/27.21 | | | REF_CLOSE: (3), (5), (19), (33) are inconsistent by sub-proof #344.
% 157.26/27.21 | | |
% 157.26/27.21 | | End of split
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #344 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (3) op(e0, e3) = all_10_0
% 157.26/27.21 (4) ~ (all_10_0 = e2)
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | ALPHA: (1) implies:
% 157.26/27.21 | (5) op(e0, e3) = e2
% 157.26/27.21 |
% 157.26/27.21 | GROUND_INST: instantiating (2) with all_10_0, e2, e3, e0, simplifying with
% 157.26/27.21 | (3), (5) gives:
% 157.26/27.21 | (6) all_10_0 = e2
% 157.26/27.21 |
% 157.26/27.21 | REDUCE: (4), (6) imply:
% 157.26/27.21 | (7) $false
% 157.26/27.21 |
% 157.26/27.21 | CLOSE: (7) is inconsistent.
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #345 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) all_58_6 = e2 & op(e1, e3) = e2
% 157.26/27.21 (2) all_58_6 = e0
% 157.26/27.21 (3) ~ (e2 = e0)
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | ALPHA: (1) implies:
% 157.26/27.21 | (4) all_58_6 = e2
% 157.26/27.21 |
% 157.26/27.21 | COMBINE_EQS: (2), (4) imply:
% 157.26/27.21 | (5) e2 = e0
% 157.26/27.21 |
% 157.26/27.21 | REDUCE: (3), (5) imply:
% 157.26/27.21 | (6) $false
% 157.26/27.21 |
% 157.26/27.21 | CLOSE: (6) is inconsistent.
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #346 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.21 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.21 (2) op(e1, e1) = all_6_2
% 157.26/27.21 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.21 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.21 (4) op(e2, e3) = all_52_1
% 157.26/27.21 (5) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.21 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.21 (6) ~ (e3 = e0)
% 157.26/27.21 (7) all_58_6 = e0
% 157.26/27.21 (8) op(e2, e3) = e2
% 157.26/27.21 (9) all_58_7 = e3
% 157.26/27.21 (10) ~ (e3 = e1)
% 157.26/27.21 (11) ~ (e2 = e1)
% 157.26/27.21 (12) ~ (e1 = e0)
% 157.26/27.21 (13) ~ (all_6_2 = e2)
% 157.26/27.21 (14) all_58_0 = e0
% 157.26/27.21 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (16) all_58_8 = e0
% 157.26/27.21 (17) ~ (e3 = e2)
% 157.26/27.21 (18) all_58_12 = e1
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (1) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (19) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 157.26/27.21 | | e1)
% 157.26/27.21 | |
% 157.26/27.21 | | BETA: splitting (19) gives:
% 157.26/27.21 | |
% 157.26/27.21 | | Case 1:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (20) all_58_6 = e1 & op(e1, e3) = e1
% 157.26/27.21 | | |
% 157.26/27.21 | | | REF_CLOSE: (7), (12), (20) are inconsistent by sub-proof #1064.
% 157.26/27.21 | | |
% 157.26/27.21 | | Case 2:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (21) all_58_7 = e1 & op(e1, e2) = e1
% 157.26/27.21 | | |
% 157.26/27.21 | | | ALPHA: (21) implies:
% 157.26/27.21 | | | (22) all_58_7 = e1
% 157.26/27.21 | | |
% 157.26/27.21 | | | REF_CLOSE: (9), (10), (22) are inconsistent by sub-proof #1330.
% 157.26/27.21 | | |
% 157.26/27.21 | | End of split
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (23) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 157.26/27.21 | | e1)
% 157.26/27.21 | |
% 157.26/27.21 | | BETA: splitting (23) gives:
% 157.26/27.21 | |
% 157.26/27.21 | | Case 1:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (24) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.21 | | |
% 157.26/27.21 | | | REF_CLOSE: (12), (16), (24) are inconsistent by sub-proof #1474.
% 157.26/27.21 | | |
% 157.26/27.21 | | Case 2:
% 157.26/27.21 | | |
% 157.26/27.21 | | | (25) all_58_11 = e1 & op(e1, e0) = e1
% 157.26/27.21 | | |
% 157.26/27.21 | | | ALPHA: (25) implies:
% 157.26/27.21 | | | (26) all_58_11 = e1
% 157.26/27.21 | | |
% 157.26/27.21 | | | BETA: splitting (5) gives:
% 157.26/27.21 | | |
% 157.26/27.21 | | | Case 1:
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | (27) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 157.26/27.21 | | | | = e2)
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | BETA: splitting (27) gives:
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | Case 1:
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | (28) all_58_6 = e2 & op(e1, e3) = e2
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | ALPHA: (28) implies:
% 157.26/27.21 | | | | | (29) all_58_6 = e2
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | REF_CLOSE: (3), (4), (6), (8), (10), (14), (15), (17), (18), (29) are
% 157.26/27.21 | | | | | inconsistent by sub-proof #1125.
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | Case 2:
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | (30) all_58_7 = e2 & op(e1, e2) = e2
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | ALPHA: (30) implies:
% 157.26/27.21 | | | | | (31) all_58_7 = e2
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | | REF_CLOSE: (9), (17), (31) are inconsistent by sub-proof #1215.
% 157.26/27.21 | | | | |
% 157.26/27.21 | | | | End of split
% 157.26/27.21 | | | |
% 157.26/27.21 | | | Case 2:
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | (32) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 157.26/27.21 | | | | = e2)
% 157.26/27.21 | | | |
% 157.26/27.21 | | | | REF_CLOSE: (2), (11), (13), (15), (26), (32) are inconsistent by
% 157.26/27.21 | | | | sub-proof #1167.
% 157.26/27.21 | | | |
% 157.26/27.21 | | | End of split
% 157.26/27.21 | | |
% 157.26/27.21 | | End of split
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #347 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 157.26/27.21 (2) ~ (e2 = e0)
% 157.26/27.21 (3) ~ (e2 = e1)
% 157.26/27.21 (4) op(e2, e3) = e1
% 157.26/27.21 (5) all_58_0 = e0
% 157.26/27.21 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (1) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.21 | |
% 157.26/27.21 | | (7) all_58_0 = e2 & op(e3, e3) = e2
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #702.
% 157.26/27.21 | |
% 157.26/27.21 | Case 2:
% 157.26/27.21 | |
% 157.26/27.21 | | (8) all_58_2 = e2 & op(e2, e3) = e2
% 157.26/27.21 | |
% 157.26/27.21 | | ALPHA: (8) implies:
% 157.26/27.21 | | (9) op(e2, e3) = e2
% 157.26/27.21 | |
% 157.26/27.21 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1430.
% 157.26/27.21 | |
% 157.26/27.21 | End of split
% 157.26/27.21 |
% 157.26/27.21 End of proof
% 157.26/27.21
% 157.26/27.21 Sub-proof #348 shows that the following formulas are inconsistent:
% 157.26/27.21 ----------------------------------------------------------------
% 157.26/27.21 (1) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.21 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.21 (2) ~ (e2 = e0)
% 157.26/27.21 (3) all_58_9 = e3
% 157.26/27.21 (4) ~ (e3 = e1)
% 157.26/27.21 (5) all_58_4 = e0 & op(e3, e1) = e0
% 157.26/27.21 (6) ~ (e2 = e1)
% 157.26/27.21 (7) ~ (e1 = e0)
% 157.26/27.21 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.21 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.21 (9) all_58_0 = e0
% 157.26/27.21 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.21 (11) ~ (e3 = e2)
% 157.26/27.21
% 157.26/27.21 Begin of proof
% 157.26/27.21 |
% 157.26/27.21 | ALPHA: (5) implies:
% 157.26/27.21 | (12) all_58_4 = e0
% 157.26/27.21 | (13) op(e3, e1) = e0
% 157.26/27.21 |
% 157.26/27.21 | BETA: splitting (1) gives:
% 157.26/27.21 |
% 157.26/27.21 | Case 1:
% 157.26/27.22 | |
% 157.26/27.22 | | (14) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 157.26/27.22 | | e2)
% 157.26/27.22 | |
% 157.26/27.22 | | BETA: splitting (14) gives:
% 157.26/27.22 | |
% 157.26/27.22 | | Case 1:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (15) all_58_0 = e2 & op(e3, e3) = e2
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (2), (9), (15) are inconsistent by sub-proof #702.
% 157.26/27.22 | | |
% 157.26/27.22 | | Case 2:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (16) all_58_1 = e2 & op(e3, e2) = e2
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (13), (16) are inconsistent
% 157.26/27.22 | | | by sub-proof #349.
% 157.26/27.22 | | |
% 157.26/27.22 | | End of split
% 157.26/27.22 | |
% 157.26/27.22 | Case 2:
% 157.26/27.22 | |
% 157.26/27.22 | | (17) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 157.26/27.22 | | e2)
% 157.26/27.22 | |
% 157.26/27.22 | | BETA: splitting (17) gives:
% 157.26/27.22 | |
% 157.26/27.22 | | Case 1:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (18) all_58_4 = e2 & op(e3, e1) = e2
% 157.26/27.22 | | |
% 157.26/27.22 | | | ALPHA: (18) implies:
% 157.26/27.22 | | | (19) all_58_4 = e2
% 157.26/27.22 | | |
% 157.26/27.22 | | | COMBINE_EQS: (12), (19) imply:
% 157.26/27.22 | | | (20) e2 = e0
% 157.26/27.22 | | |
% 157.26/27.22 | | | REDUCE: (2), (20) imply:
% 157.26/27.22 | | | (21) $false
% 157.26/27.22 | | |
% 157.26/27.22 | | | CLOSE: (21) is inconsistent.
% 157.26/27.22 | | |
% 157.26/27.22 | | Case 2:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (22) all_58_9 = e2 & op(e3, e0) = e2
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (3), (11), (22) are inconsistent by sub-proof #1353.
% 157.26/27.22 | | |
% 157.26/27.22 | | End of split
% 157.26/27.22 | |
% 157.26/27.22 | End of split
% 157.26/27.22 |
% 157.26/27.22 End of proof
% 157.26/27.22
% 157.26/27.22 Sub-proof #349 shows that the following formulas are inconsistent:
% 157.26/27.22 ----------------------------------------------------------------
% 157.26/27.22 (1) all_58_9 = e3
% 157.26/27.22 (2) ~ (e3 = e1)
% 157.26/27.22 (3) op(e3, e1) = e0
% 157.26/27.22 (4) ~ (e2 = e1)
% 157.26/27.22 (5) ~ (e1 = e0)
% 157.26/27.22 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.22 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.22 (7) all_58_1 = e2 & op(e3, e2) = e2
% 157.26/27.22 (8) all_58_0 = e0
% 157.26/27.22 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.22
% 157.26/27.22 Begin of proof
% 157.26/27.22 |
% 157.26/27.22 | ALPHA: (7) implies:
% 157.26/27.22 | (10) all_58_1 = e2
% 157.26/27.22 |
% 157.26/27.22 | BETA: splitting (6) gives:
% 157.26/27.22 |
% 157.26/27.22 | Case 1:
% 157.26/27.22 | |
% 157.26/27.22 | | (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 157.26/27.22 | | e1)
% 157.26/27.22 | |
% 157.26/27.22 | | BETA: splitting (11) gives:
% 157.26/27.22 | |
% 157.26/27.22 | | Case 1:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (12) all_58_0 = e1 & op(e3, e3) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (5), (8), (12) are inconsistent by sub-proof #1495.
% 157.26/27.22 | | |
% 157.26/27.22 | | Case 2:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (13) all_58_1 = e1 & op(e3, e2) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #1219.
% 157.26/27.22 | | |
% 157.26/27.22 | | End of split
% 157.26/27.22 | |
% 157.26/27.22 | Case 2:
% 157.26/27.22 | |
% 157.26/27.22 | | (14) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 157.26/27.22 | | e1)
% 157.26/27.22 | |
% 157.26/27.22 | | BETA: splitting (14) gives:
% 157.26/27.22 | |
% 157.26/27.22 | | Case 1:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (15) all_58_4 = e1 & op(e3, e1) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | ALPHA: (15) implies:
% 157.26/27.22 | | | (16) op(e3, e1) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (3), (5), (9), (16) are inconsistent by sub-proof #1281.
% 157.26/27.22 | | |
% 157.26/27.22 | | Case 2:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (17) all_58_9 = e1 & op(e3, e0) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (1), (2), (17) are inconsistent by sub-proof #1078.
% 157.26/27.22 | | |
% 157.26/27.22 | | End of split
% 157.26/27.22 | |
% 157.26/27.22 | End of split
% 157.26/27.22 |
% 157.26/27.22 End of proof
% 157.26/27.22
% 157.26/27.22 Sub-proof #350 shows that the following formulas are inconsistent:
% 157.26/27.22 ----------------------------------------------------------------
% 157.26/27.22 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.22 (2) all_58_9 = e3
% 157.26/27.22 (3) ~ (e3 = e1)
% 157.26/27.22 (4) ~ (all_4_2 = e1)
% 157.26/27.22 (5) op(e0, e0) = all_4_2
% 157.26/27.22 (6) all_58_11 = e2
% 157.26/27.22 (7) ~ (e2 = e1)
% 157.26/27.22 (8) ~ (e1 = e0)
% 157.26/27.22 (9) all_58_10 = e0
% 157.26/27.22 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.22
% 157.26/27.22 Begin of proof
% 157.26/27.22 |
% 157.26/27.22 | BETA: splitting (1) gives:
% 157.26/27.22 |
% 157.26/27.22 | Case 1:
% 157.26/27.22 | |
% 157.26/27.22 | | (11) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.26/27.22 | | e1)
% 157.26/27.22 | |
% 157.26/27.22 | | BETA: splitting (11) gives:
% 157.26/27.22 | |
% 157.26/27.22 | | Case 1:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (12) all_58_9 = e1 & op(e3, e0) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | ALPHA: (12) implies:
% 157.26/27.22 | | | (13) all_58_9 = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #1461.
% 157.26/27.22 | | |
% 157.26/27.22 | | Case 2:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (14) all_58_10 = e1 & op(e2, e0) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #1373.
% 157.26/27.22 | | |
% 157.26/27.22 | | End of split
% 157.26/27.22 | |
% 157.26/27.22 | Case 2:
% 157.26/27.22 | |
% 157.26/27.22 | | (15) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.22 | | e1)
% 157.26/27.22 | |
% 157.26/27.22 | | BETA: splitting (15) gives:
% 157.26/27.22 | |
% 157.26/27.22 | | Case 1:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (16) all_58_11 = e1 & op(e1, e0) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (6), (7), (16) are inconsistent by sub-proof #1455.
% 157.26/27.22 | | |
% 157.26/27.22 | | Case 2:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (17) all_58_15 = e1 & op(e0, e0) = e1
% 157.26/27.22 | | |
% 157.26/27.22 | | | REF_CLOSE: (4), (5), (10), (17) are inconsistent by sub-proof #1418.
% 157.26/27.22 | | |
% 157.26/27.22 | | End of split
% 157.26/27.22 | |
% 157.26/27.22 | End of split
% 157.26/27.22 |
% 157.26/27.22 End of proof
% 157.26/27.22
% 157.26/27.22 Sub-proof #351 shows that the following formulas are inconsistent:
% 157.26/27.22 ----------------------------------------------------------------
% 157.26/27.22 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.22 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.22 (2) op(e2, e3) = all_52_1
% 157.26/27.22 (3) ~ (e3 = e0)
% 157.26/27.22 (4) ~ (e2 = e0)
% 157.26/27.22 (5) all_58_5 = e3
% 157.26/27.22 (6) all_58_9 = e3
% 157.26/27.22 (7) op(e2, e3) = e2
% 157.26/27.22 (8) ~ (e3 = e1)
% 157.26/27.22 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.22 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.22 (10) all_58_10 = e1
% 157.26/27.22 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 157.26/27.22 (12) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.26/27.22 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.26/27.22 (13) ~ (e2 = e1)
% 157.26/27.22 (14) ~ (e1 = e0)
% 157.26/27.22 (15) ~ (all_8_2 = e1)
% 157.26/27.22 (16) op(e2, e2) = all_8_2
% 157.26/27.22 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.22 (18) ~ (e3 = e2)
% 157.26/27.22
% 157.26/27.22 Begin of proof
% 157.26/27.22 |
% 157.26/27.22 | BETA: splitting (11) gives:
% 157.26/27.22 |
% 157.26/27.22 | Case 1:
% 157.26/27.22 | |
% 157.26/27.22 | | (19) all_58_9 = e2 & op(e3, e0) = e2
% 157.26/27.22 | |
% 157.26/27.22 | | ALPHA: (19) implies:
% 157.26/27.22 | | (20) all_58_9 = e2
% 157.26/27.22 | |
% 157.26/27.22 | | COMBINE_EQS: (6), (20) imply:
% 157.26/27.22 | | (21) e3 = e2
% 157.26/27.22 | |
% 157.26/27.22 | | SIMP: (21) implies:
% 157.26/27.22 | | (22) e3 = e2
% 157.26/27.22 | |
% 157.26/27.22 | | COMBINE_EQS: (5), (22) imply:
% 157.26/27.22 | | (23) all_58_5 = e2
% 157.26/27.22 | |
% 157.26/27.22 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (13), (14), (17),
% 157.26/27.22 | | (18), (23) are inconsistent by sub-proof #896.
% 157.26/27.22 | |
% 157.26/27.22 | Case 2:
% 157.26/27.22 | |
% 157.26/27.22 | | (24) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.22 | |
% 157.26/27.22 | | ALPHA: (24) implies:
% 157.26/27.22 | | (25) all_58_10 = e2
% 157.26/27.22 | |
% 157.26/27.22 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (12), (13), (14), (15), (16),
% 157.26/27.22 | | (17), (18), (25) are inconsistent by sub-proof #905.
% 157.26/27.22 | |
% 157.26/27.22 | End of split
% 157.26/27.22 |
% 157.26/27.22 End of proof
% 157.26/27.22
% 157.26/27.22 Sub-proof #352 shows that the following formulas are inconsistent:
% 157.26/27.22 ----------------------------------------------------------------
% 157.26/27.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.22 (2) op(e2, e1) = e3
% 157.26/27.22 (3) op(e2, e1) = e1
% 157.26/27.22 (4) ~ (e3 = e1)
% 157.26/27.22
% 157.26/27.22 Begin of proof
% 157.26/27.22 |
% 157.26/27.22 | GROUND_INST: instantiating (1) with e3, e1, e1, e2, simplifying with (2), (3)
% 157.26/27.22 | gives:
% 157.26/27.22 | (5) e3 = e1
% 157.26/27.22 |
% 157.26/27.22 | REDUCE: (4), (5) imply:
% 157.26/27.22 | (6) $false
% 157.26/27.22 |
% 157.26/27.22 | CLOSE: (6) is inconsistent.
% 157.26/27.22 |
% 157.26/27.22 End of proof
% 157.26/27.22
% 157.26/27.22 Sub-proof #353 shows that the following formulas are inconsistent:
% 157.26/27.22 ----------------------------------------------------------------
% 157.26/27.22 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 157.26/27.22 (2) op(e3, e2) = all_52_4
% 157.26/27.22 (3) ~ (e3 = e0)
% 157.26/27.22 (4) op(e3, e3) = e0
% 157.26/27.22 (5) ~ (all_52_4 = e3)
% 157.26/27.22 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.22
% 157.26/27.22 Begin of proof
% 157.26/27.22 |
% 157.26/27.22 | BETA: splitting (1) gives:
% 157.26/27.22 |
% 157.26/27.22 | Case 1:
% 157.26/27.22 | |
% 157.26/27.22 | | (7) all_58_0 = e3 & op(e3, e3) = e3
% 157.26/27.22 | |
% 157.26/27.22 | | ALPHA: (7) implies:
% 157.26/27.22 | | (8) op(e3, e3) = e3
% 157.26/27.22 | |
% 157.26/27.22 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1521.
% 157.26/27.22 | |
% 157.26/27.22 | Case 2:
% 157.26/27.22 | |
% 157.26/27.22 | | (9) all_58_1 = e3 & op(e3, e2) = e3
% 157.26/27.22 | |
% 157.26/27.22 | | ALPHA: (9) implies:
% 157.26/27.22 | | (10) op(e3, e2) = e3
% 157.26/27.22 | |
% 157.26/27.22 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1540.
% 157.26/27.22 | |
% 157.26/27.22 | End of split
% 157.26/27.22 |
% 157.26/27.22 End of proof
% 157.26/27.22
% 157.26/27.22 Sub-proof #354 shows that the following formulas are inconsistent:
% 157.26/27.22 ----------------------------------------------------------------
% 157.26/27.22 (1) ~ (all_56_12 = e1) | (all_56_1 = e3 & op(e3, e1) = e3)
% 157.26/27.22 (2) ~ (all_56_13 = e3) | (all_56_3 = e2 & op(e2, e3) = e2)
% 157.26/27.22 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.26/27.22 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.26/27.22 (5) op(e0, e3) = all_52_3
% 157.26/27.22 (6) op(e3, e0) = all_52_12
% 157.26/27.22 (7) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.22 (8) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.22 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.22 (9) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.22 (10) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.22 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.22 (11) op(e3, e3) = all_10_2
% 157.26/27.22 (12) all_54_13 = all_52_7
% 157.26/27.22 (13) op(e1, e1) = all_6_2
% 157.26/27.22 (14) ~ (all_52_7 = e3)
% 157.26/27.22 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.22 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.22 e1)
% 157.26/27.22 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.22 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.22 (17) ~ (all_52_6 = all_52_14)
% 157.26/27.22 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.26/27.22 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.26/27.22 (19) all_54_10 = all_6_2
% 157.26/27.22 (20) ~ (all_52_2 = all_52_3)
% 157.26/27.22 (21) ~ (all_52_4 = all_52_6)
% 157.26/27.22 (22) all_56_12 = all_10_2
% 157.26/27.22 (23) ~ (all_52_2 = all_10_2)
% 157.26/27.22 (24) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.26/27.22 (25) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.22 (26) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 157.26/27.22 op(e1, e1) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 157.26/27.22 e2) & op(e1, e1) = all_32_1 & $i(all_32_1))
% 157.26/27.22 (27) ~ (all_52_7 = all_52_11)
% 157.26/27.22 (28) ~ (all_52_12 = all_4_2)
% 157.26/27.22 (29) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.26/27.22 (30) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.22 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.22 (31) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.22 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.22 (32) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.22 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.22 (33) all_54_1 = all_52_4
% 157.26/27.22 (34) op(e3, e2) = all_52_4
% 157.26/27.22 (35) ~ (all_52_1 = all_52_13)
% 157.26/27.22 (36) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.22 (37) ~ (all_56_15 = e2) | (all_56_10 = e0 & op(e0, e2) = e0)
% 157.26/27.22 (38) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.22 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.22 (39) ~ (all_52_12 = all_52_13)
% 157.26/27.22 (40) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.26/27.22 (41) ~ (all_52_4 = all_52_12)
% 157.26/27.22 (42) all_54_0 = all_10_2
% 157.26/27.22 (43) op(e2, e1) = all_52_9
% 157.26/27.22 (44) op(e2, e3) = all_52_1
% 157.26/27.22 (45) ~ (all_52_13 = e3)
% 157.26/27.22 (46) ~ (all_52_1 = all_52_3)
% 157.26/27.22 (47) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 157.26/27.22 op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 157.26/27.22 e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 157.26/27.22 (48) all_54_2 = all_52_8
% 157.26/27.22 (49) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.22 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.22 (50) ~ (all_52_8 = all_52_9)
% 157.26/27.22 (51) ~ (all_52_2 = all_6_2)
% 157.26/27.22 (52) ~ (e3 = e0)
% 157.26/27.22 (53) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.22 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.22 (54) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.22 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.22 (55) ~ (all_52_9 = all_52_13)
% 157.26/27.22 (56) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.22 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.22 e2)
% 157.26/27.22 (57) ~ (e2 = e0)
% 157.26/27.22 (58) ~ (all_52_9 = e3)
% 157.26/27.22 (59) ~ (all_52_11 = all_6_2)
% 157.26/27.22 (60) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.26/27.22 (61) ~ (all_52_2 = all_52_6)
% 157.26/27.22 (62) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.22 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.22 (63) all_32_2 = all_10_2
% 157.26/27.22 (64) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 &
% 157.26/27.22 op(e3, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 157.26/27.22 e0) & op(e3, e3) = all_28_1 & $i(all_28_1))
% 157.26/27.22 (65) op(e1, e3) = all_52_2
% 157.26/27.22 (66) ~ (all_52_6 = all_6_2)
% 157.26/27.22 (67) op(e2, e0) = all_52_13
% 157.26/27.22 (68) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.22 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.22 (69) ~ (all_52_8 = all_52_12)
% 157.26/27.22 (70) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.26/27.22 (71) ~ (e3 = e1)
% 157.26/27.22 (72) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.22 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.22 (73) op(e1, e2) = all_52_6
% 157.26/27.22 (74) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.26/27.22 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.22 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.26/27.22 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.26/27.22 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.26/27.22 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.22 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.26/27.22 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.26/27.22 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.26/27.22 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.22 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.26/27.22 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.26/27.22 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.26/27.22 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.26/27.22 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.26/27.22 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.26/27.22 = e0)
% 157.26/27.22 (75) ~ (all_4_2 = e1)
% 157.26/27.22 (76) ~ (all_52_4 = all_10_2)
% 157.26/27.22 (77) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.26/27.22 (78) ~ (all_52_3 = all_4_2)
% 157.26/27.22 (79) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.22 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.22 (80) op(e3, e3) = all_14_1
% 157.26/27.22 (81) ~ (all_52_3 = all_10_2)
% 157.26/27.22 (82) ~ (all_52_9 = all_6_2)
% 157.26/27.22 (83) op(e0, e0) = all_4_2
% 157.26/27.22 (84) all_54_8 = all_52_2
% 157.26/27.22 (85) all_54_7 = all_52_13
% 157.26/27.22 (86) ~ (all_52_8 = all_10_2)
% 157.26/27.22 (87) all_56_15 = all_4_2
% 157.26/27.22 (88) op(e0, e1) = all_52_11
% 157.26/27.22 (89) ~ (all_52_9 = all_52_11)
% 157.26/27.22 (90) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 157.26/27.22 (91) ~ (all_52_13 = all_4_2)
% 157.26/27.22 (92) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e3) & op(all_20_1, e0) = all_20_0 &
% 157.26/27.22 op(e2, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 157.26/27.22 e1) & op(e2, e2) = all_20_1 & $i(all_20_1))
% 157.26/27.22 (93) all_28_2 = all_6_2
% 157.26/27.22 (94) ~ (all_52_2 = all_52_14)
% 157.26/27.22 (95) ~ (all_52_6 = all_52_7)
% 157.26/27.22 (96) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.22 (97) ~ (all_52_4 = e3)
% 157.26/27.22 (98) ~ (all_52_8 = all_6_2)
% 157.26/27.22 (99) all_54_6 = all_52_9
% 157.26/27.22 (100) ~ (e2 = e1)
% 157.26/27.22 (101) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.26/27.22 (102) all_54_3 = all_52_12
% 157.26/27.22 (103) ~ (all_52_4 = all_52_7)
% 157.26/27.22 (104) ~ (all_52_8 = all_52_11)
% 157.26/27.22 (105) ~ (all_52_12 = all_10_2)
% 157.26/27.22 (106) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.26/27.22 (107) ~ (e1 = e0)
% 157.26/27.22 (108) op(e3, e1) = all_52_8
% 157.26/27.22 (109) ~ (all_6_2 = e2)
% 157.26/27.22 (110) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.22 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.22 e3)
% 157.26/27.22 (111) all_56_14 = all_6_2
% 157.26/27.22 (112) all_56_13 = e3
% 157.26/27.22 (113) ~ (all_52_1 = all_10_2)
% 157.26/27.22 (114) ~ (all_52_12 = all_52_14)
% 157.26/27.22 (115) ~ (all_14_1 = e0)
% 157.26/27.22 (116) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.22 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.22 (117) all_22_2 = e3
% 157.26/27.22 (118) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.22 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.22 (119) all_54_14 = all_52_11
% 157.26/27.22 (120) ~ (all_52_7 = all_4_2)
% 157.26/27.22 (121) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.22 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.22 (122) op(e0, e2) = all_52_7
% 157.26/27.22 (123) op(e1, e0) = all_52_14
% 157.26/27.22 (124) ~ (all_52_1 = all_52_2)
% 157.26/27.22 (125) all_54_15 = all_4_2
% 157.26/27.22 (126) all_20_2 = all_4_2
% 157.26/27.22 (127) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.26/27.22 (128) ~ (all_52_6 = e3)
% 157.26/27.22 (129) ~ (all_52_14 = all_6_2)
% 157.26/27.22 (130) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.22 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.22 (131) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.22 (132) ~ (all_52_3 = all_52_11)
% 157.26/27.22 (133) ~ (all_52_11 = all_4_2)
% 157.26/27.22 (134) all_54_11 = all_52_14
% 157.26/27.22 (135) ~ (all_52_13 = all_52_14)
% 157.26/27.22 (136) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.26/27.22 (137) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.26/27.22 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.22 (138) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.26/27.22 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.26/27.22 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.26/27.22 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.26/27.22 e0)))
% 157.26/27.22 (139) all_54_9 = all_52_6
% 157.26/27.22 (140) ~ (all_52_4 = all_52_8)
% 157.26/27.22 (141) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.26/27.22 (142) all_54_12 = all_52_3
% 157.26/27.22 (143) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.26/27.22 (144) ~ (all_52_14 = all_4_2)
% 157.26/27.22 (145) ~ (all_52_1 = all_52_9)
% 157.26/27.22 (146) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.26/27.22 (147) ~ (all_52_1 = e3)
% 157.26/27.22 (148) ~ (all_52_3 = all_52_7)
% 157.26/27.22 (149) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 157.26/27.22 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.22
% 157.26/27.22 Begin of proof
% 157.26/27.22 |
% 157.26/27.22 | BETA: splitting (2) gives:
% 157.26/27.22 |
% 157.26/27.22 | Case 1:
% 157.26/27.22 | |
% 157.26/27.22 | | (150) ~ (all_56_13 = e3)
% 157.26/27.22 | |
% 157.26/27.22 | | REDUCE: (112), (150) imply:
% 157.26/27.22 | | (151) $false
% 157.26/27.22 | |
% 157.26/27.22 | | CLOSE: (151) is inconsistent.
% 157.26/27.22 | |
% 157.26/27.22 | Case 2:
% 157.26/27.22 | |
% 157.26/27.22 | | (152) all_56_3 = e2 & op(e2, e3) = e2
% 157.26/27.22 | |
% 157.26/27.22 | | ALPHA: (152) implies:
% 157.26/27.22 | | (153) op(e2, e3) = e2
% 157.26/27.22 | |
% 157.26/27.22 | | BETA: splitting (149) gives:
% 157.26/27.22 | |
% 157.26/27.22 | | Case 1:
% 157.26/27.22 | | |
% 157.26/27.22 | | | (154) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 157.26/27.22 | | | e3)
% 157.26/27.22 | | |
% 157.26/27.22 | | | BETA: splitting (154) gives:
% 157.26/27.22 | | |
% 157.26/27.22 | | | Case 1:
% 157.26/27.22 | | | |
% 157.26/27.22 | | | | (155) all_58_1 = e3 & op(e3, e2) = e3
% 157.26/27.22 | | | |
% 157.26/27.22 | | | | ALPHA: (155) implies:
% 157.26/27.22 | | | | (156) op(e3, e2) = e3
% 157.26/27.22 | | | |
% 157.26/27.22 | | | | REF_CLOSE: (34), (97), (131), (156) are inconsistent by sub-proof #1540.
% 157.26/27.22 | | | |
% 157.26/27.22 | | | Case 2:
% 157.26/27.22 | | | |
% 157.26/27.22 | | | | (157) all_58_3 = e3 & op(e2, e2) = e3
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | ALPHA: (157) implies:
% 157.26/27.23 | | | | (158) all_58_3 = e3
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | GROUND_INST: instantiating (131) with all_52_1, e2, e3, e2, simplifying
% 157.26/27.23 | | | | with (44), (153) gives:
% 157.26/27.23 | | | | (159) all_52_1 = e2
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | GROUND_INST: instantiating (131) with all_10_2, all_14_1, e3, e3,
% 157.26/27.23 | | | | simplifying with (11), (80) gives:
% 157.26/27.23 | | | | (160) all_14_1 = all_10_2
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | REDUCE: (124), (159) imply:
% 157.26/27.23 | | | | (161) ~ (all_52_2 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | SIMP: (161) implies:
% 157.26/27.23 | | | | (162) ~ (all_52_2 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | REDUCE: (46), (159) imply:
% 157.26/27.23 | | | | (163) ~ (all_52_3 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | SIMP: (163) implies:
% 157.26/27.23 | | | | (164) ~ (all_52_3 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | REDUCE: (145), (159) imply:
% 157.26/27.23 | | | | (165) ~ (all_52_9 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | SIMP: (165) implies:
% 157.26/27.23 | | | | (166) ~ (all_52_9 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | REDUCE: (35), (159) imply:
% 157.26/27.23 | | | | (167) ~ (all_52_13 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | SIMP: (167) implies:
% 157.26/27.23 | | | | (168) ~ (all_52_13 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | REDUCE: (113), (159) imply:
% 157.26/27.23 | | | | (169) ~ (all_10_2 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | SIMP: (169) implies:
% 157.26/27.23 | | | | (170) ~ (all_10_2 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | REDUCE: (147), (159) imply:
% 157.26/27.23 | | | | (171) ~ (e3 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | SIMP: (171) implies:
% 157.26/27.23 | | | | (172) ~ (e3 = e2)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | REDUCE: (115), (160) imply:
% 157.26/27.23 | | | | (173) ~ (all_10_2 = e0)
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | BETA: splitting (92) gives:
% 157.26/27.23 | | | |
% 157.26/27.23 | | | | Case 1:
% 157.26/27.23 | | | | |
% 157.26/27.23 | | | | | (174) ~ (all_20_2 = e2)
% 157.26/27.23 | | | | |
% 157.26/27.23 | | | | | REDUCE: (126), (174) imply:
% 157.26/27.23 | | | | | (175) ~ (all_4_2 = e2)
% 157.26/27.23 | | | | |
% 157.26/27.23 | | | | | BETA: splitting (47) gives:
% 157.26/27.23 | | | | |
% 157.26/27.23 | | | | | Case 1:
% 157.26/27.23 | | | | | |
% 157.26/27.23 | | | | | | (176) ~ (all_22_2 = e3)
% 157.26/27.23 | | | | | |
% 157.26/27.23 | | | | | | REDUCE: (117), (176) imply:
% 157.26/27.23 | | | | | | (177) $false
% 157.26/27.23 | | | | | |
% 157.26/27.23 | | | | | | CLOSE: (177) is inconsistent.
% 157.26/27.23 | | | | | |
% 157.26/27.23 | | | | | Case 2:
% 157.26/27.23 | | | | | |
% 157.26/27.23 | | | | | | (178) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3,
% 157.26/27.23 | | | | | | e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 157.26/27.23 | | | | | | (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 157.26/27.23 | | | | | |
% 157.26/27.23 | | | | | | BETA: splitting (64) gives:
% 157.26/27.23 | | | | | |
% 157.26/27.23 | | | | | | Case 1:
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | (179) ~ (all_28_2 = e3)
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | REDUCE: (93), (179) imply:
% 157.26/27.23 | | | | | | | (180) ~ (all_6_2 = e3)
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | BETA: splitting (26) gives:
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | (181) ~ (all_32_2 = e1)
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | REDUCE: (63), (181) imply:
% 157.26/27.23 | | | | | | | | (182) ~ (all_10_2 = e1)
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (13), (14), (15), (16),
% 157.26/27.23 | | | | | | | | (18), (30), (31), (32), (34), (38), (42), (43), (44),
% 157.26/27.23 | | | | | | | | (45), (49), (53), (54), (56), (57), (58), (67), (68),
% 157.26/27.23 | | | | | | | | (70), (72), (73), (76), (79), (83), (96), (100),
% 157.26/27.23 | | | | | | | | (107), (109), (110), (116), (118), (121), (122),
% 157.26/27.23 | | | | | | | | (128), (130), (131), (137), (138), (153), (158),
% 157.26/27.23 | | | | | | | | (170), (173), (175), (178), (180), (182) are
% 157.26/27.23 | | | | | | | | inconsistent by sub-proof #768.
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | (183) all_32_2 = e1
% 157.26/27.23 | | | | | | | | (184) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 157.26/27.23 | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) & $i(all_32_1))
% 157.26/27.23 | | | | | | | | | ( ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 157.26/27.23 | | | | | | | | $i(all_32_1))
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | COMBINE_EQS: (63), (183) imply:
% 157.26/27.23 | | | | | | | | (185) all_10_2 = e1
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | SIMP: (185) implies:
% 157.26/27.23 | | | | | | | | (186) all_10_2 = e1
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | COMBINE_EQS: (22), (186) imply:
% 157.26/27.23 | | | | | | | | (187) all_56_12 = e1
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | REDUCE: (23), (186) imply:
% 157.26/27.23 | | | | | | | | (188) ~ (all_52_2 = e1)
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | REDUCE: (86), (186) imply:
% 157.26/27.23 | | | | | | | | (189) ~ (all_52_8 = e1)
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | REDUCE: (105), (186) imply:
% 157.26/27.23 | | | | | | | | (190) ~ (all_52_12 = e1)
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | REDUCE: (170), (186) imply:
% 157.26/27.23 | | | | | | | | (191) ~ (e2 = e1)
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | REDUCE: (11), (186) imply:
% 157.26/27.23 | | | | | | | | (192) op(e3, e3) = e1
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | BETA: splitting (178) gives:
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | (193) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 157.26/27.23 | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | ALPHA: (193) implies:
% 157.26/27.23 | | | | | | | | | (194) ~ (all_22_0 = e0)
% 157.26/27.23 | | | | | | | | | (195) op(e3, e3) = all_22_1
% 157.26/27.23 | | | | | | | | | (196) op(all_22_1, e2) = all_22_0
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | BETA: splitting (1) gives:
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | (197) ~ (all_56_12 = e1)
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | REDUCE: (187), (197) imply:
% 157.26/27.23 | | | | | | | | | | (198) $false
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | CLOSE: (198) is inconsistent.
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | (199) all_56_1 = e3 & op(e3, e1) = e3
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | ALPHA: (199) implies:
% 157.26/27.23 | | | | | | | | | | (200) all_56_1 = e3
% 157.26/27.23 | | | | | | | | | | (201) op(e3, e1) = e3
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | BETA: splitting (53) gives:
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | (202) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.26/27.23 | | | | | | | | | | | & op(e2, e3) = e1)
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | BETA: splitting (202) gives:
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | (203) all_58_0 = e1 & op(e3, e3) = e1
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | ALPHA: (203) implies:
% 157.26/27.23 | | | | | | | | | | | | (204) all_58_0 = e1
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | BETA: splitting (184) gives:
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | (205) ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 157.26/27.23 | | | | | | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) &
% 157.26/27.23 | | | | | | | | | | | | | $i(all_32_1)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | ALPHA: (205) implies:
% 157.26/27.23 | | | | | | | | | | | | | (206) op(e1, e1) = all_32_1
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | GROUND_INST: instantiating (131) with all_6_2, all_32_1, e1,
% 157.26/27.23 | | | | | | | | | | | | | e1, simplifying with (13), (206) gives:
% 157.26/27.23 | | | | | | | | | | | | | (207) all_32_1 = all_6_2
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | GROUND_INST: instantiating (131) with all_52_8, e3, e1, e3,
% 157.26/27.23 | | | | | | | | | | | | | simplifying with (108), (201) gives:
% 157.26/27.23 | | | | | | | | | | | | | (208) all_52_8 = e3
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | GROUND_INST: instantiating (131) with e1, all_22_1, e3, e3,
% 157.26/27.23 | | | | | | | | | | | | | simplifying with (192), (195) gives:
% 157.26/27.23 | | | | | | | | | | | | | (209) all_22_1 = e1
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (50), (208) imply:
% 157.26/27.23 | | | | | | | | | | | | | (210) ~ (all_52_9 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (104), (208) imply:
% 157.26/27.23 | | | | | | | | | | | | | (211) ~ (all_52_11 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | SIMP: (211) implies:
% 157.26/27.23 | | | | | | | | | | | | | (212) ~ (all_52_11 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (69), (208) imply:
% 157.26/27.23 | | | | | | | | | | | | | (213) ~ (all_52_12 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | SIMP: (213) implies:
% 157.26/27.23 | | | | | | | | | | | | | (214) ~ (all_52_12 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (98), (208) imply:
% 157.26/27.23 | | | | | | | | | | | | | (215) ~ (all_6_2 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (196), (209) imply:
% 157.26/27.23 | | | | | | | | | | | | | (216) op(e1, e2) = all_22_0
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | BETA: splitting (31) gives:
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | (217) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 157.26/27.23 | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (13), (14), (15), (16), (18),
% 157.26/27.23 | | | | | | | | | | | | | | (30), (31), (32), (34), (38), (43), (44), (45),
% 157.26/27.23 | | | | | | | | | | | | | | (49), (52), (53), (54), (56), (57), (58), (62),
% 157.26/27.23 | | | | | | | | | | | | | | (67), (68), (71), (72), (73), (79), (83), (96),
% 157.26/27.23 | | | | | | | | | | | | | | (97), (100), (107), (109), (110), (116), (118),
% 157.26/27.23 | | | | | | | | | | | | | | (121), (122), (128), (130), (131), (137), (138),
% 157.26/27.23 | | | | | | | | | | | | | | (153), (158), (172), (175), (180), (192), (195),
% 157.26/27.23 | | | | | | | | | | | | | | (201), (204), (217) are inconsistent by sub-proof
% 157.26/27.23 | | | | | | | | | | | | | | #750.
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | (218) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 157.26/27.23 | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | (219) all_58_8 = e2 & op(e1, e1) = e2
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | REF_CLOSE: (13), (109), (131), (219) are inconsistent by
% 157.26/27.23 | | | | | | | | | | | | | | | sub-proof #1440.
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | (220) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 157.26/27.23 | | | | | | | | | | | | | | | (221) all_58_14 = e2
% 157.26/27.23 | | | | | | | | | | | | | | | (222) op(e0, e1) = e2
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (9), (10), (13), (14), (15), (16),
% 157.26/27.23 | | | | | | | | | | | | | | | (17), (18), (19), (20), (21), (25), (27), (28),
% 157.26/27.23 | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (36), (38),
% 157.26/27.23 | | | | | | | | | | | | | | | (40), (41), (43), (44), (45), (49), (51), (52),
% 157.26/27.23 | | | | | | | | | | | | | | | (53), (54), (56), (57), (58), (59), (60), (61),
% 157.26/27.23 | | | | | | | | | | | | | | | (62), (66), (67), (68), (71), (72), (73), (74),
% 157.26/27.23 | | | | | | | | | | | | | | | (78), (79), (83), (84), (85), (87), (88), (89),
% 157.26/27.23 | | | | | | | | | | | | | | | (90), (91), (95), (96), (97), (100), (101), (102),
% 157.26/27.23 | | | | | | | | | | | | | | | (103), (106), (107), (109), (110), (111), (112),
% 157.26/27.23 | | | | | | | | | | | | | | | (116), (118), (120), (121), (122), (123), (125),
% 157.26/27.23 | | | | | | | | | | | | | | | (128), (129), (130), (131), (132), (133), (134),
% 157.26/27.23 | | | | | | | | | | | | | | | (135), (136), (137), (138), (139), (141), (142),
% 157.26/27.23 | | | | | | | | | | | | | | | (146), (148), (153), (158), (168), (172), (175),
% 157.26/27.23 | | | | | | | | | | | | | | | (180), (187), (188), (190), (192), (194), (195),
% 157.26/27.23 | | | | | | | | | | | | | | | (200), (204), (212), (214), (216), (221), (222)
% 157.26/27.23 | | | | | | | | | | | | | | | are inconsistent by sub-proof #364.
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | (223) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 157.26/27.23 | | | | | | | | | | | | | $i(all_32_1)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | ALPHA: (223) implies:
% 157.26/27.23 | | | | | | | | | | | | | (224) ~ (all_32_1 = e2)
% 157.26/27.23 | | | | | | | | | | | | | (225) op(e1, e1) = all_32_1
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | GROUND_INST: instantiating (131) with all_6_2, all_32_1, e1,
% 157.26/27.23 | | | | | | | | | | | | | e1, simplifying with (13), (225) gives:
% 157.26/27.23 | | | | | | | | | | | | | (226) all_32_1 = all_6_2
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | GROUND_INST: instantiating (131) with all_52_8, e3, e1, e3,
% 157.26/27.23 | | | | | | | | | | | | | simplifying with (108), (201) gives:
% 157.26/27.23 | | | | | | | | | | | | | (227) all_52_8 = e3
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | GROUND_INST: instantiating (131) with e1, all_22_1, e3, e3,
% 157.26/27.23 | | | | | | | | | | | | | simplifying with (192), (195) gives:
% 157.26/27.23 | | | | | | | | | | | | | (228) all_22_1 = e1
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (50), (227) imply:
% 157.26/27.23 | | | | | | | | | | | | | (229) ~ (all_52_9 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (104), (227) imply:
% 157.26/27.23 | | | | | | | | | | | | | (230) ~ (all_52_11 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | SIMP: (230) implies:
% 157.26/27.23 | | | | | | | | | | | | | (231) ~ (all_52_11 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (69), (227) imply:
% 157.26/27.23 | | | | | | | | | | | | | (232) ~ (all_52_12 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | SIMP: (232) implies:
% 157.26/27.23 | | | | | | | | | | | | | (233) ~ (all_52_12 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (98), (227) imply:
% 157.26/27.23 | | | | | | | | | | | | | (234) ~ (all_6_2 = e3)
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | REDUCE: (196), (228) imply:
% 157.26/27.23 | | | | | | | | | | | | | (235) op(e1, e2) = all_22_0
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | BETA: splitting (31) gives:
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | (236) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 157.26/27.23 | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (13), (14), (15), (16), (18),
% 157.26/27.23 | | | | | | | | | | | | | | (30), (31), (32), (34), (38), (43), (44), (45),
% 157.26/27.23 | | | | | | | | | | | | | | (49), (52), (53), (54), (56), (57), (58), (62),
% 157.26/27.23 | | | | | | | | | | | | | | (67), (68), (71), (72), (73), (79), (83), (96),
% 157.26/27.23 | | | | | | | | | | | | | | (97), (100), (107), (109), (110), (116), (118),
% 157.26/27.23 | | | | | | | | | | | | | | (121), (122), (128), (130), (131), (137), (138),
% 157.26/27.23 | | | | | | | | | | | | | | (153), (158), (172), (175), (180), (192), (195),
% 157.26/27.23 | | | | | | | | | | | | | | (201), (204), (236) are inconsistent by sub-proof
% 157.26/27.23 | | | | | | | | | | | | | | #750.
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | (237) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 157.26/27.23 | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | (238) all_58_8 = e2 & op(e1, e1) = e2
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | REF_CLOSE: (13), (109), (131), (238) are inconsistent by
% 157.26/27.23 | | | | | | | | | | | | | | | sub-proof #1440.
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | (239) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 157.26/27.23 | | | | | | | | | | | | | | | (240) all_58_14 = e2
% 157.26/27.23 | | | | | | | | | | | | | | | (241) op(e0, e1) = e2
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (9), (10), (13), (14), (15), (16),
% 157.26/27.23 | | | | | | | | | | | | | | | (17), (18), (19), (20), (21), (25), (27), (28),
% 157.26/27.23 | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (36), (38),
% 157.26/27.23 | | | | | | | | | | | | | | | (40), (41), (43), (44), (45), (49), (51), (52),
% 157.26/27.23 | | | | | | | | | | | | | | | (53), (54), (56), (57), (58), (59), (60), (61),
% 157.26/27.23 | | | | | | | | | | | | | | | (62), (66), (67), (68), (71), (72), (73), (74),
% 157.26/27.23 | | | | | | | | | | | | | | | (78), (79), (83), (84), (85), (87), (88), (89),
% 157.26/27.23 | | | | | | | | | | | | | | | (90), (91), (95), (96), (97), (100), (101), (102),
% 157.26/27.23 | | | | | | | | | | | | | | | (103), (106), (107), (109), (110), (111), (112),
% 157.26/27.23 | | | | | | | | | | | | | | | (116), (118), (120), (121), (122), (123), (125),
% 157.26/27.23 | | | | | | | | | | | | | | | (128), (129), (130), (131), (132), (133), (134),
% 157.26/27.23 | | | | | | | | | | | | | | | (135), (136), (137), (138), (139), (141), (142),
% 157.26/27.23 | | | | | | | | | | | | | | | (146), (148), (153), (158), (168), (172), (175),
% 157.26/27.23 | | | | | | | | | | | | | | | (180), (187), (188), (190), (192), (194), (195),
% 157.26/27.23 | | | | | | | | | | | | | | | (200), (204), (231), (233), (235), (240), (241)
% 157.26/27.23 | | | | | | | | | | | | | | | are inconsistent by sub-proof #364.
% 157.26/27.23 | | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | (242) all_58_2 = e1 & op(e2, e3) = e1
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | ALPHA: (242) implies:
% 157.26/27.23 | | | | | | | | | | | | (243) op(e2, e3) = e1
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | REF_CLOSE: (100), (131), (153), (243) are inconsistent by
% 157.26/27.23 | | | | | | | | | | | | sub-proof #1430.
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | (244) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 157.26/27.23 | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | BETA: splitting (244) gives:
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | (245) all_58_6 = e1 & op(e1, e3) = e1
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | ALPHA: (245) implies:
% 157.26/27.23 | | | | | | | | | | | | (246) all_58_6 = e1
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (13), (14), (15), (16), (18),
% 157.26/27.23 | | | | | | | | | | | | (30), (31), (32), (34), (38), (43), (44), (45),
% 157.26/27.23 | | | | | | | | | | | | (49), (52), (53), (54), (56), (57), (58), (62),
% 157.26/27.23 | | | | | | | | | | | | (67), (68), (71), (72), (73), (79), (83), (96),
% 157.26/27.23 | | | | | | | | | | | | (97), (100), (107), (109), (110), (116), (118),
% 157.26/27.23 | | | | | | | | | | | | (121), (122), (128), (130), (131), (137), (138),
% 157.26/27.23 | | | | | | | | | | | | (153), (158), (172), (175), (180), (192), (195),
% 157.26/27.23 | | | | | | | | | | | | (246) are inconsistent by sub-proof #685.
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | (247) all_58_12 = e1 & op(e0, e3) = e1
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | ALPHA: (247) implies:
% 157.26/27.23 | | | | | | | | | | | | (248) all_58_12 = e1
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (13), (14), (15), (16), (18),
% 157.26/27.23 | | | | | | | | | | | | (30), (31), (32), (34), (38), (43), (44), (45),
% 157.26/27.23 | | | | | | | | | | | | (49), (52), (53), (54), (56), (57), (58), (67),
% 157.26/27.23 | | | | | | | | | | | | (68), (71), (72), (73), (79), (83), (96), (97),
% 157.26/27.23 | | | | | | | | | | | | (100), (107), (109), (110), (116), (118), (121),
% 157.26/27.23 | | | | | | | | | | | | (122), (128), (130), (131), (137), (138), (153),
% 157.26/27.23 | | | | | | | | | | | | (158), (172), (175), (180), (192), (195), (248)
% 157.26/27.23 | | | | | | | | | | | | are inconsistent by sub-proof #747.
% 157.26/27.23 | | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | End of split
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | (249) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 157.26/27.23 | | | | | | | | | $i(all_22_1)
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | ALPHA: (249) implies:
% 157.26/27.23 | | | | | | | | | (250) ~ (all_22_1 = e1)
% 157.26/27.23 | | | | | | | | | (251) op(e3, e3) = all_22_1
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | REF_CLOSE: (131), (192), (250), (251) are inconsistent by
% 157.26/27.23 | | | | | | | | | sub-proof #668.
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | End of split
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | End of split
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | Case 2:
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | (252) all_28_2 = e3
% 157.26/27.23 | | | | | | | (253) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 &
% 157.26/27.23 | | | | | | | op(e3, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) |
% 157.26/27.23 | | | | | | | ( ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 157.26/27.23 | | | | | | | $i(all_28_1))
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | COMBINE_EQS: (93), (252) imply:
% 157.26/27.23 | | | | | | | (254) all_6_2 = e3
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | COMBINE_EQS: (111), (254) imply:
% 157.26/27.23 | | | | | | | (255) all_56_14 = e3
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | REDUCE: (51), (254) imply:
% 157.26/27.23 | | | | | | | (256) ~ (all_52_2 = e3)
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | REDUCE: (98), (254) imply:
% 157.26/27.23 | | | | | | | (257) ~ (all_52_8 = e3)
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | REDUCE: (59), (254) imply:
% 157.26/27.23 | | | | | | | (258) ~ (all_52_11 = e3)
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | REDUCE: (129), (254) imply:
% 157.26/27.23 | | | | | | | (259) ~ (all_52_14 = e3)
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | REDUCE: (13), (254) imply:
% 157.26/27.23 | | | | | | | (260) op(e1, e1) = e3
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | BETA: splitting (24) gives:
% 157.26/27.23 | | | | | | |
% 157.26/27.23 | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | (261) ~ (all_56_14 = e3)
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | REDUCE: (255), (261) imply:
% 157.26/27.23 | | | | | | | | (262) $false
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | CLOSE: (262) is inconsistent.
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | (263) all_56_6 = e1 & op(e1, e3) = e1
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | ALPHA: (263) implies:
% 157.26/27.23 | | | | | | | | (264) all_56_6 = e1
% 157.26/27.23 | | | | | | | | (265) op(e1, e3) = e1
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | BETA: splitting (1) gives:
% 157.26/27.23 | | | | | | | |
% 157.26/27.23 | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | (266) ~ (all_56_12 = e1)
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | REDUCE: (22), (266) imply:
% 157.26/27.23 | | | | | | | | | (267) ~ (all_10_2 = e1)
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (13), (14), (15), (16),
% 157.26/27.23 | | | | | | | | | (18), (22), (30), (31), (32), (34), (38), (42),
% 157.26/27.23 | | | | | | | | | (43), (44), (45), (49), (52), (53), (54), (56),
% 157.26/27.23 | | | | | | | | | (57), (58), (61), (62), (65), (67), (68), (70),
% 157.26/27.23 | | | | | | | | | (71), (72), (73), (74), (75), (76), (79), (83),
% 157.26/27.23 | | | | | | | | | (87), (88), (90), (91), (96), (97), (100), (107),
% 157.26/27.23 | | | | | | | | | (109), (110), (112), (116), (118), (120), (121),
% 157.26/27.23 | | | | | | | | | (122), (123), (128), (130), (131), (137), (138),
% 157.26/27.23 | | | | | | | | | (146), (153), (158), (162), (166), (170), (172),
% 157.26/27.23 | | | | | | | | | (173), (175), (178), (253), (255), (260), (264),
% 157.26/27.23 | | | | | | | | | (265), (267) are inconsistent by sub-proof #566.
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | (268) all_56_12 = e1
% 157.26/27.23 | | | | | | | | | (269) all_56_1 = e3 & op(e3, e1) = e3
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | ALPHA: (269) implies:
% 157.26/27.23 | | | | | | | | | (270) op(e3, e1) = e3
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | COMBINE_EQS: (22), (268) imply:
% 157.26/27.23 | | | | | | | | | (271) all_10_2 = e1
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | SIMP: (271) implies:
% 157.26/27.23 | | | | | | | | | (272) all_10_2 = e1
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | COMBINE_EQS: (63), (272) imply:
% 157.26/27.23 | | | | | | | | | (273) all_32_2 = e1
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | REDUCE: (23), (272) imply:
% 157.26/27.23 | | | | | | | | | (274) ~ (all_52_2 = e1)
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | REDUCE: (81), (272) imply:
% 157.26/27.23 | | | | | | | | | (275) ~ (all_52_3 = e1)
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | REDUCE: (86), (272) imply:
% 157.26/27.23 | | | | | | | | | (276) ~ (all_52_8 = e1)
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | REDUCE: (170), (272) imply:
% 157.26/27.23 | | | | | | | | | (277) ~ (e2 = e1)
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | REDUCE: (11), (272) imply:
% 157.26/27.23 | | | | | | | | | (278) op(e3, e3) = e1
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | BETA: splitting (26) gives:
% 157.26/27.23 | | | | | | | | |
% 157.26/27.23 | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | (279) ~ (all_32_2 = e1)
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | REDUCE: (273), (279) imply:
% 157.26/27.23 | | | | | | | | | | (280) $false
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | CLOSE: (280) is inconsistent.
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | Case 2:
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | (281) ( ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 157.26/27.23 | | | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) &
% 157.26/27.23 | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 157.26/27.23 | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | BETA: splitting (281) gives:
% 157.26/27.23 | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | Case 1:
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | (282) ~ (all_32_0 = e0) & op(all_32_1, e3) = all_32_0 &
% 157.26/27.23 | | | | | | | | | | | op(e1, e1) = all_32_1 & $i(all_32_0) &
% 157.26/27.23 | | | | | | | | | | | $i(all_32_1)
% 157.26/27.23 | | | | | | | | | | |
% 157.26/27.23 | | | | | | | | | | | ALPHA: (282) implies:
% 157.26/27.24 | | | | | | | | | | | (283) op(e1, e1) = all_32_1
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (12), (13), (14),
% 157.26/27.24 | | | | | | | | | | | (15), (16), (17), (18), (20), (21), (25), (27),
% 157.26/27.24 | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (36), (38),
% 157.26/27.24 | | | | | | | | | | | (43), (44), (45), (48), (49), (50), (52), (53),
% 157.26/27.24 | | | | | | | | | | | (54), (55), (56), (57), (58), (61), (62), (67),
% 157.26/27.24 | | | | | | | | | | | (68), (71), (72), (73), (75), (77), (78), (79),
% 157.26/27.24 | | | | | | | | | | | (83), (84), (85), (87), (89), (91), (95), (96),
% 157.26/27.24 | | | | | | | | | | | (97), (99), (100), (103), (104), (106), (107),
% 157.26/27.24 | | | | | | | | | | | (108), (109), (110), (112), (116), (118), (119),
% 157.26/27.24 | | | | | | | | | | | (120), (121), (122), (123), (125), (127), (128),
% 157.26/27.24 | | | | | | | | | | | (130), (131), (132), (133), (134), (135), (136),
% 157.26/27.24 | | | | | | | | | | | (137), (138), (139), (141), (142), (143), (144),
% 157.26/27.24 | | | | | | | | | | | (146), (148), (153), (158), (162), (164), (166),
% 157.26/27.24 | | | | | | | | | | | (168), (172), (175), (178), (253), (255), (256),
% 157.26/27.24 | | | | | | | | | | | (257), (258), (259), (260), (265), (268), (270),
% 157.26/27.24 | | | | | | | | | | | (274), (275), (276), (278), (283) are inconsistent
% 157.26/27.24 | | | | | | | | | | | by sub-proof #358.
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | (284) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 157.26/27.24 | | | | | | | | | | | $i(all_32_1)
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | ALPHA: (284) implies:
% 157.26/27.24 | | | | | | | | | | | (285) op(e1, e1) = all_32_1
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (12), (13), (14),
% 157.26/27.24 | | | | | | | | | | | (15), (16), (17), (18), (20), (21), (25), (27),
% 157.26/27.24 | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (36), (38),
% 157.26/27.24 | | | | | | | | | | | (43), (44), (45), (48), (49), (50), (52), (53),
% 157.26/27.24 | | | | | | | | | | | (54), (55), (56), (57), (58), (61), (62), (67),
% 157.26/27.24 | | | | | | | | | | | (68), (71), (72), (73), (75), (77), (78), (79),
% 157.26/27.24 | | | | | | | | | | | (83), (84), (85), (87), (89), (91), (95), (96),
% 157.26/27.24 | | | | | | | | | | | (97), (99), (100), (103), (104), (106), (107),
% 157.26/27.24 | | | | | | | | | | | (108), (109), (110), (112), (116), (118), (119),
% 157.26/27.24 | | | | | | | | | | | (120), (121), (122), (123), (125), (127), (128),
% 157.26/27.24 | | | | | | | | | | | (130), (131), (132), (133), (134), (135), (136),
% 157.26/27.24 | | | | | | | | | | | (137), (138), (139), (141), (142), (143), (144),
% 157.26/27.24 | | | | | | | | | | | (146), (148), (153), (158), (162), (164), (166),
% 157.26/27.24 | | | | | | | | | | | (168), (172), (175), (178), (253), (255), (256),
% 157.26/27.24 | | | | | | | | | | | (257), (258), (259), (260), (265), (268), (270),
% 157.26/27.24 | | | | | | | | | | | (274), (275), (276), (278), (285) are inconsistent
% 157.26/27.24 | | | | | | | | | | | by sub-proof #358.
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | End of split
% 157.26/27.24 | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | End of split
% 157.26/27.24 | | | | | | | | |
% 157.26/27.24 | | | | | | | | End of split
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | End of split
% 157.26/27.24 | | | | | | |
% 157.26/27.24 | | | | | | End of split
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | End of split
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | Case 2:
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | | (286) all_20_2 = e2
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | | COMBINE_EQS: (126), (286) imply:
% 157.26/27.24 | | | | | (287) all_4_2 = e2
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | | SIMP: (287) implies:
% 157.26/27.24 | | | | | (288) all_4_2 = e2
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | | COMBINE_EQS: (87), (288) imply:
% 157.26/27.24 | | | | | (289) all_56_15 = e2
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | | REDUCE: (120), (288) imply:
% 157.26/27.24 | | | | | (290) ~ (all_52_7 = e2)
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | | REDUCE: (83), (288) imply:
% 157.26/27.24 | | | | | (291) op(e0, e0) = e2
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | | BETA: splitting (37) gives:
% 157.26/27.24 | | | | |
% 157.26/27.24 | | | | | Case 1:
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | | (292) ~ (all_56_15 = e2)
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | | REDUCE: (289), (292) imply:
% 157.26/27.24 | | | | | | (293) $false
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | | CLOSE: (293) is inconsistent.
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | Case 2:
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | | (294) all_56_10 = e0 & op(e0, e2) = e0
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | | ALPHA: (294) implies:
% 157.26/27.24 | | | | | | (295) op(e0, e2) = e0
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | | BETA: splitting (49) gives:
% 157.26/27.24 | | | | | |
% 157.26/27.24 | | | | | | Case 1:
% 157.26/27.24 | | | | | | |
% 157.26/27.24 | | | | | | | (296) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 157.26/27.24 | | | | | | | op(e1, e2) = e2)
% 157.26/27.24 | | | | | | |
% 157.26/27.24 | | | | | | | BETA: splitting (296) gives:
% 157.26/27.24 | | | | | | |
% 157.26/27.24 | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | | (297) all_58_6 = e2 & op(e1, e3) = e2
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | | ALPHA: (297) implies:
% 157.26/27.24 | | | | | | | | (298) all_58_6 = e2
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | | REF_CLOSE: (30), (44), (52), (53), (57), (71), (100), (107),
% 157.26/27.24 | | | | | | | | (130), (131), (153), (172), (298) are inconsistent by
% 157.26/27.24 | | | | | | | | sub-proof #1152.
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | | (299) all_58_7 = e2 & op(e1, e2) = e2
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | | ALPHA: (299) implies:
% 157.26/27.24 | | | | | | | | (300) all_58_7 = e2
% 157.26/27.24 | | | | | | | | (301) op(e1, e2) = e2
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | | BETA: splitting (31) gives:
% 157.26/27.24 | | | | | | | |
% 157.26/27.24 | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | |
% 157.26/27.24 | | | | | | | | | (302) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 157.26/27.24 | | | | | | | | | op(e2, e1) = e2)
% 157.26/27.24 | | | | | | | | |
% 157.26/27.24 | | | | | | | | | BETA: splitting (302) gives:
% 157.26/27.24 | | | | | | | | |
% 157.26/27.24 | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | (303) all_58_4 = e2 & op(e3, e1) = e2
% 157.26/27.24 | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | ALPHA: (303) implies:
% 157.26/27.24 | | | | | | | | | | (304) all_58_4 = e2
% 157.26/27.24 | | | | | | | | | | (305) op(e3, e1) = e2
% 157.26/27.24 | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | BETA: splitting (56) gives:
% 157.26/27.24 | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | (306) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 157.26/27.24 | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | REF_CLOSE: (30), (44), (52), (53), (57), (71), (100), (107),
% 157.26/27.24 | | | | | | | | | | | (122), (130), (131), (153), (172), (295), (306)
% 157.26/27.24 | | | | | | | | | | | are inconsistent by sub-proof #1039.
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | (307) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 157.26/27.24 | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | BETA: splitting (307) gives:
% 157.26/27.24 | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | (308) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | ALPHA: (308) implies:
% 157.26/27.24 | | | | | | | | | | | | (309) all_58_14 = e2
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (14), (15), (16), (30), (32),
% 157.26/27.24 | | | | | | | | | | | | (34), (38), (44), (45), (52), (53), (54), (57),
% 157.26/27.24 | | | | | | | | | | | | (62), (67), (68), (71), (73), (79), (96), (97),
% 157.26/27.24 | | | | | | | | | | | | (100), (107), (110), (116), (118), (121), (122),
% 157.26/27.24 | | | | | | | | | | | | (128), (130), (131), (137), (138), (153), (158),
% 157.26/27.24 | | | | | | | | | | | | (172), (291), (295), (300), (309) are inconsistent
% 157.26/27.24 | | | | | | | | | | | | by sub-proof #604.
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | (310) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | ALPHA: (310) implies:
% 157.26/27.24 | | | | | | | | | | | | (311) all_58_15 = e2
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | GROUND_INST: instantiating (131) with all_52_7, e0, e2, e0,
% 157.26/27.24 | | | | | | | | | | | | simplifying with (122), (295) gives:
% 157.26/27.24 | | | | | | | | | | | | (312) all_52_7 = e0
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | GROUND_INST: instantiating (131) with all_52_6, e2, e2, e1,
% 157.26/27.24 | | | | | | | | | | | | simplifying with (73), (301) gives:
% 157.26/27.24 | | | | | | | | | | | | (313) all_52_6 = e2
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | GROUND_INST: instantiating (131) with all_52_8, e2, e1, e3,
% 157.26/27.24 | | | | | | | | | | | | simplifying with (108), (305) gives:
% 157.26/27.24 | | | | | | | | | | | | (314) all_52_8 = e2
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (148), (312) imply:
% 157.26/27.24 | | | | | | | | | | | | (315) ~ (all_52_3 = e0)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (103), (312) imply:
% 157.26/27.24 | | | | | | | | | | | | (316) ~ (all_52_4 = e0)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (140), (314) imply:
% 157.26/27.24 | | | | | | | | | | | | (317) ~ (all_52_4 = e2)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (17), (313) imply:
% 157.26/27.24 | | | | | | | | | | | | (318) ~ (all_52_14 = e2)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | SIMP: (318) implies:
% 157.26/27.24 | | | | | | | | | | | | (319) ~ (all_52_14 = e2)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (27), (312) imply:
% 157.26/27.24 | | | | | | | | | | | | (320) ~ (all_52_11 = e0)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | SIMP: (320) implies:
% 157.26/27.24 | | | | | | | | | | | | (321) ~ (all_52_11 = e0)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (290), (312) imply:
% 157.26/27.24 | | | | | | | | | | | | (322) ~ (e2 = e0)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (104), (314) imply:
% 157.26/27.24 | | | | | | | | | | | | (323) ~ (all_52_11 = e2)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | SIMP: (323) implies:
% 157.26/27.24 | | | | | | | | | | | | (324) ~ (all_52_11 = e2)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (69), (314) imply:
% 157.26/27.24 | | | | | | | | | | | | (325) ~ (all_52_12 = e2)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | SIMP: (325) implies:
% 157.26/27.24 | | | | | | | | | | | | (326) ~ (all_52_12 = e2)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | REDUCE: (98), (314) imply:
% 157.26/27.24 | | | | | | | | | | | | (327) ~ (all_6_2 = e2)
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | BETA: splitting (1) gives:
% 157.26/27.24 | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | (328) ~ (all_56_12 = e1)
% 157.26/27.24 | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | REDUCE: (22), (328) imply:
% 157.26/27.24 | | | | | | | | | | | | | (329) ~ (all_10_2 = e1)
% 157.26/27.24 | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | BETA: splitting (47) gives:
% 157.26/27.24 | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | (330) ~ (all_22_2 = e3)
% 157.26/27.24 | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | REDUCE: (117), (330) imply:
% 157.26/27.24 | | | | | | | | | | | | | | (331) $false
% 157.26/27.24 | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | CLOSE: (331) is inconsistent.
% 157.26/27.24 | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | (332) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0
% 157.26/27.24 | | | | | | | | | | | | | | & op(e3, e3) = all_22_1 & $i(all_22_0) &
% 157.26/27.24 | | | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3, e3)
% 157.26/27.24 | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 157.26/27.24 | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 157.26/27.24 | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | (333) all_54_0 = e3
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | COMBINE_EQS: (42), (333) imply:
% 157.26/27.24 | | | | | | | | | | | | | | | (334) all_10_2 = e3
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | SIMP: (334) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | (335) all_10_2 = e3
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | COMBINE_EQS: (22), (335) imply:
% 157.26/27.24 | | | | | | | | | | | | | | | (336) all_56_12 = e3
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | REDUCE: (23), (335) imply:
% 157.26/27.24 | | | | | | | | | | | | | | | (337) ~ (all_52_2 = e3)
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | REDUCE: (81), (335) imply:
% 157.26/27.24 | | | | | | | | | | | | | | | (338) ~ (all_52_3 = e3)
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | REDUCE: (105), (335) imply:
% 157.26/27.24 | | | | | | | | | | | | | | | (339) ~ (all_52_12 = e3)
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | REDUCE: (11), (335) imply:
% 157.26/27.24 | | | | | | | | | | | | | | | (340) op(e3, e3) = e3
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 157.26/27.24 | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | (341) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.26/27.24 | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.26/27.24 | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | (342) all_58_1 = e0 & op(e3, e2) = e0
% 157.26/27.24 | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | (343) all_58_1 = e0
% 157.26/27.24 | | | | | | | | | | | | | | | | | (344) op(e3, e2) = e0
% 157.26/27.24 | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | (345) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 157.26/27.24 | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 157.26/27.24 | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (346) all_58_12 = e3 & op(e0, e3) = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | ALPHA: (346) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (347) all_58_12 = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (14), (15), (16), (18), (25), (30),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (33), (34), (36), (38), (39), (40), (41), (43),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (44), (45), (52), (53), (54), (56), (57), (58),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (67), (68), (71), (73), (79), (85), (96), (97),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (100), (102), (106), (107), (110), (114), (116),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (118), (121), (122), (123), (128), (130), (131),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (134), (135), (138), (153), (158), (168), (172),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (291), (295), (300), (304), (311), (316), (317),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (319), (326), (339), (343), (347) are inconsistent
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | by sub-proof #399.
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (348) all_58_13 = e3 & op(e0, e2) = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (122), (131), (348) are inconsistent by
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | sub-proof #1449.
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.24 | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | (349) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 157.26/27.24 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.26/27.24 | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | BETA: splitting (349) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (350) all_58_14 = e3 & op(e0, e1) = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | (351) all_58_14 = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | (352) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | (353) all_58_9 = e3 & op(e3, e0) = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | (354) all_58_9 = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | (355) op(e3, e0) = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | (356) all_54_12 = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (338), (356) are inconsistent by sub-proof
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | #1234.
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | (357) ~ (all_54_12 = e3)
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | (358) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (359) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (359) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (360) op(e3, e3) = all_22_1
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (10), (14), (15), (16),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (25), (29), (30), (33), (34), (36),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (44), (45), (51), (52),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (59), (62), (67),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (68), (72), (73), (79), (82), (84), (85), (89),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (94), (96), (97), (99), (101), (102), (106),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (109), (110), (116), (118), (119), (121), (122),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (123), (128), (130), (131), (132), (134), (135),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (138), (142), (143), (153), (158), (162), (164),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (291), (295), (300), (304), (311),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (315), (316), (317), (319), (321), (324), (326),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (337), (338), (339), (340), (343), (351), (354),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (355), (358), (360) are inconsistent by sub-proof
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | #357.
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (362) op(e3, e3) = all_22_1
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (10), (14), (15), (16),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (25), (29), (30), (33), (34), (36),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (44), (45), (51), (52),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (59), (62), (67),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (68), (72), (73), (79), (82), (84), (85), (89),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (94), (96), (97), (99), (101), (102), (106),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (109), (110), (116), (118), (119), (121), (122),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (123), (128), (130), (131), (132), (134), (135),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (138), (142), (143), (153), (158), (162), (164),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (291), (295), (300), (304), (311),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (315), (316), (317), (319), (321), (324), (326),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (337), (338), (339), (340), (343), (351), (354),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (355), (358), (362) are inconsistent by sub-proof
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | #357.
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | (363) all_58_10 = e3 & op(e2, e0) = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (363) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | (364) op(e2, e0) = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (67), (131), (364) are inconsistent by
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | sub-proof #1364.
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | (365) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | (366) all_58_11 = e3 & op(e1, e0) = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | (367) all_58_11 = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | (368) all_54_12 = e3
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (338), (368) are inconsistent by sub-proof
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | #1234.
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | (369) ~ (all_54_12 = e3)
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | (370) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (371) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (372) op(e3, e3) = all_22_1
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (15), (16), (19), (20), (24), (25), (29), (30),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (31), (33), (34), (36), (38), (39), (40), (41),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (49), (51), (52), (53), (54), (55),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (59), (62), (67), (68), (72), (73),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (74), (79), (82), (84), (85), (89), (94), (96),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (97), (99), (101), (102), (106), (109), (110),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (111), (114), (116), (118), (119), (121), (122),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (123), (128), (130), (131), (132), (134), (135),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (138), (142), (143), (153), (158), (162), (164),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (172), (289), (291), (295), (300),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (304), (311), (315), (316), (317), (319), (321),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (324), (326), (336), (337), (338), (339), (340),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (351), (367), (370), (372) are
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #355.
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (373) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies:
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (374) op(e3, e3) = all_22_1
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (15), (16), (19), (20), (24), (25), (29), (30),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (31), (33), (34), (36), (38), (39), (40), (41),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (49), (51), (52), (53), (54), (55),
% 157.26/27.24 | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (59), (62), (67), (68), (72), (73),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (74), (79), (82), (84), (85), (89), (94), (96),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (97), (99), (101), (102), (106), (109), (110),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (111), (114), (116), (118), (119), (121), (122),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (123), (128), (130), (131), (132), (134), (135),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (138), (142), (143), (153), (158), (162), (164),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (172), (289), (291), (295), (300),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (304), (311), (315), (316), (317), (319), (321),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (324), (326), (336), (337), (338), (339), (340),
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (351), (367), (370), (374) are
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #355.
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | (375) all_58_15 = e3 & op(e0, e0) = e3
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | (376) op(e0, e0) = e3
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (131), (172), (291), (376) are inconsistent by
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | | sub-proof #1382.
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | (377) all_58_15 = e3 & op(e0, e0) = e3
% 157.26/27.25 | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | (378) op(e0, e0) = e3
% 157.26/27.25 | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (131), (172), (291), (378) are inconsistent by
% 157.26/27.25 | | | | | | | | | | | | | | | | | | | sub-proof #1382.
% 157.26/27.25 | | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | (379) all_58_3 = e0 & op(e2, e2) = e0
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (158), (379) are inconsistent by sub-proof
% 157.26/27.25 | | | | | | | | | | | | | | | | | #910.
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | (380) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.26/27.25 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.26/27.25 | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | BETA: splitting (380) gives:
% 157.26/27.25 | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | (381) all_58_7 = e0 & op(e1, e2) = e0
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | ALPHA: (381) implies:
% 157.26/27.25 | | | | | | | | | | | | | | | | | (382) all_58_7 = e0
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (382) imply:
% 157.26/27.25 | | | | | | | | | | | | | | | | | (383) e2 = e0
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (383) imply:
% 157.26/27.25 | | | | | | | | | | | | | | | | | (384) all_58_4 = e0
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (14), (15), (31), (52), (57), (71),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (79), (100), (107), (109), (110), (122), (131),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (138), (153), (158), (172), (291), (311), (384)
% 157.26/27.25 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #847.
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | (385) all_58_13 = e0 & op(e0, e2) = e0
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | ALPHA: (385) implies:
% 157.26/27.25 | | | | | | | | | | | | | | | | | (386) all_58_13 = e0
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (15), (16), (18), (19), (20), (24), (25), (29),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (30), (33), (34), (36), (38), (39), (40), (41),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (43), (44), (45), (51), (52), (53), (54), (55),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (62), (67), (68), (71),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (72), (73), (74), (79), (82), (84), (85), (89),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (94), (96), (97), (99), (100), (101), (102),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (106), (107), (109), (110), (111), (112), (114),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (116), (118), (119), (121), (122), (123), (128),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (130), (131), (132), (134), (135), (137), (138),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (141), (142), (143), (153), (158), (162), (164),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (166), (168), (172), (289), (291), (295), (300),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (304), (311), (315), (316), (317), (319), (321),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (324), (326), (332), (336), (337), (338), (339),
% 157.26/27.25 | | | | | | | | | | | | | | | | | (340), (386) are inconsistent by sub-proof #373.
% 157.26/27.25 | | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | (387) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 157.26/27.25 | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | | REF_CLOSE: (42), (170), (173), (329), (387) are inconsistent
% 157.26/27.25 | | | | | | | | | | | | | | | by sub-proof #1307.
% 157.26/27.25 | | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | (388) all_56_12 = e1
% 157.26/27.25 | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | | REF_CLOSE: (22), (33), (36), (76), (97), (316), (317), (388)
% 157.26/27.25 | | | | | | | | | | | | | are inconsistent by sub-proof #372.
% 157.26/27.25 | | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | (389) all_58_5 = e2 & op(e2, e1) = e2
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | ALPHA: (389) implies:
% 157.26/27.25 | | | | | | | | | | (390) all_58_5 = e2
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | REF_CLOSE: (10), (52), (57), (71), (79), (100), (107), (131),
% 157.26/27.25 | | | | | | | | | | (153), (158), (390) are inconsistent by sub-proof
% 157.26/27.25 | | | | | | | | | | #898.
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | End of split
% 157.26/27.25 | | | | | | | | |
% 157.26/27.25 | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | |
% 157.26/27.25 | | | | | | | | | (391) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 157.26/27.25 | | | | | | | | | op(e0, e1) = e2)
% 157.26/27.25 | | | | | | | | |
% 157.26/27.25 | | | | | | | | | REF_CLOSE: (7), (9), (10), (13), (14), (15), (16), (30), (32),
% 157.26/27.25 | | | | | | | | | (34), (38), (44), (45), (52), (53), (54), (57),
% 157.26/27.25 | | | | | | | | | (62), (67), (68), (71), (73), (79), (96), (97),
% 157.26/27.25 | | | | | | | | | (100), (107), (109), (110), (116), (118), (121),
% 157.26/27.25 | | | | | | | | | (122), (128), (130), (131), (137), (138), (153),
% 157.26/27.25 | | | | | | | | | (158), (172), (291), (295), (300), (391) are
% 157.26/27.25 | | | | | | | | | inconsistent by sub-proof #371.
% 157.26/27.25 | | | | | | | | |
% 157.26/27.25 | | | | | | | | End of split
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | End of split
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | Case 2:
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | (392) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 157.26/27.25 | | | | | | | op(e1, e0) = e2)
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | REF_CLOSE: (7), (9), (13), (14), (15), (16), (30), (38), (44),
% 157.26/27.25 | | | | | | | (45), (52), (53), (54), (56), (57), (67), (68), (71),
% 157.26/27.25 | | | | | | | (73), (79), (96), (100), (107), (109), (110), (118),
% 157.26/27.25 | | | | | | | (122), (128), (130), (131), (138), (153), (158), (172),
% 157.26/27.25 | | | | | | | (291), (295), (392) are inconsistent by sub-proof #638.
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | End of split
% 157.26/27.25 | | | | | |
% 157.26/27.25 | | | | | End of split
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | End of split
% 157.26/27.25 | | | |
% 157.26/27.25 | | | End of split
% 157.26/27.25 | | |
% 157.26/27.25 | | Case 2:
% 157.26/27.25 | | |
% 157.26/27.25 | | | (393) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2)
% 157.26/27.25 | | | = e3)
% 157.26/27.25 | | |
% 157.26/27.25 | | | BETA: splitting (393) gives:
% 157.26/27.25 | | |
% 157.26/27.25 | | | Case 1:
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | (394) all_58_7 = e3 & op(e1, e2) = e3
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | REF_CLOSE: (73), (128), (131), (394) are inconsistent by sub-proof
% 157.26/27.25 | | | | #1184.
% 157.26/27.25 | | | |
% 157.26/27.25 | | | Case 2:
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | (395) all_58_13 = e3 & op(e0, e2) = e3
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | REF_CLOSE: (14), (122), (131), (395) are inconsistent by sub-proof
% 157.26/27.25 | | | | #1449.
% 157.26/27.25 | | | |
% 157.26/27.25 | | | End of split
% 157.26/27.25 | | |
% 157.26/27.25 | | End of split
% 157.26/27.25 | |
% 157.26/27.25 | End of split
% 157.26/27.25 |
% 157.26/27.25 End of proof
% 157.26/27.25
% 157.26/27.25 Sub-proof #355 shows that the following formulas are inconsistent:
% 157.26/27.25 ----------------------------------------------------------------
% 157.26/27.25 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.26/27.25 (2) ~ (all_52_12 = e3)
% 157.26/27.25 (3) op(e0, e3) = all_52_3
% 157.26/27.25 (4) op(e3, e0) = all_52_12
% 157.26/27.25 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.25 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.25 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.25 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.25 (7) ~ (all_52_14 = e2)
% 157.26/27.25 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.25 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.25 (9) all_58_1 = e0
% 157.26/27.25 (10) ~ (all_52_12 = e2)
% 157.26/27.25 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.25 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.25 (12) all_58_14 = e3
% 157.26/27.25 (13) op(e1, e1) = all_6_2
% 157.26/27.25 (14) ~ (all_52_7 = e3)
% 157.26/27.25 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.25 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.25 e1)
% 157.26/27.25 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.25 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.25 (17) all_54_10 = all_6_2
% 157.26/27.25 (18) ~ (all_52_2 = all_52_3)
% 157.26/27.25 (19) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.26/27.25 (20) all_58_7 = e2
% 157.26/27.25 (21) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.25 (22) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.26/27.25 (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.25 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.25 (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.25 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.25 (25) all_54_1 = all_52_4
% 157.26/27.25 (26) op(e3, e2) = all_52_4
% 157.26/27.25 (27) ~ (all_52_3 = e0)
% 157.26/27.25 (28) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.25 (29) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.25 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.25 (30) ~ (all_52_12 = all_52_13)
% 157.26/27.25 (31) ~ (all_52_4 = e2)
% 157.26/27.25 (32) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.26/27.25 (33) ~ (all_52_4 = all_52_12)
% 157.26/27.25 (34) op(e2, e3) = all_52_1
% 157.26/27.25 (35) ~ (all_52_13 = e3)
% 157.26/27.25 (36) ~ (all_52_3 = e3)
% 157.26/27.25 (37) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.25 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.25 (38) ~ (all_52_2 = all_6_2)
% 157.26/27.25 (39) ~ (e3 = e0)
% 157.26/27.25 (40) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.25 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.25 (41) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.25 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.25 (42) ~ (all_52_9 = all_52_13)
% 157.26/27.25 (43) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.25 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.25 e2)
% 157.26/27.25 (44) ~ (e2 = e0)
% 157.26/27.25 (45) ~ (all_52_11 = all_6_2)
% 157.26/27.25 (46) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.25 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.25 (47) ~ (all_52_3 = e2)
% 157.26/27.25 (48) op(e2, e0) = all_52_13
% 157.26/27.25 (49) op(e2, e3) = e2
% 157.26/27.25 (50) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.25 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.25 (51) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.25 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.25 (52) op(e1, e2) = all_52_6
% 157.26/27.25 (53) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.26/27.25 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.25 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.26/27.25 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.26/27.25 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.26/27.25 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.25 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.26/27.25 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.26/27.25 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.26/27.25 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.25 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.26/27.25 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.26/27.25 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.26/27.25 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.26/27.25 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.26/27.25 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.26/27.25 = e0)
% 157.26/27.25 (54) ~ (all_52_4 = e0)
% 157.26/27.25 (55) ~ (all_52_11 = e2)
% 157.26/27.25 (56) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.25 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.25 (57) ~ (all_52_9 = all_6_2)
% 157.26/27.25 (58) all_54_8 = all_52_2
% 157.26/27.25 (59) all_54_7 = all_52_13
% 157.26/27.25 (60) all_56_12 = e3
% 157.26/27.25 (61) op(e3, e2) = e0
% 157.26/27.25 (62) ~ (all_52_2 = e3)
% 157.26/27.25 (63) ~ (all_52_13 = e2)
% 157.26/27.25 (64) op(e0, e0) = e2
% 157.26/27.25 (65) ~ (all_52_9 = all_52_11)
% 157.26/27.25 (66) all_58_4 = e2
% 157.26/27.25 (67) ~ (all_52_2 = all_52_14)
% 157.26/27.25 (68) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.25 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.25 (69) ~ (all_52_4 = e3)
% 157.26/27.25 (70) all_54_6 = all_52_9
% 157.26/27.25 (71) op(e0, e2) = e0
% 157.26/27.25 (72) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.26/27.25 (73) all_58_15 = e2
% 157.26/27.25 (74) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.26/27.25 (75) op(e3, e3) = e3
% 157.26/27.25 (76) all_54_3 = all_52_12
% 157.26/27.25 (77) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.26/27.25 (78) ~ (all_52_2 = e2)
% 157.26/27.25 (79) all_58_3 = e3
% 157.26/27.25 (80) ~ (all_6_2 = e2)
% 157.26/27.25 (81) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.25 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.25 e3)
% 157.26/27.25 (82) all_56_14 = all_6_2
% 157.26/27.25 (83) ~ (all_52_12 = all_52_14)
% 157.26/27.25 (84) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.25 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.25 (85) ~ (all_52_9 = e2)
% 157.26/27.25 (86) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.25 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.25 (87) all_54_14 = all_52_11
% 157.26/27.25 (88) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.25 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.25 (89) op(e0, e2) = all_52_7
% 157.26/27.25 (90) op(e1, e0) = all_52_14
% 157.26/27.25 (91) op(e3, e3) = all_22_1
% 157.26/27.25 (92) all_56_15 = e2
% 157.26/27.25 (93) ~ (all_52_6 = e3)
% 157.26/27.25 (94) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.25 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.25 (95) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.25 (96) ~ (all_52_3 = all_52_11)
% 157.26/27.25 (97) all_54_11 = all_52_14
% 157.26/27.25 (98) ~ (all_52_13 = all_52_14)
% 157.26/27.25 (99) ~ (e3 = e2)
% 157.26/27.25 (100) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.26/27.25 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.26/27.25 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.26/27.25 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.26/27.25 e0)))
% 157.26/27.25 (101) ~ (all_52_11 = e0)
% 157.26/27.25 (102) all_58_11 = e3
% 157.26/27.25 (103) all_54_12 = all_52_3
% 157.26/27.25 (104) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.26/27.25
% 157.26/27.25 Begin of proof
% 157.26/27.25 |
% 157.26/27.25 | BETA: splitting (28) gives:
% 157.26/27.25 |
% 157.26/27.25 | Case 1:
% 157.26/27.25 | |
% 157.26/27.25 | | (105) all_54_1 = e3
% 157.26/27.25 | |
% 157.26/27.25 | | COMBINE_EQS: (25), (105) imply:
% 157.26/27.25 | | (106) all_52_4 = e3
% 157.26/27.25 | |
% 157.26/27.25 | | REDUCE: (69), (106) imply:
% 157.26/27.25 | | (107) $false
% 157.26/27.25 | |
% 157.26/27.25 | | CLOSE: (107) is inconsistent.
% 157.26/27.25 | |
% 157.26/27.25 | Case 2:
% 157.26/27.25 | |
% 157.26/27.25 | | (108) ~ (all_54_1 = e3)
% 157.26/27.25 | | (109) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.25 | |
% 157.26/27.25 | | BETA: splitting (109) gives:
% 157.26/27.25 | |
% 157.26/27.25 | | Case 1:
% 157.26/27.25 | | |
% 157.26/27.25 | | | (110) all_54_1 = e2
% 157.26/27.25 | | |
% 157.26/27.25 | | | COMBINE_EQS: (25), (110) imply:
% 157.26/27.25 | | | (111) all_52_4 = e2
% 157.26/27.25 | | |
% 157.26/27.25 | | | REDUCE: (31), (111) imply:
% 157.26/27.25 | | | (112) $false
% 157.26/27.25 | | |
% 157.26/27.25 | | | CLOSE: (112) is inconsistent.
% 157.26/27.25 | | |
% 157.26/27.25 | | Case 2:
% 157.26/27.25 | | |
% 157.26/27.25 | | | (113) ~ (all_54_1 = e2)
% 157.26/27.25 | | | (114) all_54_1 = e1 | all_54_1 = e0
% 157.26/27.25 | | |
% 157.26/27.25 | | | BETA: splitting (114) gives:
% 157.26/27.25 | | |
% 157.26/27.25 | | | Case 1:
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | (115) all_54_1 = e1
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | COMBINE_EQS: (25), (115) imply:
% 157.26/27.25 | | | | (116) all_52_4 = e1
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | REDUCE: (33), (116) imply:
% 157.26/27.25 | | | | (117) ~ (all_52_12 = e1)
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | SIMP: (117) implies:
% 157.26/27.25 | | | | (118) ~ (all_52_12 = e1)
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | REDUCE: (69), (116) imply:
% 157.26/27.25 | | | | (119) ~ (e3 = e1)
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | SIMP: (119) implies:
% 157.26/27.25 | | | | (120) ~ (e3 = e1)
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | REDUCE: (31), (116) imply:
% 157.26/27.25 | | | | (121) ~ (e2 = e1)
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | SIMP: (121) implies:
% 157.26/27.25 | | | | (122) ~ (e2 = e1)
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | REDUCE: (54), (116) imply:
% 157.26/27.25 | | | | (123) ~ (e1 = e0)
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | REDUCE: (26), (116) imply:
% 157.26/27.25 | | | | (124) op(e3, e2) = e1
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | BETA: splitting (32) gives:
% 157.26/27.25 | | | |
% 157.26/27.25 | | | | Case 1:
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | | (125) all_54_3 = e3
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | | COMBINE_EQS: (76), (125) imply:
% 157.26/27.25 | | | | | (126) all_52_12 = e3
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | | REDUCE: (2), (126) imply:
% 157.26/27.25 | | | | | (127) $false
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | | CLOSE: (127) is inconsistent.
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | Case 2:
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | | (128) ~ (all_54_3 = e3)
% 157.26/27.25 | | | | | (129) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | | BETA: splitting (6) gives:
% 157.26/27.25 | | | | |
% 157.26/27.25 | | | | | Case 1:
% 157.26/27.25 | | | | | |
% 157.26/27.25 | | | | | | (130) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 157.26/27.25 | | | | | | e2) = e1)
% 157.26/27.25 | | | | | |
% 157.26/27.25 | | | | | | REF_CLOSE: (9), (79), (120), (123), (130) are inconsistent by
% 157.26/27.25 | | | | | | sub-proof #419.
% 157.26/27.25 | | | | | |
% 157.26/27.25 | | | | | Case 2:
% 157.26/27.25 | | | | | |
% 157.26/27.25 | | | | | | (131) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 157.26/27.25 | | | | | | op(e0, e2) = e1)
% 157.26/27.25 | | | | | |
% 157.26/27.25 | | | | | | BETA: splitting (131) gives:
% 157.26/27.25 | | | | | |
% 157.26/27.25 | | | | | | Case 1:
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | (132) all_58_7 = e1 & op(e1, e2) = e1
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | ALPHA: (132) implies:
% 157.26/27.25 | | | | | | | (133) all_58_7 = e1
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | BETA: splitting (37) gives:
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | Case 1:
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | (134) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 157.26/27.25 | | | | | | | | op(e1, e2) = e2)
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | REF_CLOSE: (11), (12), (13), (23), (24), (34), (39), (40), (44),
% 157.26/27.25 | | | | | | | | (49), (56), (66), (79), (80), (94), (95), (99),
% 157.26/27.25 | | | | | | | | (120), (122), (123), (133), (134) are inconsistent by
% 157.26/27.25 | | | | | | | | sub-proof #762.
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | (135) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 157.26/27.25 | | | | | | | | op(e1, e0) = e2)
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | REF_CLOSE: (5), (8), (13), (14), (15), (16), (23), (29), (34),
% 157.26/27.25 | | | | | | | | (35), (39), (40), (41), (43), (44), (48), (49), (50),
% 157.26/27.25 | | | | | | | | (52), (56), (64), (68), (71), (79), (80), (81), (86),
% 157.26/27.25 | | | | | | | | (89), (93), (94), (95), (99), (100), (120), (122),
% 157.26/27.25 | | | | | | | | (123), (135) are inconsistent by sub-proof #638.
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | End of split
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | Case 2:
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | (136) all_58_13 = e1 & op(e0, e2) = e1
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | ALPHA: (136) implies:
% 157.26/27.25 | | | | | | | (137) all_58_13 = e1
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | BETA: splitting (129) gives:
% 157.26/27.25 | | | | | | |
% 157.26/27.25 | | | | | | | Case 1:
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | (138) all_54_3 = e2
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | COMBINE_EQS: (76), (138) imply:
% 157.26/27.25 | | | | | | | | (139) all_52_12 = e2
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | REDUCE: (10), (139) imply:
% 157.26/27.25 | | | | | | | | (140) $false
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | CLOSE: (140) is inconsistent.
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | (141) ~ (all_54_3 = e2)
% 157.26/27.25 | | | | | | | | (142) all_54_3 = e1 | all_54_3 = e0
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | BETA: splitting (88) gives:
% 157.26/27.25 | | | | | | | |
% 157.26/27.25 | | | | | | | | Case 1:
% 157.26/27.25 | | | | | | | | |
% 157.26/27.25 | | | | | | | | | (143) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 157.26/27.25 | | | | | | | | | op(e3, e2) = e3)
% 157.26/27.25 | | | | | | | | |
% 157.26/27.25 | | | | | | | | | BETA: splitting (143) gives:
% 157.26/27.25 | | | | | | | | |
% 157.26/27.25 | | | | | | | | | Case 1:
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | (144) all_58_0 = e3 & op(e3, e3) = e3
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | ALPHA: (144) implies:
% 157.26/27.25 | | | | | | | | | | (145) all_58_0 = e3
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | BETA: splitting (100) gives:
% 157.26/27.25 | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | Case 1:
% 157.26/27.25 | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | (146) all_58_15 = e0 & op(e0, e0) = e0
% 157.26/27.25 | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | REF_CLOSE: (11), (13), (14), (15), (24), (39), (44), (49),
% 157.26/27.25 | | | | | | | | | | | (56), (64), (66), (73), (79), (80), (81), (89),
% 157.26/27.25 | | | | | | | | | | | (95), (99), (100), (120), (122), (123), (146) are
% 157.26/27.25 | | | | | | | | | | | inconsistent by sub-proof #784.
% 157.26/27.25 | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | Case 2:
% 157.26/27.25 | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | (147) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 157.26/27.25 | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.26/27.25 | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 157.26/27.25 | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 157.26/27.25 | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.26/27.25 | | | | | | | | | | |
% 157.26/27.25 | | | | | | | | | | | ALPHA: (147) implies:
% 157.26/27.26 | | | | | | | | | | | (148) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 157.26/27.26 | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 157.26/27.26 | | | | | | | | | | | e0) = e0)
% 157.26/27.26 | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | BETA: splitting (40) gives:
% 157.26/27.26 | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | (149) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.26/27.26 | | | | | | | | | | | | & op(e2, e3) = e1)
% 157.26/27.26 | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | REF_CLOSE: (49), (75), (91), (95), (120), (122), (149) are
% 157.26/27.26 | | | | | | | | | | | | inconsistent by sub-proof #863.
% 157.26/27.26 | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | (150) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 157.26/27.26 | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 157.26/27.26 | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | BETA: splitting (150) gives:
% 157.26/27.26 | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | (151) all_58_6 = e1 & op(e1, e3) = e1
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | ALPHA: (151) implies:
% 157.26/27.26 | | | | | | | | | | | | | (152) all_58_6 = e1
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | BETA: splitting (72) gives:
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | (153) all_54_12 = e2
% 157.26/27.26 | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | REF_CLOSE: (47), (103), (153) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | #1189.
% 157.26/27.26 | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | (154) ~ (all_54_12 = e2)
% 157.26/27.26 | | | | | | | | | | | | | | (155) all_54_12 = e1 | all_54_12 = e0
% 157.26/27.26 | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 157.26/27.26 | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | (156) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.26/27.26 | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | REF_CLOSE: (49), (79), (95), (120), (122), (156) are
% 157.26/27.26 | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 157.26/27.26 | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | (157) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 157.26/27.26 | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.26/27.26 | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 157.26/27.26 | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | (158) all_58_5 = e1 & op(e2, e1) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | (159) all_58_5 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | (160) all_58_9 = e0 & op(e3, e0) = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | (161) all_58_9 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (162) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (163) all_58_0 = e1 & op(e3, e3) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (164) op(e3, e3) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (91), (95), (120), (164) are inconsistent by
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | sub-proof #864.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (165) all_58_1 = e1 & op(e3, e2) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (166) all_58_1 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (166) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (167) e1 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (168) e1 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (168) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (169) all_58_13 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (14), (15), (16), (17), (18), (19), (20), (21),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (22), (23), (26), (27), (29), (30), (34), (35),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (36), (38), (39), (40), (41), (43), (44), (45),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (46), (47), (48), (49), (50), (51), (52), (53),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (55), (56), (58), (59), (60), (62), (63), (64),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (66), (68), (69), (71), (72), (73), (74), (76),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (86), (87), (88), (89), (90), (92), (93), (94),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (103), (104), (118), (120), (122), (123), (142),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (161), (166), (169) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | #386.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (170) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (171) all_58_4 = e1 & op(e3, e1) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (172) all_58_4 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (13), (24), (39), (44), (49), (56),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (79), (80), (95), (99), (120), (122), (123), (172)
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #850.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (173) all_58_9 = e1 & op(e3, e0) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (174) all_58_9 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (174) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (175) e1 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (175) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (176) all_58_13 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (14), (15), (16), (17), (18), (19), (20), (21),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (22), (23), (26), (27), (29), (30), (32), (34),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (35), (36), (38), (39), (40), (41), (43), (44),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (53), (55), (56), (58), (59), (60), (62), (63),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (64), (66), (68), (69), (71), (72), (73), (74),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (76), (77), (78), (79), (80), (81), (82), (83),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (84), (86), (87), (88), (89), (90), (92), (93),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (94), (95), (96), (97), (98), (99), (100), (101),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (102), (103), (104), (118), (120), (122), (123),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (161), (176) are inconsistent by sub-proof #385.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | (177) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 157.26/27.26 | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (178) all_58_10 = e0 & op(e2, e0) = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (179) all_58_10 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (180) all_54_12 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (180) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (181) all_52_3 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | SIMP: (181) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (182) all_52_3 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | REDUCE: (18), (182) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (183) ~ (all_52_2 = e1)
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (184) all_54_8 = e3
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (62), (184) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | #1425.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (185) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | (186) all_54_8 = e2
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (78), (186) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | #1231.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | (187) all_54_8 = e1 | all_54_8 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (188) all_54_8 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (188) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (189) all_52_2 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (189) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (190) $false
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (191) all_54_8 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (191) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (192) all_52_2 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (192) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (193) ~ (e1 = e0)
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (95) with e0, e1, e2, e3,
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | simplifying with (61), (124) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (194) e1 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (194) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (195) all_58_5 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (49), (79), (95), (120), (122), (123),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | | (179), (195) are inconsistent by sub-proof #839.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (196) all_54_12 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (103), (196) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | #1223.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (197) all_58_11 = e0 & op(e1, e0) = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (198) all_58_11 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (198) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (199) e3 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (199) imply:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (200) all_58_0 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (14), (15), (16), (20), (23),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (26), (29), (34), (35), (39), (40), (41), (43),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (44), (48), (49), (50), (52), (56), (64), (66),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (68), (69), (71), (79), (81), (84), (86), (88),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (89), (93), (94), (95), (99), (100), (102), (120),
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (122), (123), (137), (200) are inconsistent by
% 157.26/27.26 | | | | | | | | | | | | | | | | | | sub-proof #640.
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | (201) all_58_10 = e1 & op(e2, e0) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | (202) all_58_10 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | (203) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (13), (24), (39), (44), (49), (56),
% 157.26/27.26 | | | | | | | | | | | | | | | | | (79), (80), (95), (99), (120), (122), (123),
% 157.26/27.26 | | | | | | | | | | | | | | | | | (202), (203) are inconsistent by sub-proof #356.
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | (204) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 157.26/27.26 | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (205) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (206) all_58_8 = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (207) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (208) all_58_6 = e0 & op(e1, e3) = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (209) all_58_6 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (152), (209) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | #735.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (210) all_58_7 = e0 & op(e1, e2) = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (211) all_58_7 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (44), (211) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | #1086.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | (212) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (213) all_58_8 = e0 & op(e1, e1) = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (214) all_58_8 = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (206), (214) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | #1445.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | (215) all_58_11 = e0 & op(e1, e0) = e0
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (102), (215) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | | #1083.
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | (216) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (120), (216) are inconsistent by sub-proof
% 157.26/27.26 | | | | | | | | | | | | | | | | | | #844.
% 157.26/27.26 | | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | (217) all_58_12 = e1 & op(e0, e3) = e1
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | ALPHA: (217) implies:
% 157.26/27.26 | | | | | | | | | | | | | (218) all_58_12 = e1
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | | REF_CLOSE: (6), (9), (12), (20), (23), (34), (39), (40),
% 157.26/27.26 | | | | | | | | | | | | | (43), (44), (49), (79), (94), (95), (99), (100),
% 157.26/27.26 | | | | | | | | | | | | | (120), (122), (123), (137), (218) are inconsistent
% 157.26/27.26 | | | | | | | | | | | | | by sub-proof #648.
% 157.26/27.26 | | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | (219) all_58_1 = e3 & op(e3, e2) = e3
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | ALPHA: (219) implies:
% 157.26/27.26 | | | | | | | | | | (220) op(e3, e2) = e3
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | REF_CLOSE: (26), (69), (95), (220) are inconsistent by
% 157.26/27.26 | | | | | | | | | | sub-proof #1540.
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | |
% 157.26/27.26 | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | |
% 157.26/27.26 | | | | | | | | | (221) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 157.26/27.26 | | | | | | | | | op(e3, e0) = e3)
% 157.26/27.26 | | | | | | | | |
% 157.26/27.26 | | | | | | | | | BETA: splitting (221) gives:
% 157.26/27.26 | | | | | | | | |
% 157.26/27.26 | | | | | | | | | Case 1:
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | (222) all_58_4 = e3 & op(e3, e1) = e3
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | ALPHA: (222) implies:
% 157.26/27.26 | | | | | | | | | | (223) all_58_4 = e3
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | REF_CLOSE: (5), (8), (11), (13), (14), (15), (16), (23),
% 157.26/27.26 | | | | | | | | | | (24), (29), (34), (35), (39), (40), (41), (43),
% 157.26/27.26 | | | | | | | | | | (44), (48), (49), (50), (52), (56), (64), (68),
% 157.26/27.26 | | | | | | | | | | (71), (73), (79), (80), (81), (86), (89), (93),
% 157.26/27.26 | | | | | | | | | | (94), (95), (99), (100), (102), (120), (122),
% 157.26/27.26 | | | | | | | | | | (123), (223) are inconsistent by sub-proof #695.
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | Case 2:
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | (224) all_58_9 = e3 & op(e3, e0) = e3
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | ALPHA: (224) implies:
% 157.26/27.26 | | | | | | | | | | (225) all_58_9 = e3
% 157.26/27.26 | | | | | | | | | | (226) op(e3, e0) = e3
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10),
% 157.26/27.26 | | | | | | | | | | (11), (12), (14), (15), (16), (17), (18), (20),
% 157.26/27.26 | | | | | | | | | | (21), (22), (23), (25), (26), (27), (28), (29),
% 157.26/27.26 | | | | | | | | | | (30), (31), (32), (33), (34), (35), (36), (38),
% 157.26/27.26 | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46),
% 157.26/27.26 | | | | | | | | | | (47), (48), (49), (50), (51), (52), (54), (55),
% 157.26/27.26 | | | | | | | | | | (56), (57), (58), (59), (62), (63), (64), (65),
% 157.26/27.26 | | | | | | | | | | (66), (67), (68), (69), (70), (71), (72), (73),
% 157.26/27.26 | | | | | | | | | | (74), (75), (76), (77), (78), (79), (80), (81),
% 157.26/27.26 | | | | | | | | | | (84), (85), (86), (87), (88), (89), (90), (91),
% 157.26/27.26 | | | | | | | | | | (93), (94), (95), (96), (97), (98), (100), (101),
% 157.26/27.26 | | | | | | | | | | (103), (104), (225), (226) are inconsistent by
% 157.26/27.26 | | | | | | | | | | sub-proof #357.
% 157.26/27.26 | | | | | | | | | |
% 157.26/27.26 | | | | | | | | | End of split
% 157.26/27.26 | | | | | | | | |
% 157.26/27.26 | | | | | | | | End of split
% 157.26/27.26 | | | | | | | |
% 157.26/27.26 | | | | | | | End of split
% 157.26/27.26 | | | | | | |
% 157.26/27.26 | | | | | | End of split
% 157.26/27.26 | | | | | |
% 157.26/27.26 | | | | | End of split
% 157.26/27.26 | | | | |
% 157.26/27.26 | | | | End of split
% 157.26/27.26 | | | |
% 157.26/27.26 | | | Case 2:
% 157.26/27.26 | | | |
% 157.26/27.26 | | | | (227) all_54_1 = e0
% 157.26/27.26 | | | |
% 157.26/27.26 | | | | COMBINE_EQS: (25), (227) imply:
% 157.26/27.26 | | | | (228) all_52_4 = e0
% 157.26/27.26 | | | |
% 157.26/27.26 | | | | REDUCE: (54), (228) imply:
% 157.26/27.26 | | | | (229) $false
% 157.26/27.26 | | | |
% 157.26/27.26 | | | | CLOSE: (229) is inconsistent.
% 157.26/27.26 | | | |
% 157.26/27.26 | | | End of split
% 157.26/27.26 | | |
% 157.26/27.26 | | End of split
% 157.26/27.26 | |
% 157.26/27.26 | End of split
% 157.26/27.26 |
% 157.26/27.26 End of proof
% 157.26/27.26
% 157.26/27.26 Sub-proof #356 shows that the following formulas are inconsistent:
% 157.26/27.26 ----------------------------------------------------------------
% 157.26/27.26 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.26 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.26 (2) all_58_14 = e3
% 157.26/27.26 (3) op(e1, e1) = all_6_2
% 157.26/27.26 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.26 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.26 (5) ~ (e3 = e0)
% 157.26/27.26 (6) ~ (e2 = e0)
% 157.26/27.26 (7) op(e2, e3) = e2
% 157.26/27.26 (8) ~ (e3 = e1)
% 157.26/27.26 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.26 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.26 (10) all_58_10 = e1
% 157.26/27.26 (11) ~ (e2 = e1)
% 157.26/27.26 (12) ~ (e1 = e0)
% 157.26/27.26 (13) all_58_3 = e3
% 157.26/27.26 (14) ~ (all_6_2 = e2)
% 157.26/27.26 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.26 (16) ~ (e3 = e2)
% 157.26/27.26 (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 157.26/27.26
% 157.26/27.26 Begin of proof
% 157.26/27.26 |
% 157.26/27.26 | BETA: splitting (17) gives:
% 157.26/27.26 |
% 157.26/27.26 | Case 1:
% 157.26/27.26 | |
% 157.26/27.26 | | (18) all_58_4 = e1 & op(e3, e1) = e1
% 157.26/27.26 | |
% 157.26/27.26 | | ALPHA: (18) implies:
% 157.26/27.26 | | (19) all_58_4 = e1
% 157.26/27.26 | |
% 157.26/27.26 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 157.26/27.26 | | (14), (15), (16), (19) are inconsistent by sub-proof #850.
% 157.26/27.26 | |
% 157.26/27.26 | Case 2:
% 157.26/27.26 | |
% 157.26/27.26 | | (20) all_58_5 = e1 & op(e2, e1) = e1
% 157.26/27.26 | |
% 157.26/27.26 | | ALPHA: (20) implies:
% 157.26/27.26 | | (21) all_58_5 = e1
% 157.26/27.26 | |
% 157.26/27.26 | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (13), (15), (21)
% 157.26/27.26 | | are inconsistent by sub-proof #754.
% 157.26/27.26 | |
% 157.26/27.26 | End of split
% 157.26/27.26 |
% 157.26/27.26 End of proof
% 157.26/27.26
% 157.26/27.26 Sub-proof #357 shows that the following formulas are inconsistent:
% 157.26/27.26 ----------------------------------------------------------------
% 157.26/27.26 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.26/27.26 (2) ~ (all_52_12 = e3)
% 157.26/27.26 (3) op(e3, e0) = all_52_12
% 157.26/27.26 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.26 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.26 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.26 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.26 (6) ~ (all_52_14 = e2)
% 157.26/27.26 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.26 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.26 (8) all_58_1 = e0
% 157.26/27.26 (9) ~ (all_52_12 = e2)
% 157.26/27.26 (10) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.26 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.26 (11) all_58_14 = e3
% 157.26/27.26 (12) ~ (all_52_7 = e3)
% 157.26/27.26 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.26 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.26 e1)
% 157.26/27.26 (14) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.26 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.26 (15) all_54_10 = all_6_2
% 157.26/27.26 (16) ~ (all_52_2 = all_52_3)
% 157.26/27.26 (17) all_58_7 = e2
% 157.26/27.26 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.26 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.26/27.26 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.26 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.26 (21) all_54_1 = all_52_4
% 157.26/27.26 (22) op(e3, e2) = all_52_4
% 157.26/27.26 (23) ~ (all_52_3 = e0)
% 157.26/27.26 (24) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.26 (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.26 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.26 (26) ~ (all_52_12 = all_52_13)
% 157.26/27.26 (27) ~ (all_52_4 = e2)
% 157.26/27.26 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.26/27.26 (29) ~ (all_52_4 = all_52_12)
% 157.26/27.26 (30) op(e2, e3) = all_52_1
% 157.26/27.26 (31) ~ (all_52_13 = e3)
% 157.26/27.26 (32) ~ (all_52_3 = e3)
% 157.26/27.26 (33) ~ (all_52_2 = all_6_2)
% 157.26/27.26 (34) ~ (e3 = e0)
% 157.26/27.26 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.26 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.26 (36) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.26 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.26 (37) ~ (all_52_9 = all_52_13)
% 157.26/27.26 (38) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.26 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.26 e2)
% 157.26/27.26 (39) ~ (e2 = e0)
% 157.26/27.26 (40) ~ (all_52_11 = all_6_2)
% 157.26/27.26 (41) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.26 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.26 (42) ~ (all_52_3 = e2)
% 157.26/27.26 (43) all_58_9 = e3
% 157.26/27.26 (44) op(e2, e0) = all_52_13
% 157.26/27.26 (45) op(e2, e3) = e2
% 157.26/27.26 (46) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.26 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.26 (47) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.26 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.26 (48) op(e1, e2) = all_52_6
% 157.26/27.26 (49) ~ (all_52_4 = e0)
% 157.26/27.26 (50) ~ (all_52_11 = e2)
% 157.26/27.26 (51) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.26 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.26 (52) ~ (all_52_9 = all_6_2)
% 157.26/27.26 (53) all_54_8 = all_52_2
% 157.26/27.26 (54) all_54_7 = all_52_13
% 157.26/27.26 (55) ~ (all_52_2 = e3)
% 157.26/27.26 (56) ~ (all_52_13 = e2)
% 157.26/27.26 (57) op(e0, e0) = e2
% 157.26/27.26 (58) ~ (all_52_9 = all_52_11)
% 157.26/27.26 (59) all_58_4 = e2
% 157.26/27.26 (60) ~ (all_52_2 = all_52_14)
% 157.26/27.26 (61) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.26 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.26 (62) ~ (all_52_4 = e3)
% 157.26/27.26 (63) all_54_6 = all_52_9
% 157.26/27.26 (64) op(e0, e2) = e0
% 157.26/27.26 (65) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.26/27.26 (66) all_58_15 = e2
% 157.26/27.26 (67) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.26/27.26 (68) op(e3, e3) = e3
% 157.26/27.26 (69) all_54_3 = all_52_12
% 157.26/27.26 (70) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.26/27.26 (71) ~ (all_52_2 = e2)
% 157.26/27.26 (72) all_58_3 = e3
% 157.26/27.26 (73) ~ (all_6_2 = e2)
% 157.26/27.27 (74) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.27 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.27 e3)
% 157.26/27.27 (75) op(e3, e0) = e3
% 157.26/27.27 (76) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.27 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.27 (77) ~ (all_52_9 = e2)
% 157.26/27.27 (78) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.27 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.27 (79) all_54_14 = all_52_11
% 157.26/27.27 (80) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.27 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.27 (81) op(e0, e2) = all_52_7
% 157.26/27.27 (82) op(e1, e0) = all_52_14
% 157.26/27.27 (83) op(e3, e3) = all_22_1
% 157.26/27.27 (84) ~ (all_52_6 = e3)
% 157.26/27.27 (85) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.27 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.27 (86) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.27 (87) ~ (all_52_3 = all_52_11)
% 157.26/27.27 (88) all_54_11 = all_52_14
% 157.26/27.27 (89) ~ (all_52_13 = all_52_14)
% 157.26/27.27 (90) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.27 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.26/27.27 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.26/27.27 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.26/27.27 (91) ~ (all_52_11 = e0)
% 157.26/27.27 (92) all_54_12 = all_52_3
% 157.26/27.27 (93) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.26/27.27
% 157.26/27.27 Begin of proof
% 157.26/27.27 |
% 157.26/27.27 | BETA: splitting (24) gives:
% 157.26/27.27 |
% 157.26/27.27 | Case 1:
% 157.26/27.27 | |
% 157.26/27.27 | | (94) all_54_1 = e3
% 157.26/27.27 | |
% 157.26/27.27 | | COMBINE_EQS: (21), (94) imply:
% 157.26/27.27 | | (95) all_52_4 = e3
% 157.26/27.27 | |
% 157.26/27.27 | | REDUCE: (62), (95) imply:
% 157.26/27.27 | | (96) $false
% 157.26/27.27 | |
% 157.26/27.27 | | CLOSE: (96) is inconsistent.
% 157.26/27.27 | |
% 157.26/27.27 | Case 2:
% 157.26/27.27 | |
% 157.26/27.27 | | (97) ~ (all_54_1 = e3)
% 157.26/27.27 | | (98) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.27 | |
% 157.26/27.27 | | BETA: splitting (98) gives:
% 157.26/27.27 | |
% 157.26/27.27 | | Case 1:
% 157.26/27.27 | | |
% 157.26/27.27 | | | (99) all_54_1 = e2
% 157.26/27.27 | | |
% 157.26/27.27 | | | COMBINE_EQS: (21), (99) imply:
% 157.26/27.27 | | | (100) all_52_4 = e2
% 157.26/27.27 | | |
% 157.26/27.27 | | | REDUCE: (27), (100) imply:
% 157.26/27.27 | | | (101) $false
% 157.26/27.27 | | |
% 157.26/27.27 | | | CLOSE: (101) is inconsistent.
% 157.26/27.27 | | |
% 157.26/27.27 | | Case 2:
% 157.26/27.27 | | |
% 157.26/27.27 | | | (102) all_54_1 = e1 | all_54_1 = e0
% 157.26/27.27 | | |
% 157.26/27.27 | | | BETA: splitting (102) gives:
% 157.26/27.27 | | |
% 157.26/27.27 | | | Case 1:
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | (103) all_54_1 = e1
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | COMBINE_EQS: (21), (103) imply:
% 157.26/27.27 | | | | (104) all_52_4 = e1
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | REDUCE: (29), (104) imply:
% 157.26/27.27 | | | | (105) ~ (all_52_12 = e1)
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | SIMP: (105) implies:
% 157.26/27.27 | | | | (106) ~ (all_52_12 = e1)
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | BETA: splitting (65) gives:
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | Case 1:
% 157.26/27.27 | | | | |
% 157.26/27.27 | | | | | (107) all_54_12 = e2
% 157.26/27.27 | | | | |
% 157.26/27.27 | | | | | REF_CLOSE: (42), (92), (107) are inconsistent by sub-proof #1189.
% 157.26/27.27 | | | | |
% 157.26/27.27 | | | | Case 2:
% 157.26/27.27 | | | | |
% 157.26/27.27 | | | | | (108) ~ (all_54_12 = e2)
% 157.26/27.27 | | | | | (109) all_54_12 = e1 | all_54_12 = e0
% 157.26/27.27 | | | | |
% 157.26/27.27 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.26/27.27 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (22),
% 157.26/27.27 | | | | | (23), (25), (26), (28), (30), (31), (32), (33), (34), (35),
% 157.26/27.27 | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.26/27.27 | | | | | (46), (47), (48), (50), (51), (52), (53), (54), (55), (56),
% 157.26/27.27 | | | | | (57), (58), (59), (60), (61), (62), (63), (64), (66), (67),
% 157.26/27.27 | | | | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 157.26/27.27 | | | | | (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 157.26/27.27 | | | | | (88), (89), (90), (91), (92), (93), (106), (109) are
% 157.26/27.27 | | | | | inconsistent by sub-proof #377.
% 157.26/27.27 | | | | |
% 157.26/27.27 | | | | End of split
% 157.26/27.27 | | | |
% 157.26/27.27 | | | Case 2:
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | (110) all_54_1 = e0
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | COMBINE_EQS: (21), (110) imply:
% 157.26/27.27 | | | | (111) all_52_4 = e0
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | REDUCE: (49), (111) imply:
% 157.26/27.27 | | | | (112) $false
% 157.26/27.27 | | | |
% 157.26/27.27 | | | | CLOSE: (112) is inconsistent.
% 157.26/27.27 | | | |
% 157.26/27.27 | | | End of split
% 157.26/27.27 | | |
% 157.26/27.27 | | End of split
% 157.26/27.27 | |
% 157.26/27.27 | End of split
% 157.26/27.27 |
% 157.26/27.27 End of proof
% 157.26/27.27
% 157.26/27.27 Sub-proof #358 shows that the following formulas are inconsistent:
% 157.26/27.27 ----------------------------------------------------------------
% 157.26/27.27 (1) op(e1, e1) = e3
% 157.26/27.27 (2) op(e1, e1) = all_32_1
% 157.26/27.27 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.26/27.27 (4) all_56_14 = e3
% 157.26/27.27 (5) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.26/27.27 (6) ~ (all_52_3 = e1)
% 157.26/27.27 (7) op(e3, e1) = e3
% 157.26/27.27 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.27 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.27 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.27 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.27 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.27 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.27 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.27 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.27 (12) all_54_13 = all_52_7
% 157.26/27.27 (13) op(e1, e1) = all_6_2
% 157.26/27.27 (14) ~ (all_52_7 = e3)
% 157.26/27.27 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.27 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.27 e1)
% 157.26/27.27 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.27 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.27 (17) ~ (all_52_6 = all_52_14)
% 157.26/27.27 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.26/27.27 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.26/27.27 (19) ~ (all_52_11 = e3)
% 157.26/27.27 (20) ~ (all_52_2 = all_52_3)
% 157.26/27.27 (21) ~ (all_52_4 = all_52_6)
% 157.26/27.27 (22) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.27 (23) ~ (all_52_7 = all_52_11)
% 157.26/27.27 (24) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.26/27.27 (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.27 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.27 (26) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.27 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.27 (27) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.27 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.27 (28) ~ (all_52_14 = e3)
% 157.26/27.27 (29) all_54_1 = all_52_4
% 157.26/27.27 (30) op(e3, e2) = all_52_4
% 157.26/27.27 (31) ~ (all_4_2 = e2)
% 157.26/27.27 (32) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.27 (33) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.27 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.27 (34) op(e2, e1) = all_52_9
% 157.26/27.27 (35) op(e2, e3) = all_52_1
% 157.26/27.27 (36) ~ (all_52_13 = e3)
% 157.26/27.27 (37) all_54_2 = all_52_8
% 157.26/27.27 (38) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.27 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.27 (39) ~ (all_52_8 = all_52_9)
% 157.26/27.27 (40) ~ (e3 = e0)
% 157.26/27.27 (41) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.27 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.27 (42) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.27 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.27 (43) ~ (all_52_9 = all_52_13)
% 157.26/27.27 (44) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.27 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.27 e2)
% 157.26/27.27 (45) ~ (e2 = e0)
% 157.26/27.27 (46) ~ (all_52_9 = e3)
% 157.26/27.27 (47) ~ (all_52_2 = all_52_6)
% 157.26/27.27 (48) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.27 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.27 (49) ~ (all_52_3 = e2)
% 157.26/27.27 (50) op(e2, e0) = all_52_13
% 157.26/27.27 (51) op(e2, e3) = e2
% 157.26/27.27 (52) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.27 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.27 (53) ~ (e3 = e1)
% 157.26/27.27 (54) all_56_12 = e1
% 157.26/27.27 (55) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.27 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.27 (56) op(e1, e2) = all_52_6
% 157.26/27.27 (57) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 157.26/27.27 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3,
% 157.26/27.27 e3) = all_28_1 & $i(all_28_1))
% 157.26/27.27 (58) ~ (all_4_2 = e1)
% 157.26/27.27 (59) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.26/27.27 (60) ~ (all_52_3 = all_4_2)
% 157.26/27.27 (61) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.27 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.27 (62) op(e0, e0) = all_4_2
% 157.26/27.27 (63) all_54_8 = all_52_2
% 157.26/27.27 (64) all_54_7 = all_52_13
% 157.26/27.27 (65) ~ (all_52_2 = e3)
% 157.26/27.27 (66) op(e3, e3) = e1
% 157.26/27.27 (67) ~ (all_52_13 = e2)
% 157.26/27.27 (68) all_56_15 = all_4_2
% 157.26/27.27 (69) ~ (all_52_9 = all_52_11)
% 157.26/27.27 (70) ~ (all_52_13 = all_4_2)
% 157.26/27.27 (71) ~ (all_52_2 = e1)
% 157.26/27.27 (72) ~ (all_52_6 = all_52_7)
% 157.26/27.27 (73) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.27 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.27 (74) ~ (all_52_4 = e3)
% 157.26/27.27 (75) all_54_6 = all_52_9
% 157.26/27.27 (76) ~ (e2 = e1)
% 157.26/27.27 (77) ~ (all_52_4 = all_52_7)
% 157.26/27.27 (78) ~ (all_52_8 = all_52_11)
% 157.26/27.27 (79) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.26/27.27 (80) ~ (e1 = e0)
% 157.26/27.27 (81) ~ (all_52_2 = e2)
% 157.26/27.27 (82) all_58_3 = e3
% 157.26/27.27 (83) op(e3, e1) = all_52_8
% 157.26/27.27 (84) ~ (all_6_2 = e2)
% 157.26/27.27 (85) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.27 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.27 e3)
% 157.26/27.27 (86) all_56_13 = e3
% 157.26/27.27 (87) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.27 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.27 (88) ~ (all_52_9 = e2)
% 157.26/27.27 (89) ~ (all_52_8 = e3)
% 157.26/27.27 (90) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.27 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.27 (91) all_54_14 = all_52_11
% 157.26/27.27 (92) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.26/27.27 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 157.26/27.27 e3) = all_22_1 & $i(all_22_1))
% 157.26/27.27 (93) ~ (all_52_7 = all_4_2)
% 157.26/27.27 (94) op(e1, e3) = e1
% 157.26/27.27 (95) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.27 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.27 (96) op(e0, e2) = all_52_7
% 157.26/27.27 (97) op(e1, e0) = all_52_14
% 157.26/27.27 (98) all_54_15 = all_4_2
% 157.26/27.27 (99) ~ (all_52_8 = e1)
% 157.26/27.27 (100) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.26/27.27 (101) ~ (all_52_6 = e3)
% 157.26/27.27 (102) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.27 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.27 (103) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.27 (104) ~ (all_52_3 = all_52_11)
% 157.26/27.27 (105) ~ (all_52_11 = all_4_2)
% 157.26/27.27 (106) all_54_11 = all_52_14
% 157.26/27.27 (107) ~ (all_52_13 = all_52_14)
% 157.26/27.27 (108) ~ (e3 = e2)
% 157.26/27.27 (109) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.26/27.27 (110) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.26/27.27 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.27 (111) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.26/27.27 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.26/27.27 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.26/27.27 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.26/27.27 e0)))
% 157.26/27.27 (112) all_54_9 = all_52_6
% 157.26/27.27 (113) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.26/27.27 (114) all_54_12 = all_52_3
% 157.26/27.27 (115) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.26/27.27 (116) ~ (all_52_14 = all_4_2)
% 157.26/27.27 (117) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.26/27.27 (118) ~ (all_52_3 = all_52_7)
% 157.26/27.27
% 157.26/27.27 Begin of proof
% 157.26/27.27 |
% 157.26/27.27 | BETA: splitting (57) gives:
% 157.26/27.27 |
% 157.26/27.27 | Case 1:
% 157.26/27.27 | |
% 157.26/27.27 | | (119) ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 157.26/27.27 | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 157.26/27.27 | |
% 157.26/27.27 | | ALPHA: (119) implies:
% 157.26/27.27 | | (120) op(e3, e3) = all_28_1
% 157.26/27.27 | |
% 157.26/27.27 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.26/27.27 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.26/27.27 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 157.26/27.27 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.26/27.27 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 157.26/27.27 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 157.26/27.27 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 157.26/27.27 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 157.26/27.27 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 157.26/27.27 | | (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 157.26/27.27 | | (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 157.26/27.27 | | (120) are inconsistent by sub-proof #359.
% 157.26/27.27 | |
% 157.26/27.27 | Case 2:
% 157.26/27.27 | |
% 157.26/27.27 | | (121) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1)
% 157.26/27.27 | |
% 157.26/27.27 | | ALPHA: (121) implies:
% 157.26/27.27 | | (122) op(e3, e3) = all_28_1
% 157.26/27.27 | |
% 157.26/27.27 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.26/27.27 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.26/27.27 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 157.26/27.27 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.26/27.27 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 157.26/27.27 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 157.26/27.27 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 157.26/27.27 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 157.26/27.27 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 157.26/27.27 | | (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 157.26/27.27 | | (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 157.26/27.27 | | (122) are inconsistent by sub-proof #359.
% 157.26/27.27 | |
% 157.26/27.27 | End of split
% 157.26/27.27 |
% 157.26/27.27 End of proof
% 157.26/27.27
% 157.26/27.27 Sub-proof #359 shows that the following formulas are inconsistent:
% 157.26/27.27 ----------------------------------------------------------------
% 157.26/27.27 (1) op(e1, e1) = e3
% 157.26/27.27 (2) op(e1, e1) = all_32_1
% 157.26/27.27 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.26/27.27 (4) all_56_14 = e3
% 157.26/27.27 (5) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.26/27.27 (6) ~ (all_52_3 = e1)
% 157.26/27.27 (7) op(e3, e1) = e3
% 157.26/27.27 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.27 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.27 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.27 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.27 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.27 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.27 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.27 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.27 (12) all_54_13 = all_52_7
% 157.26/27.27 (13) op(e1, e1) = all_6_2
% 157.26/27.27 (14) ~ (all_52_7 = e3)
% 157.26/27.27 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.27 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.27 e1)
% 157.26/27.27 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.27 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.27 (17) ~ (all_52_6 = all_52_14)
% 157.26/27.27 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.26/27.27 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.26/27.27 (19) ~ (all_52_11 = e3)
% 157.26/27.27 (20) ~ (all_52_2 = all_52_3)
% 157.26/27.27 (21) ~ (all_52_4 = all_52_6)
% 157.26/27.27 (22) op(e3, e3) = all_28_1
% 157.26/27.27 (23) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.27 (24) ~ (all_52_7 = all_52_11)
% 157.26/27.27 (25) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.26/27.27 (26) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.27 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.27 (27) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.27 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.27 (28) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.27 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.27 (29) ~ (all_52_14 = e3)
% 157.26/27.27 (30) all_54_1 = all_52_4
% 157.26/27.27 (31) op(e3, e2) = all_52_4
% 157.26/27.27 (32) ~ (all_4_2 = e2)
% 157.26/27.27 (33) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.27 (34) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.27 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.27 (35) op(e2, e1) = all_52_9
% 157.26/27.27 (36) op(e2, e3) = all_52_1
% 157.26/27.27 (37) ~ (all_52_13 = e3)
% 157.26/27.27 (38) all_54_2 = all_52_8
% 157.26/27.27 (39) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.27 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.27 (40) ~ (all_52_8 = all_52_9)
% 157.26/27.27 (41) ~ (e3 = e0)
% 157.26/27.27 (42) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.27 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.27 (43) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.27 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.27 (44) ~ (all_52_9 = all_52_13)
% 157.26/27.27 (45) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.27 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.27 e2)
% 157.26/27.27 (46) ~ (e2 = e0)
% 157.26/27.27 (47) ~ (all_52_9 = e3)
% 157.26/27.27 (48) ~ (all_52_2 = all_52_6)
% 157.26/27.27 (49) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.27 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.27 (50) ~ (all_52_3 = e2)
% 157.26/27.27 (51) op(e2, e0) = all_52_13
% 157.26/27.27 (52) op(e2, e3) = e2
% 157.26/27.27 (53) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.27 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.27 (54) ~ (e3 = e1)
% 157.26/27.27 (55) all_56_12 = e1
% 157.26/27.27 (56) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.27 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.27 (57) op(e1, e2) = all_52_6
% 157.26/27.27 (58) ~ (all_4_2 = e1)
% 157.26/27.27 (59) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.26/27.27 (60) ~ (all_52_3 = all_4_2)
% 157.26/27.27 (61) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.27 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.27 (62) op(e0, e0) = all_4_2
% 157.26/27.27 (63) all_54_8 = all_52_2
% 157.26/27.27 (64) all_54_7 = all_52_13
% 157.26/27.27 (65) ~ (all_52_2 = e3)
% 157.26/27.27 (66) op(e3, e3) = e1
% 157.26/27.27 (67) ~ (all_52_13 = e2)
% 157.26/27.27 (68) all_56_15 = all_4_2
% 157.26/27.27 (69) ~ (all_52_9 = all_52_11)
% 157.26/27.27 (70) ~ (all_52_13 = all_4_2)
% 157.26/27.27 (71) ~ (all_52_2 = e1)
% 157.26/27.27 (72) ~ (all_52_6 = all_52_7)
% 157.26/27.28 (73) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.28 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.28 (74) ~ (all_52_4 = e3)
% 157.26/27.28 (75) all_54_6 = all_52_9
% 157.26/27.28 (76) ~ (e2 = e1)
% 157.26/27.28 (77) ~ (all_52_4 = all_52_7)
% 157.26/27.28 (78) ~ (all_52_8 = all_52_11)
% 157.26/27.28 (79) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.26/27.28 (80) ~ (e1 = e0)
% 157.26/27.28 (81) ~ (all_52_2 = e2)
% 157.26/27.28 (82) all_58_3 = e3
% 157.26/27.28 (83) op(e3, e1) = all_52_8
% 157.26/27.28 (84) ~ (all_6_2 = e2)
% 157.26/27.28 (85) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.28 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.28 e3)
% 157.26/27.28 (86) all_56_13 = e3
% 157.26/27.28 (87) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.28 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.28 (88) ~ (all_52_9 = e2)
% 157.26/27.28 (89) ~ (all_52_8 = e3)
% 157.26/27.28 (90) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.28 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.28 (91) all_54_14 = all_52_11
% 157.26/27.28 (92) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.26/27.28 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 157.26/27.28 e3) = all_22_1 & $i(all_22_1))
% 157.26/27.28 (93) ~ (all_52_7 = all_4_2)
% 157.26/27.28 (94) op(e1, e3) = e1
% 157.26/27.28 (95) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.28 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.28 (96) op(e0, e2) = all_52_7
% 157.26/27.28 (97) op(e1, e0) = all_52_14
% 157.26/27.28 (98) all_54_15 = all_4_2
% 157.26/27.28 (99) ~ (all_52_8 = e1)
% 157.26/27.28 (100) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.26/27.28 (101) ~ (all_52_6 = e3)
% 157.26/27.28 (102) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.28 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.28 (103) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.28 (104) ~ (all_52_3 = all_52_11)
% 157.26/27.28 (105) ~ (all_52_11 = all_4_2)
% 157.26/27.28 (106) all_54_11 = all_52_14
% 157.26/27.28 (107) ~ (all_52_13 = all_52_14)
% 157.26/27.28 (108) ~ (e3 = e2)
% 157.26/27.28 (109) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.26/27.28 (110) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.26/27.28 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.28 (111) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.26/27.28 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.26/27.28 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.26/27.28 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.26/27.28 e0)))
% 157.26/27.28 (112) all_54_9 = all_52_6
% 157.26/27.28 (113) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.26/27.28 (114) all_54_12 = all_52_3
% 157.26/27.28 (115) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.26/27.28 (116) ~ (all_52_14 = all_4_2)
% 157.26/27.28 (117) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.26/27.28 (118) ~ (all_52_3 = all_52_7)
% 157.26/27.28
% 157.26/27.28 Begin of proof
% 157.26/27.28 |
% 157.26/27.28 | BETA: splitting (92) gives:
% 157.26/27.28 |
% 157.26/27.28 | Case 1:
% 157.26/27.28 | |
% 157.26/27.28 | | (119) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.26/27.28 | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 157.26/27.28 | |
% 157.26/27.28 | | ALPHA: (119) implies:
% 157.26/27.28 | | (120) op(e3, e3) = all_22_1
% 157.26/27.28 | |
% 157.26/27.28 | | BETA: splitting (18) gives:
% 157.26/27.28 | |
% 157.26/27.28 | | Case 1:
% 157.26/27.28 | | |
% 157.26/27.28 | | | (121) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 157.26/27.28 | | | e3)
% 157.26/27.28 | | |
% 157.26/27.28 | | | BETA: splitting (121) gives:
% 157.26/27.28 | | |
% 157.26/27.28 | | | Case 1:
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | (122) all_58_4 = e3 & op(e3, e1) = e3
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | ALPHA: (122) implies:
% 157.26/27.28 | | | | (123) all_58_4 = e3
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | BETA: splitting (34) gives:
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | Case 1:
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | (124) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 157.26/27.28 | | | | | e2) = e3)
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | BETA: splitting (124) gives:
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | Case 1:
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | (125) all_58_6 = e3 & op(e1, e3) = e3
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | ALPHA: (125) implies:
% 157.26/27.28 | | | | | | (126) all_58_6 = e3
% 157.26/27.28 | | | | | | (127) op(e1, e3) = e3
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.26/27.28 | | | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21),
% 157.26/27.28 | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 157.26/27.28 | | | | | | (31), (32), (33), (36), (37), (38), (39), (40), (41),
% 157.26/27.28 | | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 157.26/27.28 | | | | | | (51), (52), (53), (54), (55), (56), (58), (59), (60),
% 157.26/27.28 | | | | | | (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 157.26/27.28 | | | | | | (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 157.26/27.28 | | | | | | (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 157.26/27.28 | | | | | | (88), (89), (91), (93), (94), (96), (97), (98), (99),
% 157.26/27.28 | | | | | | (100), (101), (102), (103), (104), (105), (106), (107),
% 157.26/27.28 | | | | | | (108), (109), (110), (111), (112), (113), (114), (115),
% 157.26/27.28 | | | | | | (116), (117), (118), (120), (123), (126), (127) are
% 157.26/27.28 | | | | | | inconsistent by sub-proof #535.
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | Case 2:
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | (128) all_58_7 = e3 & op(e1, e2) = e3
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | REF_CLOSE: (57), (101), (103), (128) are inconsistent by sub-proof
% 157.26/27.28 | | | | | | #1184.
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | End of split
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | Case 2:
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | (129) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 157.26/27.28 | | | | | e0) = e3)
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | BETA: splitting (129) gives:
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | Case 1:
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | (130) all_58_8 = e3 & op(e1, e1) = e3
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | ALPHA: (130) implies:
% 157.26/27.28 | | | | | | (131) all_58_8 = e3
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | BETA: splitting (26) gives:
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | Case 1:
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | (132) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 157.26/27.28 | | | | | | | op(e2, e3) = e3)
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | BETA: splitting (132) gives:
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | (133) all_58_0 = e3 & op(e3, e3) = e3
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | ALPHA: (133) implies:
% 157.26/27.28 | | | | | | | | (134) op(e3, e3) = e3
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | REF_CLOSE: (22), (54), (66), (103), (120), (134) are
% 157.26/27.28 | | | | | | | | inconsistent by sub-proof #667.
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | (135) all_58_2 = e3 & op(e2, e3) = e3
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | ALPHA: (135) implies:
% 157.26/27.28 | | | | | | | | (136) op(e2, e3) = e3
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | REF_CLOSE: (36), (52), (103), (108), (136) are inconsistent by
% 157.26/27.28 | | | | | | | | sub-proof #1159.
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | End of split
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | Case 2:
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | (137) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 157.26/27.28 | | | | | | | op(e0, e3) = e3)
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | BETA: splitting (137) gives:
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | (138) all_58_6 = e3 & op(e1, e3) = e3
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | ALPHA: (138) implies:
% 157.26/27.28 | | | | | | | | (139) all_58_6 = e3
% 157.26/27.28 | | | | | | | | (140) op(e1, e3) = e3
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.26/27.28 | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (19), (20),
% 157.26/27.28 | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 157.26/27.28 | | | | | | | | (30), (31), (32), (33), (36), (37), (38), (39), (40),
% 157.26/27.28 | | | | | | | | (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 157.26/27.28 | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (58), (59),
% 157.26/27.28 | | | | | | | | (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 157.26/27.28 | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 157.26/27.28 | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 157.26/27.28 | | | | | | | | (87), (88), (89), (91), (93), (94), (96), (97), (98),
% 157.26/27.28 | | | | | | | | (99), (100), (101), (102), (103), (104), (105),
% 157.26/27.28 | | | | | | | | (106), (107), (108), (109), (110), (111), (112),
% 157.26/27.28 | | | | | | | | (113), (114), (115), (116), (117), (118), (120),
% 157.26/27.28 | | | | | | | | (123), (139), (140) are inconsistent by sub-proof
% 157.26/27.28 | | | | | | | | #535.
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | (141) all_58_12 = e3 & op(e0, e3) = e3
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | ALPHA: (141) implies:
% 157.26/27.28 | | | | | | | | (142) all_58_12 = e3
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | BETA: splitting (102) gives:
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | (143) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 157.26/27.28 | | | | | | | | | op(e2, e3) = e0)
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | BETA: splitting (143) gives:
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | (144) all_58_0 = e0 & op(e3, e3) = e0
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | ALPHA: (144) implies:
% 157.26/27.28 | | | | | | | | | | (145) all_58_0 = e0
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | REF_CLOSE: (11), (13), (26), (27), (36), (41), (42), (46),
% 157.26/27.28 | | | | | | | | | | (52), (54), (56), (61), (73), (76), (80), (82),
% 157.26/27.28 | | | | | | | | | | (84), (103), (108), (123), (131), (142), (145) are
% 157.26/27.28 | | | | | | | | | | inconsistent by sub-proof #586.
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | (146) all_58_2 = e0 & op(e2, e3) = e0
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | ALPHA: (146) implies:
% 157.26/27.28 | | | | | | | | | | (147) op(e2, e3) = e0
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | REF_CLOSE: (46), (52), (103), (147) are inconsistent by
% 157.26/27.28 | | | | | | | | | | sub-proof #1156.
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | End of split
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | (148) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 157.26/27.28 | | | | | | | | | op(e0, e3) = e0)
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | BETA: splitting (148) gives:
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | (149) all_58_6 = e0 & op(e1, e3) = e0
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | ALPHA: (149) implies:
% 157.26/27.28 | | | | | | | | | | (150) all_58_6 = e0
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | REF_CLOSE: (11), (13), (26), (27), (36), (41), (42), (46),
% 157.26/27.28 | | | | | | | | | | (52), (54), (56), (61), (73), (76), (80), (82),
% 157.26/27.28 | | | | | | | | | | (84), (103), (108), (123), (131), (142), (150) are
% 157.26/27.28 | | | | | | | | | | inconsistent by sub-proof #570.
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | (151) all_58_12 = e0 & op(e0, e3) = e0
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | ALPHA: (151) implies:
% 157.26/27.28 | | | | | | | | | | (152) all_58_12 = e0
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | REF_CLOSE: (41), (142), (152) are inconsistent by sub-proof
% 157.26/27.28 | | | | | | | | | | #1463.
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | End of split
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | End of split
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | End of split
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | End of split
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | Case 2:
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | (153) all_58_11 = e3 & op(e1, e0) = e3
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | ALPHA: (153) implies:
% 157.26/27.28 | | | | | | (154) all_58_11 = e3
% 157.26/27.28 | | | | | | (155) op(e1, e0) = e3
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.26/27.28 | | | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21),
% 157.26/27.28 | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 157.26/27.28 | | | | | | (31), (32), (33), (36), (37), (38), (39), (40), (41),
% 157.26/27.28 | | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 157.26/27.28 | | | | | | (51), (52), (53), (54), (55), (56), (58), (59), (60),
% 157.26/27.28 | | | | | | (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 157.26/27.28 | | | | | | (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 157.26/27.28 | | | | | | (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 157.26/27.28 | | | | | | (88), (89), (90), (91), (93), (94), (96), (97), (98),
% 157.26/27.28 | | | | | | (99), (100), (101), (102), (103), (104), (105), (106),
% 157.26/27.28 | | | | | | (107), (108), (109), (110), (111), (112), (113), (114),
% 157.26/27.28 | | | | | | (115), (116), (117), (118), (120), (123), (154), (155)
% 157.26/27.28 | | | | | | are inconsistent by sub-proof #464.
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | End of split
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | End of split
% 157.26/27.28 | | | |
% 157.26/27.28 | | | Case 2:
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | (156) all_58_5 = e3 & op(e2, e1) = e3
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | ALPHA: (156) implies:
% 157.26/27.28 | | | | (157) op(e2, e1) = e3
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | REF_CLOSE: (35), (47), (103), (157) are inconsistent by sub-proof #1196.
% 157.26/27.28 | | | |
% 157.26/27.28 | | | End of split
% 157.26/27.28 | | |
% 157.26/27.28 | | Case 2:
% 157.26/27.28 | | |
% 157.26/27.28 | | | (158) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 157.26/27.28 | | | = e3)
% 157.26/27.28 | | |
% 157.26/27.28 | | | BETA: splitting (158) gives:
% 157.26/27.28 | | |
% 157.26/27.28 | | | Case 1:
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | (159) all_58_8 = e3 & op(e1, e1) = e3
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | ALPHA: (159) implies:
% 157.26/27.28 | | | | (160) all_58_8 = e3
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | BETA: splitting (42) gives:
% 157.26/27.28 | | | |
% 157.26/27.28 | | | | Case 1:
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | (161) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 157.26/27.28 | | | | | e3) = e1)
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | BETA: splitting (161) gives:
% 157.26/27.28 | | | | |
% 157.26/27.28 | | | | | Case 1:
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | (162) all_58_0 = e1 & op(e3, e3) = e1
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | ALPHA: (162) implies:
% 157.26/27.28 | | | | | | (163) all_58_0 = e1
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | BETA: splitting (117) gives:
% 157.26/27.28 | | | | | |
% 157.26/27.28 | | | | | | Case 1:
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | (164) all_56_12 = e3
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | REF_CLOSE: (54), (55), (164) are inconsistent by sub-proof #1191.
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | Case 2:
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | (165) ~ (all_56_12 = e3)
% 157.26/27.28 | | | | | | | (166) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | REDUCE: (55), (165) imply:
% 157.26/27.28 | | | | | | | (167) ~ (e3 = e1)
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | BETA: splitting (166) gives:
% 157.26/27.28 | | | | | | |
% 157.26/27.28 | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | (168) all_56_13 = e2
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | COMBINE_EQS: (86), (168) imply:
% 157.26/27.28 | | | | | | | | (169) e3 = e2
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | REDUCE: (108), (169) imply:
% 157.26/27.28 | | | | | | | | (170) $false
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | CLOSE: (170) is inconsistent.
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | (171) ~ (all_56_13 = e2)
% 157.26/27.28 | | | | | | | | (172) all_56_14 = e1 | all_56_15 = e0
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | BETA: splitting (172) gives:
% 157.26/27.28 | | | | | | | |
% 157.26/27.28 | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | (173) all_56_14 = e1
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | REF_CLOSE: (4), (54), (173) are inconsistent by sub-proof
% 157.26/27.28 | | | | | | | | | #585.
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | (174) all_56_15 = e0
% 157.26/27.28 | | | | | | | | | (175) ~ (all_56_14 = e1)
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | COMBINE_EQS: (68), (174) imply:
% 157.26/27.28 | | | | | | | | | (176) all_4_2 = e0
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | SIMP: (176) implies:
% 157.26/27.28 | | | | | | | | | (177) all_4_2 = e0
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | REDUCE: (93), (177) imply:
% 157.26/27.28 | | | | | | | | | (178) ~ (all_52_7 = e0)
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | REDUCE: (70), (177) imply:
% 157.26/27.28 | | | | | | | | | (179) ~ (all_52_13 = e0)
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | REDUCE: (32), (177) imply:
% 157.26/27.28 | | | | | | | | | (180) ~ (e2 = e0)
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | REDUCE: (58), (177) imply:
% 157.26/27.28 | | | | | | | | | (181) ~ (e1 = e0)
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | REDUCE: (62), (177) imply:
% 157.26/27.28 | | | | | | | | | (182) op(e0, e0) = e0
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | BETA: splitting (85) gives:
% 157.26/27.28 | | | | | | | | |
% 157.26/27.28 | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | (183) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 157.26/27.28 | | | | | | | | | | e3 & op(e0, e2) = e3)
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | BETA: splitting (183) gives:
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | (184) all_58_12 = e3 & op(e0, e3) = e3
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | ALPHA: (184) implies:
% 157.26/27.28 | | | | | | | | | | | (185) all_58_12 = e3
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | REF_CLOSE: (4), (5), (19), (23), (32), (37), (38), (40),
% 157.26/27.28 | | | | | | | | | | | (41), (42), (44), (47), (52), (54), (58), (59),
% 157.26/27.28 | | | | | | | | | | | (64), (67), (68), (69), (70), (75), (78), (88),
% 157.26/27.28 | | | | | | | | | | | (89), (91), (94), (99), (102), (103), (115),
% 157.26/27.28 | | | | | | | | | | | (163), (172), (185) are inconsistent by sub-proof
% 157.26/27.28 | | | | | | | | | | | #479.
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | (186) all_58_13 = e3 & op(e0, e2) = e3
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | REF_CLOSE: (14), (96), (103), (186) are inconsistent by
% 157.26/27.28 | | | | | | | | | | | sub-proof #1449.
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | End of split
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | (187) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 157.26/27.28 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | BETA: splitting (187) gives:
% 157.26/27.28 | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | (188) all_58_14 = e3 & op(e0, e1) = e3
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | ALPHA: (188) implies:
% 157.26/27.28 | | | | | | | | | | | (189) all_58_14 = e3
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | REF_CLOSE: (11), (13), (27), (41), (46), (52), (54), (56),
% 157.26/27.28 | | | | | | | | | | | (61), (73), (76), (80), (82), (84), (103), (108),
% 157.26/27.28 | | | | | | | | | | | (160), (189) are inconsistent by sub-proof #780.
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | (190) all_58_15 = e3 & op(e0, e0) = e3
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | ALPHA: (190) implies:
% 157.26/27.28 | | | | | | | | | | | (191) all_58_15 = e3
% 157.26/27.28 | | | | | | | | | | | (192) op(e0, e0) = e3
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | BETA: splitting (23) gives:
% 157.26/27.28 | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | (193) all_54_7 = e3
% 157.26/27.28 | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | COMBINE_EQS: (64), (193) imply:
% 157.26/27.28 | | | | | | | | | | | | (194) all_52_13 = e3
% 157.26/27.28 | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | REDUCE: (37), (194) imply:
% 157.26/27.28 | | | | | | | | | | | | (195) $false
% 157.26/27.28 | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 157.26/27.28 | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | (196) ~ (all_54_7 = e3)
% 157.26/27.28 | | | | | | | | | | | | (197) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.28 | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | BETA: splitting (197) gives:
% 157.26/27.28 | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | (198) all_54_7 = e2
% 157.26/27.28 | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | COMBINE_EQS: (64), (198) imply:
% 157.26/27.28 | | | | | | | | | | | | | (199) all_52_13 = e2
% 157.26/27.28 | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | REDUCE: (67), (199) imply:
% 157.26/27.28 | | | | | | | | | | | | | (200) $false
% 157.26/27.28 | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | CLOSE: (200) is inconsistent.
% 157.26/27.28 | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | (201) ~ (all_54_7 = e2)
% 157.26/27.28 | | | | | | | | | | | | | (202) all_54_7 = e1 | all_54_7 = e0
% 157.26/27.28 | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | BETA: splitting (102) gives:
% 157.26/27.28 | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | (203) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 157.26/27.28 | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 157.26/27.28 | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | REF_CLOSE: (46), (52), (66), (80), (103), (120), (203) are
% 157.26/27.28 | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 157.26/27.28 | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | (204) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 157.26/27.28 | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 157.26/27.28 | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 157.26/27.28 | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | (205) all_58_6 = e0 & op(e1, e3) = e0
% 157.26/27.28 | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 157.26/27.28 | | | | | | | | | | | | | | | (206) all_58_6 = e0
% 157.26/27.28 | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 157.26/27.28 | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | (207) all_58_15 = e0 & op(e0, e0) = e0
% 157.26/27.28 | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 157.26/27.28 | | | | | | | | | | | | | | | | (208) all_58_15 = e0
% 157.26/27.28 | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | REF_CLOSE: (41), (191), (208) are inconsistent by sub-proof
% 157.26/27.28 | | | | | | | | | | | | | | | | #1318.
% 157.26/27.28 | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | (209) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 157.26/27.28 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.26/27.28 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 157.26/27.28 | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 157.26/27.28 | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.26/27.28 | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 157.26/27.28 | | | | | | | | | | | | | | | | (210) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 157.26/27.28 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 157.26/27.28 | | | | | | | | | | | | | | | | e1) = e0)
% 157.26/27.28 | | | | | | | | | | | | | | | | (211) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 157.26/27.28 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 157.26/27.28 | | | | | | | | | | | | | | | | e0) = e0)
% 157.26/27.28 | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 157.26/27.28 | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | (212) all_58_12 = e0 & op(e0, e3) = e0
% 157.26/27.28 | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 157.26/27.28 | | | | | | | | | | | | | | | | | (213) all_58_12 = e0
% 157.26/27.28 | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (12), (13), (14),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (15), (16), (19), (22), (24), (26), (27), (28),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (31), (32), (34), (36), (37), (38), (39), (40),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (41), (42), (43), (44), (45), (46), (47), (49),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (51), (52), (53), (54), (56), (57), (58), (59),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (61), (62), (64), (66), (67), (68), (69), (73),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (74), (75), (76), (78), (80), (82), (84), (85),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (86), (88), (89), (91), (94), (95), (96), (99),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (100), (101), (102), (103), (108), (110), (111),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (115), (120), (160), (163), (166), (178), (179),
% 157.26/27.28 | | | | | | | | | | | | | | | | | (182), (191), (192), (197), (202), (211), (213)
% 157.26/27.28 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #508.
% 157.26/27.28 | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | (214) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 157.26/27.28 | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 157.26/27.28 | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 157.26/27.28 | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | (215) all_58_13 = e0 & op(e0, e2) = e0
% 157.26/27.28 | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 157.26/27.28 | | | | | | | | | | | | | | | | | | (216) op(e0, e2) = e0
% 157.26/27.28 | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (14), (19), (24), (38), (40), (44),
% 157.26/27.28 | | | | | | | | | | | | | | | | | | (47), (59), (64), (67), (69), (75), (78), (88),
% 157.26/27.28 | | | | | | | | | | | | | | | | | | (89), (91), (96), (99), (100), (103), (115),
% 157.26/27.28 | | | | | | | | | | | | | | | | | | (178), (179), (197), (216) are inconsistent by
% 157.26/27.28 | | | | | | | | | | | | | | | | | | sub-proof #559.
% 157.26/27.28 | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.28 | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | (217) all_58_14 = e0 & op(e0, e1) = e0
% 157.26/27.28 | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 157.26/27.28 | | | | | | | | | | | | | | | | | | (218) all_58_14 = e0
% 157.26/27.28 | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 157.26/27.28 | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | (219) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 157.26/27.28 | | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 157.26/27.28 | | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | (220) all_58_4 = e1 & op(e3, e1) = e1
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | (221) all_58_4 = e1
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | | (222) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 157.26/27.28 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (11), (13), (14), (15), (22), (26),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (27), (31), (34), (36), (39), (41), (42), (45),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (46), (49), (52), (54), (56), (57), (61), (66),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (73), (74), (76), (80), (82), (84), (85), (95),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (96), (101), (102), (103), (108), (120), (160),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (163), (182), (191), (192), (206), (210), (211),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (218), (222) are inconsistent by sub-proof #362.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (223) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (224) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (225) all_58_8 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (160), (225) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | #950.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (226) all_58_11 = e1 & op(e1, e0) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (227) all_58_11 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (11), (13), (15), (22), (26), (27),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (31), (34), (36), (39), (41), (42), (45), (46),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (49), (52), (54), (57), (61), (66), (74), (76),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (95), (101), (102), (103),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (108), (111), (120), (160), (163), (182), (191),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (192), (206), (210), (211), (218), (221), (227)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #484.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | (228) all_58_5 = e1 & op(e2, e1) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | (229) all_58_5 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (230) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (11), (13), (14), (15), (22), (26),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (27), (31), (34), (36), (39), (41), (42), (45),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (46), (49), (52), (54), (56), (57), (61), (66),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (73), (74), (76), (80), (82), (84), (85), (95),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (96), (101), (102), (103), (108), (120), (160),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (163), (182), (191), (192), (206), (210), (211),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (218), (230) are inconsistent by sub-proof #362.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (231) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (232) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (233) all_58_8 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (160), (233) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | #950.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (234) all_58_11 = e1 & op(e1, e0) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (235) all_58_11 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10), (11), (13), (15), (22), (26),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (27), (28), (31), (34), (36), (39), (41), (42),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (45), (46), (49), (52), (54), (57), (61), (66),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (74), (76), (80), (82), (84), (95), (101), (102),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (103), (108), (110), (111), (120), (160), (163),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (182), (191), (192), (206), (210), (211), (218),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (229), (235) are inconsistent by sub-proof #483.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | (236) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | (237) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (160), (237) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | #959.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | (238) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (218), (238) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | #482.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | (239) all_58_12 = e0 & op(e0, e3) = e0
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (12), (13), (14),
% 157.26/27.29 | | | | | | | | | | | | | | | (15), (16), (19), (22), (24), (26), (27), (28),
% 157.26/27.29 | | | | | | | | | | | | | | | (31), (32), (34), (36), (37), (38), (39), (40),
% 157.26/27.29 | | | | | | | | | | | | | | | (41), (42), (43), (44), (45), (46), (47), (49),
% 157.26/27.29 | | | | | | | | | | | | | | | (51), (52), (53), (54), (56), (57), (58), (59),
% 157.26/27.29 | | | | | | | | | | | | | | | (61), (62), (64), (66), (67), (68), (69), (73),
% 157.26/27.29 | | | | | | | | | | | | | | | (74), (75), (76), (78), (80), (82), (84), (85),
% 157.26/27.29 | | | | | | | | | | | | | | | (86), (88), (89), (91), (94), (95), (96), (99),
% 157.26/27.29 | | | | | | | | | | | | | | | (100), (101), (102), (103), (108), (110), (111),
% 157.26/27.29 | | | | | | | | | | | | | | | (115), (120), (160), (163), (166), (178), (179),
% 157.26/27.29 | | | | | | | | | | | | | | | (182), (191), (192), (197), (202), (239) are
% 157.26/27.29 | | | | | | | | | | | | | | | inconsistent by sub-proof #481.
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | End of split
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | End of split
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | End of split
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | Case 2:
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | (240) all_58_2 = e1 & op(e2, e3) = e1
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | ALPHA: (240) implies:
% 157.26/27.29 | | | | | | (241) op(e2, e3) = e1
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | REF_CLOSE: (52), (76), (103), (241) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | #1430.
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | End of split
% 157.26/27.29 | | | | |
% 157.26/27.29 | | | | Case 2:
% 157.26/27.29 | | | | |
% 157.26/27.29 | | | | | (242) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 157.26/27.29 | | | | | e3) = e1)
% 157.26/27.29 | | | | |
% 157.26/27.29 | | | | | BETA: splitting (242) gives:
% 157.26/27.29 | | | | |
% 157.26/27.29 | | | | | Case 1:
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | (243) all_58_6 = e1 & op(e1, e3) = e1
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | ALPHA: (243) implies:
% 157.26/27.29 | | | | | | (244) all_58_6 = e1
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | BETA: splitting (117) gives:
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | Case 1:
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | (245) all_56_12 = e3
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | REF_CLOSE: (54), (55), (245) are inconsistent by sub-proof #1191.
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | Case 2:
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | (246) ~ (all_56_12 = e3)
% 157.26/27.29 | | | | | | | (247) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | REDUCE: (55), (246) imply:
% 157.26/27.29 | | | | | | | (248) ~ (e3 = e1)
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | BETA: splitting (247) gives:
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | (249) all_56_13 = e2
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | COMBINE_EQS: (86), (249) imply:
% 157.26/27.29 | | | | | | | | (250) e3 = e2
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | REDUCE: (108), (250) imply:
% 157.26/27.29 | | | | | | | | (251) $false
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | CLOSE: (251) is inconsistent.
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | (252) ~ (all_56_13 = e2)
% 157.26/27.29 | | | | | | | | (253) all_56_14 = e1 | all_56_15 = e0
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | BETA: splitting (253) gives:
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | (254) all_56_14 = e1
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | REF_CLOSE: (4), (54), (254) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | #585.
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | (255) all_56_15 = e0
% 157.26/27.29 | | | | | | | | | (256) ~ (all_56_14 = e1)
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | COMBINE_EQS: (68), (255) imply:
% 157.26/27.29 | | | | | | | | | (257) all_4_2 = e0
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | SIMP: (257) implies:
% 157.26/27.29 | | | | | | | | | (258) all_4_2 = e0
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | REDUCE: (32), (258) imply:
% 157.26/27.29 | | | | | | | | | (259) ~ (e2 = e0)
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | REDUCE: (58), (258) imply:
% 157.26/27.29 | | | | | | | | | (260) ~ (e1 = e0)
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | REDUCE: (62), (258) imply:
% 157.26/27.29 | | | | | | | | | (261) op(e0, e0) = e0
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | REF_CLOSE: (11), (13), (14), (22), (26), (27), (36), (41),
% 157.26/27.29 | | | | | | | | | (46), (52), (54), (56), (61), (66), (73), (76),
% 157.26/27.29 | | | | | | | | | (80), (82), (84), (85), (96), (102), (103), (108),
% 157.26/27.29 | | | | | | | | | (120), (160), (244), (261) are inconsistent by
% 157.26/27.29 | | | | | | | | | sub-proof #363.
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | End of split
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | End of split
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | End of split
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | Case 2:
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | (262) all_58_12 = e1 & op(e0, e3) = e1
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | ALPHA: (262) implies:
% 157.26/27.29 | | | | | | (263) all_58_12 = e1
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | REF_CLOSE: (4), (8), (10), (11), (13), (14), (22), (26), (27), (28),
% 157.26/27.29 | | | | | | (31), (32), (36), (39), (41), (42), (46), (49), (52),
% 157.26/27.29 | | | | | | (54), (55), (56), (58), (61), (62), (66), (68), (73),
% 157.26/27.29 | | | | | | (74), (76), (80), (82), (84), (85), (86), (95), (96),
% 157.26/27.29 | | | | | | (102), (103), (108), (111), (117), (120), (160), (263)
% 157.26/27.29 | | | | | | are inconsistent by sub-proof #571.
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | End of split
% 157.26/27.29 | | | | |
% 157.26/27.29 | | | | End of split
% 157.26/27.29 | | | |
% 157.26/27.29 | | | Case 2:
% 157.26/27.29 | | | |
% 157.26/27.29 | | | | (264) all_58_14 = e3 & op(e0, e1) = e3
% 157.26/27.29 | | | |
% 157.26/27.29 | | | | ALPHA: (264) implies:
% 157.26/27.29 | | | | (265) all_58_14 = e3
% 157.26/27.29 | | | |
% 157.26/27.29 | | | | BETA: splitting (34) gives:
% 157.26/27.29 | | | |
% 157.26/27.29 | | | | Case 1:
% 157.26/27.29 | | | | |
% 157.26/27.29 | | | | | (266) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 157.26/27.29 | | | | | e2) = e3)
% 157.26/27.29 | | | | |
% 157.26/27.29 | | | | | BETA: splitting (266) gives:
% 157.26/27.29 | | | | |
% 157.26/27.29 | | | | | Case 1:
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | (267) all_58_6 = e3 & op(e1, e3) = e3
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | ALPHA: (267) implies:
% 157.26/27.29 | | | | | | (268) all_58_6 = e3
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | BETA: splitting (102) gives:
% 157.26/27.29 | | | | | |
% 157.26/27.29 | | | | | | Case 1:
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | (269) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 157.26/27.29 | | | | | | | op(e2, e3) = e0)
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | REF_CLOSE: (46), (52), (66), (80), (103), (120), (269) are
% 157.26/27.29 | | | | | | | inconsistent by sub-proof #761.
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | Case 2:
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | (270) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 157.26/27.29 | | | | | | | op(e0, e3) = e0)
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | BETA: splitting (270) gives:
% 157.26/27.29 | | | | | | |
% 157.26/27.29 | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | (271) all_58_6 = e0 & op(e1, e3) = e0
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | ALPHA: (271) implies:
% 157.26/27.29 | | | | | | | | (272) all_58_6 = e0
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | REF_CLOSE: (41), (268), (272) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | #1321.
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | (273) all_58_12 = e0 & op(e0, e3) = e0
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | ALPHA: (273) implies:
% 157.26/27.29 | | | | | | | | (274) all_58_12 = e0
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | BETA: splitting (15) gives:
% 157.26/27.29 | | | | | | | |
% 157.26/27.29 | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | (275) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1
% 157.26/27.29 | | | | | | | | | & op(e0, e2) = e1)
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | BETA: splitting (275) gives:
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | (276) all_58_12 = e1 & op(e0, e3) = e1
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | ALPHA: (276) implies:
% 157.26/27.29 | | | | | | | | | | (277) all_58_12 = e1
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | REF_CLOSE: (80), (274), (277) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | | #1513.
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | (278) all_58_13 = e1 & op(e0, e2) = e1
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | ALPHA: (278) implies:
% 157.26/27.29 | | | | | | | | | | (279) op(e0, e2) = e1
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | BETA: splitting (42) gives:
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | (280) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.26/27.29 | | | | | | | | | | | & op(e2, e3) = e1)
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | BETA: splitting (280) gives:
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | (281) all_58_0 = e1 & op(e3, e3) = e1
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | ALPHA: (281) implies:
% 157.26/27.29 | | | | | | | | | | | | (282) all_58_0 = e1
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | BETA: splitting (45) gives:
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | (283) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 157.26/27.29 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | REF_CLOSE: (26), (36), (41), (42), (46), (52), (54), (76),
% 157.26/27.29 | | | | | | | | | | | | | (80), (96), (102), (103), (108), (279), (283) are
% 157.26/27.29 | | | | | | | | | | | | | inconsistent by sub-proof #902.
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | (284) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 157.26/27.29 | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | BETA: splitting (284) gives:
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | (285) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | REF_CLOSE: (26), (36), (41), (52), (54), (103), (108), (265),
% 157.26/27.29 | | | | | | | | | | | | | | (268), (274), (282), (285) are inconsistent by
% 157.26/27.29 | | | | | | | | | | | | | | sub-proof #829.
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | (286) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | REF_CLOSE: (32), (62), (103), (286) are inconsistent by
% 157.26/27.29 | | | | | | | | | | | | | | sub-proof #1452.
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | (287) all_58_2 = e1 & op(e2, e3) = e1
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | ALPHA: (287) implies:
% 157.26/27.29 | | | | | | | | | | | | (288) op(e2, e3) = e1
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | REF_CLOSE: (52), (76), (103), (288) are inconsistent by
% 157.26/27.29 | | | | | | | | | | | | sub-proof #1430.
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | (289) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 157.26/27.29 | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | REF_CLOSE: (54), (80), (268), (274), (289) are inconsistent
% 157.26/27.29 | | | | | | | | | | | by sub-proof #862.
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | (290) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1
% 157.26/27.29 | | | | | | | | | & op(e0, e0) = e1)
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | BETA: splitting (290) gives:
% 157.26/27.29 | | | | | | | | |
% 157.26/27.29 | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | (291) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | ALPHA: (291) implies:
% 157.26/27.29 | | | | | | | | | | (292) all_58_14 = e1
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | REF_CLOSE: (54), (265), (292) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | | #1147.
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | (293) all_58_15 = e1 & op(e0, e0) = e1
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | ALPHA: (293) implies:
% 157.26/27.29 | | | | | | | | | | (294) op(e0, e0) = e1
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | BETA: splitting (16) gives:
% 157.26/27.29 | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | (295) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 157.26/27.29 | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | BETA: splitting (295) gives:
% 157.26/27.29 | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | (296) all_58_9 = e3 & op(e3, e0) = e3
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | ALPHA: (296) implies:
% 157.26/27.29 | | | | | | | | | | | | (297) all_58_9 = e3
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | BETA: splitting (42) gives:
% 157.26/27.29 | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | (298) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.26/27.29 | | | | | | | | | | | | | & op(e2, e3) = e1)
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | BETA: splitting (298) gives:
% 157.26/27.29 | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | (299) all_58_0 = e1 & op(e3, e3) = e1
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | ALPHA: (299) implies:
% 157.26/27.29 | | | | | | | | | | | | | | (300) all_58_0 = e1
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 157.26/27.29 | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | (301) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | (302) all_58_4 = e1 & op(e3, e1) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | (303) all_58_4 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (27), (41), (46), (52), (54), (61),
% 157.26/27.29 | | | | | | | | | | | | | | | | (76), (80), (82), (84), (103), (108), (265), (303)
% 157.26/27.29 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #850.
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | (304) all_58_5 = e1 & op(e2, e1) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | ALPHA: (304) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | (305) all_58_5 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (11), (13), (19),
% 157.26/27.29 | | | | | | | | | | | | | | | | (23), (26), (27), (28), (32), (36), (37), (38),
% 157.26/27.29 | | | | | | | | | | | | | | | | (40), (41), (44), (46), (47), (49), (52), (54),
% 157.26/27.29 | | | | | | | | | | | | | | | | (55), (56), (59), (61), (64), (67), (68), (69),
% 157.26/27.29 | | | | | | | | | | | | | | | | (70), (75), (76), (78), (80), (82), (83), (84),
% 157.26/27.29 | | | | | | | | | | | | | | | | (86), (88), (89), (91), (99), (103), (108), (115),
% 157.26/27.29 | | | | | | | | | | | | | | | | (117), (265), (268), (274), (294), (297), (300),
% 157.26/27.29 | | | | | | | | | | | | | | | | (305) are inconsistent by sub-proof #454.
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | (306) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 157.26/27.29 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 157.26/27.29 | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | (307) all_58_8 = e1 & op(e1, e1) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | (308) all_58_8 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | (309) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 157.26/27.29 | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.26/27.29 | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (46), (52), (82), (103), (309) are
% 157.26/27.29 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #755.
% 157.26/27.29 | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | (310) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 157.26/27.29 | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | (311) all_58_5 = e0 & op(e2, e1) = e0
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | (312) all_58_5 = e0
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | (313) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (26), (36), (41), (46), (52), (54), (61),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | (76), (80), (82), (103), (108), (268), (274),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | (297), (300), (313) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | #453.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | (314) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | (315) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | (316) all_58_11 = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (317) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (318) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (319) all_58_12 = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (36), (41), (42), (46), (52), (54), (76),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (80), (102), (103), (108), (319) are inconsistent
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1062.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (320) all_58_13 = e2 & op(e0, e2) = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (321) all_58_13 = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | (322) op(e0, e2) = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | (323) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (324) all_58_1 = e1 & op(e3, e2) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_1 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (26), (27), (31), (36), (41), (42),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (46), (52), (54), (61), (74), (76), (80), (82),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (84), (95), (103), (108), (110), (265), (268),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (274), (297), (300), (312), (325) are inconsistent
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #820.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_3 = e1 & op(e2, e2) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (26), (27), (31), (36), (41), (42),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (46), (52), (54), (61), (74), (76), (80), (82),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (84), (95), (103), (108), (265), (268), (274),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (297), (300), (312), (326) are inconsistent by
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #452.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | (327) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_7 = e1 & op(e1, e2) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_7 = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (13), (26), (27), (31), (36),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (41), (42), (46), (49), (52), (54), (61), (74),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (76), (80), (82), (84), (95), (103), (108), (110),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (265), (268), (274), (297), (300), (308), (312),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (316), (321), (329) are inconsistent by sub-proof
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | #449.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_13 = e1 & op(e0, e2) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | (331) op(e0, e2) = e1
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (96), (103), (322), (331) are inconsistent
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1319.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (332) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (26), (36), (41), (46), (52), (54), (76),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (80), (103), (108), (111), (265), (268), (274),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | (297), (300), (316), (332) are inconsistent by
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | | sub-proof #448.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | (333) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | (334) op(e0, e0) = e2
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (103), (294), (334) are inconsistent by
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | | sub-proof #1386.
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | (335) all_58_10 = e0 & op(e2, e0) = e0
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | (336) all_58_10 = e0
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 157.26/27.29 | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | (337) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.26/27.29 | | | | | | | | | | | | | | | | | | |
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (26), (36), (41), (46), (52), (54), (61),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | (76), (80), (82), (103), (108), (268), (274),
% 157.26/27.29 | | | | | | | | | | | | | | | | | | | (297), (300), (337) are inconsistent by sub-proof
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | #453.
% 157.26/27.30 | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | (338) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.26/27.30 | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | (339) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | (340) all_58_11 = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | (341) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | (342) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | (343) all_58_12 = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (36), (41), (42), (46), (52), (54), (76),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | (80), (102), (103), (108), (343) are inconsistent
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1062.
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | (344) all_58_13 = e2 & op(e0, e2) = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | (345) all_58_13 = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | (346) op(e0, e2) = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | (347) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (348) all_58_1 = e1 & op(e3, e2) = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (349) all_58_1 = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (26), (27), (31), (36), (41), (42),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (46), (52), (54), (61), (74), (76), (80), (82),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (84), (95), (103), (108), (110), (265), (268),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (274), (297), (300), (336), (349) are inconsistent
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #818.
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (350) all_58_3 = e1 & op(e2, e2) = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_3 = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (82), (351) are inconsistent by sub-proof
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | #841.
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | (352) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_7 = e1 & op(e1, e2) = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_7 = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (13), (26), (27), (31), (36),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (41), (42), (46), (49), (52), (54), (56), (61),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (74), (76), (80), (82), (84), (95), (103), (108),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (110), (265), (268), (274), (297), (300), (308),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (336), (340), (345), (354) are inconsistent by
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #447.
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_13 = e1 & op(e0, e2) = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (355) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | (356) op(e0, e2) = e1
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (96), (103), (346), (356) are inconsistent
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1319.
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | (357) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (26), (36), (41), (46), (52), (54), (76),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | (80), (103), (108), (111), (265), (268), (274),
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | (297), (300), (340), (357) are inconsistent by
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | | sub-proof #448.
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | (358) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (358) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | (359) op(e0, e0) = e2
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (103), (294), (359) are inconsistent by
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | | sub-proof #1386.
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | (360) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.30 | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | ALPHA: (360) implies:
% 157.26/27.30 | | | | | | | | | | | | | | | | (361) all_58_14 = e1
% 157.26/27.30 | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | | REF_CLOSE: (54), (265), (361) are inconsistent by sub-proof
% 157.26/27.30 | | | | | | | | | | | | | | | | #1147.
% 157.26/27.30 | | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | (362) all_58_2 = e1 & op(e2, e3) = e1
% 157.26/27.30 | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | ALPHA: (362) implies:
% 157.26/27.30 | | | | | | | | | | | | | | (363) op(e2, e3) = e1
% 157.26/27.30 | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | | REF_CLOSE: (52), (76), (103), (363) are inconsistent by
% 157.26/27.30 | | | | | | | | | | | | | | sub-proof #1430.
% 157.26/27.30 | | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | (364) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 157.26/27.30 | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 157.26/27.30 | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | | REF_CLOSE: (54), (80), (268), (274), (364) are inconsistent
% 157.26/27.30 | | | | | | | | | | | | | by sub-proof #862.
% 157.26/27.30 | | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | (365) all_58_10 = e3 & op(e2, e0) = e3
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | ALPHA: (365) implies:
% 157.26/27.30 | | | | | | | | | | | | (366) op(e2, e0) = e3
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | REF_CLOSE: (37), (51), (103), (366) are inconsistent by
% 157.26/27.30 | | | | | | | | | | | | sub-proof #1364.
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | (367) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 157.26/27.30 | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.26/27.30 | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | BETA: splitting (367) gives:
% 157.26/27.30 | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | (368) all_58_11 = e3 & op(e1, e0) = e3
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | ALPHA: (368) implies:
% 157.26/27.30 | | | | | | | | | | | | (369) all_58_11 = e3
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | REF_CLOSE: (9), (11), (13), (26), (28), (32), (36), (39),
% 157.26/27.30 | | | | | | | | | | | | (41), (42), (45), (46), (52), (53), (54), (61),
% 157.26/27.30 | | | | | | | | | | | | (62), (76), (80), (82), (84), (96), (102), (103),
% 157.26/27.30 | | | | | | | | | | | | (108), (265), (268), (369) are inconsistent by
% 157.26/27.30 | | | | | | | | | | | | sub-proof #360.
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | (370) all_58_15 = e3 & op(e0, e0) = e3
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | ALPHA: (370) implies:
% 157.26/27.30 | | | | | | | | | | | | (371) all_58_15 = e3
% 157.26/27.30 | | | | | | | | | | | | (372) op(e0, e0) = e3
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | | REF_CLOSE: (15), (26), (36), (41), (42), (45), (46), (52),
% 157.26/27.30 | | | | | | | | | | | | (54), (76), (80), (102), (103), (108), (265),
% 157.26/27.30 | | | | | | | | | | | | (268), (274), (371), (372) are inconsistent by
% 157.26/27.30 | | | | | | | | | | | | sub-proof #786.
% 157.26/27.30 | | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | End of split
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | End of split
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | End of split
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | Case 2:
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | (373) all_58_7 = e3 & op(e1, e2) = e3
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | REF_CLOSE: (57), (101), (103), (373) are inconsistent by sub-proof
% 157.26/27.30 | | | | | | #1184.
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | End of split
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | Case 2:
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | (374) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 157.26/27.30 | | | | | e0) = e3)
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | BETA: splitting (374) gives:
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | Case 1:
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | (375) all_58_8 = e3 & op(e1, e1) = e3
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | ALPHA: (375) implies:
% 157.26/27.30 | | | | | | (376) all_58_8 = e3
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | REF_CLOSE: (11), (13), (27), (41), (46), (52), (54), (56), (61),
% 157.26/27.30 | | | | | | (73), (76), (80), (82), (84), (103), (108), (265), (376)
% 157.26/27.30 | | | | | | are inconsistent by sub-proof #780.
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | Case 2:
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | (377) all_58_11 = e3 & op(e1, e0) = e3
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | ALPHA: (377) implies:
% 157.26/27.30 | | | | | | (378) all_58_11 = e3
% 157.26/27.30 | | | | | | (379) op(e1, e0) = e3
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | BETA: splitting (26) gives:
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | Case 1:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | (380) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 157.26/27.30 | | | | | | | op(e2, e3) = e3)
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (13),
% 157.26/27.30 | | | | | | | (14), (15), (19), (23), (24), (26), (27), (28), (36),
% 157.26/27.30 | | | | | | | (37), (38), (39), (40), (41), (42), (44), (45), (46),
% 157.26/27.30 | | | | | | | (47), (52), (53), (54), (55), (56), (59), (61), (64),
% 157.26/27.30 | | | | | | | (67), (68), (69), (70), (75), (76), (78), (80), (82),
% 157.26/27.30 | | | | | | | (83), (84), (85), (86), (87), (88), (89), (91), (93),
% 157.26/27.30 | | | | | | | (96), (99), (100), (102), (103), (108), (110), (111),
% 157.26/27.30 | | | | | | | (115), (117), (265), (378), (379), (380) are
% 157.26/27.30 | | | | | | | inconsistent by sub-proof #429.
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | Case 2:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | (381) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 157.26/27.30 | | | | | | | op(e0, e3) = e3)
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | BETA: splitting (381) gives:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | (382) all_58_6 = e3 & op(e1, e3) = e3
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | ALPHA: (382) implies:
% 157.26/27.30 | | | | | | | | (383) all_58_6 = e3
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | REF_CLOSE: (9), (11), (13), (26), (28), (32), (36), (39), (41),
% 157.26/27.30 | | | | | | | | (42), (45), (46), (52), (53), (54), (61), (62), (76),
% 157.26/27.30 | | | | | | | | (80), (82), (84), (96), (102), (103), (108), (265),
% 157.26/27.30 | | | | | | | | (378), (383) are inconsistent by sub-proof #360.
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | (384) all_58_12 = e3 & op(e0, e3) = e3
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (13),
% 157.26/27.30 | | | | | | | | (14), (15), (19), (23), (24), (26), (27), (28), (31),
% 157.26/27.30 | | | | | | | | (32), (36), (37), (38), (39), (40), (41), (42), (44),
% 157.26/27.30 | | | | | | | | (45), (46), (47), (52), (53), (54), (55), (56), (58),
% 157.26/27.30 | | | | | | | | (59), (61), (64), (67), (68), (69), (70), (74), (75),
% 157.26/27.30 | | | | | | | | (76), (78), (80), (82), (83), (84), (85), (86), (87),
% 157.26/27.30 | | | | | | | | (88), (89), (91), (93), (94), (95), (96), (99),
% 157.26/27.30 | | | | | | | | (100), (102), (103), (108), (110), (111), (115),
% 157.26/27.30 | | | | | | | | (117), (265), (378), (379), (384) are inconsistent by
% 157.26/27.30 | | | | | | | | sub-proof #423.
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | End of split
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | End of split
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | End of split
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | End of split
% 157.26/27.30 | | | |
% 157.26/27.30 | | | End of split
% 157.26/27.30 | | |
% 157.26/27.30 | | End of split
% 157.26/27.30 | |
% 157.26/27.30 | Case 2:
% 157.26/27.30 | |
% 157.26/27.30 | | (385) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 157.26/27.30 | |
% 157.26/27.30 | | ALPHA: (385) implies:
% 157.26/27.30 | | (386) ~ (all_22_1 = e1)
% 157.26/27.30 | | (387) op(e3, e3) = all_22_1
% 157.26/27.30 | |
% 157.26/27.30 | | REF_CLOSE: (66), (103), (386), (387) are inconsistent by sub-proof #668.
% 157.26/27.30 | |
% 157.26/27.30 | End of split
% 157.26/27.30 |
% 157.26/27.30 End of proof
% 157.26/27.30
% 157.26/27.30 Sub-proof #360 shows that the following formulas are inconsistent:
% 157.26/27.30 ----------------------------------------------------------------
% 157.26/27.30 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.30 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.30 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.30 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.30 (3) all_58_14 = e3
% 157.26/27.30 (4) op(e1, e1) = all_6_2
% 157.26/27.30 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.30 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.30 (6) all_58_6 = e3
% 157.26/27.30 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.30 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.30 (8) ~ (all_4_2 = e2)
% 157.26/27.30 (9) op(e2, e3) = all_52_1
% 157.26/27.30 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.30 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.30 (11) ~ (e3 = e0)
% 157.26/27.30 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.30 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.30 (13) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.30 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.30 e2)
% 157.26/27.30 (14) ~ (e2 = e0)
% 157.26/27.30 (15) op(e2, e3) = e2
% 157.26/27.30 (16) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.30 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.30 (17) ~ (e3 = e1)
% 157.26/27.30 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.30 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.30 (19) op(e0, e0) = all_4_2
% 157.26/27.30 (20) ~ (e2 = e1)
% 157.26/27.30 (21) ~ (e1 = e0)
% 157.26/27.30 (22) all_58_3 = e3
% 157.26/27.30 (23) ~ (all_6_2 = e2)
% 157.26/27.30 (24) op(e0, e2) = all_52_7
% 157.26/27.30 (25) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.30 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.30 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.30 (27) ~ (e3 = e2)
% 157.26/27.30 (28) all_58_11 = e3
% 157.26/27.30
% 157.26/27.30 Begin of proof
% 157.26/27.30 |
% 157.26/27.30 | BETA: splitting (7) gives:
% 157.26/27.30 |
% 157.26/27.30 | Case 1:
% 157.26/27.30 | |
% 157.26/27.30 | | (29) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 157.26/27.30 | | e2)
% 157.26/27.30 | |
% 157.26/27.30 | | BETA: splitting (29) gives:
% 157.26/27.30 | |
% 157.26/27.30 | | Case 1:
% 157.26/27.30 | | |
% 157.26/27.30 | | | (30) all_58_9 = e2 & op(e3, e0) = e2
% 157.26/27.30 | | |
% 157.26/27.30 | | | ALPHA: (30) implies:
% 157.26/27.30 | | | (31) all_58_9 = e2
% 157.26/27.30 | | |
% 157.26/27.30 | | | BETA: splitting (13) gives:
% 157.26/27.30 | | |
% 157.26/27.30 | | | Case 1:
% 157.26/27.30 | | | |
% 157.26/27.30 | | | | (32) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 157.26/27.30 | | | | e2) = e2)
% 157.26/27.30 | | | |
% 157.26/27.30 | | | | BETA: splitting (32) gives:
% 157.26/27.30 | | | |
% 157.26/27.30 | | | | Case 1:
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | (33) all_58_12 = e2 & op(e0, e3) = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | ALPHA: (33) implies:
% 157.26/27.30 | | | | | (34) all_58_12 = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | REF_CLOSE: (5), (9), (11), (12), (14), (15), (17), (20), (21), (25),
% 157.26/27.30 | | | | | (26), (27), (34) are inconsistent by sub-proof #1062.
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | Case 2:
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | (35) all_58_13 = e2 & op(e0, e2) = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | ALPHA: (35) implies:
% 157.26/27.30 | | | | | (36) op(e0, e2) = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | BETA: splitting (1) gives:
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | Case 1:
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | (37) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 157.26/27.30 | | | | | | e2) = e1)
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | BETA: splitting (37) gives:
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | Case 1:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | (38) all_58_1 = e1 & op(e3, e2) = e1
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | ALPHA: (38) implies:
% 157.26/27.30 | | | | | | | (39) all_58_1 = e1
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | BETA: splitting (16) gives:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 157.26/27.30 | | | | | | | | op(e2, e2) = e0)
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | BETA: splitting (40) gives:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | (41) all_58_1 = e0 & op(e3, e2) = e0
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | REF_CLOSE: (21), (39), (41) are inconsistent by sub-proof
% 157.26/27.30 | | | | | | | | | #1327.
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | (42) all_58_3 = e0 & op(e2, e2) = e0
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | REF_CLOSE: (11), (22), (42) are inconsistent by sub-proof
% 157.26/27.30 | | | | | | | | | #756.
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | End of split
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | (43) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 157.26/27.30 | | | | | | | | op(e0, e2) = e0)
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | BETA: splitting (43) gives:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | (44) all_58_7 = e0 & op(e1, e2) = e0
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | ALPHA: (44) implies:
% 157.26/27.30 | | | | | | | | | (45) all_58_7 = e0
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (10), (11), (12), (14), (15),
% 157.26/27.30 | | | | | | | | | (17), (20), (21), (23), (25), (26), (27), (28),
% 157.26/27.30 | | | | | | | | | (45) are inconsistent by sub-proof #368.
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | (46) all_58_13 = e0 & op(e0, e2) = e0
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | ALPHA: (46) implies:
% 157.26/27.30 | | | | | | | | | (47) op(e0, e2) = e0
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | REF_CLOSE: (14), (24), (26), (36), (47) are inconsistent by
% 157.26/27.30 | | | | | | | | | sub-proof #1040.
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | End of split
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | End of split
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | Case 2:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | (48) all_58_3 = e1 & op(e2, e2) = e1
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | ALPHA: (48) implies:
% 157.26/27.30 | | | | | | | (49) all_58_3 = e1
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | REF_CLOSE: (17), (22), (49) are inconsistent by sub-proof #841.
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | End of split
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | Case 2:
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | (50) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 157.26/27.30 | | | | | | e2) = e1)
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | BETA: splitting (50) gives:
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | | Case 1:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | (51) all_58_7 = e1 & op(e1, e2) = e1
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | ALPHA: (51) implies:
% 157.26/27.30 | | | | | | | (52) all_58_7 = e1
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | BETA: splitting (10) gives:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | (53) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 157.26/27.30 | | | | | | | | op(e1, e2) = e2)
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | BETA: splitting (53) gives:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | (54) all_58_6 = e2 & op(e1, e3) = e2
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | ALPHA: (54) implies:
% 157.26/27.30 | | | | | | | | | (55) all_58_6 = e2
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | REF_CLOSE: (5), (9), (11), (12), (14), (15), (17), (20), (21),
% 157.26/27.30 | | | | | | | | | (25), (26), (27), (55) are inconsistent by
% 157.26/27.30 | | | | | | | | | sub-proof #1152.
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | (56) all_58_7 = e2 & op(e1, e2) = e2
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | ALPHA: (56) implies:
% 157.26/27.30 | | | | | | | | | (57) all_58_7 = e2
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | COMBINE_EQS: (52), (57) imply:
% 157.26/27.30 | | | | | | | | | (58) e2 = e1
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | COMBINE_EQS: (31), (58) imply:
% 157.26/27.30 | | | | | | | | | (59) all_58_9 = e1
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | BETA: splitting (7) gives:
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | | Case 1:
% 157.26/27.30 | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | REF_CLOSE: (2), (11), (14), (15), (17), (18), (20), (21),
% 157.26/27.30 | | | | | | | | | | (22), (26), (29), (59) are inconsistent by
% 157.26/27.30 | | | | | | | | | | sub-proof #693.
% 157.26/27.30 | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | (60) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2
% 157.26/27.30 | | | | | | | | | | & op(e0, e0) = e2)
% 157.26/27.30 | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (11), (12), (14), (15), (17),
% 157.26/27.30 | | | | | | | | | | (19), (20), (21), (25), (26), (27), (28), (60) are
% 157.26/27.30 | | | | | | | | | | inconsistent by sub-proof #361.
% 157.26/27.30 | | | | | | | | | |
% 157.26/27.30 | | | | | | | | | End of split
% 157.26/27.30 | | | | | | | | |
% 157.26/27.30 | | | | | | | | End of split
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | Case 2:
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | (61) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 157.26/27.30 | | | | | | | | op(e1, e0) = e2)
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (11), (12), (14), (15), (17),
% 157.26/27.30 | | | | | | | | (20), (21), (23), (25), (26), (27), (28), (61) are
% 157.26/27.30 | | | | | | | | inconsistent by sub-proof #369.
% 157.26/27.30 | | | | | | | |
% 157.26/27.30 | | | | | | | End of split
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | Case 2:
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | (62) all_58_13 = e1 & op(e0, e2) = e1
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | ALPHA: (62) implies:
% 157.26/27.30 | | | | | | | (63) op(e0, e2) = e1
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | | REF_CLOSE: (20), (24), (26), (36), (63) are inconsistent by
% 157.26/27.30 | | | | | | | sub-proof #1319.
% 157.26/27.30 | | | | | | |
% 157.26/27.30 | | | | | | End of split
% 157.26/27.30 | | | | | |
% 157.26/27.30 | | | | | End of split
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | End of split
% 157.26/27.30 | | | |
% 157.26/27.30 | | | Case 2:
% 157.26/27.30 | | | |
% 157.26/27.30 | | | | (64) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 157.26/27.30 | | | | e0) = e2)
% 157.26/27.30 | | | |
% 157.26/27.30 | | | | BETA: splitting (64) gives:
% 157.26/27.30 | | | |
% 157.26/27.30 | | | | Case 1:
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | (65) all_58_14 = e2 & op(e0, e1) = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | ALPHA: (65) implies:
% 157.26/27.30 | | | | | (66) all_58_14 = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | COMBINE_EQS: (3), (66) imply:
% 157.26/27.30 | | | | | (67) e3 = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | COMBINE_EQS: (6), (67) imply:
% 157.26/27.30 | | | | | (68) all_58_6 = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | REF_CLOSE: (5), (9), (11), (12), (14), (15), (17), (20), (21), (25),
% 157.26/27.30 | | | | | (26), (27), (68) are inconsistent by sub-proof #1152.
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | Case 2:
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | (69) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | | REF_CLOSE: (8), (19), (26), (69) are inconsistent by sub-proof #1452.
% 157.26/27.30 | | | | |
% 157.26/27.30 | | | | End of split
% 157.26/27.30 | | | |
% 157.26/27.30 | | | End of split
% 157.26/27.30 | | |
% 157.26/27.30 | | Case 2:
% 157.26/27.30 | | |
% 157.26/27.30 | | | (70) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.30 | | |
% 157.26/27.30 | | | ALPHA: (70) implies:
% 157.26/27.30 | | | (71) all_58_10 = e2
% 157.26/27.30 | | |
% 157.26/27.30 | | | REF_CLOSE: (2), (11), (14), (15), (17), (18), (20), (21), (22), (26), (71)
% 157.26/27.30 | | | are inconsistent by sub-proof #906.
% 157.26/27.30 | | |
% 157.26/27.30 | | End of split
% 157.26/27.30 | |
% 157.26/27.30 | Case 2:
% 157.26/27.30 | |
% 157.26/27.30 | | (72) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.30 | | e2)
% 157.26/27.30 | |
% 157.26/27.30 | | REF_CLOSE: (5), (6), (8), (9), (11), (12), (14), (15), (17), (19), (20),
% 157.26/27.30 | | (21), (25), (26), (27), (28), (72) are inconsistent by sub-proof
% 157.26/27.30 | | #361.
% 157.26/27.30 | |
% 157.26/27.30 | End of split
% 157.26/27.30 |
% 157.26/27.30 End of proof
% 157.26/27.30
% 157.26/27.30 Sub-proof #361 shows that the following formulas are inconsistent:
% 157.26/27.30 ----------------------------------------------------------------
% 157.26/27.30 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.30 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.30 (2) all_58_6 = e3
% 157.26/27.30 (3) ~ (all_4_2 = e2)
% 157.26/27.30 (4) op(e2, e3) = all_52_1
% 157.26/27.30 (5) ~ (e3 = e0)
% 157.26/27.30 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.30 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.30 (7) ~ (e2 = e0)
% 157.26/27.30 (8) op(e2, e3) = e2
% 157.26/27.30 (9) ~ (e3 = e1)
% 157.26/27.30 (10) op(e0, e0) = all_4_2
% 157.26/27.30 (11) ~ (e2 = e1)
% 157.26/27.30 (12) ~ (e1 = e0)
% 157.26/27.30 (13) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.30 (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.30 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.30 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.30 (16) ~ (e3 = e2)
% 157.26/27.30 (17) all_58_11 = e3
% 157.26/27.30
% 157.26/27.30 Begin of proof
% 157.26/27.30 |
% 157.26/27.30 | BETA: splitting (13) gives:
% 157.26/27.30 |
% 157.26/27.30 | Case 1:
% 157.26/27.30 | |
% 157.26/27.30 | | (18) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.30 | |
% 157.26/27.30 | | ALPHA: (18) implies:
% 157.26/27.30 | | (19) all_58_11 = e2
% 157.26/27.30 | |
% 157.26/27.30 | | COMBINE_EQS: (17), (19) imply:
% 157.26/27.30 | | (20) e3 = e2
% 157.26/27.30 | |
% 157.26/27.31 | | SIMP: (20) implies:
% 157.26/27.31 | | (21) e3 = e2
% 157.26/27.31 | |
% 157.26/27.31 | | COMBINE_EQS: (2), (21) imply:
% 157.26/27.31 | | (22) all_58_6 = e2
% 157.26/27.31 | |
% 157.26/27.31 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15), (16),
% 157.26/27.31 | | (22) are inconsistent by sub-proof #1152.
% 157.26/27.31 | |
% 157.26/27.31 | Case 2:
% 157.26/27.31 | |
% 157.26/27.31 | | (23) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.31 | |
% 157.26/27.31 | | REF_CLOSE: (3), (10), (15), (23) are inconsistent by sub-proof #1452.
% 157.26/27.31 | |
% 157.26/27.31 | End of split
% 157.26/27.31 |
% 157.26/27.31 End of proof
% 157.26/27.31
% 157.26/27.31 Sub-proof #362 shows that the following formulas are inconsistent:
% 157.26/27.31 ----------------------------------------------------------------
% 157.26/27.31 (1) all_58_15 = e3
% 157.26/27.31 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.31 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.31 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.31 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.31 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.31 (5) op(e1, e1) = all_6_2
% 157.26/27.31 (6) ~ (all_52_7 = e3)
% 157.26/27.31 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.26/27.31 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.31 (8) op(e3, e3) = all_28_1
% 157.26/27.31 (9) all_58_14 = e0
% 157.26/27.31 (10) all_58_8 = e3
% 157.26/27.31 (11) all_58_0 = e1
% 157.26/27.31 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.31 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.31 (13) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.31 (14) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 157.26/27.31 (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.31 (15) op(e3, e2) = all_52_4
% 157.26/27.31 (16) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.31 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.31 (17) op(e2, e3) = all_52_1
% 157.26/27.31 (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.31 (19) ~ (e3 = e0)
% 157.26/27.31 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.31 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.31 (21) op(e0, e0) = e0
% 157.26/27.31 (22) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.31 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.31 e2)
% 157.26/27.31 (23) ~ (e2 = e0)
% 157.26/27.31 (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.31 (25) all_58_6 = e0
% 157.26/27.31 (26) op(e2, e3) = e2
% 157.26/27.31 (27) ~ (e3 = e1)
% 157.26/27.31 (28) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.31 (29) op(e1, e2) = all_52_6
% 157.26/27.31 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.31 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.31 (31) op(e3, e3) = e1
% 157.26/27.31 (32) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.31 | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.31 (33) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.31 (34) ~ (all_52_4 = e3)
% 157.26/27.31 (35) ~ (e2 = e1)
% 157.26/27.31 (36) ~ (e1 = e0)
% 157.26/27.31 (37) all_58_3 = e3
% 157.26/27.31 (38) ~ (all_6_2 = e2)
% 157.26/27.31 (39) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.31 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.31 e3)
% 157.26/27.31 (40) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.31 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.31 (41) op(e0, e2) = all_52_7
% 157.26/27.31 (42) op(e3, e3) = all_22_1
% 157.26/27.31 (43) ~ (all_52_6 = e3)
% 157.26/27.31 (44) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.31 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.31 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.31 (46) ~ (e3 = e2)
% 157.26/27.31 (47) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 157.26/27.31 (48) op(e0, e0) = e3
% 157.26/27.31
% 157.26/27.31 Begin of proof
% 157.26/27.31 |
% 157.26/27.31 | BETA: splitting (47) gives:
% 157.26/27.31 |
% 157.26/27.31 | Case 1:
% 157.26/27.31 | |
% 157.26/27.31 | | (49) all_58_6 = e1 & op(e1, e3) = e1
% 157.26/27.31 | |
% 157.26/27.31 | | ALPHA: (49) implies:
% 157.26/27.31 | | (50) all_58_6 = e1
% 157.26/27.31 | |
% 157.26/27.31 | | REF_CLOSE: (4), (5), (6), (8), (10), (12), (13), (17), (19), (21), (23),
% 157.26/27.31 | | (26), (27), (28), (30), (31), (33), (35), (36), (37), (38), (39),
% 157.26/27.31 | | (41), (42), (44), (45), (46), (50) are inconsistent by sub-proof
% 157.26/27.31 | | #363.
% 157.26/27.31 | |
% 157.26/27.31 | Case 2:
% 157.26/27.31 | |
% 157.26/27.31 | | (51) all_58_7 = e1 & op(e1, e2) = e1
% 157.26/27.31 | |
% 157.26/27.31 | | ALPHA: (51) implies:
% 157.26/27.31 | | (52) all_58_7 = e1
% 157.26/27.31 | |
% 157.26/27.31 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 157.26/27.31 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 157.26/27.31 | | (25), (26), (27), (29), (30), (31), (32), (34), (35), (36), (37),
% 157.26/27.31 | | (38), (40), (42), (43), (44), (45), (46), (48), (52) are
% 157.26/27.31 | | inconsistent by sub-proof #488.
% 157.26/27.31 | |
% 157.26/27.31 | End of split
% 157.26/27.31 |
% 157.26/27.31 End of proof
% 157.26/27.31
% 157.26/27.31 Sub-proof #363 shows that the following formulas are inconsistent:
% 157.26/27.31 ----------------------------------------------------------------
% 157.26/27.31 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.31 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.31 (2) op(e1, e1) = all_6_2
% 157.26/27.31 (3) ~ (all_52_7 = e3)
% 157.26/27.31 (4) op(e3, e3) = all_28_1
% 157.26/27.31 (5) all_58_8 = e3
% 157.26/27.31 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.31 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.31 (7) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.31 (8) all_58_6 = e1
% 157.26/27.31 (9) op(e2, e3) = all_52_1
% 157.26/27.31 (10) ~ (e3 = e0)
% 157.26/27.31 (11) op(e0, e0) = e0
% 157.26/27.31 (12) ~ (e2 = e0)
% 157.26/27.31 (13) op(e2, e3) = e2
% 157.26/27.31 (14) ~ (e3 = e1)
% 157.26/27.31 (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.31 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.31 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.31 (17) op(e3, e3) = e1
% 157.26/27.31 (18) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.31 (19) ~ (e2 = e1)
% 157.26/27.31 (20) ~ (e1 = e0)
% 157.26/27.31 (21) all_58_3 = e3
% 157.26/27.31 (22) ~ (all_6_2 = e2)
% 157.26/27.31 (23) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.31 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.31 e3)
% 157.26/27.31 (24) op(e0, e2) = all_52_7
% 157.26/27.31 (25) op(e3, e3) = all_22_1
% 157.26/27.31 (26) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.31 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.31 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.31 (28) ~ (e3 = e2)
% 157.26/27.31
% 157.26/27.31 Begin of proof
% 157.26/27.31 |
% 157.26/27.31 | BETA: splitting (26) gives:
% 157.26/27.31 |
% 157.26/27.31 | Case 1:
% 157.26/27.31 | |
% 157.26/27.31 | | (29) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 157.26/27.31 | | e0)
% 157.26/27.31 | |
% 157.26/27.31 | | REF_CLOSE: (12), (13), (17), (20), (25), (27), (29) are inconsistent by
% 157.26/27.31 | | sub-proof #761.
% 157.26/27.31 | |
% 157.26/27.31 | Case 2:
% 157.26/27.31 | |
% 157.26/27.31 | | (30) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 157.26/27.31 | | e0)
% 157.26/27.31 | |
% 157.26/27.31 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.26/27.31 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.26/27.31 | | (24), (25), (27), (28), (30) are inconsistent by sub-proof #510.
% 157.26/27.31 | |
% 157.26/27.31 | End of split
% 157.26/27.31 |
% 157.26/27.31 End of proof
% 157.26/27.31
% 157.26/27.31 Sub-proof #364 shows that the following formulas are inconsistent:
% 157.26/27.31 ----------------------------------------------------------------
% 157.26/27.31 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.26/27.31 (2) ~ (all_52_12 = e3)
% 157.26/27.31 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.31 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.31 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.31 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.31 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.31 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.31 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.31 (7) op(e1, e1) = all_6_2
% 157.26/27.31 (8) ~ (all_52_7 = e3)
% 157.26/27.31 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.26/27.31 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.31 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.31 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.31 (11) ~ (all_52_6 = all_52_14)
% 157.26/27.31 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.26/27.31 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.26/27.31 (13) all_54_10 = all_6_2
% 157.26/27.31 (14) ~ (all_52_11 = e3)
% 157.26/27.31 (15) ~ (all_52_2 = all_52_3)
% 157.26/27.31 (16) ~ (all_52_4 = all_52_6)
% 157.26/27.31 (17) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.31 (18) ~ (all_52_7 = all_52_11)
% 157.26/27.31 (19) all_58_0 = e1
% 157.26/27.31 (20) ~ (all_52_12 = all_4_2)
% 157.26/27.31 (21) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.26/27.31 (22) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.31 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.31 (23) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.31 (24) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.31 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.31 (25) all_54_1 = all_52_4
% 157.26/27.31 (26) op(e3, e2) = all_52_4
% 157.26/27.31 (27) ~ (all_4_2 = e2)
% 157.26/27.31 (28) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.31 (29) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.31 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.31 (30) all_58_14 = e2
% 157.26/27.31 (31) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.26/27.31 (32) ~ (all_52_4 = all_52_12)
% 157.26/27.31 (33) op(e2, e1) = all_52_9
% 157.26/27.31 (34) op(e2, e3) = all_52_1
% 157.26/27.31 (35) ~ (all_52_13 = e3)
% 157.26/27.31 (36) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.31 (37) ~ (all_52_2 = all_6_2)
% 157.26/27.31 (38) ~ (e3 = e0)
% 157.26/27.31 (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.31 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.31 (40) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.31 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.31 (41) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.31 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.31 e2)
% 157.26/27.31 (42) ~ (e2 = e0)
% 157.26/27.31 (43) ~ (all_52_9 = e3)
% 157.26/27.31 (44) ~ (all_52_11 = all_6_2)
% 157.26/27.31 (45) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.26/27.31 (46) ~ (all_52_2 = all_52_6)
% 157.26/27.31 (47) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.31 (48) ~ (all_52_6 = all_6_2)
% 157.26/27.31 (49) op(e2, e0) = all_52_13
% 157.26/27.31 (50) op(e2, e3) = e2
% 157.26/27.31 (51) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.31 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.31 (52) ~ (e3 = e1)
% 157.26/27.31 (53) all_56_12 = e1
% 157.26/27.31 (54) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.31 (55) op(e1, e2) = all_52_6
% 157.26/27.31 (56) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.26/27.31 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.31 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.26/27.31 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.26/27.31 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.26/27.31 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.31 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.26/27.31 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.26/27.31 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.26/27.31 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.31 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.26/27.31 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.26/27.31 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.26/27.31 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.26/27.31 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.26/27.31 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.26/27.31 = e0)
% 157.26/27.31 (57) ~ (all_52_3 = all_4_2)
% 157.26/27.31 (58) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.31 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.31 (59) ~ (all_6_2 = e3)
% 157.26/27.31 (60) op(e0, e0) = all_4_2
% 157.26/27.31 (61) all_54_8 = all_52_2
% 157.26/27.31 (62) all_54_7 = all_52_13
% 157.26/27.31 (63) op(e3, e3) = e1
% 157.26/27.31 (64) ~ (all_52_13 = e2)
% 157.26/27.31 (65) all_56_15 = all_4_2
% 157.26/27.31 (66) op(e0, e1) = e2
% 157.26/27.31 (67) op(e0, e1) = all_52_11
% 157.26/27.31 (68) ~ (all_52_9 = all_52_11)
% 157.26/27.31 (69) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 157.26/27.31 (70) ~ (all_52_13 = all_4_2)
% 157.26/27.31 (71) ~ (all_52_2 = e1)
% 157.26/27.31 (72) ~ (all_52_6 = all_52_7)
% 157.26/27.31 (73) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.31 (74) ~ (all_52_4 = e3)
% 157.26/27.31 (75) ~ (e2 = e1)
% 157.26/27.31 (76) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.26/27.31 (77) all_54_3 = all_52_12
% 157.26/27.31 (78) ~ (all_52_4 = all_52_7)
% 157.26/27.31 (79) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.26/27.31 (80) ~ (e1 = e0)
% 157.26/27.31 (81) op(e1, e2) = all_22_0
% 157.26/27.31 (82) ~ (all_22_0 = e0)
% 157.26/27.31 (83) all_58_3 = e3
% 157.26/27.31 (84) ~ (all_6_2 = e2)
% 157.26/27.31 (85) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.31 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.31 e3)
% 157.26/27.31 (86) all_56_14 = all_6_2
% 157.26/27.31 (87) all_56_13 = e3
% 157.26/27.31 (88) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.31 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.31 (89) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.31 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.31 (90) ~ (all_52_7 = all_4_2)
% 157.26/27.31 (91) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.31 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.31 (92) op(e0, e2) = all_52_7
% 157.26/27.31 (93) op(e1, e0) = all_52_14
% 157.26/27.31 (94) op(e3, e3) = all_22_1
% 157.26/27.31 (95) all_54_15 = all_4_2
% 157.26/27.31 (96) all_56_1 = e3
% 157.26/27.31 (97) ~ (all_52_6 = e3)
% 157.26/27.31 (98) ~ (all_52_14 = all_6_2)
% 157.26/27.31 (99) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.31 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.31 (100) ~ (all_52_12 = e1)
% 157.26/27.31 (101) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.31 (102) ~ (all_52_3 = all_52_11)
% 157.26/27.31 (103) ~ (all_52_11 = all_4_2)
% 157.26/27.31 (104) all_54_11 = all_52_14
% 157.26/27.31 (105) ~ (all_52_13 = all_52_14)
% 157.26/27.31 (106) ~ (e3 = e2)
% 157.26/27.31 (107) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.26/27.31 (108) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.26/27.31 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.31 (109) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.26/27.31 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.26/27.31 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.26/27.31 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.26/27.31 e0)))
% 157.26/27.31 (110) all_54_9 = all_52_6
% 157.26/27.31 (111) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.26/27.31 (112) all_54_12 = all_52_3
% 157.26/27.31 (113) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.26/27.31 (114) ~ (all_52_3 = all_52_7)
% 157.26/27.31
% 157.26/27.31 Begin of proof
% 157.26/27.31 |
% 157.26/27.31 | BETA: splitting (12) gives:
% 157.26/27.31 |
% 157.26/27.31 | Case 1:
% 157.26/27.31 | |
% 157.26/27.31 | | (115) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 157.26/27.31 | | e3)
% 157.26/27.31 | |
% 157.26/27.31 | | BETA: splitting (115) gives:
% 157.26/27.31 | |
% 157.26/27.31 | | Case 1:
% 157.26/27.31 | | |
% 157.26/27.31 | | | (116) all_58_4 = e3 & op(e3, e1) = e3
% 157.26/27.31 | | |
% 157.26/27.31 | | | ALPHA: (116) implies:
% 157.26/27.31 | | | (117) all_58_4 = e3
% 157.26/27.31 | | | (118) op(e3, e1) = e3
% 157.26/27.31 | | |
% 157.26/27.31 | | | BETA: splitting (9) gives:
% 157.26/27.31 | | |
% 157.26/27.31 | | | Case 1:
% 157.26/27.31 | | | |
% 157.26/27.31 | | | | (119) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 157.26/27.31 | | | | e2) = e1)
% 157.26/27.31 | | | |
% 157.26/27.31 | | | | BETA: splitting (119) gives:
% 157.26/27.31 | | | |
% 157.26/27.31 | | | | Case 1:
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | (120) all_58_12 = e1 & op(e0, e3) = e1
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | ALPHA: (120) implies:
% 157.26/27.31 | | | | | (121) all_58_12 = e1
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12), (22), (23),
% 157.26/27.31 | | | | | (24), (26), (27), (29), (33), (34), (35), (36), (38), (39),
% 157.26/27.31 | | | | | (40), (41), (42), (43), (49), (50), (51), (52), (54), (55),
% 157.26/27.31 | | | | | (58), (59), (60), (63), (73), (74), (75), (80), (83), (84),
% 157.26/27.31 | | | | | (85), (88), (89), (91), (92), (94), (97), (99), (101),
% 157.26/27.31 | | | | | (106), (108), (109), (121) are inconsistent by sub-proof
% 157.26/27.31 | | | | | #747.
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | Case 2:
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | (122) all_58_13 = e1 & op(e0, e2) = e1
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | ALPHA: (122) implies:
% 157.26/27.31 | | | | | (123) all_58_13 = e1
% 157.26/27.31 | | | | | (124) op(e0, e2) = e1
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | GROUND_INST: instantiating (101) with all_52_11, e2, e1, e0,
% 157.26/27.31 | | | | | simplifying with (66), (67) gives:
% 157.26/27.31 | | | | | (125) all_52_11 = e2
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | GROUND_INST: instantiating (101) with all_52_7, e1, e2, e0,
% 157.26/27.31 | | | | | simplifying with (92), (124) gives:
% 157.26/27.31 | | | | | (126) all_52_7 = e1
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | GROUND_INST: instantiating (101) with all_52_6, all_22_0, e2, e1,
% 157.26/27.31 | | | | | simplifying with (55), (81) gives:
% 157.26/27.31 | | | | | (127) all_52_6 = all_22_0
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | COMBINE_EQS: (110), (127) imply:
% 157.26/27.31 | | | | | (128) all_54_9 = all_22_0
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | REDUCE: (46), (127) imply:
% 157.26/27.31 | | | | | (129) ~ (all_52_2 = all_22_0)
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | REDUCE: (114), (126) imply:
% 157.26/27.31 | | | | | (130) ~ (all_52_3 = e1)
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | REDUCE: (102), (125) imply:
% 157.26/27.31 | | | | | (131) ~ (all_52_3 = e2)
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | REDUCE: (16), (127) imply:
% 157.26/27.31 | | | | | (132) ~ (all_52_4 = all_22_0)
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | REDUCE: (78), (126) imply:
% 157.26/27.31 | | | | | (133) ~ (all_52_4 = e1)
% 157.26/27.31 | | | | |
% 157.26/27.31 | | | | | REDUCE: (72), (126), (127) imply:
% 157.26/27.31 | | | | | (134) ~ (all_22_0 = e1)
% 157.26/27.31 | | | | |
% 157.26/27.32 | | | | | REDUCE: (11), (127) imply:
% 157.26/27.32 | | | | | (135) ~ (all_52_14 = all_22_0)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | SIMP: (135) implies:
% 157.26/27.32 | | | | | (136) ~ (all_52_14 = all_22_0)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (48), (127) imply:
% 157.26/27.32 | | | | | (137) ~ (all_22_0 = all_6_2)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (97), (127) imply:
% 157.26/27.32 | | | | | (138) ~ (all_22_0 = e3)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (18), (125), (126) imply:
% 157.26/27.32 | | | | | (139) ~ (e2 = e1)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (90), (126) imply:
% 157.26/27.32 | | | | | (140) ~ (all_4_2 = e1)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | SIMP: (140) implies:
% 157.26/27.32 | | | | | (141) ~ (all_4_2 = e1)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (8), (126) imply:
% 157.26/27.32 | | | | | (142) ~ (e3 = e1)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (68), (125) imply:
% 157.26/27.32 | | | | | (143) ~ (all_52_9 = e2)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (44), (125) imply:
% 157.26/27.32 | | | | | (144) ~ (all_6_2 = e2)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (103), (125) imply:
% 157.26/27.32 | | | | | (145) ~ (all_4_2 = e2)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | REDUCE: (14), (125) imply:
% 157.26/27.32 | | | | | (146) ~ (e3 = e2)
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | BETA: splitting (51) gives:
% 157.26/27.32 | | | | |
% 157.26/27.32 | | | | | Case 1:
% 157.26/27.32 | | | | | |
% 157.26/27.32 | | | | | | (147) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 157.26/27.32 | | | | | | e2) = e0)
% 157.26/27.32 | | | | | |
% 157.26/27.32 | | | | | | BETA: splitting (147) gives:
% 157.26/27.32 | | | | | |
% 157.26/27.32 | | | | | | Case 1:
% 157.26/27.32 | | | | | | |
% 157.26/27.32 | | | | | | | (148) all_58_1 = e0 & op(e3, e2) = e0
% 157.26/27.32 | | | | | | |
% 157.26/27.32 | | | | | | | ALPHA: (148) implies:
% 157.26/27.32 | | | | | | | (149) all_58_1 = e0
% 157.26/27.32 | | | | | | |
% 157.26/27.32 | | | | | | | BETA: splitting (89) gives:
% 157.26/27.32 | | | | | | |
% 157.26/27.32 | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | |
% 157.26/27.32 | | | | | | | | (150) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 157.26/27.32 | | | | | | | | op(e2, e2) = e2)
% 157.26/27.32 | | | | | | | |
% 157.26/27.32 | | | | | | | | BETA: splitting (150) gives:
% 157.26/27.32 | | | | | | | |
% 157.26/27.32 | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | (151) all_58_1 = e2 & op(e3, e2) = e2
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | REF_CLOSE: (42), (149), (151) are inconsistent by sub-proof
% 157.26/27.32 | | | | | | | | | #801.
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | (152) all_58_3 = e2 & op(e2, e2) = e2
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | REF_CLOSE: (83), (106), (152) are inconsistent by sub-proof
% 157.26/27.32 | | | | | | | | | #719.
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | End of split
% 157.26/27.32 | | | | | | | |
% 157.26/27.32 | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | |
% 157.26/27.32 | | | | | | | | (153) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 157.26/27.32 | | | | | | | | op(e0, e2) = e2)
% 157.26/27.32 | | | | | | | |
% 157.26/27.32 | | | | | | | | BETA: splitting (153) gives:
% 157.26/27.32 | | | | | | | |
% 157.26/27.32 | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | (154) all_58_7 = e2 & op(e1, e2) = e2
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | ALPHA: (154) implies:
% 157.26/27.32 | | | | | | | | | (155) all_58_7 = e2
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | BETA: splitting (1) gives:
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | (156) all_54_9 = e3
% 157.26/27.32 | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | REF_CLOSE: (128), (138), (156) are inconsistent by sub-proof
% 157.26/27.32 | | | | | | | | | | #370.
% 157.26/27.32 | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | (157) ~ (all_54_9 = e3)
% 157.26/27.32 | | | | | | | | | | (158) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.26/27.32 | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | BETA: splitting (40) gives:
% 157.26/27.32 | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | (159) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 157.26/27.32 | | | | | | | | | | | & op(e3, e2) = e2)
% 157.26/27.32 | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | BETA: splitting (159) gives:
% 157.26/27.32 | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | (160) all_58_0 = e2 & op(e3, e3) = e2
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | ALPHA: (160) implies:
% 157.26/27.32 | | | | | | | | | | | | (161) all_58_0 = e2
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | COMBINE_EQS: (19), (161) imply:
% 157.26/27.32 | | | | | | | | | | | | (162) e2 = e1
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | SIMP: (162) implies:
% 157.26/27.32 | | | | | | | | | | | | (163) e2 = e1
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | COMBINE_EQS: (155), (163) imply:
% 157.26/27.32 | | | | | | | | | | | | (164) all_58_7 = e1
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 157.26/27.32 | | | | | | | | | | | | (19), (22), (23), (24), (26), (27), (29), (30),
% 157.26/27.32 | | | | | | | | | | | | (33), (34), (35), (36), (38), (39), (40), (41),
% 157.26/27.32 | | | | | | | | | | | | (42), (43), (47), (49), (50), (51), (52), (54),
% 157.26/27.32 | | | | | | | | | | | | (55), (58), (59), (60), (63), (66), (67), (73),
% 157.26/27.32 | | | | | | | | | | | | (74), (75), (80), (83), (84), (85), (88), (89),
% 157.26/27.32 | | | | | | | | | | | | (91), (92), (94), (97), (99), (101), (106), (108),
% 157.26/27.32 | | | | | | | | | | | | (109), (117), (118), (123), (149), (164) are
% 157.26/27.32 | | | | | | | | | | | | inconsistent by sub-proof #723.
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | (165) all_58_1 = e2 & op(e3, e2) = e2
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | ALPHA: (165) implies:
% 157.26/27.32 | | | | | | | | | | | | (166) all_58_1 = e2
% 157.26/27.32 | | | | | | | | | | | | (167) op(e3, e2) = e2
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | COMBINE_EQS: (149), (166) imply:
% 157.26/27.32 | | | | | | | | | | | | (168) e2 = e0
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | SIMP: (168) implies:
% 157.26/27.32 | | | | | | | | | | | | (169) e2 = e0
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | COMBINE_EQS: (155), (169) imply:
% 157.26/27.32 | | | | | | | | | | | | (170) all_58_7 = e0
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.26/27.32 | | | | | | | | | | | | (12), (13), (17), (19), (22), (23), (24), (25),
% 157.26/27.32 | | | | | | | | | | | | (26), (27), (28), (29), (30), (33), (34), (35),
% 157.26/27.32 | | | | | | | | | | | | (36), (38), (39), (40), (41), (43), (45), (47),
% 157.26/27.32 | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 157.26/27.32 | | | | | | | | | | | | (58), (59), (60), (62), (63), (64), (65), (66),
% 157.26/27.32 | | | | | | | | | | | | (67), (69), (70), (73), (74), (76), (79), (80),
% 157.26/27.32 | | | | | | | | | | | | (82), (83), (85), (86), (87), (88), (89), (91),
% 157.26/27.32 | | | | | | | | | | | | (92), (93), (94), (95), (96), (97), (98), (99),
% 157.26/27.32 | | | | | | | | | | | | (101), (104), (105), (107), (108), (109), (113),
% 157.26/27.32 | | | | | | | | | | | | (117), (118), (124), (128), (132), (133), (134),
% 157.26/27.32 | | | | | | | | | | | | (136), (137), (138), (141), (143), (166), (167),
% 157.26/27.32 | | | | | | | | | | | | (170) are inconsistent by sub-proof #366.
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | (171) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 157.26/27.32 | | | | | | | | | | | & op(e3, e0) = e2)
% 157.26/27.32 | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | BETA: splitting (171) gives:
% 157.26/27.32 | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | (172) all_58_4 = e2 & op(e3, e1) = e2
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | ALPHA: (172) implies:
% 157.26/27.32 | | | | | | | | | | | | (173) all_58_4 = e2
% 157.26/27.32 | | | | | | | | | | | | (174) op(e3, e1) = e2
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 157.26/27.32 | | | | | | | | | | | | (19), (22), (23), (24), (26), (27), (29), (33),
% 157.26/27.32 | | | | | | | | | | | | (34), (35), (36), (38), (39), (40), (41), (42),
% 157.26/27.32 | | | | | | | | | | | | (43), (47), (49), (50), (51), (52), (54), (55),
% 157.26/27.32 | | | | | | | | | | | | (58), (59), (60), (63), (73), (74), (75), (80),
% 157.26/27.32 | | | | | | | | | | | | (83), (84), (85), (88), (89), (91), (92), (94),
% 157.26/27.32 | | | | | | | | | | | | (97), (99), (101), (106), (108), (109), (118),
% 157.26/27.32 | | | | | | | | | | | | (173), (174) are inconsistent by sub-proof #751.
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | (175) all_58_9 = e2 & op(e3, e0) = e2
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | ALPHA: (175) implies:
% 157.26/27.32 | | | | | | | | | | | | (176) op(e3, e0) = e2
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | BETA: splitting (158) gives:
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | (177) all_54_9 = e2
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | COMBINE_EQS: (128), (177) imply:
% 157.26/27.32 | | | | | | | | | | | | | (178) all_22_0 = e2
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | SIMP: (178) implies:
% 157.26/27.32 | | | | | | | | | | | | | (179) all_22_0 = e2
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | REDUCE: (129), (179) imply:
% 157.26/27.32 | | | | | | | | | | | | | (180) ~ (all_52_2 = e2)
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | REDUCE: (132), (179) imply:
% 157.26/27.32 | | | | | | | | | | | | | (181) ~ (all_52_4 = e2)
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | REDUCE: (81), (179) imply:
% 157.26/27.32 | | | | | | | | | | | | | (182) op(e1, e2) = e2
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | BETA: splitting (28) gives:
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | (183) all_54_1 = e3
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | COMBINE_EQS: (25), (183) imply:
% 157.26/27.32 | | | | | | | | | | | | | | (184) all_52_4 = e3
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | REDUCE: (74), (184) imply:
% 157.26/27.32 | | | | | | | | | | | | | | (185) $false
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | (186) ~ (all_54_1 = e3)
% 157.26/27.32 | | | | | | | | | | | | | | (187) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | (188) all_54_1 = e2
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | COMBINE_EQS: (25), (188) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | (189) all_52_4 = e2
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | REDUCE: (181), (189) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | (190) $false
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | (191) ~ (all_54_1 = e2)
% 157.26/27.32 | | | | | | | | | | | | | | | (192) all_54_1 = e1 | all_54_1 = e0
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | (193) all_54_1 = e1
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (193) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | (194) all_52_4 = e1
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | REDUCE: (133), (194) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | (195) $false
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | (196) all_54_1 = e0
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (196) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | (197) all_52_4 = e0
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | REDUCE: (32), (197) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | (198) ~ (all_52_12 = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | SIMP: (198) implies:
% 157.26/27.32 | | | | | | | | | | | | | | | | (199) ~ (all_52_12 = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | REDUCE: (74), (197) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | (200) ~ (e3 = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | REDUCE: (181), (197) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | (201) ~ (e2 = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | REDUCE: (133), (197) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | (202) ~ (e1 = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | REDUCE: (26), (197) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | (203) op(e3, e2) = e0
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | (204) all_54_3 = e3
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (204) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | | (205) all_52_12 = e3
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | REDUCE: (2), (205) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | | (206) $false
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent.
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | (207) ~ (all_54_3 = e3)
% 157.26/27.32 | | | | | | | | | | | | | | | | | (208) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (209) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (210) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (211) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (212) op(e2, e3) = e3
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (50), (101), (106), (212) are inconsistent
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | by sub-proof #1159.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (213) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (214) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (215) ~ (all_56_12 = e3)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (216) op(e3, e2) = e2
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with e0, e2, e2, e3,
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | simplifying with (203), (216) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (217) e2 = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (217) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (218) all_58_7 = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (12), (13), (17), (19), (22), (23), (24), (25),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (26), (27), (28), (29), (30), (33), (34), (35),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (36), (38), (39), (40), (41), (42), (43), (45),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (47), (49), (50), (51), (52), (53), (54), (55),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (56), (58), (59), (60), (62), (63), (64), (65),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (66), (67), (69), (70), (73), (74), (75), (76),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (79), (80), (82), (83), (85), (86), (87), (88),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (89), (91), (92), (93), (94), (95), (96), (97),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (98), (99), (101), (104), (105), (106), (107),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (108), (109), (113), (117), (118), (124), (128),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (132), (133), (134), (136), (137), (138), (141),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (143), (218) are inconsistent by sub-proof #365.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (219) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (21), (37), (52), (53), (57), (59),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (61), (65), (71), (76), (84), (86), (87), (106),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (111), (112), (113), (130), (131), (180), (219)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #673.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (220) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (221) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (96), (221) are inconsistent by sub-proof
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | #672.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (222) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (223) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (65), (69), (95), (107), (141), (223) are
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1294.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (224) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (225) ~ (all_56_12 = e3)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (226) op(e3, e0) = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with e0, e2, e0, e3,
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | simplifying with (176), (226) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (227) e2 = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (227) imply:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (228) all_58_7 = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (12), (13), (17), (19), (22), (23), (24), (25),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (26), (27), (28), (29), (30), (33), (34), (35),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (36), (38), (39), (40), (41), (42), (43), (45),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (47), (49), (50), (51), (52), (53), (54), (55),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (56), (58), (59), (60), (62), (63), (64), (65),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (66), (67), (69), (70), (73), (74), (75), (76),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (79), (80), (82), (83), (85), (86), (87), (88),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (89), (91), (92), (93), (94), (95), (96), (97),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (98), (99), (101), (104), (105), (106), (107),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (108), (109), (113), (117), (118), (124), (128),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (132), (133), (134), (136), (137), (138), (141),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (143), (228) are inconsistent by sub-proof #365.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (229) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (230) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (231) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (232) op(e2, e1) = e2
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (101), (143), (232) are inconsistent by
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | sub-proof #1441.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (233) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (234) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (235) op(e1, e2) = e1
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (12), (19), (20), (22), (23), (24), (26), (29),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (30), (33), (34), (35), (36), (38), (39), (40),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (41), (43), (47), (49), (50), (51), (52), (54),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (55), (58), (59), (60), (63), (66), (67), (73),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (74), (77), (80), (83), (84), (85), (88), (89),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (91), (92), (94), (97), (99), (100), (101), (108),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (109), (117), (118), (123), (149), (155), (182),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (199), (208), (235) are inconsistent by sub-proof
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | #671.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (236) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | (237) op(e0, e2) = e2
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (92), (101), (124), (237) are inconsistent
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | | by sub-proof #1319.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (238) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (239) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (240) op(e0, e2) = e0
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (52), (77), (80), (83), (100), (101), (123),
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (124), (149), (155), (199), (208), (240) are
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #670.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (241) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (66), (67), (75), (101), (241) are
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1293.
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | (242) all_54_9 = e1 | all_54_9 = e0
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | | REF_CLOSE: (82), (128), (134), (242) are inconsistent by
% 157.26/27.32 | | | | | | | | | | | | | sub-proof #367.
% 157.26/27.32 | | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | | |
% 157.26/27.32 | | | | | | | | | End of split
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | Case 2:
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | (243) all_58_13 = e2 & op(e0, e2) = e2
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | ALPHA: (243) implies:
% 157.26/27.32 | | | | | | | | | (244) op(e0, e2) = e2
% 157.26/27.32 | | | | | | | | |
% 157.26/27.32 | | | | | | | | | REF_CLOSE: (75), (92), (101), (124), (244) are inconsistent by
% 157.26/27.32 | | | | | | | | | sub-proof #1319.
% 157.26/27.32 | | | | | | | | |
% 157.26/27.33 | | | | | | | | End of split
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | End of split
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | Case 2:
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | (245) all_58_3 = e0 & op(e2, e2) = e0
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | REF_CLOSE: (38), (83), (245) are inconsistent by sub-proof #756.
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | End of split
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | Case 2:
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | (246) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 157.26/27.33 | | | | | | op(e0, e2) = e0)
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | BETA: splitting (246) gives:
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | Case 1:
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | (247) all_58_7 = e0 & op(e1, e2) = e0
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | ALPHA: (247) implies:
% 157.26/27.33 | | | | | | | (248) all_58_7 = e0
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 157.26/27.33 | | | | | | | (13), (17), (19), (22), (23), (24), (25), (26), (27),
% 157.26/27.33 | | | | | | | (28), (29), (30), (33), (34), (35), (36), (38), (39),
% 157.26/27.33 | | | | | | | (40), (41), (42), (43), (45), (47), (49), (50), (51),
% 157.26/27.33 | | | | | | | (52), (53), (54), (55), (56), (58), (59), (60), (62),
% 157.26/27.33 | | | | | | | (63), (64), (65), (66), (67), (69), (70), (73), (74),
% 157.26/27.33 | | | | | | | (75), (76), (79), (80), (82), (83), (85), (86), (87),
% 157.26/27.33 | | | | | | | (88), (89), (91), (92), (93), (94), (95), (96), (97),
% 157.26/27.33 | | | | | | | (98), (99), (101), (104), (105), (106), (107), (108),
% 157.26/27.33 | | | | | | | (109), (113), (117), (118), (124), (128), (132), (133),
% 157.26/27.33 | | | | | | | (134), (136), (137), (138), (141), (143), (248) are
% 157.26/27.33 | | | | | | | inconsistent by sub-proof #365.
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | Case 2:
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | (249) all_58_13 = e0 & op(e0, e2) = e0
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | REF_CLOSE: (80), (123), (249) are inconsistent by sub-proof #1409.
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | End of split
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | End of split
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | End of split
% 157.26/27.33 | | | |
% 157.26/27.33 | | | Case 2:
% 157.26/27.33 | | | |
% 157.26/27.33 | | | | (250) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 157.26/27.33 | | | | e0) = e1)
% 157.26/27.33 | | | |
% 157.26/27.33 | | | | BETA: splitting (250) gives:
% 157.26/27.33 | | | |
% 157.26/27.33 | | | | Case 1:
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | | (251) all_58_14 = e1 & op(e0, e1) = e1
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | | ALPHA: (251) implies:
% 157.26/27.33 | | | | | (252) op(e0, e1) = e1
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | | REF_CLOSE: (66), (67), (75), (101), (252) are inconsistent by
% 157.26/27.33 | | | | | sub-proof #1473.
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | Case 2:
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | | (253) all_58_15 = e1 & op(e0, e0) = e1
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | | ALPHA: (253) implies:
% 157.26/27.33 | | | | | (254) all_58_15 = e1
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | | BETA: splitting (85) gives:
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | | Case 1:
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | (255) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 157.26/27.33 | | | | | | op(e0, e2) = e3)
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | BETA: splitting (255) gives:
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | Case 1:
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | (256) all_58_12 = e3 & op(e0, e3) = e3
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | ALPHA: (256) implies:
% 157.26/27.33 | | | | | | | (257) all_58_12 = e3
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | BETA: splitting (109) gives:
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | | (258) all_58_15 = e0 & op(e0, e0) = e0
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | | REF_CLOSE: (80), (254), (258) are inconsistent by sub-proof
% 157.26/27.33 | | | | | | | | #1059.
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | | (259) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 157.26/27.33 | | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 157.26/27.33 | | | | | | | | e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.26/27.33 | | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0
% 157.26/27.33 | | | | | | | | & op(e0, e1) = e0))
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | | ALPHA: (259) implies:
% 157.26/27.33 | | | | | | | | (260) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.26/27.33 | | | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | | BETA: splitting (10) gives:
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | |
% 157.26/27.33 | | | | | | | | | (261) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 157.26/27.33 | | | | | | | | | op(e2, e0) = e3)
% 157.26/27.33 | | | | | | | | |
% 157.26/27.33 | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 157.26/27.33 | | | | | | | | | (19), (22), (23), (24), (26), (27), (29), (33),
% 157.26/27.33 | | | | | | | | | (34), (35), (36), (38), (39), (40), (41), (42),
% 157.26/27.33 | | | | | | | | | (43), (47), (49), (50), (51), (52), (54), (55),
% 157.26/27.33 | | | | | | | | | (58), (59), (60), (63), (73), (74), (75), (80),
% 157.26/27.33 | | | | | | | | | (83), (84), (85), (88), (89), (91), (92), (94),
% 157.26/27.33 | | | | | | | | | (97), (99), (101), (106), (108), (109), (117),
% 157.26/27.33 | | | | | | | | | (118), (257), (261) are inconsistent by sub-proof
% 157.26/27.33 | | | | | | | | | #736.
% 157.26/27.33 | | | | | | | | |
% 157.26/27.33 | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | |
% 157.26/27.33 | | | | | | | | | (262) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3
% 157.26/27.33 | | | | | | | | | & op(e0, e0) = e3)
% 157.26/27.33 | | | | | | | | |
% 157.26/27.33 | | | | | | | | | BETA: splitting (262) gives:
% 157.26/27.33 | | | | | | | | |
% 157.26/27.33 | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | (263) all_58_11 = e3 & op(e1, e0) = e3
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | ALPHA: (263) implies:
% 157.26/27.33 | | | | | | | | | | (264) all_58_11 = e3
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | BETA: splitting (260) gives:
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | (265) all_58_12 = e0 & op(e0, e3) = e0
% 157.26/27.33 | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | ALPHA: (265) implies:
% 157.26/27.33 | | | | | | | | | | | (266) all_58_12 = e0
% 157.26/27.33 | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | REF_CLOSE: (38), (257), (266) are inconsistent by sub-proof
% 157.26/27.33 | | | | | | | | | | | #1463.
% 157.26/27.33 | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | (267) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 157.26/27.33 | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 157.26/27.33 | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | BETA: splitting (267) gives:
% 157.26/27.33 | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | (268) all_58_13 = e0 & op(e0, e2) = e0
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | ALPHA: (268) implies:
% 157.26/27.33 | | | | | | | | | | | | (269) op(e0, e2) = e0
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | BETA: splitting (36) gives:
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | (270) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 157.26/27.33 | | | | | | | | | | | | | & op(e1, e2) = e2)
% 157.26/27.33 | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | BETA: splitting (270) gives:
% 157.26/27.33 | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | (271) all_58_6 = e2 & op(e1, e3) = e2
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | ALPHA: (271) implies:
% 157.26/27.33 | | | | | | | | | | | | | | (272) all_58_6 = e2
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | REF_CLOSE: (22), (34), (38), (39), (42), (50), (52), (75),
% 157.26/27.33 | | | | | | | | | | | | | | (80), (99), (101), (106), (272) are inconsistent
% 157.26/27.33 | | | | | | | | | | | | | | by sub-proof #1152.
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | (273) all_58_7 = e2 & op(e1, e2) = e2
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | ALPHA: (273) implies:
% 157.26/27.33 | | | | | | | | | | | | | | (274) all_58_7 = e2
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | (275) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.26/27.33 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.26/27.33 | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 157.26/27.33 | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | (276) all_58_9 = e2 & op(e3, e0) = e2
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 157.26/27.33 | | | | | | | | | | | | | | | | (277) all_58_9 = e2
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 157.26/27.33 | | | | | | | | | | | | | | | | (19), (22), (23), (24), (26), (27), (29), (30),
% 157.26/27.33 | | | | | | | | | | | | | | | | (33), (34), (35), (36), (38), (39), (40), (41),
% 157.26/27.33 | | | | | | | | | | | | | | | | (42), (43), (47), (49), (50), (51), (52), (54),
% 157.26/27.33 | | | | | | | | | | | | | | | | (55), (58), (59), (60), (63), (66), (67), (73),
% 157.26/27.33 | | | | | | | | | | | | | | | | (74), (75), (80), (83), (84), (85), (88), (89),
% 157.26/27.33 | | | | | | | | | | | | | | | | (91), (92), (94), (97), (99), (101), (106), (108),
% 157.26/27.33 | | | | | | | | | | | | | | | | (109), (117), (118), (254), (257), (277) are
% 157.26/27.33 | | | | | | | | | | | | | | | | inconsistent by sub-proof #729.
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | (278) all_58_10 = e2 & op(e2, e0) = e2
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 157.26/27.33 | | | | | | | | | | | | | | | | (279) all_58_10 = e2
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (38), (42), (50), (52), (58), (75), (80),
% 157.26/27.33 | | | | | | | | | | | | | | | | (83), (101), (279) are inconsistent by sub-proof
% 157.26/27.33 | | | | | | | | | | | | | | | | #906.
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | (280) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.26/27.33 | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.26/27.33 | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 157.26/27.33 | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | (281) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | REF_CLOSE: (22), (34), (38), (39), (42), (50), (52), (75),
% 157.26/27.33 | | | | | | | | | | | | | | | | (80), (99), (101), (106), (257), (264), (281) are
% 157.26/27.33 | | | | | | | | | | | | | | | | inconsistent by sub-proof #428.
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | (282) all_58_15 = e2 & op(e0, e0) = e2
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 157.26/27.33 | | | | | | | | | | | | | | | | (283) op(e0, e0) = e2
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (9), (10), (22), (24), (26), (29),
% 157.26/27.33 | | | | | | | | | | | | | | | | (30), (34), (35), (38), (39), (40), (42), (47),
% 157.26/27.33 | | | | | | | | | | | | | | | | (49), (50), (51), (52), (55), (58), (73), (74),
% 157.26/27.33 | | | | | | | | | | | | | | | | (75), (80), (83), (88), (89), (91), (92), (97),
% 157.26/27.33 | | | | | | | | | | | | | | | | (99), (101), (106), (108), (109), (257), (269),
% 157.26/27.33 | | | | | | | | | | | | | | | | (274), (283) are inconsistent by sub-proof #605.
% 157.26/27.33 | | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | (284) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 157.26/27.33 | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 157.26/27.33 | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | BETA: splitting (284) gives:
% 157.26/27.33 | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | Case 1:
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | (285) all_58_8 = e2 & op(e1, e1) = e2
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | REF_CLOSE: (30), (38), (42), (52), (54), (73), (75), (80),
% 157.26/27.33 | | | | | | | | | | | | | | (117), (285) are inconsistent by sub-proof #1338.
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | (286) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | | REF_CLOSE: (22), (34), (38), (39), (42), (50), (52), (75),
% 157.26/27.33 | | | | | | | | | | | | | | (80), (99), (101), (106), (257), (264), (286) are
% 157.26/27.33 | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 157.26/27.33 | | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | (287) all_58_14 = e0 & op(e0, e1) = e0
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | ALPHA: (287) implies:
% 157.26/27.33 | | | | | | | | | | | | (288) op(e0, e1) = e0
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | | REF_CLOSE: (42), (66), (67), (101), (288) are inconsistent by
% 157.26/27.33 | | | | | | | | | | | | sub-proof #1372.
% 157.26/27.33 | | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | Case 2:
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | (289) all_58_15 = e3 & op(e0, e0) = e3
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | ALPHA: (289) implies:
% 157.26/27.33 | | | | | | | | | | (290) all_58_15 = e3
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | COMBINE_EQS: (254), (290) imply:
% 157.26/27.33 | | | | | | | | | | (291) e3 = e1
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | COMBINE_EQS: (257), (291) imply:
% 157.26/27.33 | | | | | | | | | | (292) all_58_12 = e1
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 157.26/27.33 | | | | | | | | | | (22), (23), (24), (26), (27), (29), (33), (34),
% 157.26/27.33 | | | | | | | | | | (35), (36), (38), (39), (40), (41), (42), (43),
% 157.26/27.33 | | | | | | | | | | (49), (50), (51), (52), (54), (55), (58), (59),
% 157.26/27.33 | | | | | | | | | | (60), (63), (73), (74), (75), (80), (83), (84),
% 157.26/27.33 | | | | | | | | | | (85), (88), (89), (91), (92), (94), (97), (99),
% 157.26/27.33 | | | | | | | | | | (101), (106), (108), (109), (292) are inconsistent
% 157.26/27.33 | | | | | | | | | | by sub-proof #747.
% 157.26/27.33 | | | | | | | | | |
% 157.26/27.33 | | | | | | | | | End of split
% 157.26/27.33 | | | | | | | | |
% 157.26/27.33 | | | | | | | | End of split
% 157.26/27.33 | | | | | | | |
% 157.26/27.33 | | | | | | | End of split
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | Case 2:
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | (293) all_58_13 = e3 & op(e0, e2) = e3
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | REF_CLOSE: (8), (92), (101), (293) are inconsistent by sub-proof
% 157.26/27.33 | | | | | | | #1449.
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | End of split
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | Case 2:
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | (294) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 157.26/27.33 | | | | | | op(e0, e0) = e3)
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | BETA: splitting (294) gives:
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | | Case 1:
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | (295) all_58_14 = e3 & op(e0, e1) = e3
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | REF_CLOSE: (30), (106), (295) are inconsistent by sub-proof #1465.
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | Case 2:
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | (296) all_58_15 = e3 & op(e0, e0) = e3
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | | REF_CLOSE: (52), (254), (296) are inconsistent by sub-proof #1054.
% 157.26/27.33 | | | | | | |
% 157.26/27.33 | | | | | | End of split
% 157.26/27.33 | | | | | |
% 157.26/27.33 | | | | | End of split
% 157.26/27.33 | | | | |
% 157.26/27.33 | | | | End of split
% 157.26/27.33 | | | |
% 157.26/27.33 | | | End of split
% 157.26/27.33 | | |
% 157.26/27.33 | | Case 2:
% 157.26/27.33 | | |
% 157.26/27.33 | | | (297) all_58_5 = e3 & op(e2, e1) = e3
% 157.26/27.33 | | |
% 157.26/27.33 | | | ALPHA: (297) implies:
% 157.26/27.33 | | | (298) op(e2, e1) = e3
% 157.26/27.33 | | |
% 157.26/27.33 | | | REF_CLOSE: (33), (43), (101), (298) are inconsistent by sub-proof #1196.
% 157.26/27.33 | | |
% 157.26/27.33 | | End of split
% 157.26/27.33 | |
% 157.26/27.33 | Case 2:
% 157.26/27.33 | |
% 157.26/27.33 | | (299) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 157.26/27.33 | | e3)
% 157.26/27.33 | |
% 157.26/27.33 | | REF_CLOSE: (7), (30), (59), (101), (106), (299) are inconsistent by
% 157.26/27.33 | | sub-proof #1243.
% 157.26/27.33 | |
% 157.26/27.33 | End of split
% 157.26/27.33 |
% 157.26/27.33 End of proof
% 157.26/27.33
% 157.26/27.33 Sub-proof #365 shows that the following formulas are inconsistent:
% 157.26/27.33 ----------------------------------------------------------------
% 157.26/27.33 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.26/27.33 (2) op(e3, e1) = e3
% 157.26/27.33 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.33 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.33 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.33 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.33 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.33 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.33 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.33 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.33 (7) op(e1, e1) = all_6_2
% 157.26/27.33 (8) ~ (all_52_7 = e3)
% 157.26/27.33 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.26/27.33 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.33 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.33 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.33 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.26/27.33 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.26/27.33 (12) all_54_10 = all_6_2
% 157.26/27.33 (13) ~ (all_22_0 = all_6_2)
% 157.26/27.33 (14) ~ (all_52_14 = all_22_0)
% 157.26/27.33 (15) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.33 (16) all_58_0 = e1
% 157.26/27.33 (17) ~ (all_52_4 = all_22_0)
% 157.26/27.33 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.33 (19) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.33 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.33 (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.33 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.33 (21) all_54_1 = all_52_4
% 157.26/27.33 (22) op(e3, e2) = all_52_4
% 157.26/27.33 (23) ~ (all_4_2 = e2)
% 157.26/27.33 (24) all_58_7 = e0
% 157.26/27.33 (25) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.33 (26) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.33 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.33 (27) all_58_14 = e2
% 157.26/27.33 (28) ~ (all_22_0 = e1)
% 157.26/27.33 (29) op(e2, e1) = all_52_9
% 157.26/27.33 (30) op(e2, e3) = all_52_1
% 157.26/27.33 (31) ~ (all_52_13 = e3)
% 157.26/27.33 (32) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.33 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.33 (33) ~ (e3 = e0)
% 157.26/27.33 (34) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.33 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.33 (35) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.33 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.33 (36) op(e0, e2) = e1
% 157.26/27.33 (37) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.33 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.33 e2)
% 157.26/27.33 (38) ~ (e2 = e0)
% 157.26/27.33 (39) ~ (all_52_9 = e3)
% 157.26/27.33 (40) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.26/27.33 (41) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.33 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.33 (42) all_54_9 = all_22_0
% 157.26/27.33 (43) ~ (all_22_0 = e3)
% 157.26/27.33 (44) op(e2, e0) = all_52_13
% 157.26/27.33 (45) op(e2, e3) = e2
% 157.26/27.33 (46) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.33 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.33 (47) ~ (e3 = e1)
% 157.26/27.33 (48) all_56_12 = e1
% 157.26/27.33 (49) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.33 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.33 (50) op(e1, e2) = all_52_6
% 157.26/27.33 (51) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.26/27.33 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.33 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.26/27.33 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.26/27.33 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.26/27.33 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.33 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.26/27.33 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.26/27.33 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.26/27.33 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.33 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.26/27.33 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.26/27.33 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.26/27.33 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.26/27.33 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.26/27.33 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.26/27.33 = e0)
% 157.26/27.33 (52) ~ (all_4_2 = e1)
% 157.26/27.33 (53) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.33 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.33 (54) ~ (all_6_2 = e3)
% 157.26/27.33 (55) op(e0, e0) = all_4_2
% 157.26/27.33 (56) all_54_7 = all_52_13
% 157.26/27.33 (57) op(e3, e3) = e1
% 157.26/27.33 (58) ~ (all_52_13 = e2)
% 157.26/27.33 (59) all_56_15 = all_4_2
% 157.26/27.33 (60) op(e0, e1) = e2
% 157.26/27.33 (61) op(e0, e1) = all_52_11
% 157.26/27.33 (62) ~ (all_52_4 = e1)
% 157.26/27.33 (63) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 157.26/27.33 (64) ~ (all_52_13 = all_4_2)
% 157.26/27.33 (65) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.33 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.33 (66) ~ (all_52_4 = e3)
% 157.26/27.33 (67) ~ (e2 = e1)
% 157.26/27.33 (68) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.26/27.33 (69) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.26/27.33 (70) ~ (e1 = e0)
% 157.26/27.33 (71) all_58_4 = e3
% 157.26/27.33 (72) ~ (all_22_0 = e0)
% 157.26/27.33 (73) all_58_3 = e3
% 157.26/27.33 (74) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.33 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.33 e3)
% 157.26/27.33 (75) all_56_14 = all_6_2
% 157.26/27.33 (76) all_56_13 = e3
% 157.26/27.33 (77) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.33 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.33 (78) ~ (all_52_9 = e2)
% 157.26/27.33 (79) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.33 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.33 (80) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.33 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.33 (81) op(e0, e2) = all_52_7
% 157.26/27.33 (82) op(e1, e0) = all_52_14
% 157.26/27.33 (83) op(e3, e3) = all_22_1
% 157.26/27.33 (84) all_54_15 = all_4_2
% 157.26/27.33 (85) all_56_1 = e3
% 157.26/27.33 (86) ~ (all_52_6 = e3)
% 157.26/27.33 (87) ~ (all_52_14 = all_6_2)
% 157.26/27.33 (88) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.33 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.33 (89) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.33 (90) all_54_11 = all_52_14
% 157.26/27.33 (91) ~ (all_52_13 = all_52_14)
% 157.26/27.33 (92) ~ (e3 = e2)
% 157.26/27.33 (93) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.26/27.33 (94) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.26/27.33 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.33 (95) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.33 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.26/27.33 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.26/27.33 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.26/27.33 (96) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.26/27.33
% 157.26/27.33 Begin of proof
% 157.26/27.33 |
% 157.26/27.33 | BETA: splitting (79) gives:
% 157.26/27.33 |
% 157.26/27.33 | Case 1:
% 157.26/27.33 | |
% 157.26/27.33 | | (97) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 157.26/27.33 | | e2)
% 157.26/27.33 | |
% 157.26/27.33 | | BETA: splitting (97) gives:
% 157.26/27.33 | |
% 157.26/27.33 | | Case 1:
% 157.26/27.33 | | |
% 157.26/27.33 | | | (98) all_58_1 = e2 & op(e3, e2) = e2
% 157.26/27.33 | | |
% 157.26/27.33 | | | ALPHA: (98) implies:
% 157.26/27.33 | | | (99) all_58_1 = e2
% 157.26/27.33 | | | (100) op(e3, e2) = e2
% 157.26/27.33 | | |
% 157.26/27.34 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.26/27.34 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.26/27.34 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 157.26/27.34 | | | (33), (34), (35), (36), (37), (39), (40), (41), (42), (43),
% 157.26/27.34 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 157.26/27.34 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 157.26/27.34 | | | (64), (65), (66), (68), (69), (70), (71), (72), (73), (74),
% 157.26/27.34 | | | (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 157.26/27.34 | | | (85), (86), (87), (88), (89), (90), (91), (93), (94), (95),
% 157.26/27.34 | | | (96), (99), (100) are inconsistent by sub-proof #366.
% 157.26/27.34 | | |
% 157.26/27.34 | | Case 2:
% 157.26/27.34 | | |
% 157.26/27.34 | | | (101) all_58_3 = e2 & op(e2, e2) = e2
% 157.26/27.34 | | |
% 157.26/27.34 | | | ALPHA: (101) implies:
% 157.26/27.34 | | | (102) all_58_3 = e2
% 157.26/27.34 | | |
% 157.26/27.34 | | | COMBINE_EQS: (73), (102) imply:
% 157.26/27.34 | | | (103) e3 = e2
% 157.26/27.34 | | |
% 157.26/27.34 | | | SIMP: (103) implies:
% 157.26/27.34 | | | (104) e3 = e2
% 157.26/27.34 | | |
% 157.26/27.34 | | | REDUCE: (92), (104) imply:
% 157.26/27.34 | | | (105) $false
% 157.26/27.34 | | |
% 157.26/27.34 | | | CLOSE: (105) is inconsistent.
% 157.26/27.34 | | |
% 157.26/27.34 | | End of split
% 157.26/27.34 | |
% 157.26/27.34 | Case 2:
% 157.26/27.34 | |
% 157.26/27.34 | | (106) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 157.26/27.34 | | e2)
% 157.26/27.34 | |
% 157.26/27.34 | | REF_CLOSE: (24), (36), (38), (67), (81), (89), (106) are inconsistent by
% 157.26/27.34 | | sub-proof #740.
% 157.26/27.34 | |
% 157.26/27.34 | End of split
% 157.26/27.34 |
% 157.26/27.34 End of proof
% 157.26/27.34
% 157.26/27.34 Sub-proof #366 shows that the following formulas are inconsistent:
% 157.26/27.34 ----------------------------------------------------------------
% 157.26/27.34 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.26/27.34 (2) op(e3, e2) = e2
% 157.26/27.34 (3) op(e3, e1) = e3
% 157.26/27.34 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.34 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.34 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.34 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.34 (6) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.34 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.34 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.34 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.34 (8) op(e1, e1) = all_6_2
% 157.26/27.34 (9) ~ (all_52_7 = e3)
% 157.26/27.34 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.26/27.34 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.26/27.34 e1)
% 157.26/27.34 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.34 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.34 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.26/27.34 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.26/27.34 (13) all_54_10 = all_6_2
% 157.26/27.34 (14) ~ (all_22_0 = all_6_2)
% 157.26/27.34 (15) ~ (all_52_14 = all_22_0)
% 157.26/27.34 (16) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.26/27.34 (17) all_58_0 = e1
% 157.26/27.34 (18) ~ (all_52_4 = all_22_0)
% 157.26/27.34 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.34 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.34 (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.26/27.34 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.34 (21) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.34 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.34 (22) all_54_1 = all_52_4
% 157.26/27.34 (23) op(e3, e2) = all_52_4
% 157.26/27.34 (24) ~ (all_4_2 = e2)
% 157.26/27.34 (25) all_58_7 = e0
% 157.26/27.34 (26) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.34 (27) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.34 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.34 (28) all_58_14 = e2
% 157.26/27.34 (29) ~ (all_22_0 = e1)
% 157.26/27.34 (30) op(e2, e1) = all_52_9
% 157.26/27.34 (31) op(e2, e3) = all_52_1
% 157.26/27.34 (32) ~ (all_52_13 = e3)
% 157.26/27.34 (33) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.34 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.34 (34) ~ (e3 = e0)
% 157.26/27.34 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.34 (36) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.34 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.34 (37) op(e0, e2) = e1
% 157.26/27.34 (38) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.34 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.26/27.34 e2)
% 157.26/27.34 (39) ~ (all_52_9 = e3)
% 157.26/27.34 (40) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 157.26/27.34 (41) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.34 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.34 (42) all_54_9 = all_22_0
% 157.26/27.34 (43) ~ (all_22_0 = e3)
% 157.26/27.34 (44) op(e2, e0) = all_52_13
% 157.26/27.34 (45) op(e2, e3) = e2
% 157.26/27.34 (46) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.34 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.34 (47) ~ (e3 = e1)
% 157.26/27.34 (48) all_56_12 = e1
% 157.26/27.34 (49) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.26/27.34 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.26/27.34 (50) op(e1, e2) = all_52_6
% 157.26/27.34 (51) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.26/27.34 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.26/27.34 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.26/27.34 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.26/27.34 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.26/27.34 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.26/27.34 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.26/27.34 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.26/27.34 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.26/27.34 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.26/27.34 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.26/27.34 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.26/27.34 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.26/27.34 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.26/27.34 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.26/27.34 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.26/27.34 = e0)
% 157.26/27.34 (52) ~ (all_4_2 = e1)
% 157.26/27.34 (53) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.34 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.34 (54) ~ (all_6_2 = e3)
% 157.26/27.34 (55) op(e0, e0) = all_4_2
% 157.26/27.34 (56) all_54_7 = all_52_13
% 157.26/27.34 (57) op(e3, e3) = e1
% 157.26/27.34 (58) ~ (all_52_13 = e2)
% 157.26/27.34 (59) all_56_15 = all_4_2
% 157.26/27.34 (60) op(e0, e1) = e2
% 157.26/27.34 (61) op(e0, e1) = all_52_11
% 157.26/27.34 (62) ~ (all_52_4 = e1)
% 157.26/27.34 (63) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 157.26/27.34 (64) ~ (all_52_13 = all_4_2)
% 157.26/27.34 (65) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.34 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.34 (66) ~ (all_52_4 = e3)
% 157.26/27.34 (67) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.26/27.34 (68) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.26/27.34 (69) ~ (e1 = e0)
% 157.26/27.34 (70) all_58_4 = e3
% 157.26/27.34 (71) ~ (all_22_0 = e0)
% 157.26/27.34 (72) all_58_3 = e3
% 157.26/27.34 (73) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.34 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.34 e3)
% 157.26/27.34 (74) all_56_14 = all_6_2
% 157.26/27.34 (75) all_56_13 = e3
% 157.26/27.34 (76) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.34 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.34 (77) ~ (all_52_9 = e2)
% 157.26/27.34 (78) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.34 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.34 (79) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.34 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.34 (80) op(e0, e2) = all_52_7
% 157.26/27.34 (81) op(e1, e0) = all_52_14
% 157.26/27.34 (82) op(e3, e3) = all_22_1
% 157.26/27.34 (83) all_54_15 = all_4_2
% 157.26/27.34 (84) all_56_1 = e3
% 157.26/27.34 (85) all_58_1 = e2
% 157.26/27.34 (86) ~ (all_52_6 = e3)
% 157.26/27.34 (87) ~ (all_52_14 = all_6_2)
% 157.26/27.34 (88) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.34 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.34 (89) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.34 (90) all_54_11 = all_52_14
% 157.26/27.34 (91) ~ (all_52_13 = all_52_14)
% 157.26/27.34 (92) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.26/27.34 (93) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.26/27.34 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.34 (94) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.26/27.34 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.26/27.34 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.26/27.34 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.26/27.34 (95) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.26/27.34
% 157.26/27.34 Begin of proof
% 157.26/27.34 |
% 157.26/27.34 | BETA: splitting (1) gives:
% 157.26/27.34 |
% 157.26/27.34 | Case 1:
% 157.26/27.34 | |
% 157.26/27.34 | | (96) all_54_9 = e3
% 157.26/27.34 | |
% 157.26/27.34 | | REF_CLOSE: (42), (43), (96) are inconsistent by sub-proof #370.
% 157.26/27.34 | |
% 157.26/27.34 | Case 2:
% 157.26/27.34 | |
% 157.26/27.34 | | (97) ~ (all_54_9 = e3)
% 157.26/27.34 | | (98) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.26/27.34 | |
% 157.26/27.34 | | BETA: splitting (98) gives:
% 157.26/27.34 | |
% 157.26/27.34 | | Case 1:
% 157.26/27.34 | | |
% 157.26/27.34 | | | (99) all_54_9 = e2
% 157.26/27.34 | | |
% 157.26/27.34 | | | COMBINE_EQS: (42), (99) imply:
% 157.26/27.34 | | | (100) all_22_0 = e2
% 157.26/27.34 | | |
% 157.26/27.34 | | | SIMP: (100) implies:
% 157.26/27.34 | | | (101) all_22_0 = e2
% 157.26/27.34 | | |
% 157.26/27.34 | | | REDUCE: (18), (101) imply:
% 157.26/27.34 | | | (102) ~ (all_52_4 = e2)
% 157.26/27.34 | | |
% 157.26/27.34 | | | REDUCE: (15), (101) imply:
% 157.26/27.34 | | | (103) ~ (all_52_14 = e2)
% 157.26/27.34 | | |
% 157.26/27.34 | | | REDUCE: (14), (101) imply:
% 157.26/27.34 | | | (104) ~ (all_6_2 = e2)
% 157.26/27.34 | | |
% 157.26/27.34 | | | SIMP: (104) implies:
% 157.26/27.34 | | | (105) ~ (all_6_2 = e2)
% 157.26/27.34 | | |
% 157.26/27.34 | | | REDUCE: (43), (101) imply:
% 157.26/27.34 | | | (106) ~ (e3 = e2)
% 157.26/27.34 | | |
% 157.26/27.34 | | | SIMP: (106) implies:
% 157.26/27.34 | | | (107) ~ (e3 = e2)
% 157.26/27.34 | | |
% 157.26/27.34 | | | REDUCE: (29), (101) imply:
% 157.26/27.34 | | | (108) ~ (e2 = e1)
% 157.26/27.34 | | |
% 157.26/27.34 | | | REDUCE: (71), (101) imply:
% 157.26/27.34 | | | (109) ~ (e2 = e0)
% 157.26/27.34 | | |
% 157.26/27.34 | | | BETA: splitting (33) gives:
% 157.26/27.34 | | |
% 157.26/27.34 | | | Case 1:
% 157.26/27.34 | | | |
% 157.26/27.34 | | | | (110) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 157.26/27.34 | | | | = e2)
% 157.26/27.34 | | | |
% 157.26/27.34 | | | | REF_CLOSE: (19), (25), (31), (34), (35), (45), (47), (69), (88), (89),
% 157.26/27.34 | | | | (107), (108), (109), (110) are inconsistent by sub-proof
% 157.26/27.34 | | | | #745.
% 157.26/27.34 | | | |
% 157.26/27.34 | | | Case 2:
% 157.26/27.34 | | | |
% 157.26/27.34 | | | | (111) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 157.26/27.34 | | | | e0) = e2)
% 157.26/27.34 | | | |
% 157.26/27.34 | | | | BETA: splitting (111) gives:
% 157.26/27.34 | | | |
% 157.26/27.34 | | | | Case 1:
% 157.26/27.34 | | | | |
% 157.26/27.34 | | | | | (112) all_58_8 = e2 & op(e1, e1) = e2
% 157.26/27.34 | | | | |
% 157.26/27.34 | | | | | REF_CLOSE: (28), (34), (47), (49), (65), (69), (70), (108), (109),
% 157.26/27.34 | | | | | (112) are inconsistent by sub-proof #1338.
% 157.26/27.34 | | | | |
% 157.26/27.34 | | | | Case 2:
% 157.26/27.34 | | | | |
% 157.26/27.34 | | | | | (113) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.34 | | | | |
% 157.26/27.34 | | | | | ALPHA: (113) implies:
% 157.26/27.34 | | | | | (114) all_58_11 = e2
% 157.26/27.34 | | | | |
% 157.26/27.34 | | | | | BETA: splitting (27) gives:
% 157.26/27.34 | | | | |
% 157.26/27.34 | | | | | Case 1:
% 157.26/27.34 | | | | | |
% 157.26/27.34 | | | | | | (115) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 157.26/27.34 | | | | | | e2) = e3)
% 157.26/27.34 | | | | | |
% 157.26/27.34 | | | | | | BETA: splitting (115) gives:
% 157.26/27.34 | | | | | |
% 157.26/27.34 | | | | | | Case 1:
% 157.26/27.34 | | | | | | |
% 157.26/27.34 | | | | | | | (116) all_58_6 = e3 & op(e1, e3) = e3
% 157.26/27.34 | | | | | | |
% 157.26/27.34 | | | | | | | ALPHA: (116) implies:
% 157.26/27.34 | | | | | | | (117) all_58_6 = e3
% 157.26/27.34 | | | | | | |
% 157.26/27.34 | | | | | | | BETA: splitting (26) gives:
% 157.26/27.34 | | | | | | |
% 157.26/27.34 | | | | | | | Case 1:
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | | (118) all_54_1 = e3
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | | COMBINE_EQS: (22), (118) imply:
% 157.26/27.34 | | | | | | | | (119) all_52_4 = e3
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | | REDUCE: (66), (119) imply:
% 157.26/27.34 | | | | | | | | (120) $false
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | | CLOSE: (120) is inconsistent.
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | Case 2:
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | | (121) ~ (all_54_1 = e3)
% 157.26/27.34 | | | | | | | | (122) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | | BETA: splitting (122) gives:
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | | Case 1:
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | | (123) all_54_1 = e2
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | | COMBINE_EQS: (22), (123) imply:
% 157.26/27.34 | | | | | | | | | (124) all_52_4 = e2
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | | REDUCE: (102), (124) imply:
% 157.26/27.34 | | | | | | | | | (125) $false
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | | CLOSE: (125) is inconsistent.
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | Case 2:
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | | (126) ~ (all_54_1 = e2)
% 157.26/27.34 | | | | | | | | | (127) all_54_1 = e1 | all_54_1 = e0
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | | BETA: splitting (127) gives:
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | | Case 1:
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | (128) all_54_1 = e1
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | COMBINE_EQS: (22), (128) imply:
% 157.26/27.34 | | | | | | | | | | (129) all_52_4 = e1
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | REDUCE: (62), (129) imply:
% 157.26/27.34 | | | | | | | | | | (130) $false
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | CLOSE: (130) is inconsistent.
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | Case 2:
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | (131) all_54_1 = e0
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | COMBINE_EQS: (22), (131) imply:
% 157.26/27.34 | | | | | | | | | | (132) all_52_4 = e0
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | REDUCE: (66), (132) imply:
% 157.26/27.34 | | | | | | | | | | (133) ~ (e3 = e0)
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | REDUCE: (102), (132) imply:
% 157.26/27.34 | | | | | | | | | | (134) ~ (e2 = e0)
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | REDUCE: (62), (132) imply:
% 157.26/27.34 | | | | | | | | | | (135) ~ (e1 = e0)
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | REDUCE: (23), (132) imply:
% 157.26/27.34 | | | | | | | | | | (136) op(e3, e2) = e0
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | BETA: splitting (11) gives:
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | Case 1:
% 157.26/27.34 | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | (137) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 157.26/27.34 | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 157.26/27.34 | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.26/27.34 | | | | | | | | | | | (12), (17), (19), (20), (21), (23), (24), (27),
% 157.26/27.34 | | | | | | | | | | | (28), (30), (31), (32), (33), (34), (35), (36),
% 157.26/27.34 | | | | | | | | | | | (38), (39), (41), (44), (45), (46), (47), (49),
% 157.26/27.34 | | | | | | | | | | | (50), (53), (54), (55), (57), (65), (66), (69),
% 157.26/27.34 | | | | | | | | | | | (70), (72), (73), (76), (78), (79), (80), (82),
% 157.26/27.34 | | | | | | | | | | | (86), (88), (89), (93), (94), (105), (107), (108),
% 157.26/27.34 | | | | | | | | | | | (109), (114), (137) are inconsistent by sub-proof
% 157.26/27.34 | | | | | | | | | | | #684.
% 157.26/27.34 | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | Case 2:
% 157.26/27.34 | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | (138) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 157.26/27.34 | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 157.26/27.34 | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | BETA: splitting (138) gives:
% 157.26/27.34 | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | Case 1:
% 157.26/27.34 | | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | | (139) all_58_11 = e3 & op(e1, e0) = e3
% 157.26/27.34 | | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | | ALPHA: (139) implies:
% 157.26/27.34 | | | | | | | | | | | | (140) all_58_11 = e3
% 157.26/27.34 | | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | | REF_CLOSE: (8), (19), (25), (31), (33), (34), (35), (45),
% 157.26/27.34 | | | | | | | | | | | | (47), (69), (88), (89), (105), (107), (108),
% 157.26/27.34 | | | | | | | | | | | | (109), (117), (140) are inconsistent by sub-proof
% 157.26/27.34 | | | | | | | | | | | | #368.
% 157.26/27.34 | | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | Case 2:
% 157.26/27.34 | | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | | (141) all_58_15 = e3 & op(e0, e0) = e3
% 157.26/27.34 | | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | | ALPHA: (141) implies:
% 157.26/27.34 | | | | | | | | | | | | (142) all_58_15 = e3
% 157.26/27.34 | | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.26/27.34 | | | | | | | | | | | | (12), (13), (16), (17), (19), (20), (21), (23),
% 157.26/27.34 | | | | | | | | | | | | (24), (25), (27), (28), (30), (31), (32), (33),
% 157.26/27.34 | | | | | | | | | | | | (34), (35), (36), (37), (38), (39), (40), (41),
% 157.26/27.34 | | | | | | | | | | | | (44), (45), (46), (47), (48), (49), (50), (51),
% 157.26/27.34 | | | | | | | | | | | | (52), (53), (54), (55), (56), (57), (58), (59),
% 157.26/27.34 | | | | | | | | | | | | (60), (61), (63), (64), (65), (66), (67), (68),
% 157.26/27.34 | | | | | | | | | | | | (69), (70), (72), (73), (74), (75), (76), (77),
% 157.26/27.34 | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 157.26/27.34 | | | | | | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93),
% 157.26/27.34 | | | | | | | | | | | | (94), (95), (103), (105), (107), (108), (109),
% 157.26/27.34 | | | | | | | | | | | | (117), (136), (142) are inconsistent by sub-proof
% 157.26/27.34 | | | | | | | | | | | | #678.
% 157.26/27.34 | | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | | End of split
% 157.26/27.34 | | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | | End of split
% 157.26/27.34 | | | | | | | | | |
% 157.26/27.34 | | | | | | | | | End of split
% 157.26/27.34 | | | | | | | | |
% 157.26/27.34 | | | | | | | | End of split
% 157.26/27.34 | | | | | | | |
% 157.26/27.34 | | | | | | | End of split
% 157.26/27.34 | | | | | | |
% 157.26/27.34 | | | | | | Case 2:
% 157.26/27.34 | | | | | | |
% 157.26/27.34 | | | | | | | (143) all_58_7 = e3 & op(e1, e2) = e3
% 157.26/27.34 | | | | | | |
% 157.26/27.34 | | | | | | | REF_CLOSE: (50), (86), (89), (143) are inconsistent by sub-proof
% 157.26/27.34 | | | | | | | #1184.
% 157.26/27.34 | | | | | | |
% 157.26/27.34 | | | | | | End of split
% 157.26/27.34 | | | | | |
% 157.26/27.34 | | | | | Case 2:
% 157.26/27.34 | | | | | |
% 157.26/27.34 | | | | | | (144) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 157.26/27.34 | | | | | | op(e1, e0) = e3)
% 157.26/27.34 | | | | | |
% 157.26/27.34 | | | | | | REF_CLOSE: (28), (34), (47), (49), (65), (69), (70), (107), (108),
% 157.26/27.34 | | | | | | (109), (114), (144) are inconsistent by sub-proof #738.
% 157.26/27.34 | | | | | |
% 157.26/27.34 | | | | | End of split
% 157.26/27.34 | | | | |
% 157.26/27.34 | | | | End of split
% 157.26/27.34 | | | |
% 157.26/27.34 | | | End of split
% 157.26/27.34 | | |
% 157.26/27.34 | | Case 2:
% 157.26/27.34 | | |
% 157.26/27.34 | | | (145) all_54_9 = e1 | all_54_9 = e0
% 157.26/27.34 | | |
% 157.26/27.34 | | | REF_CLOSE: (29), (42), (71), (145) are inconsistent by sub-proof #367.
% 157.26/27.34 | | |
% 157.26/27.34 | | End of split
% 157.26/27.34 | |
% 157.26/27.34 | End of split
% 157.26/27.34 |
% 157.26/27.34 End of proof
% 157.26/27.34
% 157.26/27.34 Sub-proof #367 shows that the following formulas are inconsistent:
% 157.26/27.34 ----------------------------------------------------------------
% 157.26/27.34 (1) all_54_9 = e1 | all_54_9 = e0
% 157.26/27.34 (2) all_54_9 = all_22_0
% 157.26/27.34 (3) ~ (all_22_0 = e1)
% 157.26/27.34 (4) ~ (all_22_0 = e0)
% 157.26/27.34
% 157.26/27.34 Begin of proof
% 157.26/27.34 |
% 157.26/27.34 | BETA: splitting (1) gives:
% 157.26/27.34 |
% 157.26/27.34 | Case 1:
% 157.26/27.34 | |
% 157.26/27.34 | | (5) all_54_9 = e1
% 157.26/27.34 | |
% 157.26/27.34 | | COMBINE_EQS: (2), (5) imply:
% 157.26/27.34 | | (6) all_22_0 = e1
% 157.26/27.34 | |
% 157.26/27.34 | | SIMP: (6) implies:
% 157.26/27.34 | | (7) all_22_0 = e1
% 157.26/27.34 | |
% 157.26/27.34 | | REDUCE: (3), (7) imply:
% 157.26/27.34 | | (8) $false
% 157.26/27.34 | |
% 157.26/27.34 | | CLOSE: (8) is inconsistent.
% 157.26/27.34 | |
% 157.26/27.34 | Case 2:
% 157.26/27.34 | |
% 157.26/27.34 | | (9) all_54_9 = e0
% 157.26/27.34 | |
% 157.26/27.34 | | COMBINE_EQS: (2), (9) imply:
% 157.26/27.34 | | (10) all_22_0 = e0
% 157.26/27.34 | |
% 157.26/27.34 | | SIMP: (10) implies:
% 157.26/27.34 | | (11) all_22_0 = e0
% 157.26/27.34 | |
% 157.26/27.34 | | REDUCE: (4), (11) imply:
% 157.26/27.34 | | (12) $false
% 157.26/27.34 | |
% 157.26/27.34 | | CLOSE: (12) is inconsistent.
% 157.26/27.34 | |
% 157.26/27.34 | End of split
% 157.26/27.34 |
% 157.26/27.34 End of proof
% 157.26/27.34
% 157.26/27.34 Sub-proof #368 shows that the following formulas are inconsistent:
% 157.26/27.34 ----------------------------------------------------------------
% 157.26/27.34 (1) op(e1, e1) = all_6_2
% 157.26/27.34 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.34 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.34 (3) all_58_6 = e3
% 157.26/27.34 (4) all_58_7 = e0
% 157.26/27.34 (5) op(e2, e3) = all_52_1
% 157.26/27.34 (6) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.26/27.34 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.34 (7) ~ (e3 = e0)
% 157.26/27.34 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.34 (9) ~ (e2 = e0)
% 157.26/27.34 (10) op(e2, e3) = e2
% 157.26/27.34 (11) ~ (e3 = e1)
% 157.26/27.34 (12) ~ (e2 = e1)
% 157.26/27.34 (13) ~ (e1 = e0)
% 157.26/27.34 (14) ~ (all_6_2 = e2)
% 157.26/27.34 (15) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.34 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.34 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.34 (17) ~ (e3 = e2)
% 157.26/27.34 (18) all_58_11 = e3
% 157.26/27.34
% 157.26/27.34 Begin of proof
% 157.26/27.34 |
% 157.26/27.34 | BETA: splitting (6) gives:
% 157.26/27.34 |
% 157.26/27.34 | Case 1:
% 157.26/27.34 | |
% 157.26/27.34 | | (19) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 157.26/27.34 | | e2)
% 157.26/27.34 | |
% 157.26/27.34 | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (15), (16),
% 157.26/27.34 | | (17), (19) are inconsistent by sub-proof #744.
% 157.26/27.34 | |
% 157.26/27.34 | Case 2:
% 157.26/27.34 | |
% 157.26/27.34 | | (20) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 157.26/27.34 | | e2)
% 157.26/27.34 | |
% 157.26/27.34 | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 157.26/27.34 | | (15), (16), (17), (18), (20) are inconsistent by sub-proof #369.
% 157.26/27.34 | |
% 157.26/27.34 | End of split
% 157.26/27.34 |
% 157.26/27.34 End of proof
% 157.26/27.34
% 157.26/27.34 Sub-proof #369 shows that the following formulas are inconsistent:
% 157.26/27.34 ----------------------------------------------------------------
% 157.26/27.34 (1) op(e1, e1) = all_6_2
% 157.26/27.34 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.34 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.34 (3) all_58_6 = e3
% 157.26/27.34 (4) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.26/27.34 (5) op(e2, e3) = all_52_1
% 157.26/27.34 (6) ~ (e3 = e0)
% 157.26/27.34 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.34 (8) ~ (e2 = e0)
% 157.26/27.34 (9) op(e2, e3) = e2
% 157.26/27.34 (10) ~ (e3 = e1)
% 157.26/27.34 (11) ~ (e2 = e1)
% 157.26/27.34 (12) ~ (e1 = e0)
% 157.26/27.34 (13) ~ (all_6_2 = e2)
% 157.26/27.34 (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.34 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.26/27.35 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.26/27.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.26/27.35 (16) ~ (e3 = e2)
% 157.26/27.35 (17) all_58_11 = e3
% 157.26/27.35
% 157.26/27.35 Begin of proof
% 157.26/27.35 |
% 157.26/27.35 | BETA: splitting (4) gives:
% 157.26/27.35 |
% 157.26/27.35 | Case 1:
% 157.26/27.35 | |
% 157.26/27.35 | | (18) all_58_8 = e2 & op(e1, e1) = e2
% 157.26/27.35 | |
% 157.26/27.35 | | REF_CLOSE: (1), (13), (15), (18) are inconsistent by sub-proof #1440.
% 157.26/27.35 | |
% 157.26/27.35 | Case 2:
% 157.26/27.35 | |
% 157.26/27.35 | | (19) all_58_11 = e2 & op(e1, e0) = e2
% 157.26/27.35 | |
% 157.26/27.35 | | ALPHA: (19) implies:
% 157.26/27.35 | | (20) all_58_11 = e2
% 157.26/27.35 | |
% 157.26/27.35 | | COMBINE_EQS: (17), (20) imply:
% 157.26/27.35 | | (21) e3 = e2
% 157.26/27.35 | |
% 157.26/27.35 | | COMBINE_EQS: (3), (21) imply:
% 157.26/27.35 | | (22) all_58_6 = e2
% 157.26/27.35 | |
% 157.26/27.35 | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15), (16),
% 157.26/27.35 | | (22) are inconsistent by sub-proof #1152.
% 157.26/27.35 | |
% 157.26/27.35 | End of split
% 157.26/27.35 |
% 157.26/27.35 End of proof
% 157.26/27.35
% 157.26/27.35 Sub-proof #370 shows that the following formulas are inconsistent:
% 157.26/27.35 ----------------------------------------------------------------
% 157.26/27.35 (1) all_54_9 = all_22_0
% 157.26/27.35 (2) all_54_9 = e3
% 157.26/27.35 (3) ~ (all_22_0 = e3)
% 157.26/27.35
% 157.26/27.35 Begin of proof
% 157.26/27.35 |
% 157.26/27.35 | COMBINE_EQS: (1), (2) imply:
% 157.26/27.35 | (4) all_22_0 = e3
% 157.26/27.35 |
% 157.26/27.35 | SIMP: (4) implies:
% 157.26/27.35 | (5) all_22_0 = e3
% 157.26/27.35 |
% 157.26/27.35 | REDUCE: (3), (5) imply:
% 157.26/27.35 | (6) $false
% 157.26/27.35 |
% 157.26/27.35 | CLOSE: (6) is inconsistent.
% 157.26/27.35 |
% 157.26/27.35 End of proof
% 157.26/27.35
% 157.26/27.35 Sub-proof #371 shows that the following formulas are inconsistent:
% 157.26/27.35 ----------------------------------------------------------------
% 157.26/27.35 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.26/27.35 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.26/27.35 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.26/27.35 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.35 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.26/27.35 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.26/27.35 (4) op(e1, e1) = all_6_2
% 157.26/27.35 (5) ~ (all_52_7 = e3)
% 157.26/27.35 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.26/27.35 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.26/27.35 (7) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.26/27.35 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.26/27.35 (8) all_58_7 = e2
% 157.26/27.35 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.26/27.35 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.26/27.35 (10) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.26/27.35 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.26/27.35 (11) op(e3, e2) = all_52_4
% 157.26/27.35 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.26/27.35 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.26/27.35 (13) op(e2, e3) = all_52_1
% 157.26/27.35 (14) ~ (all_52_13 = e3)
% 157.26/27.35 (15) ~ (e3 = e0)
% 157.26/27.35 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.26/27.35 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.26/27.35 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.26/27.35 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.26/27.35 (18) ~ (e2 = e0)
% 157.26/27.35 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.26/27.35 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.26/27.35 (20) op(e2, e0) = all_52_13
% 157.26/27.35 (21) op(e2, e3) = e2
% 157.26/27.35 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.35 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.26/27.35 (23) ~ (e3 = e1)
% 157.26/27.35 (24) op(e1, e2) = all_52_6
% 157.26/27.35 (25) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.26/27.35 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.26/27.35 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.26/27.35 (27) op(e0, e0) = e2
% 157.26/27.35 (28) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.26/27.35 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.26/27.35 (29) ~ (all_52_4 = e3)
% 157.26/27.35 (30) op(e0, e2) = e0
% 157.26/27.35 (31) ~ (e2 = e1)
% 157.26/27.35 (32) ~ (e1 = e0)
% 157.26/27.35 (33) all_58_3 = e3
% 157.26/27.35 (34) ~ (all_6_2 = e2)
% 157.26/27.35 (35) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.26/27.35 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.26/27.35 e3)
% 157.26/27.35 (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.26/27.35 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.26/27.35 (37) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.26/27.35 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.26/27.35 (38) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.26/27.35 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.26/27.35 (39) op(e0, e2) = all_52_7
% 157.26/27.35 (40) ~ (all_52_6 = e3)
% 157.26/27.35 (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.26/27.35 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.56/27.35 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.56/27.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.56/27.35 (43) ~ (e3 = e2)
% 157.56/27.35 (44) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.56/27.35 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.56/27.35 (45) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.56/27.35 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.56/27.35 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.56/27.35 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.56/27.35
% 157.56/27.35 Begin of proof
% 157.56/27.35 |
% 157.56/27.35 | BETA: splitting (25) gives:
% 157.56/27.35 |
% 157.56/27.35 | Case 1:
% 157.56/27.35 | |
% 157.56/27.35 | | (46) all_58_8 = e2 & op(e1, e1) = e2
% 157.56/27.35 | |
% 157.56/27.35 | | REF_CLOSE: (4), (34), (42), (46) are inconsistent by sub-proof #1440.
% 157.56/27.35 | |
% 157.56/27.35 | Case 2:
% 157.56/27.35 | |
% 157.56/27.35 | | (47) all_58_14 = e2 & op(e0, e1) = e2
% 157.56/27.35 | |
% 157.56/27.35 | | ALPHA: (47) implies:
% 157.56/27.35 | | (48) all_58_14 = e2
% 157.56/27.35 | |
% 157.56/27.35 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 157.56/27.35 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 157.56/27.35 | | (26), (27), (28), (29), (30), (31), (32), (33), (35), (36), (37),
% 157.56/27.35 | | (38), (39), (40), (41), (42), (43), (44), (45), (48) are
% 157.56/27.35 | | inconsistent by sub-proof #604.
% 157.56/27.35 | |
% 157.56/27.35 | End of split
% 157.56/27.35 |
% 157.56/27.35 End of proof
% 157.56/27.35
% 157.56/27.35 Sub-proof #372 shows that the following formulas are inconsistent:
% 157.56/27.35 ----------------------------------------------------------------
% 157.56/27.35 (1) all_56_12 = all_10_2
% 157.56/27.35 (2) all_54_1 = all_52_4
% 157.56/27.35 (3) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.56/27.35 (4) ~ (all_52_4 = e2)
% 157.56/27.35 (5) all_56_12 = e1
% 157.56/27.35 (6) ~ (all_52_4 = all_10_2)
% 157.56/27.35 (7) ~ (all_52_4 = e0)
% 157.56/27.35 (8) ~ (all_52_4 = e3)
% 157.56/27.35
% 157.56/27.35 Begin of proof
% 157.56/27.35 |
% 157.56/27.35 | COMBINE_EQS: (1), (5) imply:
% 157.56/27.35 | (9) all_10_2 = e1
% 157.56/27.35 |
% 157.56/27.35 | REDUCE: (6), (9) imply:
% 157.56/27.35 | (10) ~ (all_52_4 = e1)
% 157.56/27.35 |
% 157.56/27.35 | BETA: splitting (3) gives:
% 157.56/27.35 |
% 157.56/27.35 | Case 1:
% 157.56/27.35 | |
% 157.56/27.35 | | (11) all_54_1 = e3
% 157.56/27.35 | |
% 157.56/27.35 | | COMBINE_EQS: (2), (11) imply:
% 157.56/27.35 | | (12) all_52_4 = e3
% 157.56/27.35 | |
% 157.56/27.35 | | REDUCE: (8), (12) imply:
% 157.56/27.35 | | (13) $false
% 157.56/27.35 | |
% 157.56/27.35 | | CLOSE: (13) is inconsistent.
% 157.56/27.35 | |
% 157.56/27.35 | Case 2:
% 157.56/27.35 | |
% 157.56/27.35 | | (14) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.56/27.35 | |
% 157.56/27.35 | | REF_CLOSE: (2), (4), (7), (10), (14) are inconsistent by sub-proof #1107.
% 157.56/27.35 | |
% 157.56/27.35 | End of split
% 157.56/27.35 |
% 157.56/27.35 End of proof
% 157.56/27.35
% 157.56/27.35 Sub-proof #373 shows that the following formulas are inconsistent:
% 157.56/27.35 ----------------------------------------------------------------
% 157.56/27.35 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.56/27.35 (2) ~ (all_52_12 = e3)
% 157.56/27.35 (3) all_58_13 = e0
% 157.56/27.35 (4) op(e0, e3) = all_52_3
% 157.56/27.35 (5) op(e3, e0) = all_52_12
% 157.56/27.35 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.56/27.35 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.56/27.35 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.56/27.35 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.56/27.35 (8) ~ (all_52_14 = e2)
% 157.56/27.35 (9) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.56/27.35 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.56/27.35 (10) ~ (all_52_12 = e2)
% 157.56/27.35 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.56/27.35 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.56/27.35 (12) op(e1, e1) = all_6_2
% 157.56/27.35 (13) ~ (all_52_7 = e3)
% 157.56/27.35 (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.56/27.35 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.56/27.35 e1)
% 157.56/27.35 (15) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.56/27.35 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.56/27.35 (16) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.56/27.35 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.56/27.35 (17) all_54_10 = all_6_2
% 157.56/27.35 (18) ~ (all_52_2 = all_52_3)
% 157.56/27.35 (19) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.56/27.35 (20) all_58_7 = e2
% 157.56/27.35 (21) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.56/27.35 (22) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.56/27.35 (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.56/27.35 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.56/27.35 (24) all_54_1 = all_52_4
% 157.56/27.35 (25) op(e3, e2) = all_52_4
% 157.56/27.35 (26) ~ (all_52_3 = e0)
% 157.56/27.35 (27) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.56/27.35 (28) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.56/27.35 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.56/27.35 (29) ~ (all_52_12 = all_52_13)
% 157.56/27.35 (30) ~ (all_52_4 = e2)
% 157.56/27.35 (31) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.56/27.35 (32) ~ (all_52_4 = all_52_12)
% 157.56/27.35 (33) op(e2, e1) = all_52_9
% 157.56/27.35 (34) op(e2, e3) = all_52_1
% 157.56/27.35 (35) ~ (all_52_13 = e3)
% 157.56/27.35 (36) ~ (all_52_3 = e3)
% 157.56/27.35 (37) ~ (all_52_2 = all_6_2)
% 157.56/27.35 (38) ~ (e3 = e0)
% 157.56/27.35 (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.56/27.35 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.56/27.35 (40) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.56/27.35 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.56/27.35 (41) ~ (all_52_9 = all_52_13)
% 157.56/27.35 (42) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.56/27.35 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.56/27.35 e2)
% 157.56/27.35 (43) ~ (e2 = e0)
% 157.56/27.35 (44) ~ (all_52_9 = e3)
% 157.56/27.35 (45) ~ (all_52_11 = all_6_2)
% 157.56/27.35 (46) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.56/27.35 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.56/27.35 (47) ~ (all_52_3 = e2)
% 157.56/27.35 (48) op(e2, e0) = all_52_13
% 157.56/27.35 (49) op(e2, e3) = e2
% 157.56/27.35 (50) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.56/27.35 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.56/27.35 (51) ~ (e3 = e1)
% 157.56/27.35 (52) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.56/27.35 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.56/27.35 (53) op(e1, e2) = all_52_6
% 157.56/27.35 (54) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.56/27.35 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.56/27.35 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.56/27.35 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.56/27.35 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.56/27.35 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.56/27.35 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.56/27.35 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.56/27.35 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.56/27.35 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.56/27.35 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.56/27.35 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.56/27.35 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.56/27.35 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.56/27.35 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.56/27.35 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.56/27.35 = e0)
% 157.56/27.35 (55) ~ (all_52_4 = e0)
% 157.56/27.35 (56) ~ (all_52_11 = e2)
% 157.56/27.35 (57) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.56/27.35 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.56/27.35 (58) ~ (all_52_9 = all_6_2)
% 157.56/27.35 (59) all_54_8 = all_52_2
% 157.56/27.35 (60) all_54_7 = all_52_13
% 157.56/27.35 (61) all_56_12 = e3
% 157.56/27.35 (62) ~ (all_52_2 = e3)
% 157.56/27.35 (63) ~ (all_52_13 = e2)
% 157.56/27.35 (64) op(e0, e0) = e2
% 157.56/27.35 (65) ~ (all_52_9 = all_52_11)
% 157.56/27.35 (66) all_58_4 = e2
% 157.56/27.35 (67) ~ (all_52_2 = all_52_14)
% 157.56/27.35 (68) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.56/27.35 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.56/27.35 (69) ~ (all_52_4 = e3)
% 157.56/27.35 (70) all_54_6 = all_52_9
% 157.56/27.35 (71) op(e0, e2) = e0
% 157.56/27.35 (72) all_58_15 = e2
% 157.56/27.35 (73) ~ (e2 = e1)
% 157.56/27.35 (74) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.56/27.35 (75) op(e3, e3) = e3
% 157.56/27.35 (76) all_54_3 = all_52_12
% 157.56/27.35 (77) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.56/27.35 (78) ~ (e1 = e0)
% 157.56/27.35 (79) ~ (all_52_2 = e2)
% 157.56/27.35 (80) all_58_3 = e3
% 157.56/27.35 (81) ~ (all_6_2 = e2)
% 157.56/27.35 (82) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.56/27.35 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.56/27.35 e3)
% 157.56/27.35 (83) all_56_14 = all_6_2
% 157.56/27.35 (84) all_56_13 = e3
% 157.56/27.35 (85) ~ (all_52_12 = all_52_14)
% 157.56/27.35 (86) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.56/27.35 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.56/27.35 (87) ~ (all_52_9 = e2)
% 157.56/27.35 (88) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.56/27.35 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.56/27.35 (89) all_54_14 = all_52_11
% 157.56/27.35 (90) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.56/27.35 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 157.56/27.35 e3) = all_22_1 & $i(all_22_1))
% 157.56/27.35 (91) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.56/27.35 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.56/27.35 (92) op(e0, e2) = all_52_7
% 157.56/27.35 (93) op(e1, e0) = all_52_14
% 157.56/27.35 (94) all_56_15 = e2
% 157.56/27.35 (95) ~ (all_52_6 = e3)
% 157.56/27.35 (96) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.56/27.35 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.56/27.35 (97) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.56/27.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.56/27.35 (98) ~ (all_52_3 = all_52_11)
% 157.56/27.35 (99) all_54_11 = all_52_14
% 157.56/27.35 (100) ~ (all_52_13 = all_52_14)
% 157.56/27.35 (101) ~ (e3 = e2)
% 157.56/27.35 (102) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.56/27.35 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.56/27.35 (103) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.56/27.35 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.56/27.35 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.56/27.35 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.56/27.35 e0)))
% 157.56/27.35 (104) ~ (all_52_11 = e0)
% 157.56/27.35 (105) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.56/27.35 (106) all_54_12 = all_52_3
% 157.56/27.35 (107) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.56/27.35
% 157.56/27.35 Begin of proof
% 157.56/27.35 |
% 157.56/27.35 | BETA: splitting (82) gives:
% 157.56/27.35 |
% 157.56/27.35 | Case 1:
% 157.56/27.35 | |
% 157.56/27.35 | | (108) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 157.56/27.35 | | e3)
% 157.56/27.35 | |
% 157.56/27.35 | | BETA: splitting (108) gives:
% 157.56/27.35 | |
% 157.56/27.35 | | Case 1:
% 157.56/27.35 | | |
% 157.56/27.35 | | | (109) all_58_12 = e3 & op(e0, e3) = e3
% 157.56/27.35 | | |
% 157.56/27.35 | | | ALPHA: (109) implies:
% 157.56/27.35 | | | (110) all_58_12 = e3
% 157.56/27.35 | | |
% 157.56/27.35 | | | BETA: splitting (102) gives:
% 157.56/27.35 | | |
% 157.56/27.35 | | | Case 1:
% 157.56/27.35 | | | |
% 157.56/27.35 | | | | (111) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 157.56/27.35 | | | | = e0)
% 157.56/27.35 | | | |
% 157.56/27.35 | | | | BETA: splitting (111) gives:
% 157.56/27.35 | | | |
% 157.56/27.35 | | | | Case 1:
% 157.56/27.35 | | | | |
% 157.56/27.35 | | | | | (112) all_58_0 = e0 & op(e3, e3) = e0
% 157.56/27.35 | | | | |
% 157.56/27.35 | | | | | ALPHA: (112) implies:
% 157.56/27.35 | | | | | (113) all_58_0 = e0
% 157.56/27.35 | | | | | (114) op(e3, e3) = e0
% 157.56/27.35 | | | | |
% 157.56/27.35 | | | | | BETA: splitting (15) gives:
% 157.56/27.35 | | | | |
% 157.56/27.35 | | | | | Case 1:
% 157.56/27.35 | | | | | |
% 157.56/27.35 | | | | | | (115) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 157.56/27.35 | | | | | | op(e2, e0) = e3)
% 157.56/27.35 | | | | | |
% 157.56/27.35 | | | | | | BETA: splitting (115) gives:
% 157.56/27.35 | | | | | |
% 157.56/27.35 | | | | | | Case 1:
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | (116) all_58_9 = e3 & op(e3, e0) = e3
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | ALPHA: (116) implies:
% 157.56/27.35 | | | | | | | (117) all_58_9 = e3
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | BETA: splitting (105) gives:
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | Case 1:
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | | (118) all_54_12 = e3
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | | REF_CLOSE: (36), (106), (118) are inconsistent by sub-proof
% 157.56/27.35 | | | | | | | | #1234.
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | Case 2:
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | | (119) ~ (all_54_12 = e3)
% 157.56/27.35 | | | | | | | | (120) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | | BETA: splitting (90) gives:
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | | Case 1:
% 157.56/27.35 | | | | | | | | |
% 157.56/27.35 | | | | | | | | | (121) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 157.56/27.35 | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 157.56/27.35 | | | | | | | | |
% 157.56/27.35 | | | | | | | | | ALPHA: (121) implies:
% 157.56/27.35 | | | | | | | | | (122) op(e3, e3) = all_22_1
% 157.56/27.35 | | | | | | | | |
% 157.56/27.35 | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (12),
% 157.56/27.35 | | | | | | | | | (16), (17), (18), (19), (20), (21), (22), (23),
% 157.56/27.35 | | | | | | | | | (24), (26), (27), (28), (29), (30), (31), (32),
% 157.56/27.35 | | | | | | | | | (33), (34), (35), (36), (37), (38), (39), (43),
% 157.56/27.35 | | | | | | | | | (44), (45), (46), (47), (49), (51), (53), (55),
% 157.56/27.35 | | | | | | | | | (56), (57), (58), (59), (60), (62), (63), (64),
% 157.56/27.35 | | | | | | | | | (66), (68), (69), (70), (73), (74), (75), (76),
% 157.56/27.35 | | | | | | | | | (77), (78), (79), (80), (81), (83), (85), (86),
% 157.56/27.35 | | | | | | | | | (87), (89), (93), (95), (96), (97), (98), (99),
% 157.56/27.35 | | | | | | | | | (100), (101), (104), (106), (107), (110), (113),
% 157.56/27.35 | | | | | | | | | (114), (117), (120), (122) are inconsistent by
% 157.56/27.35 | | | | | | | | | sub-proof #406.
% 157.56/27.35 | | | | | | | | |
% 157.56/27.35 | | | | | | | | Case 2:
% 157.56/27.35 | | | | | | | | |
% 157.56/27.35 | | | | | | | | | (123) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 157.56/27.35 | | | | | | | | | $i(all_22_1)
% 157.56/27.35 | | | | | | | | |
% 157.56/27.35 | | | | | | | | | ALPHA: (123) implies:
% 157.56/27.35 | | | | | | | | | (124) op(e3, e3) = all_22_1
% 157.56/27.35 | | | | | | | | |
% 157.56/27.35 | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (12),
% 157.56/27.35 | | | | | | | | | (16), (17), (18), (19), (20), (21), (22), (23),
% 157.56/27.35 | | | | | | | | | (24), (26), (27), (28), (29), (30), (31), (32),
% 157.56/27.35 | | | | | | | | | (33), (34), (35), (36), (37), (38), (39), (43),
% 157.56/27.35 | | | | | | | | | (44), (45), (46), (47), (49), (51), (53), (55),
% 157.56/27.35 | | | | | | | | | (56), (57), (58), (59), (60), (62), (63), (64),
% 157.56/27.35 | | | | | | | | | (66), (68), (69), (70), (73), (74), (75), (76),
% 157.56/27.35 | | | | | | | | | (77), (78), (79), (80), (81), (83), (85), (86),
% 157.56/27.35 | | | | | | | | | (87), (89), (93), (95), (96), (97), (98), (99),
% 157.56/27.35 | | | | | | | | | (100), (101), (104), (106), (107), (110), (113),
% 157.56/27.35 | | | | | | | | | (114), (117), (120), (124) are inconsistent by
% 157.56/27.35 | | | | | | | | | sub-proof #406.
% 157.56/27.35 | | | | | | | | |
% 157.56/27.35 | | | | | | | | End of split
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | End of split
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | Case 2:
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | (125) all_58_10 = e3 & op(e2, e0) = e3
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | ALPHA: (125) implies:
% 157.56/27.35 | | | | | | | (126) op(e2, e0) = e3
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | REF_CLOSE: (35), (48), (97), (126) are inconsistent by sub-proof
% 157.56/27.35 | | | | | | | #1364.
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | End of split
% 157.56/27.35 | | | | | |
% 157.56/27.35 | | | | | Case 2:
% 157.56/27.35 | | | | | |
% 157.56/27.35 | | | | | | (127) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 157.56/27.35 | | | | | | op(e0, e0) = e3)
% 157.56/27.35 | | | | | |
% 157.56/27.35 | | | | | | BETA: splitting (127) gives:
% 157.56/27.35 | | | | | |
% 157.56/27.35 | | | | | | Case 1:
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | (128) all_58_11 = e3 & op(e1, e0) = e3
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | ALPHA: (128) implies:
% 157.56/27.35 | | | | | | | (129) all_58_11 = e3
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | BETA: splitting (90) gives:
% 157.56/27.35 | | | | | | |
% 157.56/27.35 | | | | | | | Case 1:
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | | (130) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 157.56/27.35 | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 157.56/27.35 | | | | | | | |
% 157.56/27.35 | | | | | | | | ALPHA: (130) implies:
% 157.56/27.35 | | | | | | | | (131) op(e3, e3) = all_22_1
% 157.56/27.35 | | | | | | | |
% 157.56/27.36 | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (13), (14), (15),
% 157.56/27.36 | | | | | | | | (16), (20), (21), (23), (24), (25), (27), (28), (29),
% 157.56/27.36 | | | | | | | | (30), (31), (32), (33), (34), (35), (38), (39), (40),
% 157.56/27.36 | | | | | | | | (42), (43), (44), (46), (48), (49), (50), (53), (55),
% 157.56/27.36 | | | | | | | | (57), (60), (63), (64), (66), (68), (69), (71), (72),
% 157.56/27.36 | | | | | | | | (75), (76), (80), (82), (86), (88), (91), (92), (95),
% 157.56/27.36 | | | | | | | | (96), (97), (101), (103), (110), (113), (129), (131)
% 157.56/27.36 | | | | | | | | are inconsistent by sub-proof #403.
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | Case 2:
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | (132) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 157.56/27.36 | | | | | | | | $i(all_22_1)
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | ALPHA: (132) implies:
% 157.56/27.36 | | | | | | | | (133) op(e3, e3) = all_22_1
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (13), (14), (15),
% 157.56/27.36 | | | | | | | | (16), (20), (21), (23), (24), (25), (27), (28), (29),
% 157.56/27.36 | | | | | | | | (30), (31), (32), (33), (34), (35), (38), (39), (40),
% 157.56/27.36 | | | | | | | | (42), (43), (44), (46), (48), (49), (50), (53), (55),
% 157.56/27.36 | | | | | | | | (57), (60), (63), (64), (66), (68), (69), (71), (72),
% 157.56/27.36 | | | | | | | | (75), (76), (80), (82), (86), (88), (91), (92), (95),
% 157.56/27.36 | | | | | | | | (96), (97), (101), (103), (110), (113), (129), (133)
% 157.56/27.36 | | | | | | | | are inconsistent by sub-proof #403.
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | End of split
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | Case 2:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | (134) all_58_15 = e3 & op(e0, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | ALPHA: (134) implies:
% 157.56/27.36 | | | | | | | (135) op(e0, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | REF_CLOSE: (64), (97), (101), (135) are inconsistent by sub-proof
% 157.56/27.36 | | | | | | | #1382.
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | End of split
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | End of split
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | Case 2:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | (136) all_58_1 = e0 & op(e3, e2) = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | ALPHA: (136) implies:
% 157.56/27.36 | | | | | (137) all_58_1 = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | REF_CLOSE: (2), (6), (7), (8), (9), (10), (13), (14), (15), (16),
% 157.56/27.36 | | | | | (20), (21), (23), (24), (25), (27), (28), (29), (30), (31),
% 157.56/27.36 | | | | | (32), (33), (34), (35), (38), (39), (40), (42), (43), (44),
% 157.56/27.36 | | | | | (48), (49), (50), (51), (53), (55), (57), (60), (63), (64),
% 157.56/27.36 | | | | | (66), (68), (69), (71), (72), (73), (76), (77), (78), (80),
% 157.56/27.36 | | | | | (82), (85), (86), (88), (91), (92), (93), (95), (96), (97),
% 157.56/27.36 | | | | | (99), (100), (101), (103), (110), (137) are inconsistent by
% 157.56/27.36 | | | | | sub-proof #399.
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | End of split
% 157.56/27.36 | | | |
% 157.56/27.36 | | | Case 2:
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | (138) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 157.56/27.36 | | | | = e0)
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | BETA: splitting (138) gives:
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | Case 1:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | (139) all_58_4 = e0 & op(e3, e1) = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | ALPHA: (139) implies:
% 157.56/27.36 | | | | | (140) all_58_4 = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | REF_CLOSE: (43), (66), (140) are inconsistent by sub-proof #1447.
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | Case 2:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | (141) all_58_9 = e0 & op(e3, e0) = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | ALPHA: (141) implies:
% 157.56/27.36 | | | | | (142) all_58_9 = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | BETA: splitting (15) gives:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | Case 1:
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | (143) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 157.56/27.36 | | | | | | op(e2, e0) = e3)
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | REF_CLOSE: (35), (38), (48), (97), (142), (143) are inconsistent by
% 157.56/27.36 | | | | | | sub-proof #398.
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | Case 2:
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | (144) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 157.56/27.36 | | | | | | op(e0, e0) = e3)
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | BETA: splitting (144) gives:
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | Case 1:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | (145) all_58_11 = e3 & op(e1, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | ALPHA: (145) implies:
% 157.56/27.36 | | | | | | | (146) all_58_11 = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | BETA: splitting (90) gives:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | Case 1:
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | (147) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 157.56/27.36 | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | ALPHA: (147) implies:
% 157.56/27.36 | | | | | | | | (148) op(e3, e3) = all_22_1
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (13), (14),
% 157.56/27.36 | | | | | | | | (15), (16), (20), (21), (23), (24), (25), (27), (28),
% 157.56/27.36 | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (38), (39),
% 157.56/27.36 | | | | | | | | (40), (42), (43), (44), (46), (48), (49), (50), (53),
% 157.56/27.36 | | | | | | | | (55), (57), (60), (63), (64), (66), (68), (69), (71),
% 157.56/27.36 | | | | | | | | (72), (76), (77), (80), (82), (85), (86), (88), (91),
% 157.56/27.36 | | | | | | | | (92), (93), (95), (96), (97), (99), (100), (101),
% 157.56/27.36 | | | | | | | | (103), (110), (142), (146), (148) are inconsistent by
% 157.56/27.36 | | | | | | | | sub-proof #396.
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | Case 2:
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | (149) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 157.56/27.36 | | | | | | | | $i(all_22_1)
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | ALPHA: (149) implies:
% 157.56/27.36 | | | | | | | | (150) op(e3, e3) = all_22_1
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (13), (14),
% 157.56/27.36 | | | | | | | | (15), (16), (20), (21), (23), (24), (25), (27), (28),
% 157.56/27.36 | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (38), (39),
% 157.56/27.36 | | | | | | | | (40), (42), (43), (44), (46), (48), (49), (50), (53),
% 157.56/27.36 | | | | | | | | (55), (57), (60), (63), (64), (66), (68), (69), (71),
% 157.56/27.36 | | | | | | | | (72), (76), (77), (80), (82), (85), (86), (88), (91),
% 157.56/27.36 | | | | | | | | (92), (93), (95), (96), (97), (99), (100), (101),
% 157.56/27.36 | | | | | | | | (103), (110), (142), (146), (150) are inconsistent by
% 157.56/27.36 | | | | | | | | sub-proof #396.
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | End of split
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | Case 2:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | (151) all_58_15 = e3 & op(e0, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | ALPHA: (151) implies:
% 157.56/27.36 | | | | | | | (152) op(e0, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | REF_CLOSE: (64), (97), (101), (152) are inconsistent by sub-proof
% 157.56/27.36 | | | | | | | #1382.
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | End of split
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | End of split
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | End of split
% 157.56/27.36 | | | |
% 157.56/27.36 | | | End of split
% 157.56/27.36 | | |
% 157.56/27.36 | | Case 2:
% 157.56/27.36 | | |
% 157.56/27.36 | | | (153) all_58_13 = e3 & op(e0, e2) = e3
% 157.56/27.36 | | |
% 157.56/27.36 | | | REF_CLOSE: (13), (92), (97), (153) are inconsistent by sub-proof #1449.
% 157.56/27.36 | | |
% 157.56/27.36 | | End of split
% 157.56/27.36 | |
% 157.56/27.36 | Case 2:
% 157.56/27.36 | |
% 157.56/27.36 | | (154) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.56/27.36 | | e3)
% 157.56/27.36 | |
% 157.56/27.36 | | BETA: splitting (154) gives:
% 157.56/27.36 | |
% 157.56/27.36 | | Case 1:
% 157.56/27.36 | | |
% 157.56/27.36 | | | (155) all_58_14 = e3 & op(e0, e1) = e3
% 157.56/27.36 | | |
% 157.56/27.36 | | | ALPHA: (155) implies:
% 157.56/27.36 | | | (156) all_58_14 = e3
% 157.56/27.36 | | |
% 157.56/27.36 | | | BETA: splitting (102) gives:
% 157.56/27.36 | | |
% 157.56/27.36 | | | Case 1:
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | (157) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 157.56/27.36 | | | | = e0)
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | BETA: splitting (157) gives:
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | Case 1:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | (158) all_58_0 = e0 & op(e3, e3) = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | ALPHA: (158) implies:
% 157.56/27.36 | | | | | (159) all_58_0 = e0
% 157.56/27.36 | | | | | (160) op(e3, e3) = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | BETA: splitting (15) gives:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | Case 1:
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | (161) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 157.56/27.36 | | | | | | op(e2, e0) = e3)
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | BETA: splitting (161) gives:
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | Case 1:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | (162) all_58_9 = e3 & op(e3, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | ALPHA: (162) implies:
% 157.56/27.36 | | | | | | | (163) all_58_9 = e3
% 157.56/27.36 | | | | | | | (164) op(e3, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.56/27.36 | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 157.56/27.36 | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 157.56/27.36 | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 157.56/27.36 | | | | | | | (39), (40), (41), (42), (43), (45), (46), (47), (48),
% 157.56/27.36 | | | | | | | (49), (50), (52), (53), (54), (55), (56), (57), (58),
% 157.56/27.36 | | | | | | | (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 157.56/27.36 | | | | | | | (68), (69), (70), (71), (72), (74), (75), (76), (77),
% 157.56/27.36 | | | | | | | (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 157.56/27.36 | | | | | | | (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 157.56/27.36 | | | | | | | (97), (98), (99), (100), (103), (104), (105), (106),
% 157.56/27.36 | | | | | | | (107), (156), (159), (160), (163), (164) are
% 157.56/27.36 | | | | | | | inconsistent by sub-proof #374.
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | Case 2:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | (165) all_58_10 = e3 & op(e2, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | ALPHA: (165) implies:
% 157.56/27.36 | | | | | | | (166) op(e2, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | REF_CLOSE: (35), (48), (97), (166) are inconsistent by sub-proof
% 157.56/27.36 | | | | | | | #1364.
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | End of split
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | Case 2:
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | (167) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 157.56/27.36 | | | | | | op(e0, e0) = e3)
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | BETA: splitting (167) gives:
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | | Case 1:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | (168) all_58_11 = e3 & op(e1, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | ALPHA: (168) implies:
% 157.56/27.36 | | | | | | | (169) all_58_11 = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | BETA: splitting (91) gives:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | Case 1:
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | (170) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 157.56/27.36 | | | | | | | | op(e3, e2) = e3)
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | REF_CLOSE: (25), (38), (69), (97), (159), (170) are inconsistent
% 157.56/27.36 | | | | | | | | by sub-proof #645.
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | Case 2:
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | (171) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 157.56/27.36 | | | | | | | | op(e3, e0) = e3)
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | BETA: splitting (171) gives:
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | | Case 1:
% 157.56/27.36 | | | | | | | | |
% 157.56/27.36 | | | | | | | | | (172) all_58_4 = e3 & op(e3, e1) = e3
% 157.56/27.36 | | | | | | | | |
% 157.56/27.36 | | | | | | | | | REF_CLOSE: (6), (9), (13), (14), (15), (23), (28), (34), (35),
% 157.56/27.36 | | | | | | | | | (38), (39), (40), (42), (43), (48), (49), (50),
% 157.56/27.36 | | | | | | | | | (51), (53), (57), (64), (66), (68), (71), (73),
% 157.56/27.36 | | | | | | | | | (78), (80), (82), (88), (92), (95), (96), (97),
% 157.56/27.36 | | | | | | | | | (101), (103), (169), (172) are inconsistent by
% 157.56/27.36 | | | | | | | | | sub-proof #644.
% 157.56/27.36 | | | | | | | | |
% 157.56/27.36 | | | | | | | | Case 2:
% 157.56/27.36 | | | | | | | | |
% 157.56/27.36 | | | | | | | | | (173) all_58_9 = e3 & op(e3, e0) = e3
% 157.56/27.36 | | | | | | | | |
% 157.56/27.36 | | | | | | | | | ALPHA: (173) implies:
% 157.56/27.36 | | | | | | | | | (174) all_58_9 = e3
% 157.56/27.36 | | | | | | | | | (175) op(e3, e0) = e3
% 157.56/27.36 | | | | | | | | |
% 157.56/27.36 | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.56/27.36 | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 157.56/27.36 | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 157.56/27.36 | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 157.56/27.36 | | | | | | | | | (35), (36), (37), (39), (40), (41), (42), (43),
% 157.56/27.36 | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (53),
% 157.56/27.36 | | | | | | | | | (54), (55), (56), (57), (58), (59), (60), (61),
% 157.56/27.36 | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 157.56/27.36 | | | | | | | | | (70), (71), (72), (74), (75), (76), (77), (79),
% 157.56/27.36 | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 157.56/27.36 | | | | | | | | | (88), (89), (90), (91), (92), (93), (94), (95),
% 157.56/27.36 | | | | | | | | | (96), (97), (98), (99), (100), (103), (104), (105),
% 157.56/27.36 | | | | | | | | | (106), (107), (156), (159), (160), (174), (175) are
% 157.56/27.36 | | | | | | | | | inconsistent by sub-proof #374.
% 157.56/27.36 | | | | | | | | |
% 157.56/27.36 | | | | | | | | End of split
% 157.56/27.36 | | | | | | | |
% 157.56/27.36 | | | | | | | End of split
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | Case 2:
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | (176) all_58_15 = e3 & op(e0, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | ALPHA: (176) implies:
% 157.56/27.36 | | | | | | | (177) op(e0, e0) = e3
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | | REF_CLOSE: (64), (97), (101), (177) are inconsistent by sub-proof
% 157.56/27.36 | | | | | | | #1382.
% 157.56/27.36 | | | | | | |
% 157.56/27.36 | | | | | | End of split
% 157.56/27.36 | | | | | |
% 157.56/27.36 | | | | | End of split
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | Case 2:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | (178) all_58_1 = e0 & op(e3, e2) = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | ALPHA: (178) implies:
% 157.56/27.36 | | | | | (179) all_58_1 = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | REF_CLOSE: (3), (7), (20), (51), (73), (78), (80), (179) are
% 157.56/27.36 | | | | | inconsistent by sub-proof #857.
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | End of split
% 157.56/27.36 | | | |
% 157.56/27.36 | | | Case 2:
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | (180) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 157.56/27.36 | | | | = e0)
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | BETA: splitting (180) gives:
% 157.56/27.36 | | | |
% 157.56/27.36 | | | | Case 1:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | (181) all_58_4 = e0 & op(e3, e1) = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | ALPHA: (181) implies:
% 157.56/27.36 | | | | | (182) all_58_4 = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | REF_CLOSE: (43), (66), (182) are inconsistent by sub-proof #1447.
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | Case 2:
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | (183) all_58_9 = e0 & op(e3, e0) = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | ALPHA: (183) implies:
% 157.56/27.36 | | | | | (184) all_58_9 = e0
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 157.56/27.36 | | | | | (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 157.56/27.36 | | | | | (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 157.56/27.36 | | | | | (37), (38), (39), (40), (42), (43), (45), (46), (47), (48),
% 157.56/27.36 | | | | | (49), (50), (52), (53), (54), (55), (56), (57), (59), (60),
% 157.56/27.36 | | | | | (61), (62), (63), (64), (66), (68), (69), (71), (72), (74),
% 157.56/27.36 | | | | | (76), (77), (79), (80), (81), (82), (83), (85), (86), (88),
% 157.56/27.36 | | | | | (89), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 157.56/27.36 | | | | | (100), (101), (103), (104), (105), (106), (107), (156),
% 157.56/27.36 | | | | | (184) are inconsistent by sub-proof #383.
% 157.56/27.36 | | | | |
% 157.56/27.36 | | | | End of split
% 157.56/27.36 | | | |
% 157.56/27.36 | | | End of split
% 157.56/27.36 | | |
% 157.56/27.36 | | Case 2:
% 157.56/27.36 | | |
% 157.56/27.36 | | | (185) all_58_15 = e3 & op(e0, e0) = e3
% 157.56/27.36 | | |
% 157.56/27.36 | | | ALPHA: (185) implies:
% 157.56/27.36 | | | (186) op(e0, e0) = e3
% 157.56/27.36 | | |
% 157.56/27.36 | | | REF_CLOSE: (64), (97), (101), (186) are inconsistent by sub-proof #1382.
% 157.56/27.36 | | |
% 157.56/27.36 | | End of split
% 157.56/27.36 | |
% 157.56/27.36 | End of split
% 157.56/27.36 |
% 157.56/27.36 End of proof
% 157.56/27.36
% 157.56/27.36 Sub-proof #374 shows that the following formulas are inconsistent:
% 157.56/27.36 ----------------------------------------------------------------
% 157.56/27.36 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.56/27.36 (2) ~ (all_52_12 = e3)
% 157.56/27.36 (3) all_58_13 = e0
% 157.56/27.36 (4) op(e0, e3) = all_52_3
% 157.56/27.36 (5) op(e3, e0) = all_52_12
% 157.56/27.36 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.56/27.36 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.56/27.36 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.56/27.36 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.56/27.36 (8) ~ (all_52_14 = e2)
% 157.56/27.36 (9) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.56/27.36 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.56/27.36 (10) ~ (all_52_12 = e2)
% 157.56/27.36 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.56/27.36 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.56/27.36 (12) all_58_14 = e3
% 157.56/27.36 (13) op(e1, e1) = all_6_2
% 157.56/27.36 (14) ~ (all_52_7 = e3)
% 157.56/27.36 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.56/27.36 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.56/27.36 e1)
% 157.56/27.36 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.56/27.36 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.56/27.36 (17) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.56/27.36 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.56/27.36 (18) all_54_10 = all_6_2
% 157.56/27.36 (19) ~ (all_52_2 = all_52_3)
% 157.56/27.36 (20) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.56/27.36 (21) all_58_7 = e2
% 157.56/27.36 (22) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.56/27.36 (23) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.56/27.36 (24) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.56/27.36 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.56/27.36 (25) all_54_1 = all_52_4
% 157.56/27.36 (26) op(e3, e2) = all_52_4
% 157.56/27.36 (27) ~ (all_52_3 = e0)
% 157.56/27.36 (28) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.56/27.36 (29) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.56/27.36 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.56/27.36 (30) ~ (all_52_12 = all_52_13)
% 157.56/27.36 (31) ~ (all_52_4 = e2)
% 157.56/27.36 (32) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.56/27.36 (33) ~ (all_52_4 = all_52_12)
% 157.56/27.36 (34) op(e2, e1) = all_52_9
% 157.56/27.36 (35) op(e2, e3) = all_52_1
% 157.56/27.36 (36) ~ (all_52_13 = e3)
% 157.56/27.36 (37) ~ (all_52_3 = e3)
% 157.56/27.36 (38) ~ (all_52_2 = all_6_2)
% 157.56/27.36 (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.56/27.36 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.56/27.36 (40) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.56/27.36 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.56/27.36 (41) ~ (all_52_9 = all_52_13)
% 157.56/27.36 (42) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.56/27.36 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.56/27.36 e2)
% 157.56/27.36 (43) ~ (e2 = e0)
% 157.56/27.36 (44) op(e3, e3) = e0
% 157.56/27.36 (45) ~ (all_52_11 = all_6_2)
% 157.56/27.36 (46) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.56/27.36 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.56/27.36 (47) ~ (all_52_3 = e2)
% 157.56/27.36 (48) all_58_9 = e3
% 157.56/27.36 (49) op(e2, e0) = all_52_13
% 157.56/27.36 (50) op(e2, e3) = e2
% 157.56/27.36 (51) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.56/27.36 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.56/27.36 (52) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.56/27.36 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.56/27.36 (53) op(e1, e2) = all_52_6
% 157.68/27.36 (54) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.68/27.36 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.68/27.36 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.68/27.36 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.68/27.36 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.68/27.36 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.68/27.36 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.68/27.36 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.68/27.36 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.68/27.36 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.68/27.36 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.68/27.36 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.68/27.36 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.68/27.36 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.68/27.36 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.68/27.36 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.68/27.36 = e0)
% 157.68/27.36 (55) ~ (all_52_4 = e0)
% 157.68/27.36 (56) ~ (all_52_11 = e2)
% 157.68/27.36 (57) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.36 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.68/27.36 (58) ~ (all_52_9 = all_6_2)
% 157.68/27.36 (59) all_54_8 = all_52_2
% 157.68/27.36 (60) all_54_7 = all_52_13
% 157.68/27.36 (61) all_56_12 = e3
% 157.68/27.36 (62) ~ (all_52_2 = e3)
% 157.68/27.36 (63) ~ (all_52_13 = e2)
% 157.68/27.36 (64) op(e0, e0) = e2
% 157.68/27.36 (65) ~ (all_52_9 = all_52_11)
% 157.68/27.36 (66) all_58_4 = e2
% 157.68/27.36 (67) ~ (all_52_2 = all_52_14)
% 157.68/27.36 (68) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.68/27.36 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.36 (69) ~ (all_52_4 = e3)
% 157.68/27.36 (70) all_54_6 = all_52_9
% 157.68/27.36 (71) op(e0, e2) = e0
% 157.68/27.36 (72) all_58_15 = e2
% 157.68/27.36 (73) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.68/27.36 (74) op(e3, e3) = e3
% 157.68/27.36 (75) all_54_3 = all_52_12
% 157.68/27.36 (76) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.68/27.36 (77) ~ (all_52_2 = e2)
% 157.68/27.36 (78) all_58_3 = e3
% 157.68/27.36 (79) ~ (all_6_2 = e2)
% 157.68/27.36 (80) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.68/27.36 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.68/27.36 e3)
% 157.68/27.36 (81) all_56_14 = all_6_2
% 157.68/27.36 (82) all_56_13 = e3
% 157.68/27.36 (83) op(e3, e0) = e3
% 157.68/27.36 (84) ~ (all_52_12 = all_52_14)
% 157.68/27.36 (85) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.68/27.36 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.68/27.36 (86) ~ (all_52_9 = e2)
% 157.68/27.36 (87) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.68/27.36 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.36 (88) all_54_14 = all_52_11
% 157.68/27.36 (89) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.68/27.36 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 157.68/27.36 e3) = all_22_1 & $i(all_22_1))
% 157.68/27.36 (90) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.68/27.36 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.68/27.36 (91) op(e0, e2) = all_52_7
% 157.68/27.36 (92) op(e1, e0) = all_52_14
% 157.68/27.36 (93) all_58_0 = e0
% 157.68/27.36 (94) all_56_15 = e2
% 157.68/27.36 (95) ~ (all_52_6 = e3)
% 157.68/27.36 (96) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.68/27.36 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.68/27.36 (97) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.36 (98) ~ (all_52_3 = all_52_11)
% 157.68/27.36 (99) all_54_11 = all_52_14
% 157.68/27.36 (100) ~ (all_52_13 = all_52_14)
% 157.68/27.36 (101) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.68/27.36 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.68/27.36 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.68/27.36 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.68/27.36 e0)))
% 157.68/27.36 (102) ~ (all_52_11 = e0)
% 157.68/27.36 (103) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.68/27.36 (104) all_54_12 = all_52_3
% 157.68/27.36 (105) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.68/27.36
% 157.68/27.36 Begin of proof
% 157.68/27.36 |
% 157.68/27.36 | BETA: splitting (103) gives:
% 157.68/27.36 |
% 157.68/27.36 | Case 1:
% 157.68/27.36 | |
% 157.68/27.36 | | (106) all_54_12 = e3
% 157.68/27.36 | |
% 157.68/27.36 | | REF_CLOSE: (37), (104), (106) are inconsistent by sub-proof #1234.
% 157.68/27.36 | |
% 157.68/27.36 | Case 2:
% 157.68/27.36 | |
% 157.68/27.36 | | (107) ~ (all_54_12 = e3)
% 157.68/27.36 | | (108) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.68/27.36 | |
% 157.68/27.36 | | BETA: splitting (89) gives:
% 157.68/27.36 | |
% 157.68/27.36 | | Case 1:
% 157.68/27.36 | | |
% 157.68/27.36 | | | (109) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.68/27.36 | | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 157.68/27.36 | | |
% 157.68/27.36 | | | ALPHA: (109) implies:
% 157.68/27.36 | | | (110) op(e3, e3) = all_22_1
% 157.68/27.36 | | |
% 157.68/27.36 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.68/27.36 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.68/27.37 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 157.68/27.37 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 157.68/27.37 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 157.68/27.37 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 157.68/27.37 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 157.68/27.37 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 157.68/27.37 | | | (83), (84), (85), (86), (87), (88), (90), (91), (92), (93),
% 157.68/27.37 | | | (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 157.68/27.37 | | | (104), (105), (108), (110) are inconsistent by sub-proof #375.
% 157.68/27.37 | | |
% 157.68/27.37 | | Case 2:
% 157.68/27.37 | | |
% 157.68/27.37 | | | (111) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 157.68/27.37 | | |
% 157.68/27.37 | | | ALPHA: (111) implies:
% 157.68/27.37 | | | (112) op(e3, e3) = all_22_1
% 157.68/27.37 | | |
% 157.68/27.37 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.68/27.37 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.68/27.37 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 157.68/27.37 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 157.68/27.37 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 157.68/27.37 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 157.68/27.37 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 157.68/27.37 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 157.68/27.37 | | | (83), (84), (85), (86), (87), (88), (90), (91), (92), (93),
% 157.68/27.37 | | | (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 157.68/27.37 | | | (104), (105), (108), (112) are inconsistent by sub-proof #375.
% 157.68/27.37 | | |
% 157.68/27.37 | | End of split
% 157.68/27.37 | |
% 157.68/27.37 | End of split
% 157.68/27.37 |
% 157.68/27.37 End of proof
% 157.68/27.37
% 157.68/27.37 Sub-proof #375 shows that the following formulas are inconsistent:
% 157.68/27.37 ----------------------------------------------------------------
% 157.68/27.37 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.68/27.37 (2) ~ (all_52_12 = e3)
% 157.68/27.37 (3) all_58_13 = e0
% 157.68/27.37 (4) op(e0, e3) = all_52_3
% 157.68/27.37 (5) op(e3, e0) = all_52_12
% 157.68/27.37 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.68/27.37 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.68/27.37 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.37 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.37 (8) ~ (all_52_14 = e2)
% 157.68/27.37 (9) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.68/27.37 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.37 (10) ~ (all_52_12 = e2)
% 157.68/27.37 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.37 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.68/27.37 (12) all_58_14 = e3
% 157.68/27.37 (13) op(e1, e1) = all_6_2
% 157.68/27.37 (14) ~ (all_52_7 = e3)
% 157.68/27.37 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.37 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.68/27.37 e1)
% 157.68/27.37 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.68/27.37 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.68/27.37 (17) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.68/27.37 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.68/27.37 (18) all_54_10 = all_6_2
% 157.68/27.37 (19) ~ (all_52_2 = all_52_3)
% 157.68/27.37 (20) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.68/27.37 (21) all_58_7 = e2
% 157.68/27.37 (22) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.68/27.37 (23) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.68/27.37 (24) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.68/27.37 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.68/27.37 (25) all_54_1 = all_52_4
% 157.68/27.37 (26) op(e3, e2) = all_52_4
% 157.68/27.37 (27) ~ (all_52_3 = e0)
% 157.68/27.37 (28) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.68/27.37 (29) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.68/27.37 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.68/27.37 (30) ~ (all_52_12 = all_52_13)
% 157.68/27.37 (31) ~ (all_52_4 = e2)
% 157.68/27.37 (32) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.37 (33) ~ (all_52_4 = all_52_12)
% 157.68/27.37 (34) op(e2, e1) = all_52_9
% 157.68/27.37 (35) op(e2, e3) = all_52_1
% 157.68/27.37 (36) ~ (all_52_13 = e3)
% 157.68/27.37 (37) ~ (all_52_3 = e3)
% 157.68/27.37 (38) ~ (all_52_2 = all_6_2)
% 157.68/27.37 (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.68/27.37 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.68/27.37 (40) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.68/27.37 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.68/27.37 (41) ~ (all_52_9 = all_52_13)
% 157.68/27.37 (42) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.37 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.68/27.37 e2)
% 157.68/27.37 (43) ~ (e2 = e0)
% 157.68/27.37 (44) op(e3, e3) = e0
% 157.68/27.37 (45) ~ (all_52_11 = all_6_2)
% 157.68/27.37 (46) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.68/27.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.68/27.37 (47) ~ (all_52_3 = e2)
% 157.68/27.37 (48) all_58_9 = e3
% 157.68/27.37 (49) op(e2, e0) = all_52_13
% 157.68/27.37 (50) op(e2, e3) = e2
% 157.68/27.37 (51) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.37 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.68/27.37 (52) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.68/27.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.68/27.37 (53) op(e1, e2) = all_52_6
% 157.68/27.37 (54) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.68/27.37 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.68/27.37 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.68/27.37 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.68/27.37 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.68/27.37 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.68/27.37 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.68/27.37 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.68/27.37 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.68/27.37 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.68/27.37 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.68/27.37 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.68/27.37 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.68/27.37 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.68/27.37 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.68/27.37 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.68/27.37 = e0)
% 157.68/27.37 (55) ~ (all_52_4 = e0)
% 157.68/27.37 (56) ~ (all_52_11 = e2)
% 157.68/27.37 (57) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.37 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.68/27.37 (58) ~ (all_52_9 = all_6_2)
% 157.68/27.37 (59) all_54_8 = all_52_2
% 157.68/27.37 (60) all_54_7 = all_52_13
% 157.68/27.37 (61) all_56_12 = e3
% 157.68/27.37 (62) ~ (all_52_2 = e3)
% 157.68/27.37 (63) ~ (all_52_13 = e2)
% 157.68/27.37 (64) op(e0, e0) = e2
% 157.68/27.37 (65) ~ (all_52_9 = all_52_11)
% 157.68/27.37 (66) all_58_4 = e2
% 157.68/27.37 (67) ~ (all_52_2 = all_52_14)
% 157.68/27.37 (68) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.68/27.37 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.37 (69) ~ (all_52_4 = e3)
% 157.68/27.37 (70) all_54_6 = all_52_9
% 157.68/27.37 (71) op(e0, e2) = e0
% 157.68/27.37 (72) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.68/27.37 (73) all_58_15 = e2
% 157.68/27.37 (74) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.68/27.37 (75) op(e3, e3) = e3
% 157.68/27.37 (76) all_54_3 = all_52_12
% 157.68/27.37 (77) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.68/27.37 (78) ~ (all_52_2 = e2)
% 157.68/27.37 (79) all_58_3 = e3
% 157.68/27.37 (80) ~ (all_6_2 = e2)
% 157.68/27.37 (81) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.68/27.37 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.68/27.37 e3)
% 157.68/27.37 (82) all_56_14 = all_6_2
% 157.68/27.37 (83) all_56_13 = e3
% 157.68/27.37 (84) op(e3, e0) = e3
% 157.68/27.37 (85) ~ (all_52_12 = all_52_14)
% 157.68/27.37 (86) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.68/27.37 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.68/27.37 (87) ~ (all_52_9 = e2)
% 157.68/27.37 (88) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.68/27.37 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.37 (89) all_54_14 = all_52_11
% 157.68/27.37 (90) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.68/27.37 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.68/27.37 (91) op(e0, e2) = all_52_7
% 157.68/27.37 (92) op(e1, e0) = all_52_14
% 157.68/27.37 (93) op(e3, e3) = all_22_1
% 157.68/27.37 (94) all_58_0 = e0
% 157.68/27.37 (95) all_56_15 = e2
% 157.68/27.37 (96) ~ (all_52_6 = e3)
% 157.68/27.37 (97) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.68/27.37 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.68/27.37 (98) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.37 (99) ~ (all_52_3 = all_52_11)
% 157.68/27.37 (100) all_54_11 = all_52_14
% 157.68/27.37 (101) ~ (all_52_13 = all_52_14)
% 157.68/27.37 (102) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.68/27.37 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.68/27.37 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.68/27.37 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.68/27.37 e0)))
% 157.68/27.37 (103) ~ (all_52_11 = e0)
% 157.68/27.37 (104) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.68/27.37 (105) all_54_12 = all_52_3
% 157.68/27.37 (106) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.68/27.37
% 157.68/27.37 Begin of proof
% 157.68/27.37 |
% 157.68/27.37 | BETA: splitting (28) gives:
% 157.68/27.37 |
% 157.68/27.37 | Case 1:
% 157.68/27.37 | |
% 157.68/27.37 | | (107) all_54_1 = e3
% 157.68/27.37 | |
% 157.68/27.37 | | COMBINE_EQS: (25), (107) imply:
% 157.68/27.37 | | (108) all_52_4 = e3
% 157.68/27.37 | |
% 157.68/27.37 | | REDUCE: (69), (108) imply:
% 157.68/27.37 | | (109) $false
% 157.68/27.37 | |
% 157.68/27.37 | | CLOSE: (109) is inconsistent.
% 157.68/27.37 | |
% 157.68/27.37 | Case 2:
% 157.68/27.37 | |
% 157.68/27.37 | | (110) ~ (all_54_1 = e3)
% 157.68/27.37 | | (111) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.68/27.37 | |
% 157.68/27.37 | | BETA: splitting (111) gives:
% 157.68/27.37 | |
% 157.68/27.37 | | Case 1:
% 157.68/27.37 | | |
% 157.68/27.37 | | | (112) all_54_1 = e2
% 157.68/27.37 | | |
% 157.68/27.37 | | | COMBINE_EQS: (25), (112) imply:
% 157.68/27.37 | | | (113) all_52_4 = e2
% 157.68/27.37 | | |
% 157.68/27.37 | | | REDUCE: (31), (113) imply:
% 157.68/27.37 | | | (114) $false
% 157.68/27.37 | | |
% 157.68/27.37 | | | CLOSE: (114) is inconsistent.
% 157.68/27.37 | | |
% 157.68/27.37 | | Case 2:
% 157.68/27.37 | | |
% 157.68/27.37 | | | (115) ~ (all_54_1 = e2)
% 157.68/27.37 | | | (116) all_54_1 = e1 | all_54_1 = e0
% 157.68/27.37 | | |
% 157.68/27.37 | | | BETA: splitting (116) gives:
% 157.68/27.37 | | |
% 157.68/27.37 | | | Case 1:
% 157.68/27.37 | | | |
% 157.68/27.37 | | | | (117) all_54_1 = e1
% 157.68/27.37 | | | |
% 157.68/27.37 | | | | COMBINE_EQS: (25), (117) imply:
% 157.68/27.37 | | | | (118) all_52_4 = e1
% 157.68/27.37 | | | |
% 157.68/27.37 | | | | REDUCE: (33), (118) imply:
% 157.68/27.37 | | | | (119) ~ (all_52_12 = e1)
% 157.68/27.37 | | | |
% 157.68/27.37 | | | | SIMP: (119) implies:
% 157.68/27.37 | | | | (120) ~ (all_52_12 = e1)
% 157.68/27.37 | | | |
% 157.68/27.37 | | | | BETA: splitting (72) gives:
% 157.68/27.37 | | | |
% 157.68/27.37 | | | | Case 1:
% 157.68/27.37 | | | | |
% 157.68/27.37 | | | | | (121) all_54_12 = e2
% 157.68/27.37 | | | | |
% 157.68/27.37 | | | | | REF_CLOSE: (47), (105), (121) are inconsistent by sub-proof #1189.
% 157.68/27.37 | | | | |
% 157.68/27.37 | | | | Case 2:
% 157.68/27.37 | | | | |
% 157.68/27.37 | | | | | (122) ~ (all_54_12 = e2)
% 157.68/27.37 | | | | | (123) all_54_12 = e1 | all_54_12 = e0
% 157.68/27.37 | | | | |
% 157.68/27.37 | | | | | BETA: splitting (123) gives:
% 157.68/27.37 | | | | |
% 157.68/27.37 | | | | | Case 1:
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | (124) all_54_12 = e1
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | COMBINE_EQS: (105), (124) imply:
% 157.68/27.37 | | | | | | (125) all_52_3 = e1
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | SIMP: (125) implies:
% 157.68/27.37 | | | | | | (126) all_52_3 = e1
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | REDUCE: (19), (126) imply:
% 157.68/27.37 | | | | | | (127) ~ (all_52_2 = e1)
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | REDUCE: (99), (126) imply:
% 157.68/27.37 | | | | | | (128) ~ (all_52_11 = e1)
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | SIMP: (128) implies:
% 157.68/27.37 | | | | | | (129) ~ (all_52_11 = e1)
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | REDUCE: (47), (126) imply:
% 157.68/27.37 | | | | | | (130) ~ (e2 = e1)
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | SIMP: (130) implies:
% 157.68/27.37 | | | | | | (131) ~ (e2 = e1)
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | REDUCE: (27), (126) imply:
% 157.68/27.37 | | | | | | (132) ~ (e1 = e0)
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | REDUCE: (4), (126) imply:
% 157.68/27.37 | | | | | | (133) op(e0, e3) = e1
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | BETA: splitting (23) gives:
% 157.68/27.37 | | | | | |
% 157.68/27.37 | | | | | | Case 1:
% 157.68/27.37 | | | | | | |
% 157.68/27.37 | | | | | | | (134) all_54_8 = e3
% 157.68/27.37 | | | | | | |
% 157.68/27.37 | | | | | | | COMBINE_EQS: (59), (134) imply:
% 157.68/27.37 | | | | | | | (135) all_52_2 = e3
% 157.68/27.37 | | | | | | |
% 157.68/27.37 | | | | | | | REDUCE: (62), (135) imply:
% 157.68/27.37 | | | | | | | (136) $false
% 157.68/27.37 | | | | | | |
% 157.68/27.37 | | | | | | | CLOSE: (136) is inconsistent.
% 157.68/27.37 | | | | | | |
% 157.68/27.37 | | | | | | Case 2:
% 157.68/27.37 | | | | | | |
% 157.68/27.37 | | | | | | | (137) ~ (all_54_8 = e3)
% 157.68/27.37 | | | | | | | (138) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.68/27.37 | | | | | | |
% 157.68/27.37 | | | | | | | BETA: splitting (138) gives:
% 157.68/27.37 | | | | | | |
% 157.68/27.37 | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | |
% 157.68/27.37 | | | | | | | | (139) all_54_8 = e2
% 157.68/27.37 | | | | | | | |
% 157.68/27.37 | | | | | | | | COMBINE_EQS: (59), (139) imply:
% 157.68/27.37 | | | | | | | | (140) all_52_2 = e2
% 157.68/27.37 | | | | | | | |
% 157.68/27.37 | | | | | | | | REDUCE: (78), (140) imply:
% 157.68/27.37 | | | | | | | | (141) $false
% 157.68/27.37 | | | | | | | |
% 157.68/27.37 | | | | | | | | CLOSE: (141) is inconsistent.
% 157.68/27.37 | | | | | | | |
% 157.68/27.37 | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | |
% 157.68/27.37 | | | | | | | | (142) ~ (all_54_8 = e2)
% 157.68/27.37 | | | | | | | | (143) all_54_8 = e1 | all_54_8 = e0
% 157.68/27.37 | | | | | | | |
% 157.68/27.37 | | | | | | | | BETA: splitting (32) gives:
% 157.68/27.37 | | | | | | | |
% 157.68/27.37 | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | |
% 157.68/27.37 | | | | | | | | | (144) all_54_3 = e3
% 157.68/27.37 | | | | | | | | |
% 157.68/27.37 | | | | | | | | | COMBINE_EQS: (76), (144) imply:
% 157.68/27.37 | | | | | | | | | (145) all_52_12 = e3
% 157.68/27.37 | | | | | | | | |
% 157.68/27.37 | | | | | | | | | REDUCE: (2), (145) imply:
% 157.68/27.37 | | | | | | | | | (146) $false
% 157.68/27.37 | | | | | | | | |
% 157.68/27.37 | | | | | | | | | CLOSE: (146) is inconsistent.
% 157.68/27.37 | | | | | | | | |
% 157.68/27.37 | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | |
% 157.68/27.37 | | | | | | | | | (147) ~ (all_54_3 = e3)
% 157.68/27.37 | | | | | | | | | (148) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.37 | | | | | | | | |
% 157.68/27.37 | | | | | | | | | BETA: splitting (106) gives:
% 157.68/27.37 | | | | | | | | |
% 157.68/27.37 | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | (149) all_54_14 = e3
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | COMBINE_EQS: (89), (149) imply:
% 157.68/27.37 | | | | | | | | | | (150) all_52_11 = e3
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | SIMP: (150) implies:
% 157.68/27.37 | | | | | | | | | | (151) all_52_11 = e3
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | REDUCE: (65), (151) imply:
% 157.68/27.37 | | | | | | | | | | (152) ~ (all_52_9 = e3)
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | REDUCE: (45), (151) imply:
% 157.68/27.37 | | | | | | | | | | (153) ~ (all_6_2 = e3)
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | SIMP: (153) implies:
% 157.68/27.37 | | | | | | | | | | (154) ~ (all_6_2 = e3)
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | REDUCE: (56), (151) imply:
% 157.68/27.37 | | | | | | | | | | (155) ~ (e3 = e2)
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | REDUCE: (129), (151) imply:
% 157.68/27.37 | | | | | | | | | | (156) ~ (e3 = e1)
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | REDUCE: (103), (151) imply:
% 157.68/27.37 | | | | | | | | | | (157) ~ (e3 = e0)
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | BETA: splitting (7) gives:
% 157.68/27.37 | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | (158) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 157.68/27.37 | | | | | | | | | | | & op(e2, e2) = e1)
% 157.68/27.37 | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | BETA: splitting (158) gives:
% 157.68/27.37 | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | (159) all_58_1 = e1 & op(e3, e2) = e1
% 157.68/27.37 | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | ALPHA: (159) implies:
% 157.68/27.37 | | | | | | | | | | | | (160) all_58_1 = e1
% 157.68/27.37 | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | BETA: splitting (46) gives:
% 157.68/27.37 | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | (161) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 157.68/27.37 | | | | | | | | | | | | | & op(e1, e2) = e0)
% 157.68/27.37 | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | BETA: splitting (161) gives:
% 157.68/27.37 | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | (162) all_58_6 = e0 & op(e1, e3) = e0
% 157.68/27.37 | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | ALPHA: (162) implies:
% 157.68/27.37 | | | | | | | | | | | | | | (163) all_58_6 = e0
% 157.68/27.37 | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 157.68/27.37 | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | (164) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 157.68/27.37 | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 157.68/27.37 | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 157.68/27.37 | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | (165) all_58_6 = e3 & op(e1, e3) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 157.68/27.37 | | | | | | | | | | | | | | | | (166) all_58_6 = e3
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (166) imply:
% 157.68/27.37 | | | | | | | | | | | | | | | | (167) e3 = e0
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 157.68/27.37 | | | | | | | | | | | | | | | | (168) e3 = e0
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (168) imply:
% 157.68/27.37 | | | | | | | | | | | | | | | | (169) all_58_9 = e0
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.68/27.37 | | | | | | | | | | | | | | | | (12), (14), (15), (16), (18), (19), (20), (21),
% 157.68/27.37 | | | | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29),
% 157.68/27.37 | | | | | | | | | | | | | | | | (30), (31), (32), (33), (35), (36), (37), (38),
% 157.68/27.37 | | | | | | | | | | | | | | | | (39), (40), (42), (43), (45), (46), (47), (49),
% 157.68/27.37 | | | | | | | | | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (57),
% 157.68/27.37 | | | | | | | | | | | | | | | | (59), (60), (61), (62), (63), (64), (66), (68),
% 157.68/27.37 | | | | | | | | | | | | | | | | (69), (71), (73), (74), (76), (77), (78), (79),
% 157.68/27.37 | | | | | | | | | | | | | | | | (80), (81), (82), (85), (86), (88), (89), (90),
% 157.68/27.37 | | | | | | | | | | | | | | | | (91), (92), (95), (96), (97), (98), (99), (100),
% 157.68/27.37 | | | | | | | | | | | | | | | | (101), (102), (103), (104), (105), (106), (155),
% 157.68/27.37 | | | | | | | | | | | | | | | | (157), (169) are inconsistent by sub-proof #383.
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | (170) all_58_7 = e3 & op(e1, e2) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | REF_CLOSE: (53), (96), (98), (170) are inconsistent by
% 157.68/27.37 | | | | | | | | | | | | | | | | sub-proof #1184.
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | End of split
% 157.68/27.37 | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | (171) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 157.68/27.37 | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 157.68/27.37 | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 157.68/27.37 | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | (172) all_58_8 = e3 & op(e1, e1) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 157.68/27.37 | | | | | | | | | | | | | | | | (173) all_58_8 = e3
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | (174) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 157.68/27.37 | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (175) all_58_4 = e1 & op(e3, e1) = e1
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (131), (175) are inconsistent by sub-proof
% 157.68/27.37 | | | | | | | | | | | | | | | | | | #1476.
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (176) all_58_5 = e1 & op(e2, e1) = e1
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (12), (14), (15), (16), (18), (19), (20), (21),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (30), (31), (32), (33), (35), (36), (37), (38),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (39), (40), (42), (43), (45), (46), (47), (48),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (57), (59), (60), (61), (62), (63), (64), (66),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (68), (69), (71), (73), (74), (76), (77), (78),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (79), (80), (81), (82), (85), (86), (88), (89),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (90), (91), (92), (95), (96), (97), (98), (99),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (100), (101), (102), (103), (104), (105), (106),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (120), (131), (148), (155), (156), (157), (160),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (173), (176) are inconsistent by sub-proof #382.
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | (177) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 157.68/27.37 | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (178) all_58_8 = e1 & op(e1, e1) = e1
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (173), (178) are inconsistent by sub-proof
% 157.68/27.37 | | | | | | | | | | | | | | | | | | #959.
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (179) all_58_14 = e1 & op(e0, e1) = e1
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (156), (179) are inconsistent by sub-proof
% 157.68/27.37 | | | | | | | | | | | | | | | | | | #844.
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | End of split
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | (180) all_58_11 = e3 & op(e1, e0) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 157.68/27.37 | | | | | | | | | | | | | | | | (181) all_58_11 = e3
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 157.68/27.37 | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | (182) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (183) all_58_0 = e3 & op(e3, e3) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (184) all_58_0 = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (184) imply:
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (185) e3 = e0
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (12), (14), (15), (16), (18), (19), (20), (21),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (30), (31), (32), (33), (35), (36), (37), (38),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (39), (40), (42), (43), (45), (46), (47), (48),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (57), (59), (60), (61), (62), (63), (64), (66),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (68), (69), (71), (73), (74), (76), (77), (78),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (79), (80), (81), (82), (85), (86), (88), (89),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (90), (91), (92), (95), (96), (97), (98), (99),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (100), (101), (102), (103), (104), (105), (106),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (155), (157), (181), (185) are inconsistent by
% 157.68/27.37 | | | | | | | | | | | | | | | | | | sub-proof #381.
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (186) all_58_2 = e3 & op(e2, e3) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (187) op(e2, e3) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (50), (98), (155), (187) are inconsistent by
% 157.68/27.37 | | | | | | | | | | | | | | | | | | sub-proof #1159.
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | (188) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 157.68/27.37 | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 157.68/27.37 | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (189) all_58_6 = e3 & op(e1, e3) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (190) all_58_6 = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (190) imply:
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (191) e3 = e0
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (12), (14), (15), (16), (18), (19), (20), (21),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (30), (31), (32), (33), (35), (36), (37), (38),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (39), (40), (42), (43), (45), (46), (47), (48),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (57), (59), (60), (61), (62), (63), (64), (66),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (68), (69), (71), (73), (74), (76), (77), (78),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (79), (80), (81), (82), (85), (86), (88), (89),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (90), (91), (92), (95), (96), (97), (98), (99),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (100), (101), (102), (103), (104), (105), (106),
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (155), (157), (181), (191) are inconsistent by
% 157.68/27.37 | | | | | | | | | | | | | | | | | | sub-proof #381.
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (192) all_58_12 = e3 & op(e0, e3) = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.37 | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 157.68/27.37 | | | | | | | | | | | | | | | | | | (193) all_58_12 = e3
% 157.68/27.37 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (13),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (17), (18), (19), (20), (21), (22), (23), (24),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (25), (27), (29), (30), (31), (32), (33), (34),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (43), (44), (45),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (46), (47), (48), (50), (53), (55), (56), (57),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (58), (59), (60), (62), (63), (64), (66), (68),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (69), (70), (72), (74), (75), (76), (77), (78),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (79), (80), (82), (85), (86), (87), (89), (92),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (93), (94), (96), (97), (98), (99), (100), (101),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (103), (105), (106), (111), (131), (132), (152),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (155), (156), (157), (193) are inconsistent by
% 157.68/27.38 | | | | | | | | | | | | | | | | | | sub-proof #407.
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | (194) all_58_7 = e0 & op(e1, e2) = e0
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | REF_CLOSE: (21), (43), (194) are inconsistent by sub-proof
% 157.68/27.38 | | | | | | | | | | | | | | #1468.
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | (195) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 157.68/27.38 | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 157.68/27.38 | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | BETA: splitting (195) gives:
% 157.68/27.38 | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | (196) all_58_8 = e0 & op(e1, e1) = e0
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | ALPHA: (196) implies:
% 157.68/27.38 | | | | | | | | | | | | | | (197) all_58_8 = e0
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | (198) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | (199) all_58_6 = e1 & op(e1, e3) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | (200) all_58_6 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (21), (29), (43), (48), (50),
% 157.68/27.38 | | | | | | | | | | | | | | | | (53), (57), (64), (66), (68), (79), (96), (98),
% 157.68/27.38 | | | | | | | | | | | | | | | | (131), (132), (156), (157), (160), (197), (200)
% 157.68/27.38 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #411.
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | (201) all_58_7 = e1 & op(e1, e2) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | REF_CLOSE: (21), (131), (201) are inconsistent by sub-proof
% 157.68/27.38 | | | | | | | | | | | | | | | | #1045.
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | (202) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 157.68/27.38 | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | (203) all_58_8 = e1 & op(e1, e1) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | (204) all_58_8 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (204) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | (205) e1 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | (206) e1 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (206) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | (207) all_58_1 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11),
% 157.68/27.38 | | | | | | | | | | | | | | | | (12), (14), (15), (16), (18), (19), (21), (22),
% 157.68/27.38 | | | | | | | | | | | | | | | | (23), (24), (26), (27), (29), (30), (32), (35),
% 157.68/27.38 | | | | | | | | | | | | | | | | (36), (37), (38), (39), (40), (41), (42), (43),
% 157.68/27.38 | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 157.68/27.38 | | | | | | | | | | | | | | | | (53), (56), (57), (58), (59), (60), (62), (63),
% 157.68/27.38 | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71),
% 157.68/27.38 | | | | | | | | | | | | | | | | (73), (74), (75), (76), (77), (78), (79), (80),
% 157.68/27.38 | | | | | | | | | | | | | | | | (81), (84), (86), (87), (88), (89), (90), (91),
% 157.68/27.38 | | | | | | | | | | | | | | | | (92), (93), (96), (97), (98), (99), (100), (101),
% 157.68/27.38 | | | | | | | | | | | | | | | | (102), (103), (105), (106), (120), (123), (157),
% 157.68/27.38 | | | | | | | | | | | | | | | | (207) are inconsistent by sub-proof #377.
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | (208) all_58_11 = e1 & op(e1, e0) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | (209) op(e1, e0) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (22), (30), (36), (60), (63), (76),
% 157.68/27.38 | | | | | | | | | | | | | | | | (77), (85), (92), (98), (100), (101), (120),
% 157.68/27.38 | | | | | | | | | | | | | | | | (148), (209) are inconsistent by sub-proof #417.
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | (210) all_58_11 = e0 & op(e1, e0) = e0
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | ALPHA: (210) implies:
% 157.68/27.38 | | | | | | | | | | | | | | (211) all_58_11 = e0
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 157.68/27.38 | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | (212) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | (213) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.68/27.38 | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.68/27.38 | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (214) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | (215) op(e2, e3) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (50), (98), (155), (215) are inconsistent by
% 157.68/27.38 | | | | | | | | | | | | | | | | | sub-proof #1159.
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (216) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (217) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (218) ~ (all_56_12 = e3)
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | REDUCE: (61), (218) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (219) $false
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (220) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (221) ~ (all_56_14 = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | REDUCE: (82), (221) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (222) ~ (all_6_2 = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (38), (59), (74), (80), (127), (143), (154),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (222) are inconsistent by sub-proof #1230.
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | (223) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.68/27.38 | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.68/27.38 | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (224) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | (225) ~ (all_56_12 = e3)
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | REDUCE: (61), (225) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | (226) $false
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent.
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (227) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (228) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (229) ~ (all_56_15 = e0)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (230) op(e0, e3) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (231) all_54_3 = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (231) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (232) all_52_12 = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | REDUCE: (10), (232) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (233) $false
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (234) ~ (all_54_3 = e2)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (235) all_54_3 = e1 | all_54_3 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (236) all_58_15 = e0 & op(e0, e0) = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (73), (236) are inconsistent by sub-proof
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | #885.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (237) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (238) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (239) all_54_3 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (120), (239) are inconsistent by sub-proof
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | #1291.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (240) all_54_3 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (240) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (241) all_52_12 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | SIMP: (241) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (242) all_52_12 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (242) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (243) ~ (e3 = e0)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (242) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (244) ~ (e2 = e0)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (242) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (245) ~ (e1 = e0)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (98) with e1, e3, e3, e0,
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | simplifying with (133), (230) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (246) e3 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (98) with e3, all_22_1, e3, e3,
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | simplifying with (75), (93) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (247) all_22_1 = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (98) with e0, all_22_1, e3, e3,
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | simplifying with (44), (93) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (248) all_22_1 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (248) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (249) e3 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | SIMP: (249) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (250) e3 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (250) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (251) e1 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | SIMP: (251) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (252) e1 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (252) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (253) all_58_1 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (12), (14), (15), (16), (21), (24),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (26), (29), (35), (36), (39), (40), (42), (43),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (57),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (64), (66), (68), (69), (71), (79), (81), (86),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (88), (90), (91), (94), (96), (97), (98), (102),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (131), (132), (155), (156), (157), (238), (253)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #392.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (254) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (255) ~ (all_56_12 = e3)
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | REDUCE: (61), (255) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (256) $false
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | (257) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.68/27.38 | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 157.68/27.38 | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | (258) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.68/27.38 | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.68/27.38 | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (259) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | (260) ~ (all_56_14 = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | REDUCE: (82), (260) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | (261) ~ (all_6_2 = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (38), (59), (74), (80), (127), (143), (154),
% 157.68/27.38 | | | | | | | | | | | | | | | | | (261) are inconsistent by sub-proof #1230.
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (262) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (263) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (264) op(e2, e1) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (265) all_54_3 = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (265) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (266) all_52_12 = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | REDUCE: (10), (266) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (267) $false
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (268) all_54_3 = e1 | all_54_3 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (269) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (270) all_58_6 = e1 & op(e1, e3) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (271) all_58_6 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (21), (29), (43), (48), (50),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (53), (57), (64), (66), (68), (79), (96), (98),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (131), (132), (156), (157), (160), (211), (271)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #410.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (272) all_58_7 = e1 & op(e1, e2) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (131), (272) are inconsistent by sub-proof
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | #1045.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (273) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (274) all_58_8 = e1 & op(e1, e1) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (275) all_58_8 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (12), (21), (43), (52), (66), (76),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (79), (98), (120), (131), (132), (156), (157),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (160), (264), (268), (275) are inconsistent by
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | sub-proof #389.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (276) all_58_11 = e1 & op(e1, e0) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (277) op(e1, e0) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22), (30), (36), (60), (63), (76), (77),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (85), (92), (98), (100), (101), (120), (268),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (277) are inconsistent by sub-proof #418.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (278) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (279) op(e0, e2) = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (71), (91), (98), (279) are inconsistent by
% 157.68/27.38 | | | | | | | | | | | | | | | | | | sub-proof #1040.
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | (280) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.68/27.38 | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.68/27.38 | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.68/27.38 | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | (281) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | (282) ~ (all_56_13 = e2)
% 157.68/27.38 | | | | | | | | | | | | | | | | | (283) op(e2, e0) = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (284) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (285) all_58_6 = e3 & op(e1, e3) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (286) all_58_6 = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (287) all_54_3 = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (287) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (288) all_52_12 = e2
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (288) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (289) $false
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | CLOSE: (289) is inconsistent.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (290) all_54_3 = e1 | all_54_3 = e0
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (291) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (292) all_58_9 = e1 & op(e3, e0) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (293) all_58_9 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (293) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (294) e3 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (294) imply:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (295) all_58_6 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (21), (29), (43), (48), (50),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (53), (57), (64), (66), (68), (79), (96), (98),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (131), (132), (156), (157), (160), (211), (295)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #410.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (296) all_58_10 = e1 & op(e2, e0) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (297) op(e2, e0) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (21), (76), (79), (98), (120), (131),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | (156), (160), (283), (290), (297) are inconsistent
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #388.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (298) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22), (30), (36), (60), (63), (64), (76),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (77), (85), (92), (98), (100), (101), (120),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (131), (290), (298) are inconsistent by sub-proof
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | #387.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (299) all_58_7 = e3 & op(e1, e2) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (96), (98), (299) are inconsistent by
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | sub-proof #1184.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | (300) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (301) all_58_8 = e3 & op(e1, e1) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (302) all_58_8 = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (303) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (79), (98), (131), (156), (303) are
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (304) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (305) all_58_5 = e1 & op(e2, e1) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (12), (14), (15), (16), (18), (19), (20), (21),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (30), (31), (32), (33), (35), (36), (37), (38),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (39), (40), (42), (43), (45), (46), (47), (48),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (57), (59), (60), (61), (62), (63), (64), (66),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (68), (69), (71), (73), (74), (76), (77), (78),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (79), (80), (81), (82), (85), (86), (88), (89),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (90), (91), (92), (95), (96), (97), (98), (99),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (100), (101), (102), (103), (104), (105), (106),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (120), (131), (148), (155), (156), (157), (160),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (302), (305) are inconsistent by sub-proof #382.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (306) all_58_10 = e1 & op(e2, e0) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (21), (76), (79), (98), (120),
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (131), (148), (156), (160), (283), (306) are
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #376.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (307) all_58_11 = e3 & op(e1, e0) = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | (308) all_58_11 = e3
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (309) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (79), (98), (131), (156), (309) are
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | (310) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | (311) all_58_5 = e1 & op(e2, e1) = e1
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | | (312) all_58_5 = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (21), (43), (48), (50), (57), (64),
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | | (79), (98), (131), (132), (156), (157), (160),
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | | (308), (312) are inconsistent by sub-proof #412.
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | | (313) all_58_10 = e1 & op(e2, e0) = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (21), (76), (79), (98), (120),
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | | (131), (148), (156), (160), (283), (313) are
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #376.
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | (314) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.68/27.39 | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.68/27.39 | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.68/27.39 | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (315) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.68/27.39 | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (316) op(e1, e0) = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (22), (30), (36), (60), (63), (76),
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (77), (85), (92), (98), (100), (101), (120),
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (148), (316) are inconsistent by sub-proof #417.
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (317) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.68/27.39 | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (318) ~ (all_56_14 = e1)
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | REDUCE: (82), (318) imply:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (319) ~ (all_6_2 = e1)
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (38), (59), (74), (80), (127), (143), (154),
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (319) are inconsistent by sub-proof #1230.
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | (320) all_58_3 = e1 & op(e2, e2) = e1
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | REF_CLOSE: (79), (156), (320) are inconsistent by sub-proof
% 157.68/27.39 | | | | | | | | | | | | #912.
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | (321) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 157.68/27.39 | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | REF_CLOSE: (3), (21), (131), (132), (321) are inconsistent by
% 157.68/27.39 | | | | | | | | | | | sub-proof #858.
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | (322) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | REF_CLOSE: (56), (89), (103), (129), (322) are inconsistent
% 157.68/27.39 | | | | | | | | | | by sub-proof #1149.
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | End of split
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | End of split
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | End of split
% 157.68/27.39 | | | | | |
% 157.68/27.39 | | | | | Case 2:
% 157.68/27.39 | | | | | |
% 157.68/27.39 | | | | | | (323) all_54_12 = e0
% 157.68/27.39 | | | | | |
% 157.68/27.39 | | | | | | REF_CLOSE: (27), (105), (323) are inconsistent by sub-proof #1223.
% 157.68/27.39 | | | | | |
% 157.68/27.39 | | | | | End of split
% 157.68/27.39 | | | | |
% 157.68/27.39 | | | | End of split
% 157.68/27.39 | | | |
% 157.68/27.39 | | | Case 2:
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | (324) all_54_1 = e0
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | COMBINE_EQS: (25), (324) imply:
% 157.68/27.39 | | | | (325) all_52_4 = e0
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | REDUCE: (55), (325) imply:
% 157.68/27.39 | | | | (326) $false
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | CLOSE: (326) is inconsistent.
% 157.68/27.39 | | | |
% 157.68/27.39 | | | End of split
% 157.68/27.39 | | |
% 157.68/27.39 | | End of split
% 157.68/27.39 | |
% 157.68/27.39 | End of split
% 157.68/27.39 |
% 157.68/27.39 End of proof
% 157.68/27.39
% 157.68/27.39 Sub-proof #376 shows that the following formulas are inconsistent:
% 157.68/27.39 ----------------------------------------------------------------
% 157.68/27.39 (1) all_58_13 = e0
% 157.68/27.39 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.39 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.39 (3) ~ (all_52_12 = e2)
% 157.68/27.39 (4) all_58_7 = e2
% 157.68/27.39 (5) ~ (e3 = e1)
% 157.68/27.39 (6) all_58_1 = e1
% 157.68/27.39 (7) all_58_10 = e1 & op(e2, e0) = e1
% 157.68/27.39 (8) ~ (e2 = e1)
% 157.68/27.39 (9) all_54_3 = all_52_12
% 157.68/27.39 (10) all_58_3 = e3
% 157.68/27.39 (11) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.39 (12) op(e2, e0) = e0
% 157.68/27.39 (13) ~ (all_52_12 = e1)
% 157.68/27.39 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.39
% 157.68/27.39 Begin of proof
% 157.68/27.39 |
% 157.68/27.39 | ALPHA: (7) implies:
% 157.68/27.39 | (15) op(e2, e0) = e1
% 157.68/27.39 |
% 157.68/27.39 | BETA: splitting (11) gives:
% 157.68/27.39 |
% 157.68/27.39 | Case 1:
% 157.68/27.39 | |
% 157.68/27.39 | | (16) all_54_3 = e2
% 157.68/27.39 | |
% 157.68/27.39 | | COMBINE_EQS: (9), (16) imply:
% 157.68/27.39 | | (17) all_52_12 = e2
% 157.68/27.39 | |
% 157.68/27.39 | | REDUCE: (3), (17) imply:
% 157.68/27.39 | | (18) $false
% 157.68/27.39 | |
% 157.68/27.39 | | CLOSE: (18) is inconsistent.
% 157.68/27.39 | |
% 157.68/27.39 | Case 2:
% 157.68/27.39 | |
% 157.68/27.39 | | (19) all_54_3 = e1 | all_54_3 = e0
% 157.68/27.39 | |
% 157.68/27.39 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (12), (13), (14), (15),
% 157.68/27.39 | | (19) are inconsistent by sub-proof #388.
% 157.68/27.39 | |
% 157.68/27.39 | End of split
% 157.68/27.39 |
% 157.68/27.39 End of proof
% 157.68/27.39
% 157.68/27.39 Sub-proof #377 shows that the following formulas are inconsistent:
% 157.68/27.39 ----------------------------------------------------------------
% 157.68/27.39 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.68/27.39 (2) ~ (all_52_12 = e3)
% 157.68/27.39 (3) op(e3, e0) = all_52_12
% 157.68/27.39 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.68/27.39 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.68/27.39 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.39 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.39 (6) ~ (all_52_14 = e2)
% 157.68/27.39 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.68/27.39 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.39 (8) all_58_1 = e0
% 157.68/27.39 (9) ~ (all_52_12 = e2)
% 157.68/27.39 (10) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.39 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.68/27.39 (11) all_58_14 = e3
% 157.68/27.39 (12) ~ (all_52_7 = e3)
% 157.68/27.39 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.39 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.68/27.39 e1)
% 157.68/27.39 (14) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.68/27.39 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.68/27.39 (15) all_54_10 = all_6_2
% 157.68/27.39 (16) ~ (all_52_2 = all_52_3)
% 157.68/27.39 (17) all_58_7 = e2
% 157.68/27.39 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.68/27.39 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.68/27.39 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.68/27.39 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.68/27.39 (21) op(e3, e2) = all_52_4
% 157.68/27.39 (22) ~ (all_52_3 = e0)
% 157.68/27.39 (23) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.68/27.39 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.68/27.39 (24) ~ (all_52_12 = all_52_13)
% 157.68/27.39 (25) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.39 (26) op(e2, e3) = all_52_1
% 157.68/27.39 (27) ~ (all_52_13 = e3)
% 157.68/27.39 (28) ~ (all_52_3 = e3)
% 157.68/27.39 (29) ~ (all_52_2 = all_6_2)
% 157.68/27.39 (30) ~ (e3 = e0)
% 157.68/27.39 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.68/27.39 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.68/27.39 (32) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.68/27.39 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.68/27.39 (33) ~ (all_52_9 = all_52_13)
% 157.68/27.39 (34) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.39 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.68/27.39 e2)
% 157.68/27.39 (35) ~ (e2 = e0)
% 157.68/27.39 (36) ~ (all_52_11 = all_6_2)
% 157.68/27.39 (37) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.68/27.39 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.68/27.39 (38) ~ (all_52_3 = e2)
% 157.68/27.39 (39) all_58_9 = e3
% 157.68/27.39 (40) op(e2, e0) = all_52_13
% 157.68/27.39 (41) op(e2, e3) = e2
% 157.68/27.39 (42) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.39 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.68/27.39 (43) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.68/27.39 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.68/27.39 (44) op(e1, e2) = all_52_6
% 157.68/27.39 (45) ~ (all_52_11 = e2)
% 157.68/27.39 (46) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.39 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.68/27.39 (47) all_54_12 = e1 | all_54_12 = e0
% 157.68/27.39 (48) ~ (all_52_9 = all_6_2)
% 157.68/27.39 (49) all_54_8 = all_52_2
% 157.68/27.39 (50) all_54_7 = all_52_13
% 157.68/27.39 (51) ~ (all_52_2 = e3)
% 157.68/27.39 (52) ~ (all_52_13 = e2)
% 157.68/27.39 (53) op(e0, e0) = e2
% 157.68/27.39 (54) ~ (all_52_9 = all_52_11)
% 157.68/27.39 (55) all_58_4 = e2
% 157.68/27.39 (56) ~ (all_52_2 = all_52_14)
% 157.68/27.39 (57) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.68/27.39 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.39 (58) ~ (all_52_4 = e3)
% 157.68/27.39 (59) all_54_6 = all_52_9
% 157.68/27.39 (60) op(e0, e2) = e0
% 157.68/27.39 (61) all_58_15 = e2
% 157.68/27.39 (62) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.68/27.39 (63) op(e3, e3) = e3
% 157.68/27.39 (64) all_54_3 = all_52_12
% 157.68/27.39 (65) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.68/27.39 (66) ~ (all_52_2 = e2)
% 157.68/27.39 (67) all_58_3 = e3
% 157.68/27.39 (68) ~ (all_6_2 = e2)
% 157.68/27.39 (69) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.68/27.39 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.68/27.39 e3)
% 157.68/27.39 (70) op(e3, e0) = e3
% 157.68/27.39 (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.68/27.39 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.68/27.39 (72) ~ (all_52_9 = e2)
% 157.68/27.39 (73) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.68/27.39 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.39 (74) all_54_14 = all_52_11
% 157.68/27.39 (75) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.68/27.39 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.68/27.39 (76) op(e0, e2) = all_52_7
% 157.68/27.39 (77) op(e1, e0) = all_52_14
% 157.68/27.39 (78) op(e3, e3) = all_22_1
% 157.68/27.39 (79) ~ (all_52_6 = e3)
% 157.68/27.39 (80) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.68/27.39 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.68/27.39 (81) ~ (all_52_12 = e1)
% 157.68/27.39 (82) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.39 (83) ~ (all_52_3 = all_52_11)
% 157.68/27.39 (84) all_54_11 = all_52_14
% 157.68/27.39 (85) ~ (all_52_13 = all_52_14)
% 157.68/27.39 (86) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.68/27.39 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.68/27.39 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.68/27.39 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.68/27.39 (87) ~ (all_52_11 = e0)
% 157.68/27.39 (88) all_54_12 = all_52_3
% 157.68/27.39 (89) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.68/27.39
% 157.68/27.39 Begin of proof
% 157.68/27.39 |
% 157.68/27.39 | BETA: splitting (47) gives:
% 157.68/27.39 |
% 157.68/27.39 | Case 1:
% 157.68/27.39 | |
% 157.68/27.39 | | (90) all_54_12 = e1
% 157.68/27.39 | |
% 157.68/27.39 | | COMBINE_EQS: (88), (90) imply:
% 157.68/27.39 | | (91) all_52_3 = e1
% 157.68/27.39 | |
% 157.68/27.39 | | SIMP: (91) implies:
% 157.68/27.39 | | (92) all_52_3 = e1
% 157.68/27.39 | |
% 157.68/27.39 | | REDUCE: (16), (92) imply:
% 157.68/27.39 | | (93) ~ (all_52_2 = e1)
% 157.68/27.39 | |
% 157.68/27.39 | | REDUCE: (83), (92) imply:
% 157.68/27.39 | | (94) ~ (all_52_11 = e1)
% 157.68/27.39 | |
% 157.68/27.39 | | SIMP: (94) implies:
% 157.68/27.39 | | (95) ~ (all_52_11 = e1)
% 157.68/27.39 | |
% 157.68/27.39 | | REDUCE: (28), (92) imply:
% 157.68/27.39 | | (96) ~ (e3 = e1)
% 157.68/27.39 | |
% 157.68/27.39 | | SIMP: (96) implies:
% 157.68/27.39 | | (97) ~ (e3 = e1)
% 157.68/27.39 | |
% 157.68/27.39 | | REDUCE: (38), (92) imply:
% 157.68/27.39 | | (98) ~ (e2 = e1)
% 157.68/27.39 | |
% 157.68/27.39 | | SIMP: (98) implies:
% 157.68/27.39 | | (99) ~ (e2 = e1)
% 157.68/27.39 | |
% 157.68/27.39 | | REDUCE: (22), (92) imply:
% 157.68/27.39 | | (100) ~ (e1 = e0)
% 157.68/27.39 | |
% 157.68/27.39 | | BETA: splitting (19) gives:
% 157.68/27.39 | |
% 157.68/27.39 | | Case 1:
% 157.68/27.39 | | |
% 157.68/27.39 | | | (101) all_54_8 = e3
% 157.68/27.39 | | |
% 157.68/27.39 | | | COMBINE_EQS: (49), (101) imply:
% 157.68/27.39 | | | (102) all_52_2 = e3
% 157.68/27.39 | | |
% 157.68/27.39 | | | REDUCE: (51), (102) imply:
% 157.68/27.39 | | | (103) $false
% 157.68/27.39 | | |
% 157.68/27.39 | | | CLOSE: (103) is inconsistent.
% 157.68/27.39 | | |
% 157.68/27.39 | | Case 2:
% 157.68/27.39 | | |
% 157.68/27.39 | | | (104) ~ (all_54_8 = e3)
% 157.68/27.39 | | | (105) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.68/27.39 | | |
% 157.68/27.39 | | | BETA: splitting (105) gives:
% 157.68/27.39 | | |
% 157.68/27.39 | | | Case 1:
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | (106) all_54_8 = e2
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | COMBINE_EQS: (49), (106) imply:
% 157.68/27.39 | | | | (107) all_52_2 = e2
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | REDUCE: (66), (107) imply:
% 157.68/27.39 | | | | (108) $false
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | CLOSE: (108) is inconsistent.
% 157.68/27.39 | | | |
% 157.68/27.39 | | | Case 2:
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | (109) ~ (all_54_8 = e2)
% 157.68/27.39 | | | | (110) all_54_8 = e1 | all_54_8 = e0
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | BETA: splitting (86) gives:
% 157.68/27.39 | | | |
% 157.68/27.39 | | | | Case 1:
% 157.68/27.39 | | | | |
% 157.68/27.39 | | | | | (111) all_58_15 = e0 & op(e0, e0) = e0
% 157.68/27.39 | | | | |
% 157.68/27.39 | | | | | REF_CLOSE: (35), (61), (111) are inconsistent by sub-proof #885.
% 157.68/27.39 | | | | |
% 157.68/27.39 | | | | Case 2:
% 157.68/27.39 | | | | |
% 157.68/27.39 | | | | | (112) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 157.68/27.39 | | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 157.68/27.39 | | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.68/27.39 | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.68/27.39 | | | | |
% 157.68/27.39 | | | | | ALPHA: (112) implies:
% 157.68/27.39 | | | | | (113) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 157.68/27.39 | | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.68/27.39 | | | | |
% 157.68/27.39 | | | | | BETA: splitting (113) gives:
% 157.68/27.39 | | | | |
% 157.68/27.39 | | | | | Case 1:
% 157.68/27.39 | | | | | |
% 157.68/27.39 | | | | | | (114) all_58_12 = e0 & op(e0, e3) = e0
% 157.68/27.39 | | | | | |
% 157.68/27.39 | | | | | | ALPHA: (114) implies:
% 157.68/27.39 | | | | | | (115) all_58_12 = e0
% 157.68/27.39 | | | | | |
% 157.68/27.39 | | | | | | BETA: splitting (25) gives:
% 157.68/27.39 | | | | | |
% 157.68/27.39 | | | | | | Case 1:
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | | (116) all_54_3 = e3
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | | COMBINE_EQS: (64), (116) imply:
% 157.68/27.39 | | | | | | | (117) all_52_12 = e3
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | | REDUCE: (2), (117) imply:
% 157.68/27.39 | | | | | | | (118) $false
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | | CLOSE: (118) is inconsistent.
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | Case 2:
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | | (119) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | | BETA: splitting (119) gives:
% 157.68/27.39 | | | | | | |
% 157.68/27.39 | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | | (120) all_54_3 = e2
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | | COMBINE_EQS: (64), (120) imply:
% 157.68/27.39 | | | | | | | | (121) all_52_12 = e2
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | | REDUCE: (9), (121) imply:
% 157.68/27.39 | | | | | | | | (122) $false
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | | CLOSE: (122) is inconsistent.
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | | (123) all_54_3 = e1 | all_54_3 = e0
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | | BETA: splitting (89) gives:
% 157.68/27.39 | | | | | | | |
% 157.68/27.39 | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | (124) all_54_14 = e3
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | COMBINE_EQS: (74), (124) imply:
% 157.68/27.39 | | | | | | | | | (125) all_52_11 = e3
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | SIMP: (125) implies:
% 157.68/27.39 | | | | | | | | | (126) all_52_11 = e3
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | REDUCE: (54), (126) imply:
% 157.68/27.39 | | | | | | | | | (127) ~ (all_52_9 = e3)
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | REDUCE: (36), (126) imply:
% 157.68/27.39 | | | | | | | | | (128) ~ (all_6_2 = e3)
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | SIMP: (128) implies:
% 157.68/27.39 | | | | | | | | | (129) ~ (all_6_2 = e3)
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | REDUCE: (45), (126) imply:
% 157.68/27.39 | | | | | | | | | (130) ~ (e3 = e2)
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | BETA: splitting (31) gives:
% 157.68/27.39 | | | | | | | | |
% 157.68/27.39 | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | (131) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.68/27.39 | | | | | | | | | | & op(e2, e3) = e1)
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | BETA: splitting (131) gives:
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | (132) all_58_0 = e1 & op(e3, e3) = e1
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | ALPHA: (132) implies:
% 157.68/27.39 | | | | | | | | | | | (133) all_58_0 = e1
% 157.68/27.39 | | | | | | | | | | | (134) op(e3, e3) = e1
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | BETA: splitting (5) gives:
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | (135) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 157.68/27.39 | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | BETA: splitting (135) gives:
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | (136) all_58_1 = e1 & op(e3, e2) = e1
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | ALPHA: (136) implies:
% 157.68/27.39 | | | | | | | | | | | | | (137) all_58_1 = e1
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | COMBINE_EQS: (8), (137) imply:
% 157.68/27.39 | | | | | | | | | | | | | (138) e1 = e0
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | SIMP: (138) implies:
% 157.68/27.39 | | | | | | | | | | | | | (139) e1 = e0
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | COMBINE_EQS: (133), (139) imply:
% 157.68/27.39 | | | | | | | | | | | | | (140) all_58_0 = e0
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (11), (12), (13), (14), (17),
% 157.68/27.39 | | | | | | | | | | | | | (20), (21), (23), (26), (27), (30), (31), (32),
% 157.68/27.39 | | | | | | | | | | | | | (34), (35), (37), (39), (40), (41), (42), (43),
% 157.68/27.39 | | | | | | | | | | | | | (44), (46), (53), (55), (57), (58), (60), (67),
% 157.68/27.39 | | | | | | | | | | | | | (69), (71), (73), (75), (76), (79), (80), (82),
% 157.68/27.39 | | | | | | | | | | | | | (86), (97), (99), (100), (115), (130), (140) are
% 157.68/27.39 | | | | | | | | | | | | | inconsistent by sub-proof #393.
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | (141) all_58_3 = e1 & op(e2, e2) = e1
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | REF_CLOSE: (67), (97), (141) are inconsistent by sub-proof
% 157.68/27.39 | | | | | | | | | | | | | #912.
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | (142) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 157.68/27.39 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | REF_CLOSE: (3), (5), (8), (17), (18), (24), (27), (39), (50),
% 157.68/27.39 | | | | | | | | | | | | (52), (55), (63), (64), (67), (70), (71), (78),
% 157.68/27.39 | | | | | | | | | | | | (81), (82), (99), (123), (133), (134), (142) are
% 157.68/27.39 | | | | | | | | | | | | inconsistent by sub-proof #405.
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | (143) all_58_2 = e1 & op(e2, e3) = e1
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | ALPHA: (143) implies:
% 157.68/27.39 | | | | | | | | | | | (144) op(e2, e3) = e1
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | REF_CLOSE: (41), (82), (99), (144) are inconsistent by
% 157.68/27.39 | | | | | | | | | | | sub-proof #1430.
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | (145) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 157.68/27.39 | | | | | | | | | | & op(e0, e3) = e1)
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | BETA: splitting (145) gives:
% 157.68/27.39 | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | (146) all_58_6 = e1 & op(e1, e3) = e1
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | ALPHA: (146) implies:
% 157.68/27.39 | | | | | | | | | | | (147) all_58_6 = e1
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | BETA: splitting (110) gives:
% 157.68/27.39 | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | (148) all_54_8 = e1
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | COMBINE_EQS: (49), (148) imply:
% 157.68/27.39 | | | | | | | | | | | | (149) all_52_2 = e1
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | REDUCE: (93), (149) imply:
% 157.68/27.39 | | | | | | | | | | | | (150) $false
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | (151) all_54_8 = e0
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | COMBINE_EQS: (49), (151) imply:
% 157.68/27.39 | | | | | | | | | | | | (152) all_52_2 = e0
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | REDUCE: (56), (152) imply:
% 157.68/27.39 | | | | | | | | | | | | (153) ~ (all_52_14 = e0)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | SIMP: (153) implies:
% 157.68/27.39 | | | | | | | | | | | | (154) ~ (all_52_14 = e0)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | REDUCE: (29), (152) imply:
% 157.68/27.39 | | | | | | | | | | | | (155) ~ (all_6_2 = e0)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | SIMP: (155) implies:
% 157.68/27.39 | | | | | | | | | | | | (156) ~ (all_6_2 = e0)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | REDUCE: (51), (152) imply:
% 157.68/27.39 | | | | | | | | | | | | (157) ~ (e3 = e0)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | REDUCE: (66), (152) imply:
% 157.68/27.39 | | | | | | | | | | | | (158) ~ (e2 = e0)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | REDUCE: (93), (152) imply:
% 157.68/27.39 | | | | | | | | | | | | (159) ~ (e1 = e0)
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | BETA: splitting (23) gives:
% 157.68/27.39 | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | (160) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 157.68/27.39 | | | | | | | | | | | | | & op(e1, e2) = e3)
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | REF_CLOSE: (44), (79), (82), (97), (147), (160) are
% 157.68/27.39 | | | | | | | | | | | | | inconsistent by sub-proof #718.
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | (161) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 157.68/27.39 | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | BETA: splitting (161) gives:
% 157.68/27.39 | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | (162) all_58_8 = e3 & op(e1, e1) = e3
% 157.68/27.39 | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (11), (17), (23), (30), (35), (37),
% 157.68/27.39 | | | | | | | | | | | | | | (39), (41), (43), (44), (46), (53), (55), (57),
% 157.68/27.39 | | | | | | | | | | | | | | (67), (79), (82), (97), (99), (100), (147), (162)
% 157.68/27.39 | | | | | | | | | | | | | | are inconsistent by sub-proof #394.
% 157.68/27.39 | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | (163) all_58_11 = e3 & op(e1, e0) = e3
% 157.68/27.39 | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | ALPHA: (163) implies:
% 157.68/27.39 | | | | | | | | | | | | | | (164) all_58_11 = e3
% 157.68/27.39 | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 157.68/27.39 | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | (165) all_54_10 = e3
% 157.68/27.39 | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | REF_CLOSE: (15), (129), (165) are inconsistent by sub-proof
% 157.68/27.39 | | | | | | | | | | | | | | | #1531.
% 157.68/27.39 | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | (166) ~ (all_54_10 = e3)
% 157.68/27.39 | | | | | | | | | | | | | | | (167) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.68/27.39 | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 157.68/27.39 | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | (168) all_54_10 = e2
% 157.68/27.39 | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (68), (168) are inconsistent by sub-proof
% 157.68/27.39 | | | | | | | | | | | | | | | | #1530.
% 157.68/27.39 | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | (169) ~ (all_54_10 = e2)
% 157.68/27.39 | | | | | | | | | | | | | | | | (170) all_54_10 = e1 | all_54_10 = e0
% 157.68/27.39 | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 157.68/27.39 | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | (171) all_54_10 = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (171) imply:
% 157.68/27.39 | | | | | | | | | | | | | | | | | (172) all_6_2 = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | SIMP: (172) implies:
% 157.68/27.39 | | | | | | | | | | | | | | | | | (173) all_6_2 = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | REDUCE: (48), (173) imply:
% 157.68/27.39 | | | | | | | | | | | | | | | | | (174) ~ (all_52_9 = e1)
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 157.68/27.39 | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (175) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | (176) all_58_1 = e1 & op(e3, e2) = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (100), (176) are inconsistent by sub-proof
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | #1424.
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | (177) all_58_3 = e1 & op(e2, e2) = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (97), (177) are inconsistent by sub-proof
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | #912.
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | (178) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 157.68/27.39 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 157.68/27.39 | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | (179) all_58_7 = e1 & op(e1, e2) = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (99), (179) are inconsistent by sub-proof
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | #1045.
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | (180) all_58_13 = e1 & op(e0, e2) = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | (181) all_58_13 = e1
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | |
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.39 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | (182) all_54_6 = e3
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (182) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | (183) all_52_9 = e3
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (183) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | (184) $false
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | (185) ~ (all_54_6 = e3)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | (186) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | (187) all_54_6 = e2
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (187) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | (188) all_52_9 = e2
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (188) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | (189) $false
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | (190) ~ (all_54_6 = e2)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | (191) all_54_6 = e1 | all_54_6 = e0
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | (192) all_54_6 = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (192) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | (193) all_52_9 = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (193) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | (194) $false
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | (195) all_54_6 = e0
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (195) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | (196) all_52_9 = e0
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (196) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | (197) ~ (all_52_13 = e0)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | (198) ~ (all_52_13 = e0)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | (199) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (67), (82), (97), (99), (199) are
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | (200) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | (201) all_58_5 = e1 & op(e2, e1) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | (202) all_58_5 = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_54_7 = e3
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (203) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_52_13 = e3
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (204) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (205) $false
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (206) ~ (all_54_7 = e3)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_54_7 = e2
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (208) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_52_13 = e2
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (209) imply:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (210) $false
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_54_7 = e1 | all_54_7 = e0
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_58_9 = e1 & op(e3, e0) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (97), (213) are inconsistent by sub-proof
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1078.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_58_10 = e1 & op(e2, e0) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_10 = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (11), (12), (13), (14), (17),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (23), (26), (27), (30), (31), (32),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (35), (37), (39), (40), (41), (42), (44),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (53), (55), (57), (58), (60), (67), (69),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (73), (75), (76), (79), (80), (82), (86),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (97), (99), (100), (130), (147), (164), (202),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) are inconsistent by sub-proof #378.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_58_11 = e1 & op(e1, e0) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) op(e1, e0) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (50), (65), (77), (82), (84), (85), (154),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (211), (218) are inconsistent by sub-proof
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1111.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_15 = e1 & op(e0, e0) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) op(e0, e0) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (82), (99), (220) are inconsistent by
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1386.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_10 = e1 & op(e2, e0) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_10 = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (223) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_58_4 = e1 & op(e3, e1) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (99), (224) are inconsistent by sub-proof
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | #1476.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_58_5 = e1 & op(e2, e1) = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_5 = e1
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (11), (12), (13), (14), (17),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (23), (26), (27), (30), (31), (32),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (35), (37), (39), (40), (41), (42), (44),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (53), (55), (57), (58), (60), (67), (69),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (73), (75), (76), (79), (80), (82), (86),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (97), (99), (100), (130), (147), (164), (222),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (226) are inconsistent by sub-proof #378.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (227) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (11), (12), (13), (14), (17),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (23), (26), (27), (30), (31), (32),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (34), (35), (37), (39), (40), (41), (42), (44),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (46), (53), (55), (57), (58), (60), (67), (69),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (71), (73), (75), (76), (79), (80), (82), (86),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (97), (99), (100), (130), (147), (164), (181),
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | | (222), (227) are inconsistent by sub-proof #380.
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | (228) all_54_10 = e0
% 157.68/27.40 | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (156), (228) are inconsistent by sub-proof
% 157.68/27.40 | | | | | | | | | | | | | | | | | #1528.
% 157.68/27.40 | | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | (229) all_58_12 = e1 & op(e0, e3) = e1
% 157.68/27.40 | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | | REF_CLOSE: (100), (115), (229) are inconsistent by sub-proof
% 157.68/27.40 | | | | | | | | | | | #1422.
% 157.68/27.40 | | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | | |
% 157.68/27.40 | | | | | | | | | End of split
% 157.68/27.40 | | | | | | | | |
% 157.68/27.40 | | | | | | | | Case 2:
% 157.68/27.40 | | | | | | | | |
% 157.68/27.40 | | | | | | | | | (230) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.68/27.40 | | | | | | | | |
% 157.68/27.40 | | | | | | | | | REF_CLOSE: (45), (74), (87), (95), (230) are inconsistent by
% 157.68/27.40 | | | | | | | | | sub-proof #1149.
% 157.68/27.40 | | | | | | | | |
% 157.68/27.40 | | | | | | | | End of split
% 157.68/27.40 | | | | | | | |
% 157.68/27.40 | | | | | | | End of split
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | End of split
% 157.68/27.40 | | | | | |
% 157.68/27.40 | | | | | Case 2:
% 157.68/27.40 | | | | | |
% 157.68/27.40 | | | | | | (231) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 157.68/27.40 | | | | | | op(e0, e1) = e0)
% 157.68/27.40 | | | | | |
% 157.68/27.40 | | | | | | BETA: splitting (231) gives:
% 157.68/27.40 | | | | | |
% 157.68/27.40 | | | | | | Case 1:
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | | (232) all_58_13 = e0 & op(e0, e2) = e0
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | | ALPHA: (232) implies:
% 157.68/27.40 | | | | | | | (233) all_58_13 = e0
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | | REF_CLOSE: (5), (8), (17), (67), (97), (99), (100), (233) are
% 157.68/27.40 | | | | | | | inconsistent by sub-proof #857.
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | Case 2:
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | | (234) all_58_14 = e0 & op(e0, e1) = e0
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | | ALPHA: (234) implies:
% 157.68/27.40 | | | | | | | (235) all_58_14 = e0
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | | REF_CLOSE: (11), (30), (235) are inconsistent by sub-proof #1444.
% 157.68/27.40 | | | | | | |
% 157.68/27.40 | | | | | | End of split
% 157.68/27.40 | | | | | |
% 157.68/27.40 | | | | | End of split
% 157.68/27.40 | | | | |
% 157.68/27.40 | | | | End of split
% 157.68/27.40 | | | |
% 157.68/27.40 | | | End of split
% 157.68/27.40 | | |
% 157.68/27.40 | | End of split
% 157.68/27.40 | |
% 157.68/27.40 | Case 2:
% 157.68/27.40 | |
% 157.68/27.40 | | (236) all_54_12 = e0
% 157.68/27.40 | |
% 157.68/27.40 | | REF_CLOSE: (22), (88), (236) are inconsistent by sub-proof #1223.
% 157.68/27.40 | |
% 157.68/27.40 | End of split
% 157.68/27.40 |
% 157.68/27.40 End of proof
% 157.68/27.40
% 157.68/27.40 Sub-proof #378 shows that the following formulas are inconsistent:
% 157.68/27.40 ----------------------------------------------------------------
% 157.68/27.40 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.68/27.40 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.68/27.40 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.40 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.40 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.68/27.40 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.40 (4) all_58_1 = e0
% 157.68/27.40 (5) all_58_14 = e3
% 157.68/27.40 (6) ~ (all_52_7 = e3)
% 157.68/27.40 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.68/27.40 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.40 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.68/27.40 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.68/27.40 (9) all_58_7 = e2
% 157.68/27.40 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.68/27.40 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.68/27.40 (11) op(e3, e2) = all_52_4
% 157.68/27.40 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.68/27.40 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.68/27.40 (13) all_58_6 = e1
% 157.68/27.40 (14) op(e2, e3) = all_52_1
% 157.68/27.40 (15) ~ (all_52_13 = e3)
% 157.68/27.40 (16) ~ (e3 = e0)
% 157.68/27.40 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.68/27.40 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.68/27.40 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.68/27.40 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.68/27.40 (19) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.40 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.68/27.40 e2)
% 157.68/27.40 (20) ~ (e2 = e0)
% 157.68/27.40 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.68/27.40 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.68/27.40 (22) all_58_9 = e3
% 157.68/27.40 (23) op(e2, e0) = all_52_13
% 157.68/27.40 (24) op(e2, e3) = e2
% 157.68/27.40 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.40 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.68/27.40 (26) ~ (e3 = e1)
% 157.68/27.40 (27) all_58_5 = e1
% 157.68/27.40 (28) op(e1, e2) = all_52_6
% 157.68/27.40 (29) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.40 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.68/27.40 (30) all_58_10 = e1
% 157.68/27.40 (31) op(e0, e0) = e2
% 157.68/27.40 (32) all_58_4 = e2
% 157.68/27.40 (33) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.68/27.40 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.40 (34) ~ (all_52_4 = e3)
% 157.68/27.40 (35) op(e0, e2) = e0
% 157.68/27.40 (36) ~ (e2 = e1)
% 157.68/27.40 (37) ~ (e1 = e0)
% 157.68/27.40 (38) all_58_3 = e3
% 157.68/27.40 (39) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.68/27.40 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.68/27.40 e3)
% 157.68/27.40 (40) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.68/27.40 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.68/27.40 (41) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.68/27.40 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.40 (42) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.68/27.40 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.68/27.40 (43) op(e0, e2) = all_52_7
% 157.68/27.40 (44) ~ (all_52_6 = e3)
% 157.68/27.40 (45) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.68/27.40 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.68/27.40 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.40 (47) ~ (e3 = e2)
% 157.68/27.40 (48) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.68/27.40 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.68/27.40 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.68/27.40 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.68/27.40 (49) all_58_11 = e3
% 157.68/27.40
% 157.68/27.40 Begin of proof
% 157.68/27.40 |
% 157.68/27.40 | BETA: splitting (29) gives:
% 157.68/27.40 |
% 157.68/27.40 | Case 1:
% 157.68/27.40 | |
% 157.68/27.40 | | (50) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 157.68/27.40 | | e0)
% 157.68/27.40 | |
% 157.68/27.40 | | REF_CLOSE: (16), (20), (24), (38), (46), (50) are inconsistent by sub-proof
% 157.68/27.40 | | #909.
% 157.68/27.40 | |
% 157.68/27.40 | Case 2:
% 157.68/27.40 | |
% 157.68/27.40 | | (51) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 157.68/27.40 | | e0)
% 157.68/27.40 | |
% 157.68/27.40 | | BETA: splitting (51) gives:
% 157.68/27.40 | |
% 157.68/27.40 | | Case 1:
% 157.68/27.40 | | |
% 157.68/27.40 | | | (52) all_58_5 = e0 & op(e2, e1) = e0
% 157.68/27.40 | | |
% 157.68/27.40 | | | ALPHA: (52) implies:
% 157.68/27.40 | | | (53) all_58_5 = e0
% 157.68/27.40 | | |
% 157.68/27.40 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.68/27.40 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.68/27.40 | | | (23), (24), (25), (26), (28), (29), (30), (31), (32), (33),
% 157.68/27.40 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 157.68/27.40 | | | (44), (45), (46), (47), (48), (49), (53) are inconsistent by
% 157.68/27.40 | | | sub-proof #379.
% 157.68/27.40 | | |
% 157.68/27.40 | | Case 2:
% 157.68/27.40 | | |
% 157.68/27.40 | | | (54) all_58_10 = e0 & op(e2, e0) = e0
% 157.68/27.40 | | |
% 157.68/27.40 | | | ALPHA: (54) implies:
% 157.68/27.40 | | | (55) all_58_10 = e0
% 157.68/27.40 | | |
% 157.68/27.40 | | | COMBINE_EQS: (30), (55) imply:
% 157.68/27.40 | | | (56) e1 = e0
% 157.68/27.40 | | |
% 157.68/27.40 | | | COMBINE_EQS: (27), (56) imply:
% 157.68/27.40 | | | (57) all_58_5 = e0
% 157.68/27.40 | | |
% 157.68/27.40 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.68/27.40 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.68/27.40 | | | (23), (24), (25), (26), (28), (29), (30), (31), (32), (33),
% 157.68/27.40 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 157.68/27.40 | | | (44), (45), (46), (47), (48), (49), (57) are inconsistent by
% 157.68/27.40 | | | sub-proof #379.
% 157.68/27.40 | | |
% 157.68/27.40 | | End of split
% 157.68/27.40 | |
% 157.68/27.40 | End of split
% 157.68/27.40 |
% 157.68/27.40 End of proof
% 157.68/27.40
% 157.68/27.40 Sub-proof #379 shows that the following formulas are inconsistent:
% 157.68/27.40 ----------------------------------------------------------------
% 157.68/27.40 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.68/27.40 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.68/27.40 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.40 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.40 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.68/27.40 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.40 (4) all_58_1 = e0
% 157.68/27.40 (5) all_58_14 = e3
% 157.68/27.40 (6) ~ (all_52_7 = e3)
% 157.68/27.40 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.68/27.40 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.40 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.68/27.40 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.68/27.40 (9) all_58_7 = e2
% 157.68/27.40 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.68/27.40 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.68/27.40 (11) op(e3, e2) = all_52_4
% 157.68/27.40 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.68/27.40 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.68/27.40 (13) all_58_6 = e1
% 157.68/27.40 (14) op(e2, e3) = all_52_1
% 157.68/27.40 (15) ~ (all_52_13 = e3)
% 157.68/27.40 (16) ~ (e3 = e0)
% 157.68/27.40 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.68/27.40 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.68/27.40 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.68/27.40 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.68/27.40 (19) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.40 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.68/27.40 e2)
% 157.68/27.40 (20) ~ (e2 = e0)
% 157.68/27.40 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.68/27.40 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.68/27.40 (22) all_58_9 = e3
% 157.68/27.40 (23) op(e2, e0) = all_52_13
% 157.68/27.40 (24) op(e2, e3) = e2
% 157.68/27.40 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.40 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.68/27.40 (26) ~ (e3 = e1)
% 157.68/27.40 (27) op(e1, e2) = all_52_6
% 157.68/27.40 (28) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.40 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.68/27.40 (29) all_58_10 = e1
% 157.68/27.40 (30) all_58_5 = e0
% 157.68/27.40 (31) op(e0, e0) = e2
% 157.68/27.40 (32) all_58_4 = e2
% 157.68/27.40 (33) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.68/27.40 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.40 (34) ~ (all_52_4 = e3)
% 157.68/27.40 (35) op(e0, e2) = e0
% 157.68/27.40 (36) ~ (e2 = e1)
% 157.68/27.40 (37) ~ (e1 = e0)
% 157.68/27.40 (38) all_58_3 = e3
% 157.68/27.40 (39) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.68/27.40 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.68/27.40 e3)
% 157.68/27.40 (40) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.68/27.40 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.68/27.40 (41) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.68/27.40 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.40 (42) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.68/27.40 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.68/27.40 (43) op(e0, e2) = all_52_7
% 157.68/27.40 (44) ~ (all_52_6 = e3)
% 157.68/27.40 (45) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.68/27.40 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.68/27.40 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.40 (47) ~ (e3 = e2)
% 157.68/27.40 (48) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.68/27.40 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.68/27.40 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.68/27.40 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.68/27.40 (49) all_58_11 = e3
% 157.68/27.40
% 157.68/27.40 Begin of proof
% 157.68/27.40 |
% 157.68/27.40 | BETA: splitting (2) gives:
% 157.68/27.40 |
% 157.68/27.40 | Case 1:
% 157.68/27.40 | |
% 157.68/27.40 | | (50) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 157.68/27.40 | | e1)
% 157.68/27.40 | |
% 157.68/27.40 | | BETA: splitting (50) gives:
% 157.68/27.40 | |
% 157.68/27.40 | | Case 1:
% 157.68/27.40 | | |
% 157.68/27.40 | | | (51) all_58_1 = e1 & op(e3, e2) = e1
% 157.68/27.40 | | |
% 157.68/27.40 | | | REF_CLOSE: (4), (37), (51) are inconsistent by sub-proof #1424.
% 157.68/27.40 | | |
% 157.68/27.40 | | Case 2:
% 157.68/27.40 | | |
% 157.68/27.40 | | | (52) all_58_3 = e1 & op(e2, e2) = e1
% 157.68/27.40 | | |
% 157.68/27.40 | | | REF_CLOSE: (26), (38), (52) are inconsistent by sub-proof #912.
% 157.68/27.40 | | |
% 157.68/27.40 | | End of split
% 157.68/27.40 | |
% 157.68/27.40 | Case 2:
% 157.68/27.40 | |
% 157.68/27.40 | | (53) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 157.68/27.40 | | e1)
% 157.68/27.40 | |
% 157.68/27.40 | | BETA: splitting (53) gives:
% 157.68/27.40 | |
% 157.68/27.40 | | Case 1:
% 157.68/27.40 | | |
% 157.68/27.40 | | | (54) all_58_7 = e1 & op(e1, e2) = e1
% 157.68/27.40 | | |
% 157.68/27.40 | | | REF_CLOSE: (9), (36), (54) are inconsistent by sub-proof #1045.
% 157.68/27.40 | | |
% 157.68/27.40 | | Case 2:
% 157.68/27.40 | | |
% 157.68/27.40 | | | (55) all_58_13 = e1 & op(e0, e2) = e1
% 157.68/27.40 | | |
% 157.68/27.40 | | | ALPHA: (55) implies:
% 157.68/27.40 | | | (56) all_58_13 = e1
% 157.68/27.40 | | |
% 157.68/27.40 | | | BETA: splitting (33) gives:
% 157.68/27.40 | | |
% 157.68/27.40 | | | Case 1:
% 157.68/27.40 | | | |
% 157.68/27.40 | | | | (57) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 157.68/27.40 | | | | = e1)
% 157.68/27.40 | | | |
% 157.68/27.40 | | | | REF_CLOSE: (2), (3), (5), (9), (12), (13), (16), (20), (21), (22), (24),
% 157.68/27.40 | | | | (26), (27), (28), (30), (31), (32), (33), (36), (37), (38),
% 157.68/27.40 | | | | (44), (46), (56), (57) are inconsistent by sub-proof #395.
% 157.68/27.40 | | | |
% 157.68/27.40 | | | Case 2:
% 157.68/27.40 | | | |
% 157.68/27.40 | | | | (58) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 157.68/27.40 | | | | = e1)
% 157.68/27.40 | | | |
% 157.68/27.40 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.68/27.40 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 157.68/27.40 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (31), (32),
% 157.68/27.40 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 157.68/27.40 | | | | (43), (44), (45), (46), (47), (48), (49), (56), (58) are
% 157.68/27.40 | | | | inconsistent by sub-proof #380.
% 157.68/27.40 | | | |
% 157.68/27.40 | | | End of split
% 157.68/27.40 | | |
% 157.68/27.40 | | End of split
% 157.68/27.40 | |
% 157.68/27.40 | End of split
% 157.68/27.40 |
% 157.68/27.40 End of proof
% 157.68/27.40
% 157.68/27.40 Sub-proof #380 shows that the following formulas are inconsistent:
% 157.68/27.40 ----------------------------------------------------------------
% 157.68/27.40 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.68/27.40 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.68/27.41 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.41 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.41 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.68/27.41 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.41 (4) all_58_1 = e0
% 157.68/27.41 (5) all_58_14 = e3
% 157.68/27.41 (6) ~ (all_52_7 = e3)
% 157.68/27.41 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.68/27.41 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.41 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.68/27.41 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.68/27.41 (9) all_58_7 = e2
% 157.68/27.41 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.68/27.41 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.68/27.41 (11) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.41 (12) op(e3, e2) = all_52_4
% 157.68/27.41 (13) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.68/27.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.68/27.41 (14) all_58_6 = e1
% 157.68/27.41 (15) op(e2, e3) = all_52_1
% 157.68/27.41 (16) ~ (all_52_13 = e3)
% 157.68/27.41 (17) all_58_13 = e1
% 157.68/27.41 (18) ~ (e3 = e0)
% 157.68/27.41 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.68/27.41 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.68/27.41 (20) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.68/27.41 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.68/27.41 (21) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.41 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.68/27.41 e2)
% 157.68/27.41 (22) ~ (e2 = e0)
% 157.68/27.41 (23) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.68/27.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.68/27.41 (24) all_58_9 = e3
% 157.68/27.41 (25) op(e2, e0) = all_52_13
% 157.68/27.41 (26) op(e2, e3) = e2
% 157.68/27.41 (27) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.41 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.68/27.41 (28) ~ (e3 = e1)
% 157.68/27.41 (29) op(e1, e2) = all_52_6
% 157.68/27.41 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.41 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.68/27.41 (31) all_58_10 = e1
% 157.68/27.41 (32) op(e0, e0) = e2
% 157.68/27.41 (33) all_58_4 = e2
% 157.68/27.41 (34) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.68/27.41 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.41 (35) ~ (all_52_4 = e3)
% 157.68/27.41 (36) op(e0, e2) = e0
% 157.68/27.41 (37) ~ (e2 = e1)
% 157.68/27.41 (38) ~ (e1 = e0)
% 157.68/27.41 (39) all_58_3 = e3
% 157.68/27.41 (40) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.68/27.41 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.68/27.41 e3)
% 157.68/27.41 (41) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.68/27.41 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.68/27.41 (42) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.68/27.41 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.41 (43) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.68/27.41 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.68/27.41 (44) op(e0, e2) = all_52_7
% 157.68/27.41 (45) ~ (all_52_6 = e3)
% 157.68/27.41 (46) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.68/27.41 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.68/27.41 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.41 (48) ~ (e3 = e2)
% 157.68/27.41 (49) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.68/27.41 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.68/27.41 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.68/27.41 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.68/27.41 (50) all_58_11 = e3
% 157.68/27.41
% 157.68/27.41 Begin of proof
% 157.68/27.41 |
% 157.68/27.41 | BETA: splitting (11) gives:
% 157.68/27.41 |
% 157.68/27.41 | Case 1:
% 157.68/27.41 | |
% 157.68/27.41 | | (51) all_58_8 = e1 & op(e1, e1) = e1
% 157.68/27.41 | |
% 157.68/27.41 | | ALPHA: (51) implies:
% 157.68/27.41 | | (52) all_58_8 = e1
% 157.68/27.41 | |
% 157.68/27.41 | | BETA: splitting (41) gives:
% 157.68/27.41 | |
% 157.68/27.41 | | Case 1:
% 157.68/27.41 | | |
% 157.68/27.41 | | | (53) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 157.68/27.41 | | | e1)
% 157.68/27.41 | | |
% 157.68/27.41 | | | BETA: splitting (53) gives:
% 157.68/27.41 | | |
% 157.68/27.41 | | | Case 1:
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | (54) all_58_0 = e1 & op(e3, e3) = e1
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | ALPHA: (54) implies:
% 157.68/27.41 | | | | (55) all_58_0 = e1
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | BETA: splitting (23) gives:
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | Case 1:
% 157.68/27.41 | | | | |
% 157.68/27.41 | | | | | (56) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 157.68/27.41 | | | | | e2) = e0)
% 157.68/27.41 | | | | |
% 157.68/27.41 | | | | | BETA: splitting (56) gives:
% 157.68/27.41 | | | | |
% 157.68/27.41 | | | | | Case 1:
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | (57) all_58_6 = e0 & op(e1, e3) = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | ALPHA: (57) implies:
% 157.68/27.41 | | | | | | (58) all_58_6 = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | COMBINE_EQS: (14), (58) imply:
% 157.68/27.41 | | | | | | (59) e1 = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | COMBINE_EQS: (55), (59) imply:
% 157.68/27.41 | | | | | | (60) all_58_0 = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13),
% 157.68/27.41 | | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (25),
% 157.68/27.41 | | | | | | (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 157.68/27.41 | | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 157.68/27.41 | | | | | | (45), (46), (47), (48), (49), (50), (60) are inconsistent
% 157.68/27.41 | | | | | | by sub-proof #640.
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | Case 2:
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | (61) all_58_7 = e0 & op(e1, e2) = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | REF_CLOSE: (9), (22), (61) are inconsistent by sub-proof #1468.
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | End of split
% 157.68/27.41 | | | | |
% 157.68/27.41 | | | | Case 2:
% 157.68/27.41 | | | | |
% 157.68/27.41 | | | | | (62) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1,
% 157.68/27.41 | | | | | e0) = e0)
% 157.68/27.41 | | | | |
% 157.68/27.41 | | | | | BETA: splitting (62) gives:
% 157.68/27.41 | | | | |
% 157.68/27.41 | | | | | Case 1:
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | (63) all_58_8 = e0 & op(e1, e1) = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | ALPHA: (63) implies:
% 157.68/27.41 | | | | | | (64) all_58_8 = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | COMBINE_EQS: (52), (64) imply:
% 157.68/27.41 | | | | | | (65) e1 = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | COMBINE_EQS: (55), (65) imply:
% 157.68/27.41 | | | | | | (66) all_58_0 = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13),
% 157.68/27.41 | | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (25),
% 157.68/27.41 | | | | | | (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 157.68/27.41 | | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 157.68/27.41 | | | | | | (45), (46), (47), (48), (49), (50), (66) are inconsistent
% 157.68/27.41 | | | | | | by sub-proof #640.
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | Case 2:
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | (67) all_58_11 = e0 & op(e1, e0) = e0
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | | REF_CLOSE: (18), (50), (67) are inconsistent by sub-proof #1083.
% 157.68/27.41 | | | | | |
% 157.68/27.41 | | | | | End of split
% 157.68/27.41 | | | | |
% 157.68/27.41 | | | | End of split
% 157.68/27.41 | | | |
% 157.68/27.41 | | | Case 2:
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | (68) all_58_1 = e1 & op(e3, e2) = e1
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | ALPHA: (68) implies:
% 157.68/27.41 | | | | (69) all_58_1 = e1
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | COMBINE_EQS: (4), (69) imply:
% 157.68/27.41 | | | | (70) e1 = e0
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | SIMP: (70) implies:
% 157.68/27.41 | | | | (71) e1 = e0
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | COMBINE_EQS: (17), (71) imply:
% 157.68/27.41 | | | | (72) all_58_13 = e0
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | COMBINE_EQS: (31), (71) imply:
% 157.68/27.41 | | | | (73) all_58_10 = e0
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | REF_CLOSE: (2), (3), (9), (24), (28), (32), (37), (38), (39), (47),
% 157.68/27.41 | | | | (50), (69), (72), (73) are inconsistent by sub-proof #413.
% 157.68/27.41 | | | |
% 157.68/27.41 | | | End of split
% 157.68/27.41 | | |
% 157.68/27.41 | | Case 2:
% 157.68/27.41 | | |
% 157.68/27.41 | | | (74) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 157.68/27.41 | | | e1)
% 157.68/27.41 | | |
% 157.68/27.41 | | | BETA: splitting (74) gives:
% 157.68/27.41 | | |
% 157.68/27.41 | | | Case 1:
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | (75) all_58_4 = e1 & op(e3, e1) = e1
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | REF_CLOSE: (33), (37), (75) are inconsistent by sub-proof #1476.
% 157.68/27.41 | | | |
% 157.68/27.41 | | | Case 2:
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | (76) all_58_9 = e1 & op(e3, e0) = e1
% 157.68/27.41 | | | |
% 157.68/27.41 | | | | REF_CLOSE: (24), (28), (76) are inconsistent by sub-proof #1078.
% 157.68/27.41 | | | |
% 157.68/27.41 | | | End of split
% 157.68/27.41 | | |
% 157.68/27.41 | | End of split
% 157.68/27.41 | |
% 157.68/27.41 | Case 2:
% 157.68/27.41 | |
% 157.68/27.41 | | (77) all_58_14 = e1 & op(e0, e1) = e1
% 157.68/27.41 | |
% 157.68/27.41 | | REF_CLOSE: (5), (28), (77) are inconsistent by sub-proof #844.
% 157.68/27.41 | |
% 157.68/27.41 | End of split
% 157.68/27.41 |
% 157.68/27.41 End of proof
% 157.68/27.41
% 157.68/27.41 Sub-proof #381 shows that the following formulas are inconsistent:
% 157.68/27.41 ----------------------------------------------------------------
% 157.68/27.41 (1) ~ (all_52_12 = e3)
% 157.68/27.41 (2) all_58_13 = e0
% 157.68/27.41 (3) op(e0, e3) = all_52_3
% 157.68/27.41 (4) op(e3, e0) = all_52_12
% 157.68/27.41 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.68/27.41 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.68/27.41 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.41 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.41 (7) ~ (all_52_14 = e2)
% 157.68/27.41 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.68/27.41 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.41 (9) ~ (all_52_12 = e2)
% 157.68/27.41 (10) all_58_14 = e3
% 157.68/27.41 (11) ~ (all_52_7 = e3)
% 157.68/27.41 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.41 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.68/27.41 e1)
% 157.68/27.41 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.68/27.41 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.68/27.41 (14) all_54_10 = all_6_2
% 157.68/27.41 (15) ~ (all_52_2 = all_52_3)
% 157.68/27.41 (16) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.68/27.41 (17) all_58_7 = e2
% 157.68/27.41 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.68/27.41 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.68/27.41 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.68/27.41 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.68/27.41 (21) all_54_1 = all_52_4
% 157.68/27.41 (22) op(e3, e2) = all_52_4
% 157.68/27.41 (23) ~ (all_52_3 = e0)
% 157.68/27.41 (24) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.68/27.41 (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.68/27.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.68/27.41 (26) ~ (all_52_12 = all_52_13)
% 157.68/27.41 (27) ~ (all_52_4 = e2)
% 157.68/27.41 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.41 (29) ~ (all_52_4 = all_52_12)
% 157.68/27.41 (30) op(e2, e3) = all_52_1
% 157.68/27.41 (31) ~ (all_52_13 = e3)
% 157.68/27.41 (32) ~ (all_52_3 = e3)
% 157.68/27.41 (33) ~ (all_52_2 = all_6_2)
% 157.68/27.41 (34) ~ (e3 = e0)
% 157.68/27.41 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.68/27.41 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.68/27.41 (36) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.68/27.41 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.68/27.41 (37) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.41 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.68/27.41 e2)
% 157.68/27.41 (38) ~ (e2 = e0)
% 157.68/27.41 (39) ~ (all_52_11 = all_6_2)
% 157.68/27.41 (40) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.68/27.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.68/27.41 (41) ~ (all_52_3 = e2)
% 157.68/27.41 (42) all_58_9 = e3
% 157.68/27.41 (43) op(e2, e0) = all_52_13
% 157.68/27.41 (44) op(e2, e3) = e2
% 157.68/27.41 (45) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.41 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.68/27.41 (46) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.68/27.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.68/27.41 (47) op(e1, e2) = all_52_6
% 157.68/27.41 (48) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.68/27.41 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.68/27.41 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.68/27.41 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.68/27.41 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.68/27.41 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.68/27.41 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.68/27.41 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.68/27.41 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.68/27.41 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.68/27.41 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.68/27.41 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.68/27.41 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.68/27.41 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.68/27.41 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.68/27.41 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.68/27.41 = e0)
% 157.68/27.41 (49) ~ (all_52_4 = e0)
% 157.68/27.41 (50) ~ (all_52_11 = e2)
% 157.68/27.41 (51) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.41 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.68/27.41 (52) all_54_8 = all_52_2
% 157.68/27.41 (53) all_54_7 = all_52_13
% 157.68/27.41 (54) all_56_12 = e3
% 157.68/27.41 (55) ~ (all_52_2 = e3)
% 157.68/27.41 (56) ~ (all_52_13 = e2)
% 157.68/27.41 (57) op(e0, e0) = e2
% 157.68/27.41 (58) all_58_4 = e2
% 157.68/27.41 (59) e3 = e0
% 157.68/27.41 (60) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.68/27.41 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.41 (61) ~ (all_52_4 = e3)
% 157.68/27.41 (62) op(e0, e2) = e0
% 157.68/27.41 (63) all_58_15 = e2
% 157.68/27.41 (64) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.68/27.41 (65) all_54_3 = all_52_12
% 157.68/27.41 (66) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.68/27.41 (67) ~ (all_52_2 = e2)
% 157.68/27.41 (68) all_58_3 = e3
% 157.68/27.41 (69) ~ (all_6_2 = e2)
% 157.68/27.41 (70) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.68/27.41 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.68/27.41 e3)
% 157.68/27.41 (71) all_56_14 = all_6_2
% 157.68/27.41 (72) ~ (all_52_12 = all_52_14)
% 157.68/27.41 (73) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.68/27.41 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.68/27.41 (74) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.68/27.41 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.41 (75) all_54_14 = all_52_11
% 157.68/27.41 (76) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.68/27.41 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.68/27.41 (77) op(e0, e2) = all_52_7
% 157.68/27.41 (78) op(e1, e0) = all_52_14
% 157.68/27.41 (79) all_56_15 = e2
% 157.68/27.41 (80) ~ (all_52_6 = e3)
% 157.68/27.41 (81) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.68/27.41 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.68/27.41 (82) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.41 (83) ~ (all_52_3 = all_52_11)
% 157.68/27.41 (84) all_54_11 = all_52_14
% 157.68/27.41 (85) ~ (all_52_13 = all_52_14)
% 157.68/27.41 (86) ~ (e3 = e2)
% 157.68/27.41 (87) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.68/27.41 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.68/27.41 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.68/27.41 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.68/27.41 (88) ~ (all_52_11 = e0)
% 157.68/27.41 (89) all_58_11 = e3
% 157.68/27.41 (90) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.68/27.41 (91) all_54_12 = all_52_3
% 157.68/27.41 (92) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.68/27.41
% 157.68/27.41 Begin of proof
% 157.68/27.41 |
% 157.68/27.41 | SIMP: (59) implies:
% 157.68/27.41 | (93) e3 = e0
% 157.68/27.41 |
% 157.68/27.41 | COMBINE_EQS: (42), (93) imply:
% 157.68/27.41 | (94) all_58_9 = e0
% 157.68/27.41 |
% 157.68/27.41 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.68/27.41 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.68/27.41 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 157.68/27.41 | (35), (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 157.68/27.41 | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 157.68/27.41 | (58), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 157.68/27.41 | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 157.68/27.41 | (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 157.68/27.41 | (92), (94) are inconsistent by sub-proof #384.
% 157.68/27.41 |
% 157.68/27.41 End of proof
% 157.68/27.41
% 157.68/27.41 Sub-proof #382 shows that the following formulas are inconsistent:
% 157.68/27.41 ----------------------------------------------------------------
% 157.68/27.41 (1) ~ (all_52_12 = e3)
% 157.68/27.41 (2) all_58_13 = e0
% 157.68/27.41 (3) op(e0, e3) = all_52_3
% 157.68/27.41 (4) op(e3, e0) = all_52_12
% 157.68/27.41 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.68/27.41 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.68/27.41 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.41 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.41 (7) ~ (all_52_14 = e2)
% 157.68/27.41 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.68/27.41 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.41 (9) ~ (all_52_12 = e2)
% 157.68/27.41 (10) all_58_14 = e3
% 157.68/27.41 (11) ~ (all_52_7 = e3)
% 157.68/27.41 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.41 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.68/27.41 e1)
% 157.68/27.41 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.68/27.41 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.68/27.41 (14) all_54_10 = all_6_2
% 157.68/27.41 (15) ~ (all_52_2 = all_52_3)
% 157.68/27.41 (16) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.68/27.41 (17) all_58_7 = e2
% 157.68/27.41 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.68/27.41 (19) all_58_8 = e3
% 157.68/27.41 (20) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.68/27.41 (21) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.68/27.41 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.68/27.41 (22) all_54_1 = all_52_4
% 157.68/27.41 (23) op(e3, e2) = all_52_4
% 157.68/27.41 (24) ~ (all_52_3 = e0)
% 157.68/27.41 (25) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.68/27.41 (26) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.68/27.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.68/27.41 (27) ~ (all_52_12 = all_52_13)
% 157.68/27.41 (28) ~ (all_52_4 = e2)
% 157.68/27.41 (29) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.41 (30) ~ (all_52_4 = all_52_12)
% 157.68/27.41 (31) op(e2, e3) = all_52_1
% 157.68/27.41 (32) ~ (all_52_13 = e3)
% 157.68/27.41 (33) ~ (all_52_3 = e3)
% 157.68/27.41 (34) ~ (all_52_2 = all_6_2)
% 157.68/27.41 (35) ~ (e3 = e0)
% 157.68/27.41 (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.68/27.41 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.68/27.41 (37) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.68/27.41 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.68/27.41 (38) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.41 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.68/27.41 e2)
% 157.68/27.41 (39) ~ (e2 = e0)
% 157.68/27.41 (40) ~ (all_52_11 = all_6_2)
% 157.68/27.41 (41) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.68/27.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.68/27.41 (42) ~ (all_52_3 = e2)
% 157.68/27.41 (43) all_58_9 = e3
% 157.68/27.41 (44) op(e2, e0) = all_52_13
% 157.68/27.41 (45) op(e2, e3) = e2
% 157.68/27.41 (46) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.41 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.68/27.41 (47) ~ (e3 = e1)
% 157.68/27.41 (48) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.68/27.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.68/27.41 (49) op(e1, e2) = all_52_6
% 157.68/27.41 (50) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.68/27.41 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.68/27.41 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.68/27.41 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.68/27.41 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.68/27.41 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.68/27.41 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.68/27.41 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.68/27.41 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.68/27.41 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.68/27.41 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.68/27.41 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.68/27.41 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.68/27.41 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.68/27.41 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.68/27.41 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.68/27.41 = e0)
% 157.68/27.41 (51) all_58_1 = e1
% 157.68/27.41 (52) ~ (all_52_4 = e0)
% 157.68/27.41 (53) ~ (all_52_11 = e2)
% 157.68/27.41 (54) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.41 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.68/27.41 (55) all_54_8 = all_52_2
% 157.68/27.41 (56) all_54_7 = all_52_13
% 157.68/27.41 (57) all_56_12 = e3
% 157.68/27.41 (58) ~ (all_52_2 = e3)
% 157.68/27.41 (59) ~ (all_52_13 = e2)
% 157.68/27.41 (60) op(e0, e0) = e2
% 157.68/27.41 (61) all_58_4 = e2
% 157.68/27.41 (62) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.68/27.41 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.68/27.41 (63) ~ (all_52_4 = e3)
% 157.68/27.42 (64) op(e0, e2) = e0
% 157.68/27.42 (65) all_58_15 = e2
% 157.68/27.42 (66) ~ (e2 = e1)
% 157.68/27.42 (67) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.68/27.42 (68) all_54_3 = all_52_12
% 157.68/27.42 (69) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.68/27.42 (70) ~ (all_52_2 = e2)
% 157.68/27.42 (71) all_58_3 = e3
% 157.68/27.42 (72) ~ (all_6_2 = e2)
% 157.68/27.42 (73) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.68/27.42 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.68/27.42 e3)
% 157.68/27.42 (74) all_56_14 = all_6_2
% 157.68/27.42 (75) ~ (all_52_12 = all_52_14)
% 157.68/27.42 (76) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.68/27.42 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.68/27.42 (77) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.68/27.42 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.42 (78) all_54_14 = all_52_11
% 157.68/27.42 (79) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.42 (80) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.68/27.42 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.68/27.42 (81) op(e0, e2) = all_52_7
% 157.68/27.42 (82) op(e1, e0) = all_52_14
% 157.68/27.42 (83) all_58_5 = e1 & op(e2, e1) = e1
% 157.68/27.42 (84) all_56_15 = e2
% 157.68/27.42 (85) ~ (all_52_6 = e3)
% 157.68/27.42 (86) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.68/27.42 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.68/27.42 (87) ~ (all_52_12 = e1)
% 157.68/27.42 (88) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.68/27.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.68/27.42 (89) ~ (all_52_3 = all_52_11)
% 157.68/27.42 (90) all_54_11 = all_52_14
% 157.68/27.42 (91) ~ (all_52_13 = all_52_14)
% 157.68/27.42 (92) ~ (e3 = e2)
% 157.68/27.42 (93) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.68/27.42 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.68/27.42 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.68/27.42 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.68/27.42 (94) ~ (all_52_11 = e0)
% 157.68/27.42 (95) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.68/27.42 (96) all_54_12 = all_52_3
% 157.68/27.42 (97) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.68/27.42
% 157.68/27.42 Begin of proof
% 157.68/27.42 |
% 157.68/27.42 | ALPHA: (83) implies:
% 157.68/27.42 | (98) op(e2, e1) = e1
% 157.68/27.42 |
% 157.68/27.42 | BETA: splitting (48) gives:
% 157.68/27.42 |
% 157.68/27.42 | Case 1:
% 157.68/27.42 | |
% 157.68/27.42 | | (99) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 157.68/27.42 | | e0)
% 157.68/27.42 | |
% 157.68/27.42 | | BETA: splitting (99) gives:
% 157.68/27.42 | |
% 157.68/27.42 | | Case 1:
% 157.68/27.42 | | |
% 157.68/27.42 | | | (100) all_58_4 = e0 & op(e3, e1) = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | REF_CLOSE: (39), (61), (100) are inconsistent by sub-proof #1365.
% 157.68/27.42 | | |
% 157.68/27.42 | | Case 2:
% 157.68/27.42 | | |
% 157.68/27.42 | | | (101) all_58_5 = e0 & op(e2, e1) = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | ALPHA: (101) implies:
% 157.68/27.42 | | | (102) op(e2, e1) = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | BETA: splitting (79) gives:
% 157.68/27.42 | | |
% 157.68/27.42 | | | Case 1:
% 157.68/27.42 | | | |
% 157.68/27.42 | | | | (103) all_54_3 = e2
% 157.68/27.42 | | | |
% 157.68/27.42 | | | | COMBINE_EQS: (68), (103) imply:
% 157.68/27.42 | | | | (104) all_52_12 = e2
% 157.68/27.42 | | | |
% 157.68/27.42 | | | | REDUCE: (9), (104) imply:
% 157.68/27.42 | | | | (105) $false
% 157.68/27.42 | | | |
% 157.68/27.42 | | | | CLOSE: (105) is inconsistent.
% 157.68/27.42 | | | |
% 157.68/27.42 | | | Case 2:
% 157.68/27.42 | | | |
% 157.68/27.42 | | | | (106) all_54_3 = e1 | all_54_3 = e0
% 157.68/27.42 | | | |
% 157.68/27.42 | | | | REF_CLOSE: (2), (6), (17), (47), (51), (66), (68), (71), (87), (88),
% 157.68/27.42 | | | | (98), (102), (106) are inconsistent by sub-proof #390.
% 157.68/27.42 | | | |
% 157.68/27.42 | | | End of split
% 157.68/27.42 | | |
% 157.68/27.42 | | End of split
% 157.68/27.42 | |
% 157.68/27.42 | Case 2:
% 157.68/27.42 | |
% 157.68/27.42 | | (107) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.68/27.42 | | e0)
% 157.68/27.42 | |
% 157.68/27.42 | | BETA: splitting (107) gives:
% 157.68/27.42 | |
% 157.68/27.42 | | Case 1:
% 157.68/27.42 | | |
% 157.68/27.42 | | | (108) all_58_8 = e0 & op(e1, e1) = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | ALPHA: (108) implies:
% 157.68/27.42 | | | (109) all_58_8 = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | COMBINE_EQS: (19), (109) imply:
% 157.68/27.42 | | | (110) e3 = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | COMBINE_EQS: (43), (110) imply:
% 157.68/27.42 | | | (111) all_58_9 = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.68/27.42 | | | (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 157.68/27.42 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 157.68/27.42 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (44),
% 157.68/27.42 | | | (45), (46), (48), (49), (50), (52), (53), (54), (55), (56),
% 157.68/27.42 | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (67),
% 157.68/27.42 | | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 157.68/27.42 | | | (78), (80), (81), (82), (84), (85), (86), (88), (89), (90),
% 157.68/27.42 | | | (91), (92), (93), (94), (95), (96), (97), (111) are
% 157.68/27.42 | | | inconsistent by sub-proof #383.
% 157.68/27.42 | | |
% 157.68/27.42 | | Case 2:
% 157.68/27.42 | | |
% 157.68/27.42 | | | (112) all_58_14 = e0 & op(e0, e1) = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | ALPHA: (112) implies:
% 157.68/27.42 | | | (113) all_58_14 = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | COMBINE_EQS: (10), (113) imply:
% 157.68/27.42 | | | (114) e3 = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | COMBINE_EQS: (43), (114) imply:
% 157.68/27.42 | | | (115) all_58_9 = e0
% 157.68/27.42 | | |
% 157.68/27.42 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.68/27.42 | | | (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 157.68/27.42 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 157.68/27.42 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (44),
% 157.68/27.42 | | | (45), (46), (48), (49), (50), (52), (53), (54), (55), (56),
% 157.68/27.42 | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (67),
% 157.68/27.42 | | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 157.68/27.42 | | | (78), (80), (81), (82), (84), (85), (86), (88), (89), (90),
% 157.68/27.42 | | | (91), (92), (93), (94), (95), (96), (97), (115) are
% 157.68/27.42 | | | inconsistent by sub-proof #383.
% 157.68/27.42 | | |
% 157.68/27.42 | | End of split
% 157.68/27.42 | |
% 157.68/27.42 | End of split
% 157.68/27.42 |
% 157.68/27.42 End of proof
% 157.68/27.42
% 157.68/27.42 Sub-proof #383 shows that the following formulas are inconsistent:
% 157.68/27.42 ----------------------------------------------------------------
% 157.68/27.42 (1) ~ (all_52_12 = e3)
% 157.68/27.42 (2) all_58_13 = e0
% 157.68/27.42 (3) op(e0, e3) = all_52_3
% 157.68/27.42 (4) op(e3, e0) = all_52_12
% 157.68/27.42 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.68/27.42 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.68/27.42 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.68/27.42 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.42 (7) ~ (all_52_14 = e2)
% 157.68/27.42 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.68/27.42 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.68/27.42 (9) ~ (all_52_12 = e2)
% 157.68/27.42 (10) all_58_14 = e3
% 157.68/27.42 (11) ~ (all_52_7 = e3)
% 157.68/27.42 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.68/27.42 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.68/27.42 e1)
% 157.68/27.42 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.68/27.42 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.68/27.42 (14) all_54_10 = all_6_2
% 157.68/27.42 (15) ~ (all_52_2 = all_52_3)
% 157.68/27.42 (16) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.68/27.42 (17) all_58_7 = e2
% 157.68/27.42 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.68/27.42 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.68/27.42 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.68/27.42 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.68/27.42 (21) all_54_1 = all_52_4
% 157.68/27.42 (22) op(e3, e2) = all_52_4
% 157.68/27.42 (23) ~ (all_52_3 = e0)
% 157.68/27.42 (24) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.68/27.42 (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.68/27.42 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.68/27.42 (26) ~ (all_52_12 = all_52_13)
% 157.68/27.42 (27) ~ (all_52_4 = e2)
% 157.68/27.42 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.68/27.42 (29) ~ (all_52_4 = all_52_12)
% 157.68/27.42 (30) op(e2, e3) = all_52_1
% 157.68/27.42 (31) ~ (all_52_13 = e3)
% 157.68/27.42 (32) ~ (all_52_3 = e3)
% 157.68/27.42 (33) ~ (all_52_2 = all_6_2)
% 157.68/27.42 (34) ~ (e3 = e0)
% 157.68/27.42 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.68/27.42 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.68/27.42 (36) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.68/27.42 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.68/27.42 (37) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.68/27.42 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.68/27.42 e2)
% 157.68/27.42 (38) ~ (e2 = e0)
% 157.68/27.42 (39) ~ (all_52_11 = all_6_2)
% 157.68/27.42 (40) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.68/27.42 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.68/27.42 (41) ~ (all_52_3 = e2)
% 157.68/27.42 (42) op(e2, e0) = all_52_13
% 157.68/27.42 (43) op(e2, e3) = e2
% 157.68/27.42 (44) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.68/27.42 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.79/27.42 (45) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.79/27.42 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.42 (46) op(e1, e2) = all_52_6
% 157.79/27.42 (47) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.79/27.42 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.79/27.42 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.79/27.42 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.79/27.42 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.79/27.42 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.79/27.42 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.79/27.42 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.79/27.42 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.79/27.42 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.79/27.42 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.79/27.42 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.79/27.42 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.79/27.42 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.79/27.42 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.79/27.42 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.79/27.42 = e0)
% 157.79/27.42 (48) all_58_9 = e0
% 157.79/27.42 (49) ~ (all_52_4 = e0)
% 157.79/27.42 (50) ~ (all_52_11 = e2)
% 157.79/27.42 (51) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.42 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.79/27.42 (52) all_54_8 = all_52_2
% 157.79/27.42 (53) all_54_7 = all_52_13
% 157.79/27.42 (54) all_56_12 = e3
% 157.79/27.42 (55) ~ (all_52_2 = e3)
% 157.79/27.42 (56) ~ (all_52_13 = e2)
% 157.79/27.42 (57) op(e0, e0) = e2
% 157.79/27.42 (58) all_58_4 = e2
% 157.79/27.42 (59) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.79/27.42 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.79/27.42 (60) ~ (all_52_4 = e3)
% 157.79/27.42 (61) op(e0, e2) = e0
% 157.79/27.42 (62) all_58_15 = e2
% 157.79/27.42 (63) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.79/27.42 (64) all_54_3 = all_52_12
% 157.79/27.42 (65) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.79/27.42 (66) ~ (all_52_2 = e2)
% 157.79/27.42 (67) all_58_3 = e3
% 157.79/27.42 (68) ~ (all_6_2 = e2)
% 157.79/27.42 (69) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.79/27.42 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.42 e3)
% 157.79/27.42 (70) all_56_14 = all_6_2
% 157.79/27.42 (71) ~ (all_52_12 = all_52_14)
% 157.79/27.42 (72) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.79/27.42 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.79/27.42 (73) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.79/27.42 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.42 (74) all_54_14 = all_52_11
% 157.79/27.42 (75) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.79/27.42 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.79/27.42 (76) op(e0, e2) = all_52_7
% 157.79/27.42 (77) op(e1, e0) = all_52_14
% 157.79/27.42 (78) all_56_15 = e2
% 157.79/27.42 (79) ~ (all_52_6 = e3)
% 157.79/27.42 (80) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.79/27.42 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.79/27.42 (81) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.42 (82) ~ (all_52_3 = all_52_11)
% 157.79/27.42 (83) all_54_11 = all_52_14
% 157.79/27.42 (84) ~ (all_52_13 = all_52_14)
% 157.79/27.42 (85) ~ (e3 = e2)
% 157.79/27.42 (86) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.79/27.42 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.79/27.42 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.79/27.42 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.79/27.42 (87) ~ (all_52_11 = e0)
% 157.79/27.42 (88) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.79/27.42 (89) all_54_12 = all_52_3
% 157.79/27.42 (90) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.79/27.42
% 157.79/27.42 Begin of proof
% 157.79/27.42 |
% 157.79/27.42 | BETA: splitting (13) gives:
% 157.79/27.42 |
% 157.79/27.42 | Case 1:
% 157.79/27.42 | |
% 157.79/27.42 | | (91) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 157.79/27.42 | | e3)
% 157.79/27.42 | |
% 157.79/27.42 | | REF_CLOSE: (31), (34), (42), (48), (81), (91) are inconsistent by sub-proof
% 157.79/27.42 | | #398.
% 157.79/27.42 | |
% 157.79/27.42 | Case 2:
% 157.79/27.42 | |
% 157.79/27.42 | | (92) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.42 | | e3)
% 157.79/27.42 | |
% 157.79/27.42 | | BETA: splitting (92) gives:
% 157.79/27.42 | |
% 157.79/27.42 | | Case 1:
% 157.79/27.42 | | |
% 157.79/27.42 | | | (93) all_58_11 = e3 & op(e1, e0) = e3
% 157.79/27.42 | | |
% 157.79/27.42 | | | ALPHA: (93) implies:
% 157.79/27.42 | | | (94) all_58_11 = e3
% 157.79/27.42 | | |
% 157.79/27.42 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.79/27.42 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.79/27.42 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 157.79/27.42 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 157.79/27.42 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 157.79/27.42 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 157.79/27.42 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 157.79/27.42 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 157.79/27.42 | | | (83), (84), (85), (86), (87), (88), (89), (90), (94) are
% 157.79/27.42 | | | inconsistent by sub-proof #384.
% 157.79/27.42 | | |
% 157.79/27.42 | | Case 2:
% 157.79/27.42 | | |
% 157.79/27.42 | | | (95) all_58_15 = e3 & op(e0, e0) = e3
% 157.79/27.42 | | |
% 157.79/27.42 | | | ALPHA: (95) implies:
% 157.79/27.42 | | | (96) op(e0, e0) = e3
% 157.79/27.42 | | |
% 157.79/27.42 | | | REF_CLOSE: (57), (81), (85), (96) are inconsistent by sub-proof #1382.
% 157.79/27.42 | | |
% 157.79/27.42 | | End of split
% 157.79/27.42 | |
% 157.79/27.42 | End of split
% 157.79/27.42 |
% 157.79/27.42 End of proof
% 157.79/27.42
% 157.79/27.42 Sub-proof #384 shows that the following formulas are inconsistent:
% 157.79/27.42 ----------------------------------------------------------------
% 157.79/27.42 (1) ~ (all_52_12 = e3)
% 157.79/27.42 (2) all_58_13 = e0
% 157.79/27.42 (3) op(e0, e3) = all_52_3
% 157.79/27.42 (4) op(e3, e0) = all_52_12
% 157.79/27.42 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.79/27.42 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.79/27.42 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.42 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.42 (7) ~ (all_52_14 = e2)
% 157.79/27.42 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.79/27.42 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.42 (9) ~ (all_52_12 = e2)
% 157.79/27.42 (10) all_58_14 = e3
% 157.79/27.42 (11) ~ (all_52_7 = e3)
% 157.79/27.42 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.42 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.79/27.42 e1)
% 157.79/27.42 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.79/27.42 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.79/27.42 (14) all_54_10 = all_6_2
% 157.79/27.42 (15) ~ (all_52_2 = all_52_3)
% 157.79/27.42 (16) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.79/27.42 (17) all_58_7 = e2
% 157.79/27.42 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.79/27.42 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.79/27.42 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.79/27.42 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.79/27.42 (21) all_54_1 = all_52_4
% 157.79/27.42 (22) op(e3, e2) = all_52_4
% 157.79/27.42 (23) ~ (all_52_3 = e0)
% 157.79/27.42 (24) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.79/27.42 (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.79/27.42 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.79/27.42 (26) ~ (all_52_12 = all_52_13)
% 157.79/27.42 (27) ~ (all_52_4 = e2)
% 157.79/27.42 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.79/27.42 (29) ~ (all_52_4 = all_52_12)
% 157.79/27.42 (30) op(e2, e3) = all_52_1
% 157.79/27.42 (31) ~ (all_52_13 = e3)
% 157.79/27.42 (32) ~ (all_52_3 = e3)
% 157.79/27.42 (33) ~ (all_52_2 = all_6_2)
% 157.79/27.42 (34) ~ (e3 = e0)
% 157.79/27.42 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.79/27.42 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.79/27.42 (36) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.79/27.42 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.79/27.42 (37) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.42 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.79/27.42 e2)
% 157.79/27.42 (38) ~ (e2 = e0)
% 157.79/27.42 (39) ~ (all_52_11 = all_6_2)
% 157.79/27.42 (40) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.79/27.42 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.79/27.42 (41) ~ (all_52_3 = e2)
% 157.79/27.42 (42) op(e2, e0) = all_52_13
% 157.79/27.42 (43) op(e2, e3) = e2
% 157.79/27.42 (44) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.42 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.79/27.42 (45) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.79/27.42 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.42 (46) op(e1, e2) = all_52_6
% 157.79/27.42 (47) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.79/27.42 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.79/27.42 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.79/27.42 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.79/27.42 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.79/27.42 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.79/27.42 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.79/27.42 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.79/27.42 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.79/27.42 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.79/27.42 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.79/27.42 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.79/27.42 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.79/27.42 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.79/27.42 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.79/27.42 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.79/27.42 = e0)
% 157.79/27.42 (48) all_58_9 = e0
% 157.79/27.42 (49) ~ (all_52_4 = e0)
% 157.79/27.42 (50) ~ (all_52_11 = e2)
% 157.79/27.42 (51) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.42 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.79/27.42 (52) all_54_8 = all_52_2
% 157.79/27.42 (53) all_54_7 = all_52_13
% 157.79/27.42 (54) all_56_12 = e3
% 157.79/27.42 (55) ~ (all_52_2 = e3)
% 157.79/27.42 (56) ~ (all_52_13 = e2)
% 157.79/27.42 (57) op(e0, e0) = e2
% 157.79/27.42 (58) all_58_4 = e2
% 157.79/27.42 (59) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.79/27.42 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.79/27.42 (60) ~ (all_52_4 = e3)
% 157.79/27.42 (61) op(e0, e2) = e0
% 157.79/27.42 (62) all_58_15 = e2
% 157.79/27.42 (63) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.79/27.42 (64) all_54_3 = all_52_12
% 157.79/27.42 (65) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.79/27.42 (66) ~ (all_52_2 = e2)
% 157.79/27.42 (67) all_58_3 = e3
% 157.79/27.42 (68) ~ (all_6_2 = e2)
% 157.79/27.42 (69) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.79/27.42 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.42 e3)
% 157.79/27.42 (70) all_56_14 = all_6_2
% 157.79/27.42 (71) ~ (all_52_12 = all_52_14)
% 157.79/27.42 (72) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.79/27.42 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.79/27.42 (73) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.79/27.42 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.42 (74) all_54_14 = all_52_11
% 157.79/27.42 (75) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.79/27.42 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.79/27.42 (76) op(e0, e2) = all_52_7
% 157.79/27.42 (77) op(e1, e0) = all_52_14
% 157.79/27.42 (78) all_56_15 = e2
% 157.79/27.42 (79) ~ (all_52_6 = e3)
% 157.79/27.42 (80) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.79/27.42 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.79/27.42 (81) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.42 (82) ~ (all_52_3 = all_52_11)
% 157.79/27.42 (83) all_54_11 = all_52_14
% 157.79/27.42 (84) ~ (all_52_13 = all_52_14)
% 157.79/27.42 (85) ~ (e3 = e2)
% 157.79/27.43 (86) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.79/27.43 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.79/27.43 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.79/27.43 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.79/27.43 (87) ~ (all_52_11 = e0)
% 157.79/27.43 (88) all_58_11 = e3
% 157.79/27.43 (89) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.79/27.43 (90) all_54_12 = all_52_3
% 157.79/27.43 (91) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.79/27.43
% 157.79/27.43 Begin of proof
% 157.79/27.43 |
% 157.79/27.43 | BETA: splitting (89) gives:
% 157.79/27.43 |
% 157.79/27.43 | Case 1:
% 157.79/27.43 | |
% 157.79/27.43 | | (92) all_54_12 = e3
% 157.79/27.43 | |
% 157.79/27.43 | | REF_CLOSE: (32), (90), (92) are inconsistent by sub-proof #1234.
% 157.79/27.43 | |
% 157.79/27.43 | Case 2:
% 157.79/27.43 | |
% 157.79/27.43 | | (93) ~ (all_54_12 = e3)
% 157.79/27.43 | | (94) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.79/27.43 | |
% 157.79/27.43 | | BETA: splitting (24) gives:
% 157.79/27.43 | |
% 157.79/27.43 | | Case 1:
% 157.79/27.43 | | |
% 157.79/27.43 | | | (95) all_54_1 = e3
% 157.79/27.43 | | |
% 157.79/27.43 | | | COMBINE_EQS: (21), (95) imply:
% 157.79/27.43 | | | (96) all_52_4 = e3
% 157.79/27.43 | | |
% 157.79/27.43 | | | REDUCE: (60), (96) imply:
% 157.79/27.43 | | | (97) $false
% 157.79/27.43 | | |
% 157.79/27.43 | | | CLOSE: (97) is inconsistent.
% 157.79/27.43 | | |
% 157.79/27.43 | | Case 2:
% 157.79/27.43 | | |
% 157.79/27.43 | | | (98) ~ (all_54_1 = e3)
% 157.79/27.43 | | | (99) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.79/27.43 | | |
% 157.79/27.43 | | | BETA: splitting (99) gives:
% 157.79/27.43 | | |
% 157.79/27.43 | | | Case 1:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | (100) all_54_1 = e2
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | COMBINE_EQS: (21), (100) imply:
% 157.79/27.43 | | | | (101) all_52_4 = e2
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | REDUCE: (27), (101) imply:
% 157.79/27.43 | | | | (102) $false
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | CLOSE: (102) is inconsistent.
% 157.79/27.43 | | | |
% 157.79/27.43 | | | Case 2:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | (103) ~ (all_54_1 = e2)
% 157.79/27.43 | | | | (104) all_54_1 = e1 | all_54_1 = e0
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | BETA: splitting (104) gives:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | Case 1:
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | (105) all_54_1 = e1
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | COMBINE_EQS: (21), (105) imply:
% 157.79/27.43 | | | | | (106) all_52_4 = e1
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | REDUCE: (29), (106) imply:
% 157.79/27.43 | | | | | (107) ~ (all_52_12 = e1)
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | SIMP: (107) implies:
% 157.79/27.43 | | | | | (108) ~ (all_52_12 = e1)
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | REDUCE: (60), (106) imply:
% 157.79/27.43 | | | | | (109) ~ (e3 = e1)
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | SIMP: (109) implies:
% 157.79/27.43 | | | | | (110) ~ (e3 = e1)
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | REDUCE: (27), (106) imply:
% 157.79/27.43 | | | | | (111) ~ (e2 = e1)
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | SIMP: (111) implies:
% 157.79/27.43 | | | | | (112) ~ (e2 = e1)
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | REDUCE: (49), (106) imply:
% 157.79/27.43 | | | | | (113) ~ (e1 = e0)
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.79/27.43 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (22),
% 157.79/27.43 | | | | | (23), (25), (26), (28), (30), (31), (32), (33), (34), (35),
% 157.79/27.43 | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.79/27.43 | | | | | (46), (47), (48), (50), (51), (52), (53), (54), (55), (56),
% 157.79/27.43 | | | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 157.79/27.43 | | | | | (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 157.79/27.43 | | | | | (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 157.79/27.43 | | | | | (87), (88), (90), (91), (94), (108), (110), (112), (113)
% 157.79/27.43 | | | | | are inconsistent by sub-proof #385.
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | Case 2:
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | (114) all_54_1 = e0
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | COMBINE_EQS: (21), (114) imply:
% 157.79/27.43 | | | | | (115) all_52_4 = e0
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | REDUCE: (49), (115) imply:
% 157.79/27.43 | | | | | (116) $false
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | CLOSE: (116) is inconsistent.
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | End of split
% 157.79/27.43 | | | |
% 157.79/27.43 | | | End of split
% 157.79/27.43 | | |
% 157.79/27.43 | | End of split
% 157.79/27.43 | |
% 157.79/27.43 | End of split
% 157.79/27.43 |
% 157.79/27.43 End of proof
% 157.79/27.43
% 157.79/27.43 Sub-proof #385 shows that the following formulas are inconsistent:
% 157.79/27.43 ----------------------------------------------------------------
% 157.79/27.43 (1) ~ (all_52_12 = e3)
% 157.79/27.43 (2) all_58_13 = e0
% 157.79/27.43 (3) op(e0, e3) = all_52_3
% 157.79/27.43 (4) op(e3, e0) = all_52_12
% 157.79/27.43 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.79/27.43 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.79/27.43 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.43 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.43 (7) ~ (all_52_14 = e2)
% 157.79/27.43 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.79/27.43 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.43 (9) ~ (all_52_12 = e2)
% 157.79/27.43 (10) all_58_14 = e3
% 157.79/27.43 (11) ~ (all_52_7 = e3)
% 157.79/27.43 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.43 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.79/27.43 e1)
% 157.79/27.43 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.79/27.43 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.79/27.43 (14) all_54_10 = all_6_2
% 157.79/27.43 (15) ~ (all_52_2 = all_52_3)
% 157.79/27.43 (16) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.79/27.43 (17) all_58_7 = e2
% 157.79/27.43 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.79/27.43 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.79/27.43 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.79/27.43 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.79/27.43 (21) op(e3, e2) = all_52_4
% 157.79/27.43 (22) ~ (all_52_3 = e0)
% 157.79/27.43 (23) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.79/27.43 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.79/27.43 (24) ~ (all_52_12 = all_52_13)
% 157.79/27.43 (25) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.79/27.43 (26) op(e2, e3) = all_52_1
% 157.79/27.43 (27) ~ (all_52_13 = e3)
% 157.79/27.43 (28) ~ (all_52_3 = e3)
% 157.79/27.43 (29) ~ (all_52_2 = all_6_2)
% 157.79/27.43 (30) ~ (e3 = e0)
% 157.79/27.43 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.79/27.43 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.79/27.43 (32) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.79/27.43 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.79/27.43 (33) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.43 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.79/27.43 e2)
% 157.79/27.43 (34) ~ (e2 = e0)
% 157.79/27.43 (35) ~ (all_52_11 = all_6_2)
% 157.79/27.43 (36) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.79/27.43 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.79/27.43 (37) ~ (all_52_3 = e2)
% 157.79/27.43 (38) op(e2, e0) = all_52_13
% 157.79/27.43 (39) op(e2, e3) = e2
% 157.79/27.43 (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.43 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.79/27.43 (41) ~ (e3 = e1)
% 157.79/27.43 (42) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.79/27.43 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.43 (43) op(e1, e2) = all_52_6
% 157.79/27.43 (44) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.79/27.43 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.79/27.43 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.79/27.43 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.79/27.43 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.79/27.43 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.79/27.43 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.79/27.43 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.79/27.43 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.79/27.43 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.79/27.43 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.79/27.43 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.79/27.43 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.79/27.43 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.79/27.43 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.79/27.43 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.79/27.43 = e0)
% 157.79/27.43 (45) all_58_9 = e0
% 157.79/27.43 (46) ~ (all_52_11 = e2)
% 157.79/27.43 (47) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.43 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.79/27.43 (48) all_54_8 = all_52_2
% 157.79/27.43 (49) all_54_7 = all_52_13
% 157.79/27.43 (50) all_56_12 = e3
% 157.79/27.43 (51) ~ (all_52_2 = e3)
% 157.79/27.43 (52) ~ (all_52_13 = e2)
% 157.79/27.43 (53) op(e0, e0) = e2
% 157.79/27.43 (54) all_58_4 = e2
% 157.79/27.43 (55) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.79/27.43 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.79/27.43 (56) ~ (all_52_4 = e3)
% 157.79/27.43 (57) op(e0, e2) = e0
% 157.79/27.43 (58) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.79/27.43 (59) all_58_15 = e2
% 157.79/27.43 (60) ~ (e2 = e1)
% 157.79/27.43 (61) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.79/27.43 (62) all_54_3 = all_52_12
% 157.79/27.43 (63) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.79/27.43 (64) ~ (e1 = e0)
% 157.79/27.43 (65) ~ (all_52_2 = e2)
% 157.79/27.43 (66) all_58_3 = e3
% 157.79/27.43 (67) ~ (all_6_2 = e2)
% 157.79/27.43 (68) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.79/27.43 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.43 e3)
% 157.79/27.43 (69) all_56_14 = all_6_2
% 157.79/27.43 (70) ~ (all_52_12 = all_52_14)
% 157.79/27.43 (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.79/27.43 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.79/27.43 (72) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.79/27.43 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.43 (73) all_54_14 = all_52_11
% 157.79/27.43 (74) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.79/27.43 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.79/27.43 (75) op(e0, e2) = all_52_7
% 157.79/27.43 (76) op(e1, e0) = all_52_14
% 157.79/27.43 (77) all_56_15 = e2
% 157.79/27.43 (78) ~ (all_52_6 = e3)
% 157.79/27.43 (79) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.79/27.43 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.79/27.43 (80) ~ (all_52_12 = e1)
% 157.79/27.43 (81) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.43 (82) ~ (all_52_3 = all_52_11)
% 157.79/27.43 (83) all_54_11 = all_52_14
% 157.79/27.43 (84) ~ (all_52_13 = all_52_14)
% 157.79/27.43 (85) ~ (e3 = e2)
% 157.79/27.43 (86) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.79/27.43 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.79/27.43 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.79/27.43 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.79/27.43 (87) ~ (all_52_11 = e0)
% 157.79/27.43 (88) all_58_11 = e3
% 157.79/27.43 (89) all_54_12 = all_52_3
% 157.79/27.43 (90) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.79/27.43
% 157.79/27.43 Begin of proof
% 157.79/27.43 |
% 157.79/27.43 | BETA: splitting (25) gives:
% 157.79/27.43 |
% 157.79/27.43 | Case 1:
% 157.79/27.43 | |
% 157.79/27.43 | | (91) all_54_3 = e3
% 157.79/27.43 | |
% 157.79/27.43 | | COMBINE_EQS: (62), (91) imply:
% 157.79/27.43 | | (92) all_52_12 = e3
% 157.79/27.43 | |
% 157.79/27.43 | | REDUCE: (1), (92) imply:
% 157.79/27.43 | | (93) $false
% 157.79/27.43 | |
% 157.79/27.43 | | CLOSE: (93) is inconsistent.
% 157.79/27.43 | |
% 157.79/27.43 | Case 2:
% 157.79/27.43 | |
% 157.79/27.43 | | (94) ~ (all_54_3 = e3)
% 157.79/27.43 | | (95) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.79/27.43 | |
% 157.79/27.43 | | BETA: splitting (6) gives:
% 157.79/27.43 | |
% 157.79/27.43 | | Case 1:
% 157.79/27.43 | | |
% 157.79/27.43 | | | (96) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 157.79/27.43 | | | e1)
% 157.79/27.43 | | |
% 157.79/27.43 | | | BETA: splitting (96) gives:
% 157.79/27.43 | | |
% 157.79/27.43 | | | Case 1:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | (97) all_58_1 = e1 & op(e3, e2) = e1
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | ALPHA: (97) implies:
% 157.79/27.43 | | | | (98) all_58_1 = e1
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | BETA: splitting (95) gives:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | Case 1:
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | (99) all_54_3 = e2
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | COMBINE_EQS: (62), (99) imply:
% 157.79/27.43 | | | | | (100) all_52_12 = e2
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | REDUCE: (9), (100) imply:
% 157.79/27.43 | | | | | (101) $false
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | CLOSE: (101) is inconsistent.
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | Case 2:
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | (102) ~ (all_54_3 = e2)
% 157.79/27.43 | | | | | (103) all_54_3 = e1 | all_54_3 = e0
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.79/27.43 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 157.79/27.43 | | | | | (22), (23), (24), (26), (27), (28), (29), (30), (31), (32),
% 157.79/27.43 | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 157.79/27.43 | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 157.79/27.43 | | | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 157.79/27.43 | | | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 157.79/27.43 | | | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 157.79/27.43 | | | | | (83), (84), (85), (86), (87), (88), (89), (90), (98), (103)
% 157.79/27.43 | | | | | are inconsistent by sub-proof #386.
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | End of split
% 157.79/27.43 | | | |
% 157.79/27.43 | | | Case 2:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | (104) all_58_3 = e1 & op(e2, e2) = e1
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | REF_CLOSE: (41), (66), (104) are inconsistent by sub-proof #912.
% 157.79/27.43 | | | |
% 157.79/27.43 | | | End of split
% 157.79/27.43 | | |
% 157.79/27.43 | | Case 2:
% 157.79/27.43 | | |
% 157.79/27.43 | | | (105) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 157.79/27.43 | | | = e1)
% 157.79/27.43 | | |
% 157.79/27.43 | | | BETA: splitting (105) gives:
% 157.79/27.43 | | |
% 157.79/27.43 | | | Case 1:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | (106) all_58_7 = e1 & op(e1, e2) = e1
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | REF_CLOSE: (17), (60), (106) are inconsistent by sub-proof #1045.
% 157.79/27.43 | | | |
% 157.79/27.43 | | | Case 2:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | (107) all_58_13 = e1 & op(e0, e2) = e1
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | REF_CLOSE: (2), (64), (107) are inconsistent by sub-proof #1085.
% 157.79/27.43 | | | |
% 157.79/27.43 | | | End of split
% 157.79/27.43 | | |
% 157.79/27.43 | | End of split
% 157.79/27.43 | |
% 157.79/27.43 | End of split
% 157.79/27.43 |
% 157.79/27.43 End of proof
% 157.79/27.43
% 157.79/27.43 Sub-proof #386 shows that the following formulas are inconsistent:
% 157.79/27.43 ----------------------------------------------------------------
% 157.79/27.43 (1) ~ (all_52_12 = e3)
% 157.79/27.43 (2) all_58_13 = e0
% 157.79/27.43 (3) op(e0, e3) = all_52_3
% 157.79/27.43 (4) op(e3, e0) = all_52_12
% 157.79/27.43 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.79/27.43 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.79/27.43 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.43 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.43 (7) ~ (all_52_14 = e2)
% 157.79/27.43 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.79/27.43 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.43 (9) ~ (all_52_12 = e2)
% 157.79/27.43 (10) all_58_14 = e3
% 157.79/27.43 (11) ~ (all_52_7 = e3)
% 157.79/27.43 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.43 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.79/27.43 e1)
% 157.79/27.43 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.79/27.43 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.79/27.43 (14) all_54_10 = all_6_2
% 157.79/27.43 (15) ~ (all_52_2 = all_52_3)
% 157.79/27.43 (16) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.79/27.43 (17) all_58_7 = e2
% 157.79/27.43 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.79/27.43 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.79/27.43 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.79/27.43 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.79/27.43 (21) op(e3, e2) = all_52_4
% 157.79/27.43 (22) ~ (all_52_3 = e0)
% 157.79/27.43 (23) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.79/27.43 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.79/27.43 (24) ~ (all_52_12 = all_52_13)
% 157.79/27.43 (25) op(e2, e3) = all_52_1
% 157.79/27.43 (26) ~ (all_52_13 = e3)
% 157.79/27.43 (27) ~ (all_52_3 = e3)
% 157.79/27.43 (28) ~ (all_52_2 = all_6_2)
% 157.79/27.43 (29) all_54_3 = e1 | all_54_3 = e0
% 157.79/27.43 (30) ~ (e3 = e0)
% 157.79/27.43 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.79/27.43 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.79/27.43 (32) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.79/27.43 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.79/27.43 (33) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.43 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.79/27.43 e2)
% 157.79/27.43 (34) ~ (e2 = e0)
% 157.79/27.43 (35) ~ (all_52_11 = all_6_2)
% 157.79/27.43 (36) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.79/27.43 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.79/27.43 (37) ~ (all_52_3 = e2)
% 157.79/27.43 (38) op(e2, e0) = all_52_13
% 157.79/27.43 (39) op(e2, e3) = e2
% 157.79/27.43 (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.43 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.79/27.43 (41) ~ (e3 = e1)
% 157.79/27.43 (42) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.79/27.43 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.43 (43) op(e1, e2) = all_52_6
% 157.79/27.43 (44) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 157.79/27.43 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.79/27.43 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 157.79/27.43 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.79/27.43 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 157.79/27.43 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.79/27.43 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 157.79/27.43 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 157.79/27.43 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 157.79/27.43 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.79/27.43 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 157.79/27.43 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 157.79/27.43 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 157.79/27.43 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 157.79/27.43 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 157.79/27.43 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 157.79/27.43 = e0)
% 157.79/27.43 (45) all_58_1 = e1
% 157.79/27.43 (46) all_58_9 = e0
% 157.79/27.43 (47) ~ (all_52_11 = e2)
% 157.79/27.43 (48) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.43 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.79/27.43 (49) all_54_8 = all_52_2
% 157.79/27.43 (50) all_54_7 = all_52_13
% 157.79/27.43 (51) all_56_12 = e3
% 157.79/27.43 (52) ~ (all_52_2 = e3)
% 157.79/27.43 (53) ~ (all_52_13 = e2)
% 157.79/27.43 (54) op(e0, e0) = e2
% 157.79/27.43 (55) all_58_4 = e2
% 157.79/27.43 (56) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.79/27.43 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.79/27.43 (57) ~ (all_52_4 = e3)
% 157.79/27.43 (58) op(e0, e2) = e0
% 157.79/27.43 (59) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.79/27.43 (60) all_58_15 = e2
% 157.79/27.43 (61) ~ (e2 = e1)
% 157.79/27.43 (62) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.79/27.43 (63) all_54_3 = all_52_12
% 157.79/27.43 (64) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.79/27.43 (65) ~ (e1 = e0)
% 157.79/27.43 (66) ~ (all_52_2 = e2)
% 157.79/27.43 (67) all_58_3 = e3
% 157.79/27.43 (68) ~ (all_6_2 = e2)
% 157.79/27.43 (69) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.79/27.43 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.43 e3)
% 157.79/27.43 (70) all_56_14 = all_6_2
% 157.79/27.43 (71) ~ (all_52_12 = all_52_14)
% 157.79/27.43 (72) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.79/27.43 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.79/27.43 (73) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.79/27.43 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.43 (74) all_54_14 = all_52_11
% 157.79/27.43 (75) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.79/27.43 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.79/27.43 (76) op(e0, e2) = all_52_7
% 157.79/27.43 (77) op(e1, e0) = all_52_14
% 157.79/27.43 (78) all_56_15 = e2
% 157.79/27.43 (79) ~ (all_52_6 = e3)
% 157.79/27.43 (80) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.79/27.43 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.79/27.43 (81) ~ (all_52_12 = e1)
% 157.79/27.43 (82) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.43 (83) ~ (all_52_3 = all_52_11)
% 157.79/27.43 (84) all_54_11 = all_52_14
% 157.79/27.43 (85) ~ (all_52_13 = all_52_14)
% 157.79/27.43 (86) ~ (e3 = e2)
% 157.79/27.43 (87) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.79/27.43 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.79/27.43 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.79/27.43 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.79/27.43 (88) ~ (all_52_11 = e0)
% 157.79/27.43 (89) all_58_11 = e3
% 157.79/27.43 (90) all_54_12 = all_52_3
% 157.79/27.43 (91) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.79/27.43
% 157.79/27.43 Begin of proof
% 157.79/27.43 |
% 157.79/27.43 | BETA: splitting (75) gives:
% 157.79/27.43 |
% 157.79/27.43 | Case 1:
% 157.79/27.43 | |
% 157.79/27.43 | | (92) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 157.79/27.43 | | e3)
% 157.79/27.43 | |
% 157.79/27.43 | | BETA: splitting (92) gives:
% 157.79/27.43 | |
% 157.79/27.43 | | Case 1:
% 157.79/27.43 | | |
% 157.79/27.43 | | | (93) all_58_0 = e3 & op(e3, e3) = e3
% 157.79/27.43 | | |
% 157.79/27.43 | | | ALPHA: (93) implies:
% 157.79/27.43 | | | (94) all_58_0 = e3
% 157.79/27.43 | | |
% 157.79/27.43 | | | BETA: splitting (59) gives:
% 157.79/27.43 | | |
% 157.79/27.43 | | | Case 1:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | (95) all_54_12 = e2
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | REF_CLOSE: (37), (90), (95) are inconsistent by sub-proof #1189.
% 157.79/27.43 | | | |
% 157.79/27.43 | | | Case 2:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | (96) ~ (all_54_12 = e2)
% 157.79/27.43 | | | | (97) all_54_12 = e1 | all_54_12 = e0
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | BETA: splitting (8) gives:
% 157.79/27.43 | | | |
% 157.79/27.43 | | | | Case 1:
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | (98) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 157.79/27.43 | | | | | e0) = e1)
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | BETA: splitting (98) gives:
% 157.79/27.43 | | | | |
% 157.79/27.43 | | | | | Case 1:
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | (99) all_58_9 = e1 & op(e3, e0) = e1
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | ALPHA: (99) implies:
% 157.79/27.43 | | | | | | (100) all_58_9 = e1
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | COMBINE_EQS: (46), (100) imply:
% 157.79/27.43 | | | | | | (101) e1 = e0
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | COMBINE_EQS: (45), (101) imply:
% 157.79/27.43 | | | | | | (102) all_58_1 = e0
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | REF_CLOSE: (2), (6), (17), (41), (61), (65), (67), (102) are
% 157.79/27.43 | | | | | | inconsistent by sub-proof #857.
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | Case 2:
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | (103) all_58_10 = e1 & op(e2, e0) = e1
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | ALPHA: (103) implies:
% 157.79/27.43 | | | | | | (104) op(e2, e0) = e1
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | BETA: splitting (80) gives:
% 157.79/27.43 | | | | | |
% 157.79/27.43 | | | | | | Case 1:
% 157.79/27.43 | | | | | | |
% 157.79/27.44 | | | | | | | (105) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 157.79/27.44 | | | | | | | op(e2, e3) = e0)
% 157.79/27.44 | | | | | | |
% 157.79/27.44 | | | | | | | REF_CLOSE: (30), (34), (39), (82), (94), (105) are inconsistent by
% 157.79/27.44 | | | | | | | sub-proof #615.
% 157.79/27.44 | | | | | | |
% 157.79/27.44 | | | | | | Case 2:
% 157.79/27.44 | | | | | | |
% 157.79/27.44 | | | | | | | (106) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 157.79/27.44 | | | | | | | op(e0, e3) = e0)
% 157.79/27.44 | | | | | | |
% 157.79/27.44 | | | | | | | BETA: splitting (106) gives:
% 157.79/27.44 | | | | | | |
% 157.79/27.44 | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | |
% 157.79/27.44 | | | | | | | | (107) all_58_6 = e0 & op(e1, e3) = e0
% 157.79/27.44 | | | | | | | |
% 157.79/27.44 | | | | | | | | ALPHA: (107) implies:
% 157.79/27.44 | | | | | | | | (108) all_58_6 = e0
% 157.79/27.44 | | | | | | | |
% 157.79/27.44 | | | | | | | | BETA: splitting (29) gives:
% 157.79/27.44 | | | | | | | |
% 157.79/27.44 | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | (109) all_54_3 = e1
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | COMBINE_EQS: (63), (109) imply:
% 157.79/27.44 | | | | | | | | | (110) all_52_12 = e1
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | REDUCE: (81), (110) imply:
% 157.79/27.44 | | | | | | | | | (111) $false
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | CLOSE: (111) is inconsistent.
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | (112) all_54_3 = e0
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | COMBINE_EQS: (63), (112) imply:
% 157.79/27.44 | | | | | | | | | (113) all_52_12 = e0
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | REDUCE: (24), (113) imply:
% 157.79/27.44 | | | | | | | | | (114) ~ (all_52_13 = e0)
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | SIMP: (114) implies:
% 157.79/27.44 | | | | | | | | | (115) ~ (all_52_13 = e0)
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | REDUCE: (71), (113) imply:
% 157.79/27.44 | | | | | | | | | (116) ~ (all_52_14 = e0)
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | SIMP: (116) implies:
% 157.79/27.44 | | | | | | | | | (117) ~ (all_52_14 = e0)
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | REDUCE: (1), (113) imply:
% 157.79/27.44 | | | | | | | | | (118) ~ (e3 = e0)
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | REDUCE: (9), (113) imply:
% 157.79/27.44 | | | | | | | | | (119) ~ (e2 = e0)
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | REDUCE: (81), (113) imply:
% 157.79/27.44 | | | | | | | | | (120) ~ (e1 = e0)
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | REDUCE: (4), (113) imply:
% 157.79/27.44 | | | | | | | | | (121) op(e3, e0) = e0
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | BETA: splitting (18) gives:
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | (122) all_54_7 = e3
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | COMBINE_EQS: (50), (122) imply:
% 157.79/27.44 | | | | | | | | | | (123) all_52_13 = e3
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | REDUCE: (26), (123) imply:
% 157.79/27.44 | | | | | | | | | | (124) $false
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | CLOSE: (124) is inconsistent.
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | (125) ~ (all_54_7 = e3)
% 157.79/27.44 | | | | | | | | | | (126) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | BETA: splitting (5) gives:
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | (127) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 157.79/27.44 | | | | | | | | | | | & op(e1, e2) = e1)
% 157.79/27.44 | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | BETA: splitting (127) gives:
% 157.79/27.44 | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | (128) all_58_6 = e1 & op(e1, e3) = e1
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | REF_CLOSE: (2), (6), (17), (41), (45), (61), (65), (67),
% 157.79/27.44 | | | | | | | | | | | | (108), (128) are inconsistent by sub-proof #611.
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | (129) all_58_7 = e1 & op(e1, e2) = e1
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | ALPHA: (129) implies:
% 157.79/27.44 | | | | | | | | | | | | (130) all_58_7 = e1
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | REF_CLOSE: (17), (61), (130) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | | | | | #721.
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | (131) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 157.79/27.44 | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 157.79/27.44 | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | BETA: splitting (131) gives:
% 157.79/27.44 | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | (132) all_58_8 = e1 & op(e1, e1) = e1
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | ALPHA: (132) implies:
% 157.79/27.44 | | | | | | | | | | | | (133) all_58_8 = e1
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | BETA: splitting (97) gives:
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | (134) all_54_12 = e1
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | COMBINE_EQS: (90), (134) imply:
% 157.79/27.44 | | | | | | | | | | | | | (135) all_52_3 = e1
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | SIMP: (135) implies:
% 157.79/27.44 | | | | | | | | | | | | | (136) all_52_3 = e1
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | REDUCE: (15), (136) imply:
% 157.79/27.44 | | | | | | | | | | | | | (137) ~ (all_52_2 = e1)
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | REDUCE: (83), (136) imply:
% 157.79/27.44 | | | | | | | | | | | | | (138) ~ (all_52_11 = e1)
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | SIMP: (138) implies:
% 157.79/27.44 | | | | | | | | | | | | | (139) ~ (all_52_11 = e1)
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | REDUCE: (27), (136) imply:
% 157.79/27.44 | | | | | | | | | | | | | (140) ~ (e3 = e1)
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | REDUCE: (37), (136) imply:
% 157.79/27.44 | | | | | | | | | | | | | (141) ~ (e2 = e1)
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | REDUCE: (3), (136) imply:
% 157.79/27.44 | | | | | | | | | | | | | (142) op(e0, e3) = e1
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | BETA: splitting (16) gives:
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | (143) ~ (all_56_14 = e3)
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | REDUCE: (70), (143) imply:
% 157.79/27.44 | | | | | | | | | | | | | | (144) ~ (all_6_2 = e3)
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | (145) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.79/27.44 | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 157.79/27.44 | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | (146) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 157.79/27.44 | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.79/27.44 | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (147) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | (148) op(e2, e3) = e3
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (39), (82), (86), (148) are inconsistent by
% 157.79/27.44 | | | | | | | | | | | | | | | | | sub-proof #1159.
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (149) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (150) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (151) ~ (all_56_12 = e3)
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REDUCE: (51), (151) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (152) $false
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (153) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (154) ~ (all_56_14 = e1)
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REDUCE: (70), (154) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (155) ~ (all_6_2 = e1)
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (28), (49), (52), (62), (66), (68),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (137), (144), (155) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | | | | | | | | | | | #1229.
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | (156) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 157.79/27.44 | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.79/27.44 | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (157) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | (158) ~ (all_56_12 = e3)
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | REDUCE: (51), (158) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | (159) $false
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (160) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (161) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (162) ~ (all_56_15 = e0)
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (163) op(e0, e3) = e3
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (164) op(e3, e0) = e3
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | (165) all_54_7 = e2
% 157.79/27.44 | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (53), (165) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | #1427.
% 157.79/27.44 | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | (166) ~ (all_54_7 = e2)
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | (167) all_54_7 = e1 | all_54_7 = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (168) all_54_7 = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (168) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (169) all_52_13 = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | SIMP: (169) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (170) all_52_13 = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with e1, e3, e3, e0,
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | simplifying with (142), (163) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (171) e3 = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (82) with e0, e3, e0, e3,
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | simplifying with (121), (164) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (172) e3 = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (172) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (173) e1 = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (174) e1 = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (174) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (175) all_58_1 = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (172) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (176) all_58_0 = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (10), (11), (12), (13), (17), (20),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (21), (23), (25), (26), (30), (31), (32), (33),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (34), (36), (38), (39), (40), (41), (42), (43),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (48), (54), (55), (56), (57), (58), (60), (61),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (72), (73), (75), (76), (79),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (80), (82), (86), (87), (175), (176) are
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #391.
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | (177) all_54_7 = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (115), (177) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | | #1112.
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (178) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (179) ~ (all_56_12 = e3)
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REDUCE: (51), (179) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (180) $false
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent.
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | (181) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.79/27.44 | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.79/27.44 | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 157.79/27.44 | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | (182) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 157.79/27.44 | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.79/27.44 | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (183) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | (184) ~ (all_56_14 = e1)
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | REDUCE: (70), (184) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | (185) ~ (all_6_2 = e1)
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (28), (49), (52), (62), (66), (68),
% 157.79/27.44 | | | | | | | | | | | | | | | | | (137), (144), (185) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | | | | | | | | | | #1229.
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (186) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (187) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (188) op(e2, e1) = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (10), (17), (29), (30), (34), (41),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (42), (45), (55), (61), (63), (65), (67), (81),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (82), (133), (188) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | | | | | | | | | | | #389.
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (189) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (190) op(e0, e2) = e2
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (58), (76), (82), (190) are inconsistent by
% 157.79/27.44 | | | | | | | | | | | | | | | | | | sub-proof #1040.
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | (191) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 157.79/27.44 | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.79/27.44 | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (192) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | (193) op(e2, e0) = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (17), (29), (41), (45), (61), (63),
% 157.79/27.44 | | | | | | | | | | | | | | | | | (67), (81), (82), (104), (193) are inconsistent by
% 157.79/27.44 | | | | | | | | | | | | | | | | | sub-proof #388.
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (194) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 157.79/27.44 | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | Case 1:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (195) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (196) op(e1, e0) = e1
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18), (26), (50), (53), (64), (77), (82),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (84), (85), (115), (117), (196) are inconsistent
% 157.79/27.44 | | | | | | | | | | | | | | | | | | by sub-proof #680.
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (197) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 157.79/27.44 | | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (198) ~ (all_56_14 = e1)
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REDUCE: (70), (198) imply:
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (199) ~ (all_6_2 = e1)
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (28), (49), (52), (62), (66), (68),
% 157.79/27.44 | | | | | | | | | | | | | | | | | | (137), (144), (199) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | | | | | | | | | | | #1229.
% 157.79/27.44 | | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | (200) all_56_14 = e3
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | COMBINE_EQS: (70), (200) imply:
% 157.79/27.44 | | | | | | | | | | | | | | (201) all_6_2 = e3
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | | REF_CLOSE: (35), (47), (74), (88), (91), (139), (201) are
% 157.79/27.44 | | | | | | | | | | | | | | inconsistent by sub-proof #408.
% 157.79/27.44 | | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | (202) all_54_12 = e0
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | | REF_CLOSE: (22), (90), (202) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | | | | | | #1223.
% 157.79/27.44 | | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | (203) all_58_11 = e1 & op(e1, e0) = e1
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | ALPHA: (203) implies:
% 157.79/27.44 | | | | | | | | | | | | (204) op(e1, e0) = e1
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | | REF_CLOSE: (7), (18), (26), (50), (53), (64), (77), (82),
% 157.79/27.44 | | | | | | | | | | | | (84), (85), (115), (117), (204) are inconsistent
% 157.79/27.44 | | | | | | | | | | | | by sub-proof #680.
% 157.79/27.44 | | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | | |
% 157.79/27.44 | | | | | | | | | End of split
% 157.79/27.44 | | | | | | | | |
% 157.79/27.44 | | | | | | | | End of split
% 157.79/27.44 | | | | | | | |
% 157.79/27.44 | | | | | | | Case 2:
% 157.79/27.44 | | | | | | | |
% 157.79/27.44 | | | | | | | | (205) all_58_12 = e0 & op(e0, e3) = e0
% 157.79/27.44 | | | | | | | |
% 157.79/27.44 | | | | | | | | REF_CLOSE: (2), (6), (10), (12), (17), (41), (45), (54), (61),
% 157.79/27.44 | | | | | | | | (65), (67), (82), (205) are inconsistent by sub-proof
% 157.79/27.44 | | | | | | | | #434.
% 157.79/27.44 | | | | | | | |
% 157.79/27.44 | | | | | | | End of split
% 157.79/27.44 | | | | | | |
% 157.79/27.44 | | | | | | End of split
% 157.79/27.44 | | | | | |
% 157.79/27.44 | | | | | End of split
% 157.79/27.44 | | | | |
% 157.79/27.44 | | | | Case 2:
% 157.79/27.44 | | | | |
% 157.79/27.44 | | | | | (206) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 157.79/27.44 | | | | | e0) = e1)
% 157.79/27.44 | | | | |
% 157.79/27.44 | | | | | REF_CLOSE: (7), (18), (24), (26), (29), (50), (53), (54), (61), (63),
% 157.79/27.44 | | | | | (64), (71), (77), (81), (82), (84), (85), (206) are
% 157.79/27.44 | | | | | inconsistent by sub-proof #387.
% 157.79/27.44 | | | | |
% 157.79/27.44 | | | | End of split
% 157.79/27.44 | | | |
% 157.79/27.44 | | | End of split
% 157.79/27.44 | | |
% 157.79/27.44 | | Case 2:
% 157.79/27.44 | | |
% 157.79/27.44 | | | (207) all_58_1 = e3 & op(e3, e2) = e3
% 157.79/27.44 | | |
% 157.79/27.44 | | | ALPHA: (207) implies:
% 157.79/27.44 | | | (208) op(e3, e2) = e3
% 157.79/27.44 | | |
% 157.79/27.44 | | | REF_CLOSE: (21), (57), (82), (208) are inconsistent by sub-proof #1540.
% 157.79/27.44 | | |
% 157.79/27.44 | | End of split
% 157.79/27.44 | |
% 157.79/27.44 | Case 2:
% 157.79/27.44 | |
% 157.79/27.44 | | (209) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 157.79/27.44 | | e3)
% 157.79/27.44 | |
% 157.79/27.44 | | REF_CLOSE: (5), (8), (11), (12), (13), (20), (23), (25), (26), (30), (31),
% 157.79/27.44 | | (32), (33), (34), (38), (39), (40), (41), (43), (46), (48), (54),
% 157.79/27.44 | | (55), (56), (58), (61), (65), (67), (69), (73), (76), (79), (80),
% 157.79/27.44 | | (82), (86), (87), (89), (209) are inconsistent by sub-proof #397.
% 157.79/27.44 | |
% 157.79/27.44 | End of split
% 157.79/27.44 |
% 157.79/27.44 End of proof
% 157.79/27.44
% 157.79/27.44 Sub-proof #387 shows that the following formulas are inconsistent:
% 157.79/27.44 ----------------------------------------------------------------
% 157.79/27.44 (1) ~ (all_52_14 = e2)
% 157.79/27.44 (2) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.79/27.44 (3) ~ (all_52_12 = all_52_13)
% 157.79/27.44 (4) ~ (all_52_13 = e3)
% 157.79/27.44 (5) all_54_3 = e1 | all_54_3 = e0
% 157.79/27.44 (6) all_54_7 = all_52_13
% 157.79/27.44 (7) ~ (all_52_13 = e2)
% 157.79/27.44 (8) op(e0, e0) = e2
% 157.79/27.44 (9) ~ (e2 = e1)
% 157.79/27.44 (10) all_54_3 = all_52_12
% 157.79/27.44 (11) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.79/27.44 (12) ~ (all_52_12 = all_52_14)
% 157.79/27.44 (13) op(e1, e0) = all_52_14
% 157.79/27.44 (14) ~ (all_52_12 = e1)
% 157.79/27.44 (15) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.44 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.44 (17) all_54_11 = all_52_14
% 157.79/27.44 (18) ~ (all_52_13 = all_52_14)
% 157.79/27.44
% 157.79/27.44 Begin of proof
% 157.79/27.44 |
% 157.79/27.44 | BETA: splitting (15) gives:
% 157.79/27.44 |
% 157.79/27.44 | Case 1:
% 157.79/27.44 | |
% 157.79/27.44 | | (19) all_58_11 = e1 & op(e1, e0) = e1
% 157.79/27.44 | |
% 157.79/27.44 | | ALPHA: (19) implies:
% 157.79/27.44 | | (20) op(e1, e0) = e1
% 157.79/27.44 | |
% 157.79/27.44 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 157.79/27.44 | | (16), (17), (18), (20) are inconsistent by sub-proof #418.
% 157.79/27.44 | |
% 157.79/27.44 | Case 2:
% 157.79/27.44 | |
% 157.79/27.44 | | (21) all_58_15 = e1 & op(e0, e0) = e1
% 157.79/27.44 | |
% 157.79/27.44 | | ALPHA: (21) implies:
% 157.79/27.44 | | (22) op(e0, e0) = e1
% 157.79/27.44 | |
% 157.79/27.44 | | REF_CLOSE: (8), (9), (16), (22) are inconsistent by sub-proof #1386.
% 157.79/27.44 | |
% 157.79/27.44 | End of split
% 157.79/27.44 |
% 157.79/27.44 End of proof
% 157.79/27.44
% 157.79/27.44 Sub-proof #388 shows that the following formulas are inconsistent:
% 157.79/27.44 ----------------------------------------------------------------
% 157.79/27.44 (1) all_58_13 = e0
% 157.79/27.44 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.44 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.44 (3) all_58_7 = e2
% 157.79/27.44 (4) op(e2, e0) = e1
% 157.79/27.44 (5) all_54_3 = e1 | all_54_3 = e0
% 157.79/27.44 (6) ~ (e3 = e1)
% 157.79/27.44 (7) all_58_1 = e1
% 157.79/27.44 (8) ~ (e2 = e1)
% 157.79/27.44 (9) all_54_3 = all_52_12
% 157.79/27.44 (10) all_58_3 = e3
% 157.79/27.44 (11) op(e2, e0) = e0
% 157.79/27.44 (12) ~ (all_52_12 = e1)
% 157.79/27.44 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.44
% 157.79/27.44 Begin of proof
% 157.79/27.44 |
% 157.79/27.44 | BETA: splitting (5) gives:
% 157.79/27.44 |
% 157.79/27.44 | Case 1:
% 157.79/27.44 | |
% 157.79/27.44 | | (14) all_54_3 = e1
% 157.79/27.44 | |
% 157.79/27.44 | | COMBINE_EQS: (9), (14) imply:
% 157.79/27.44 | | (15) all_52_12 = e1
% 157.79/27.44 | |
% 157.79/27.44 | | REDUCE: (12), (15) imply:
% 157.79/27.44 | | (16) $false
% 157.79/27.44 | |
% 157.79/27.44 | | CLOSE: (16) is inconsistent.
% 157.79/27.44 | |
% 157.79/27.44 | Case 2:
% 157.79/27.44 | |
% 157.79/27.44 | | (17) all_54_3 = e0
% 157.79/27.44 | |
% 157.79/27.44 | | COMBINE_EQS: (9), (17) imply:
% 157.79/27.44 | | (18) all_52_12 = e0
% 157.79/27.44 | |
% 157.79/27.44 | | REDUCE: (12), (18) imply:
% 157.79/27.44 | | (19) ~ (e1 = e0)
% 157.79/27.44 | |
% 157.79/27.44 | | SIMP: (19) implies:
% 157.79/27.44 | | (20) ~ (e1 = e0)
% 157.79/27.44 | |
% 157.79/27.44 | | GROUND_INST: instantiating (13) with e0, e1, e0, e2, simplifying with (4),
% 157.79/27.44 | | (11) gives:
% 157.79/27.44 | | (21) e1 = e0
% 157.79/27.44 | |
% 157.79/27.44 | | COMBINE_EQS: (7), (21) imply:
% 157.79/27.44 | | (22) all_58_1 = e0
% 157.79/27.44 | |
% 157.79/27.44 | | REF_CLOSE: (1), (2), (3), (6), (8), (10), (20), (22) are inconsistent by
% 157.79/27.44 | | sub-proof #857.
% 157.79/27.44 | |
% 157.79/27.44 | End of split
% 157.79/27.44 |
% 157.79/27.44 End of proof
% 157.79/27.44
% 157.79/27.44 Sub-proof #389 shows that the following formulas are inconsistent:
% 157.79/27.44 ----------------------------------------------------------------
% 157.79/27.44 (1) all_58_13 = e0
% 157.79/27.44 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.44 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.44 (3) all_58_14 = e3
% 157.79/27.44 (4) all_58_7 = e2
% 157.79/27.44 (5) all_54_3 = e1 | all_54_3 = e0
% 157.79/27.44 (6) ~ (e3 = e0)
% 157.79/27.44 (7) ~ (e2 = e0)
% 157.79/27.44 (8) ~ (e3 = e1)
% 157.79/27.44 (9) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.79/27.44 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.44 (10) all_58_1 = e1
% 157.79/27.44 (11) op(e2, e1) = e1
% 157.79/27.44 (12) all_58_4 = e2
% 157.79/27.44 (13) ~ (e2 = e1)
% 157.79/27.44 (14) all_54_3 = all_52_12
% 157.79/27.44 (15) ~ (e1 = e0)
% 157.79/27.44 (16) all_58_3 = e3
% 157.79/27.44 (17) ~ (all_52_12 = e1)
% 157.79/27.44 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.44 (19) all_58_8 = e1
% 157.79/27.44
% 157.79/27.44 Begin of proof
% 157.79/27.44 |
% 157.79/27.44 | BETA: splitting (9) gives:
% 157.79/27.44 |
% 157.79/27.44 | Case 1:
% 157.79/27.44 | |
% 157.79/27.44 | | (20) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 157.79/27.44 | | e0)
% 157.79/27.44 | |
% 157.79/27.44 | | BETA: splitting (20) gives:
% 157.79/27.44 | |
% 157.79/27.44 | | Case 1:
% 157.79/27.44 | | |
% 157.79/27.44 | | | (21) all_58_4 = e0 & op(e3, e1) = e0
% 157.79/27.44 | | |
% 157.79/27.44 | | | REF_CLOSE: (7), (12), (21) are inconsistent by sub-proof #1365.
% 157.79/27.44 | | |
% 157.79/27.44 | | Case 2:
% 157.79/27.44 | | |
% 157.79/27.44 | | | (22) all_58_5 = e0 & op(e2, e1) = e0
% 157.79/27.44 | | |
% 157.79/27.44 | | | ALPHA: (22) implies:
% 157.79/27.44 | | | (23) op(e2, e1) = e0
% 157.79/27.44 | | |
% 157.79/27.44 | | | REF_CLOSE: (1), (2), (4), (5), (8), (10), (11), (13), (14), (16), (17),
% 157.79/27.44 | | | (18), (23) are inconsistent by sub-proof #390.
% 157.79/27.44 | | |
% 157.79/27.44 | | End of split
% 157.79/27.44 | |
% 157.79/27.44 | Case 2:
% 157.79/27.44 | |
% 157.79/27.44 | | (24) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.79/27.44 | | e0)
% 157.79/27.44 | |
% 157.79/27.44 | | BETA: splitting (24) gives:
% 157.79/27.44 | |
% 157.79/27.44 | | Case 1:
% 157.79/27.44 | | |
% 157.79/27.44 | | | (25) all_58_8 = e0 & op(e1, e1) = e0
% 157.79/27.44 | | |
% 157.79/27.44 | | | ALPHA: (25) implies:
% 157.79/27.44 | | | (26) all_58_8 = e0
% 157.79/27.44 | | |
% 157.79/27.44 | | | COMBINE_EQS: (19), (26) imply:
% 157.79/27.44 | | | (27) e1 = e0
% 157.79/27.44 | | |
% 157.79/27.44 | | | COMBINE_EQS: (10), (27) imply:
% 157.79/27.44 | | | (28) all_58_1 = e0
% 157.79/27.44 | | |
% 157.79/27.44 | | | REF_CLOSE: (1), (2), (4), (8), (13), (15), (16), (28) are inconsistent by
% 157.79/27.44 | | | sub-proof #857.
% 157.79/27.44 | | |
% 157.79/27.44 | | Case 2:
% 157.79/27.44 | | |
% 157.79/27.44 | | | (29) all_58_14 = e0 & op(e0, e1) = e0
% 157.79/27.44 | | |
% 157.79/27.44 | | | REF_CLOSE: (3), (6), (29) are inconsistent by sub-proof #882.
% 157.79/27.44 | | |
% 157.79/27.44 | | End of split
% 157.79/27.44 | |
% 157.79/27.44 | End of split
% 157.79/27.44 |
% 157.79/27.44 End of proof
% 157.79/27.44
% 157.79/27.44 Sub-proof #390 shows that the following formulas are inconsistent:
% 157.79/27.44 ----------------------------------------------------------------
% 157.79/27.44 (1) all_58_13 = e0
% 157.79/27.44 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.44 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.44 (3) all_58_7 = e2
% 157.79/27.44 (4) all_54_3 = e1 | all_54_3 = e0
% 157.79/27.44 (5) ~ (e3 = e1)
% 157.79/27.44 (6) all_58_1 = e1
% 157.79/27.44 (7) op(e2, e1) = e1
% 157.79/27.44 (8) ~ (e2 = e1)
% 157.79/27.44 (9) all_54_3 = all_52_12
% 157.79/27.44 (10) all_58_3 = e3
% 157.79/27.44 (11) ~ (all_52_12 = e1)
% 157.79/27.44 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.44 (13) op(e2, e1) = e0
% 157.79/27.44
% 157.79/27.44 Begin of proof
% 157.79/27.44 |
% 157.79/27.44 | BETA: splitting (4) gives:
% 157.79/27.44 |
% 157.79/27.44 | Case 1:
% 157.79/27.44 | |
% 157.79/27.44 | | (14) all_54_3 = e1
% 157.79/27.44 | |
% 157.79/27.45 | | REF_CLOSE: (9), (11), (14) are inconsistent by sub-proof #1291.
% 157.79/27.45 | |
% 157.79/27.45 | Case 2:
% 157.79/27.45 | |
% 157.79/27.45 | | (15) all_54_3 = e0
% 157.79/27.45 | |
% 157.79/27.45 | | COMBINE_EQS: (9), (15) imply:
% 157.79/27.45 | | (16) all_52_12 = e0
% 157.79/27.45 | |
% 157.79/27.45 | | SIMP: (16) implies:
% 157.79/27.45 | | (17) all_52_12 = e0
% 157.79/27.45 | |
% 157.79/27.45 | | REDUCE: (11), (17) imply:
% 157.79/27.45 | | (18) ~ (e1 = e0)
% 157.79/27.45 | |
% 157.79/27.45 | | SIMP: (18) implies:
% 157.79/27.45 | | (19) ~ (e1 = e0)
% 157.79/27.45 | |
% 157.79/27.45 | | GROUND_INST: instantiating (12) with e0, e1, e1, e2, simplifying with (7),
% 157.79/27.45 | | (13) gives:
% 157.79/27.45 | | (20) e1 = e0
% 157.79/27.45 | |
% 157.79/27.45 | | COMBINE_EQS: (6), (20) imply:
% 157.79/27.45 | | (21) all_58_1 = e0
% 157.79/27.45 | |
% 157.79/27.45 | | REF_CLOSE: (1), (2), (3), (5), (8), (10), (19), (21) are inconsistent by
% 157.79/27.45 | | sub-proof #857.
% 157.79/27.45 | |
% 157.79/27.45 | End of split
% 157.79/27.45 |
% 157.79/27.45 End of proof
% 157.79/27.45
% 157.79/27.45 Sub-proof #391 shows that the following formulas are inconsistent:
% 157.79/27.45 ----------------------------------------------------------------
% 157.79/27.45 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.79/27.45 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.79/27.45 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.45 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.45 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.79/27.45 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.45 (4) all_58_1 = e0
% 157.79/27.45 (5) all_58_14 = e3
% 157.79/27.45 (6) ~ (all_52_7 = e3)
% 157.79/27.45 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.79/27.45 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.45 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.79/27.45 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.79/27.45 (9) all_58_7 = e2
% 157.79/27.45 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.79/27.45 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.79/27.45 (11) op(e3, e2) = all_52_4
% 157.79/27.45 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.79/27.45 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.79/27.45 (13) op(e2, e3) = all_52_1
% 157.79/27.45 (14) ~ (all_52_13 = e3)
% 157.79/27.45 (15) ~ (e3 = e0)
% 157.79/27.45 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.79/27.45 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.79/27.45 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.79/27.45 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.79/27.45 (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.45 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.79/27.45 e2)
% 157.79/27.45 (19) ~ (e2 = e0)
% 157.79/27.45 (20) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.79/27.45 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.79/27.45 (21) op(e2, e0) = all_52_13
% 157.79/27.45 (22) op(e2, e3) = e2
% 157.79/27.45 (23) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.45 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.79/27.45 (24) ~ (e3 = e1)
% 157.79/27.45 (25) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.79/27.45 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.45 (26) op(e1, e2) = all_52_6
% 157.79/27.45 (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.45 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.79/27.45 (28) op(e0, e0) = e2
% 157.79/27.45 (29) all_58_4 = e2
% 157.79/27.45 (30) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.79/27.45 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.79/27.45 (31) ~ (all_52_4 = e3)
% 157.79/27.45 (32) op(e0, e2) = e0
% 157.79/27.45 (33) all_58_15 = e2
% 157.79/27.45 (34) ~ (e2 = e1)
% 157.79/27.45 (35) ~ (e1 = e0)
% 157.79/27.45 (36) all_58_3 = e3
% 157.79/27.45 (37) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.79/27.45 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.45 e3)
% 157.79/27.45 (38) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.79/27.45 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.79/27.45 (39) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.79/27.45 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.45 (40) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.79/27.45 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.79/27.45 (41) op(e0, e2) = all_52_7
% 157.79/27.45 (42) all_58_0 = e0
% 157.79/27.45 (43) ~ (all_52_6 = e3)
% 157.79/27.45 (44) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.79/27.45 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.79/27.45 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.45 (46) ~ (e3 = e2)
% 157.79/27.45 (47) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.79/27.45 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.79/27.45 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.79/27.45 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.79/27.45
% 157.79/27.45 Begin of proof
% 157.79/27.45 |
% 157.79/27.45 | BETA: splitting (8) gives:
% 157.79/27.45 |
% 157.79/27.45 | Case 1:
% 157.79/27.45 | |
% 157.79/27.45 | | (48) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 157.79/27.45 | | e3)
% 157.79/27.45 | |
% 157.79/27.45 | | BETA: splitting (48) gives:
% 157.79/27.45 | |
% 157.79/27.45 | | Case 1:
% 157.79/27.45 | | |
% 157.79/27.45 | | | (49) all_58_9 = e3 & op(e3, e0) = e3
% 157.79/27.45 | | |
% 157.79/27.45 | | | ALPHA: (49) implies:
% 157.79/27.45 | | | (50) all_58_9 = e3
% 157.79/27.45 | | |
% 157.79/27.45 | | | BETA: splitting (47) gives:
% 157.79/27.45 | | |
% 157.79/27.45 | | | Case 1:
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | (51) all_58_15 = e0 & op(e0, e0) = e0
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | REF_CLOSE: (19), (33), (51) are inconsistent by sub-proof #885.
% 157.79/27.45 | | | |
% 157.79/27.45 | | | Case 2:
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | (52) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 157.79/27.45 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 157.79/27.45 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 157.79/27.45 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | ALPHA: (52) implies:
% 157.79/27.45 | | | | (53) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 157.79/27.45 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.79/27.45 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 157.79/27.45 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 157.79/27.45 | | | | (32), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 157.79/27.45 | | | | (43), (44), (45), (46), (47), (50), (53) are inconsistent by
% 157.79/27.45 | | | | sub-proof #392.
% 157.79/27.45 | | | |
% 157.79/27.45 | | | End of split
% 157.79/27.45 | | |
% 157.79/27.45 | | Case 2:
% 157.79/27.45 | | |
% 157.79/27.45 | | | (54) all_58_10 = e3 & op(e2, e0) = e3
% 157.79/27.45 | | |
% 157.79/27.45 | | | ALPHA: (54) implies:
% 157.79/27.45 | | | (55) op(e2, e0) = e3
% 157.79/27.45 | | |
% 157.79/27.45 | | | REF_CLOSE: (14), (21), (45), (55) are inconsistent by sub-proof #1364.
% 157.79/27.45 | | |
% 157.79/27.45 | | End of split
% 157.79/27.45 | |
% 157.79/27.45 | Case 2:
% 157.79/27.45 | |
% 157.79/27.45 | | (56) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.45 | | e3)
% 157.79/27.45 | |
% 157.79/27.45 | | BETA: splitting (56) gives:
% 157.79/27.45 | |
% 157.79/27.45 | | Case 1:
% 157.79/27.45 | | |
% 157.79/27.45 | | | (57) all_58_11 = e3 & op(e1, e0) = e3
% 157.79/27.45 | | |
% 157.79/27.45 | | | ALPHA: (57) implies:
% 157.79/27.45 | | | (58) all_58_11 = e3
% 157.79/27.45 | | |
% 157.79/27.45 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 157.79/27.45 | | | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 157.79/27.45 | | | (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 157.79/27.45 | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 157.79/27.45 | | | (47), (58) are inconsistent by sub-proof #639.
% 157.79/27.45 | | |
% 157.79/27.45 | | Case 2:
% 157.79/27.45 | | |
% 157.79/27.45 | | | (59) all_58_15 = e3 & op(e0, e0) = e3
% 157.79/27.45 | | |
% 157.79/27.45 | | | ALPHA: (59) implies:
% 157.79/27.45 | | | (60) op(e0, e0) = e3
% 157.79/27.45 | | |
% 157.79/27.45 | | | REF_CLOSE: (28), (45), (46), (60) are inconsistent by sub-proof #1382.
% 157.79/27.45 | | |
% 157.79/27.45 | | End of split
% 157.79/27.45 | |
% 157.79/27.45 | End of split
% 157.79/27.45 |
% 157.79/27.45 End of proof
% 157.79/27.45
% 157.79/27.45 Sub-proof #392 shows that the following formulas are inconsistent:
% 157.79/27.45 ----------------------------------------------------------------
% 157.79/27.45 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.79/27.45 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.79/27.45 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.45 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.45 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.79/27.45 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.45 (4) all_58_1 = e0
% 157.79/27.45 (5) all_58_14 = e3
% 157.79/27.45 (6) ~ (all_52_7 = e3)
% 157.79/27.45 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.79/27.45 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.45 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.79/27.45 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.79/27.45 (9) all_58_7 = e2
% 157.79/27.45 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.79/27.45 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.79/27.45 (11) op(e3, e2) = all_52_4
% 157.79/27.45 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.79/27.45 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.79/27.45 (13) op(e2, e3) = all_52_1
% 157.79/27.45 (14) ~ (all_52_13 = e3)
% 157.79/27.45 (15) ~ (e3 = e0)
% 157.79/27.45 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.79/27.45 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.79/27.45 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.79/27.45 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.79/27.45 (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.45 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.79/27.45 e2)
% 157.79/27.45 (19) ~ (e2 = e0)
% 157.79/27.45 (20) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.79/27.45 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.79/27.45 (21) all_58_9 = e3
% 157.79/27.45 (22) op(e2, e0) = all_52_13
% 157.79/27.45 (23) op(e2, e3) = e2
% 157.79/27.45 (24) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.45 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.79/27.45 (25) ~ (e3 = e1)
% 157.79/27.45 (26) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.79/27.45 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.45 (27) op(e1, e2) = all_52_6
% 157.79/27.45 (28) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.45 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.79/27.45 (29) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.79/27.45 | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.45 (30) op(e0, e0) = e2
% 157.79/27.45 (31) all_58_4 = e2
% 157.79/27.45 (32) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.79/27.45 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.79/27.45 (33) ~ (all_52_4 = e3)
% 157.79/27.45 (34) op(e0, e2) = e0
% 157.79/27.45 (35) ~ (e2 = e1)
% 157.79/27.45 (36) ~ (e1 = e0)
% 157.79/27.45 (37) all_58_3 = e3
% 157.79/27.45 (38) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.79/27.45 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.45 e3)
% 157.79/27.45 (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.79/27.45 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.79/27.45 (40) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.79/27.45 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.45 (41) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.79/27.45 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.79/27.45 (42) op(e0, e2) = all_52_7
% 157.79/27.45 (43) all_58_0 = e0
% 157.79/27.45 (44) ~ (all_52_6 = e3)
% 157.79/27.45 (45) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.79/27.45 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.79/27.45 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.45 (47) ~ (e3 = e2)
% 157.79/27.45 (48) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.79/27.45 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.79/27.45 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.79/27.45 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.79/27.45
% 157.79/27.45 Begin of proof
% 157.79/27.45 |
% 157.79/27.45 | BETA: splitting (29) gives:
% 157.79/27.45 |
% 157.79/27.45 | Case 1:
% 157.79/27.45 | |
% 157.79/27.45 | | (49) all_58_12 = e0 & op(e0, e3) = e0
% 157.79/27.45 | |
% 157.79/27.45 | | ALPHA: (49) implies:
% 157.79/27.45 | | (50) all_58_12 = e0
% 157.79/27.45 | |
% 157.79/27.45 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.79/27.45 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.79/27.45 | | (24), (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 157.79/27.45 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 157.79/27.45 | | (47), (48), (50) are inconsistent by sub-proof #393.
% 157.79/27.45 | |
% 157.79/27.45 | Case 2:
% 157.79/27.45 | |
% 157.79/27.45 | | (51) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.79/27.45 | | e0)
% 157.79/27.45 | |
% 157.79/27.45 | | REF_CLOSE: (2), (4), (5), (9), (15), (25), (35), (36), (37), (51) are
% 157.79/27.45 | | inconsistent by sub-proof #649.
% 157.79/27.45 | |
% 157.79/27.45 | End of split
% 157.79/27.45 |
% 157.79/27.45 End of proof
% 157.79/27.45
% 157.79/27.45 Sub-proof #393 shows that the following formulas are inconsistent:
% 157.79/27.45 ----------------------------------------------------------------
% 157.79/27.45 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.79/27.45 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.79/27.45 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.45 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.45 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.79/27.45 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.45 (4) all_58_1 = e0
% 157.79/27.45 (5) all_58_14 = e3
% 157.79/27.45 (6) ~ (all_52_7 = e3)
% 157.79/27.45 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.79/27.45 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.45 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.79/27.45 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.79/27.45 (9) all_58_7 = e2
% 157.79/27.45 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.79/27.45 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.79/27.45 (11) all_58_12 = e0
% 157.79/27.45 (12) op(e3, e2) = all_52_4
% 157.79/27.45 (13) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.79/27.45 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.79/27.45 (14) op(e2, e3) = all_52_1
% 157.79/27.45 (15) ~ (all_52_13 = e3)
% 157.79/27.45 (16) ~ (e3 = e0)
% 157.79/27.45 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.79/27.45 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.79/27.45 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.79/27.45 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.79/27.45 (19) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.45 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.79/27.45 e2)
% 157.79/27.45 (20) ~ (e2 = e0)
% 157.79/27.45 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.79/27.45 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.79/27.45 (22) all_58_9 = e3
% 157.79/27.45 (23) op(e2, e0) = all_52_13
% 157.79/27.45 (24) op(e2, e3) = e2
% 157.79/27.45 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.45 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.79/27.45 (26) ~ (e3 = e1)
% 157.79/27.45 (27) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.79/27.45 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.79/27.45 (28) op(e1, e2) = all_52_6
% 157.79/27.45 (29) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.79/27.45 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.79/27.45 (30) op(e0, e0) = e2
% 157.79/27.45 (31) all_58_4 = e2
% 157.79/27.45 (32) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.79/27.45 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.79/27.45 (33) ~ (all_52_4 = e3)
% 157.79/27.45 (34) op(e0, e2) = e0
% 157.79/27.45 (35) ~ (e2 = e1)
% 157.79/27.45 (36) ~ (e1 = e0)
% 157.79/27.45 (37) all_58_3 = e3
% 157.79/27.45 (38) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.79/27.45 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.79/27.45 e3)
% 157.79/27.45 (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.79/27.45 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.79/27.45 (40) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.79/27.45 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.79/27.45 (41) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.79/27.45 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.79/27.45 (42) op(e0, e2) = all_52_7
% 157.79/27.45 (43) all_58_0 = e0
% 157.79/27.45 (44) ~ (all_52_6 = e3)
% 157.79/27.45 (45) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.79/27.45 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.79/27.45 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.79/27.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.79/27.45 (47) ~ (e3 = e2)
% 157.79/27.45 (48) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.79/27.45 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.79/27.45 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.79/27.45 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.79/27.45
% 157.79/27.45 Begin of proof
% 157.79/27.45 |
% 157.79/27.45 | BETA: splitting (17) gives:
% 157.79/27.45 |
% 157.79/27.45 | Case 1:
% 157.79/27.45 | |
% 157.79/27.45 | | (49) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 157.79/27.45 | | e1)
% 157.79/27.45 | |
% 157.79/27.45 | | REF_CLOSE: (24), (35), (36), (43), (46), (49) are inconsistent by sub-proof
% 157.79/27.45 | | #1160.
% 157.79/27.45 | |
% 157.79/27.45 | Case 2:
% 157.79/27.45 | |
% 157.79/27.45 | | (50) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 157.79/27.45 | | e1)
% 157.79/27.45 | |
% 157.79/27.45 | | BETA: splitting (50) gives:
% 157.79/27.45 | |
% 157.79/27.45 | | Case 1:
% 157.79/27.45 | | |
% 157.79/27.45 | | | (51) all_58_6 = e1 & op(e1, e3) = e1
% 157.79/27.45 | | |
% 157.79/27.45 | | | ALPHA: (51) implies:
% 157.79/27.45 | | | (52) all_58_6 = e1
% 157.79/27.45 | | |
% 157.79/27.45 | | | BETA: splitting (13) gives:
% 157.79/27.45 | | |
% 157.79/27.45 | | | Case 1:
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | (53) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 157.79/27.45 | | | | = e3)
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | REF_CLOSE: (26), (28), (44), (46), (52), (53) are inconsistent by
% 157.79/27.45 | | | | sub-proof #718.
% 157.79/27.45 | | | |
% 157.79/27.45 | | | Case 2:
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | (54) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 157.79/27.45 | | | | = e3)
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | BETA: splitting (54) gives:
% 157.79/27.45 | | | |
% 157.79/27.45 | | | | Case 1:
% 157.79/27.45 | | | | |
% 157.79/27.45 | | | | | (55) all_58_8 = e3 & op(e1, e1) = e3
% 157.79/27.45 | | | | |
% 157.79/27.45 | | | | | REF_CLOSE: (2), (3), (4), (5), (9), (13), (16), (20), (21), (22),
% 157.79/27.45 | | | | | (24), (26), (27), (28), (29), (30), (31), (32), (35), (36),
% 157.79/27.45 | | | | | (37), (44), (46), (52), (55) are inconsistent by sub-proof
% 157.79/27.45 | | | | | #394.
% 157.79/27.45 | | | | |
% 157.79/27.45 | | | | Case 2:
% 157.79/27.45 | | | | |
% 157.79/27.45 | | | | | (56) all_58_11 = e3 & op(e1, e0) = e3
% 157.79/27.45 | | | | |
% 157.79/27.45 | | | | | ALPHA: (56) implies:
% 157.79/27.45 | | | | | (57) all_58_11 = e3
% 157.79/27.45 | | | | |
% 157.79/27.45 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13),
% 157.79/27.45 | | | | | (14), (15), (16), (17), (18), (19), (20), (23), (24), (25),
% 157.79/27.45 | | | | | (26), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 157.79/27.45 | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 157.79/27.45 | | | | | (47), (48), (57) are inconsistent by sub-proof #639.
% 157.79/27.45 | | | | |
% 157.79/27.45 | | | | End of split
% 157.79/27.45 | | | |
% 157.79/27.45 | | | End of split
% 157.79/27.45 | | |
% 157.79/27.45 | | Case 2:
% 157.79/27.45 | | |
% 157.79/27.45 | | | (58) all_58_12 = e1 & op(e0, e3) = e1
% 157.79/27.45 | | |
% 157.79/27.45 | | | ALPHA: (58) implies:
% 157.79/27.45 | | | (59) all_58_12 = e1
% 157.79/27.45 | | |
% 157.79/27.45 | | | REF_CLOSE: (11), (36), (59) are inconsistent by sub-proof #1513.
% 157.79/27.45 | | |
% 157.79/27.45 | | End of split
% 157.79/27.45 | |
% 157.79/27.45 | End of split
% 157.79/27.45 |
% 157.79/27.45 End of proof
% 157.79/27.45
% 157.79/27.45 Sub-proof #394 shows that the following formulas are inconsistent:
% 157.79/27.45 ----------------------------------------------------------------
% 157.79/27.45 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.79/27.45 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.79/27.45 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.79/27.45 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.79/27.45 (3) all_58_1 = e0
% 157.79/27.45 (4) all_58_14 = e3
% 157.82/27.45 (5) all_58_7 = e2
% 157.82/27.45 (6) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.45 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.45 (7) all_58_6 = e1
% 157.82/27.45 (8) ~ (e3 = e0)
% 157.82/27.45 (9) ~ (e2 = e0)
% 157.82/27.45 (10) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.45 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.45 (11) all_58_9 = e3
% 157.82/27.45 (12) op(e2, e3) = e2
% 157.82/27.45 (13) ~ (e3 = e1)
% 157.82/27.45 (14) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.45 (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.82/27.45 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.82/27.45 (16) op(e1, e2) = all_52_6
% 157.82/27.45 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.45 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.45 (18) op(e0, e0) = e2
% 157.82/27.45 (19) all_58_4 = e2
% 157.82/27.45 (20) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.45 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.45 (21) ~ (e2 = e1)
% 157.82/27.45 (22) ~ (e1 = e0)
% 157.82/27.45 (23) all_58_3 = e3
% 157.82/27.45 (24) ~ (all_52_6 = e3)
% 157.82/27.45 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.45
% 157.82/27.45 Begin of proof
% 157.82/27.45 |
% 157.82/27.45 | ALPHA: (14) implies:
% 157.82/27.45 | (26) all_58_8 = e3
% 157.82/27.45 |
% 157.82/27.45 | BETA: splitting (15) gives:
% 157.82/27.45 |
% 157.82/27.45 | Case 1:
% 157.82/27.45 | |
% 157.82/27.45 | | (27) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 157.82/27.45 | | e0)
% 157.82/27.45 | |
% 157.82/27.45 | | BETA: splitting (27) gives:
% 157.82/27.45 | |
% 157.82/27.45 | | Case 1:
% 157.82/27.45 | | |
% 157.82/27.45 | | | (28) all_58_4 = e0 & op(e3, e1) = e0
% 157.82/27.45 | | |
% 157.82/27.45 | | | REF_CLOSE: (9), (19), (28) are inconsistent by sub-proof #1365.
% 157.82/27.45 | | |
% 157.82/27.45 | | Case 2:
% 157.82/27.45 | | |
% 157.82/27.45 | | | (29) all_58_5 = e0 & op(e2, e1) = e0
% 157.82/27.45 | | |
% 157.82/27.45 | | | ALPHA: (29) implies:
% 157.82/27.45 | | | (30) all_58_5 = e0
% 157.82/27.45 | | |
% 157.82/27.45 | | | BETA: splitting (1) gives:
% 157.82/27.45 | | |
% 157.82/27.45 | | | Case 1:
% 157.82/27.45 | | | |
% 157.82/27.46 | | | | (31) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 157.82/27.46 | | | | = e1)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | BETA: splitting (31) gives:
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | Case 1:
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | (32) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | REF_CLOSE: (3), (22), (32) are inconsistent by sub-proof #1424.
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | Case 2:
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | (33) all_58_3 = e1 & op(e2, e2) = e1
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | REF_CLOSE: (13), (23), (33) are inconsistent by sub-proof #912.
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | End of split
% 157.82/27.46 | | | |
% 157.82/27.46 | | | Case 2:
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | (34) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 157.82/27.46 | | | | = e1)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | BETA: splitting (34) gives:
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | Case 1:
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | (35) all_58_7 = e1 & op(e1, e2) = e1
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | REF_CLOSE: (5), (21), (35) are inconsistent by sub-proof #1045.
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | Case 2:
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | (36) all_58_13 = e1 & op(e0, e2) = e1
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | ALPHA: (36) implies:
% 157.82/27.46 | | | | | (37) all_58_13 = e1
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | BETA: splitting (20) gives:
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | Case 1:
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | (38) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 157.82/27.46 | | | | | | e1) = e1)
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.82/27.46 | | | | | | (13), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.82/27.46 | | | | | | (24), (25), (30), (37), (38) are inconsistent by
% 157.82/27.46 | | | | | | sub-proof #395.
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | Case 2:
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | (39) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 157.82/27.46 | | | | | | e1) = e1)
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | BETA: splitting (39) gives:
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | Case 1:
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | (40) all_58_8 = e1 & op(e1, e1) = e1
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | REF_CLOSE: (13), (26), (40) are inconsistent by sub-proof #959.
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | Case 2:
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | (41) all_58_14 = e1 & op(e0, e1) = e1
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | REF_CLOSE: (4), (13), (41) are inconsistent by sub-proof #844.
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | End of split
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | End of split
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | End of split
% 157.82/27.46 | | | |
% 157.82/27.46 | | | End of split
% 157.82/27.46 | | |
% 157.82/27.46 | | End of split
% 157.82/27.46 | |
% 157.82/27.46 | Case 2:
% 157.82/27.46 | |
% 157.82/27.46 | | (42) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.82/27.46 | | e0)
% 157.82/27.46 | |
% 157.82/27.46 | | BETA: splitting (42) gives:
% 157.82/27.46 | |
% 157.82/27.46 | | Case 1:
% 157.82/27.46 | | |
% 157.82/27.46 | | | (43) all_58_8 = e0 & op(e1, e1) = e0
% 157.82/27.46 | | |
% 157.82/27.46 | | | REF_CLOSE: (8), (26), (43) are inconsistent by sub-proof #598.
% 157.82/27.46 | | |
% 157.82/27.46 | | Case 2:
% 157.82/27.46 | | |
% 157.82/27.46 | | | (44) all_58_14 = e0 & op(e0, e1) = e0
% 157.82/27.46 | | |
% 157.82/27.46 | | | REF_CLOSE: (4), (8), (44) are inconsistent by sub-proof #882.
% 157.82/27.46 | | |
% 157.82/27.46 | | End of split
% 157.82/27.46 | |
% 157.82/27.46 | End of split
% 157.82/27.46 |
% 157.82/27.46 End of proof
% 157.82/27.46
% 157.82/27.46 Sub-proof #395 shows that the following formulas are inconsistent:
% 157.82/27.46 ----------------------------------------------------------------
% 157.82/27.46 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.46 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.46 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.46 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.46 (3) all_58_14 = e3
% 157.82/27.46 (4) all_58_7 = e2
% 157.82/27.46 (5) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.46 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.46 (6) all_58_6 = e1
% 157.82/27.46 (7) all_58_13 = e1
% 157.82/27.46 (8) ~ (e3 = e0)
% 157.82/27.46 (9) ~ (e2 = e0)
% 157.82/27.46 (10) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.46 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.46 (11) all_58_9 = e3
% 157.82/27.46 (12) op(e2, e3) = e2
% 157.82/27.46 (13) ~ (e3 = e1)
% 157.82/27.46 (14) op(e1, e2) = all_52_6
% 157.82/27.46 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.46 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.46 (16) all_58_5 = e0
% 157.82/27.46 (17) op(e0, e0) = e2
% 157.82/27.46 (18) all_58_4 = e2
% 157.82/27.46 (19) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.46 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.46 (20) ~ (e2 = e1)
% 157.82/27.46 (21) ~ (e1 = e0)
% 157.82/27.46 (22) all_58_3 = e3
% 157.82/27.46 (23) ~ (all_52_6 = e3)
% 157.82/27.46 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.46 (25) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 157.82/27.46
% 157.82/27.46 Begin of proof
% 157.82/27.46 |
% 157.82/27.46 | BETA: splitting (25) gives:
% 157.82/27.46 |
% 157.82/27.46 | Case 1:
% 157.82/27.46 | |
% 157.82/27.46 | | (26) all_58_4 = e1 & op(e3, e1) = e1
% 157.82/27.46 | |
% 157.82/27.46 | | REF_CLOSE: (18), (20), (26) are inconsistent by sub-proof #1476.
% 157.82/27.46 | |
% 157.82/27.46 | Case 2:
% 157.82/27.46 | |
% 157.82/27.46 | | (27) all_58_5 = e1 & op(e2, e1) = e1
% 157.82/27.46 | |
% 157.82/27.46 | | ALPHA: (27) implies:
% 157.82/27.46 | | (28) all_58_5 = e1
% 157.82/27.46 | |
% 157.82/27.46 | | COMBINE_EQS: (16), (28) imply:
% 157.82/27.46 | | (29) e1 = e0
% 157.82/27.46 | |
% 157.82/27.46 | | SIMP: (29) implies:
% 157.82/27.46 | | (30) e1 = e0
% 157.82/27.46 | |
% 157.82/27.46 | | COMBINE_EQS: (7), (30) imply:
% 157.82/27.46 | | (31) all_58_13 = e0
% 157.82/27.46 | |
% 157.82/27.46 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 157.82/27.46 | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (31)
% 157.82/27.46 | | are inconsistent by sub-proof #409.
% 157.82/27.46 | |
% 157.82/27.46 | End of split
% 157.82/27.46 |
% 157.82/27.46 End of proof
% 157.82/27.46
% 157.82/27.46 Sub-proof #396 shows that the following formulas are inconsistent:
% 157.82/27.46 ----------------------------------------------------------------
% 157.82/27.46 (1) ~ (all_52_12 = e3)
% 157.82/27.46 (2) all_58_13 = e0
% 157.82/27.46 (3) op(e3, e0) = all_52_12
% 157.82/27.46 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.46 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.46 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.46 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.46 (6) ~ (all_52_14 = e2)
% 157.82/27.46 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.46 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.46 (8) ~ (all_52_12 = e2)
% 157.82/27.46 (9) ~ (all_52_7 = e3)
% 157.82/27.46 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.46 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.82/27.46 e1)
% 157.82/27.46 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.46 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.46 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.46 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.46 (13) all_58_12 = e3
% 157.82/27.46 (14) all_58_7 = e2
% 157.82/27.46 (15) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.46 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.46 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.46 (17) all_54_1 = all_52_4
% 157.82/27.46 (18) op(e3, e2) = all_52_4
% 157.82/27.46 (19) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.46 (20) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.46 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.46 (21) ~ (all_52_12 = all_52_13)
% 157.82/27.46 (22) ~ (all_52_4 = e2)
% 157.82/27.46 (23) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.46 (24) ~ (all_52_4 = all_52_12)
% 157.82/27.46 (25) op(e2, e1) = all_52_9
% 157.82/27.46 (26) op(e2, e3) = all_52_1
% 157.82/27.46 (27) ~ (all_52_13 = e3)
% 157.82/27.46 (28) ~ (e3 = e0)
% 157.82/27.46 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.46 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.46 (30) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.46 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.46 (31) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.46 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.46 e2)
% 157.82/27.46 (32) ~ (e2 = e0)
% 157.82/27.46 (33) ~ (all_52_9 = e3)
% 157.82/27.46 (34) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.46 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.46 (35) op(e2, e0) = all_52_13
% 157.82/27.46 (36) op(e2, e3) = e2
% 157.82/27.46 (37) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.46 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.46 (38) op(e1, e2) = all_52_6
% 157.82/27.46 (39) all_58_9 = e0
% 157.82/27.46 (40) ~ (all_52_4 = e0)
% 157.82/27.46 (41) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.46 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.46 (42) all_54_7 = all_52_13
% 157.82/27.46 (43) ~ (all_52_13 = e2)
% 157.82/27.46 (44) op(e0, e0) = e2
% 157.82/27.46 (45) all_58_4 = e2
% 157.82/27.46 (46) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.46 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.46 (47) ~ (all_52_4 = e3)
% 157.82/27.46 (48) op(e0, e2) = e0
% 157.82/27.46 (49) all_58_15 = e2
% 157.82/27.46 (50) all_54_3 = all_52_12
% 157.82/27.46 (51) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.46 (52) all_58_3 = e3
% 157.82/27.46 (53) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.46 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.46 e3)
% 157.82/27.46 (54) ~ (all_52_12 = all_52_14)
% 157.82/27.46 (55) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.46 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.46 (56) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.46 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.46 (57) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.46 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.46 (58) op(e0, e2) = all_52_7
% 157.82/27.46 (59) op(e1, e0) = all_52_14
% 157.82/27.46 (60) op(e3, e3) = all_22_1
% 157.82/27.46 (61) ~ (all_52_6 = e3)
% 157.82/27.46 (62) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.46 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.46 (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.46 (64) all_54_11 = all_52_14
% 157.82/27.46 (65) ~ (all_52_13 = all_52_14)
% 157.82/27.46 (66) ~ (e3 = e2)
% 157.82/27.46 (67) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.46 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.46 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.82/27.46 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.82/27.46 (68) all_58_11 = e3
% 157.82/27.46
% 157.82/27.46 Begin of proof
% 157.82/27.46 |
% 157.82/27.46 | BETA: splitting (19) gives:
% 157.82/27.46 |
% 157.82/27.46 | Case 1:
% 157.82/27.46 | |
% 157.82/27.46 | | (69) all_54_1 = e3
% 157.82/27.46 | |
% 157.82/27.46 | | COMBINE_EQS: (17), (69) imply:
% 157.82/27.46 | | (70) all_52_4 = e3
% 157.82/27.46 | |
% 157.82/27.46 | | REDUCE: (47), (70) imply:
% 157.82/27.46 | | (71) $false
% 157.82/27.46 | |
% 157.82/27.46 | | CLOSE: (71) is inconsistent.
% 157.82/27.46 | |
% 157.82/27.46 | Case 2:
% 157.82/27.46 | |
% 157.82/27.46 | | (72) ~ (all_54_1 = e3)
% 157.82/27.46 | | (73) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.46 | |
% 157.82/27.46 | | BETA: splitting (73) gives:
% 157.82/27.46 | |
% 157.82/27.46 | | Case 1:
% 157.82/27.46 | | |
% 157.82/27.46 | | | (74) all_54_1 = e2
% 157.82/27.46 | | |
% 157.82/27.46 | | | COMBINE_EQS: (17), (74) imply:
% 157.82/27.46 | | | (75) all_52_4 = e2
% 157.82/27.46 | | |
% 157.82/27.46 | | | REDUCE: (22), (75) imply:
% 157.82/27.46 | | | (76) $false
% 157.82/27.46 | | |
% 157.82/27.46 | | | CLOSE: (76) is inconsistent.
% 157.82/27.46 | | |
% 157.82/27.46 | | Case 2:
% 157.82/27.46 | | |
% 157.82/27.46 | | | (77) ~ (all_54_1 = e2)
% 157.82/27.46 | | | (78) all_54_1 = e1 | all_54_1 = e0
% 157.82/27.46 | | |
% 157.82/27.46 | | | BETA: splitting (78) gives:
% 157.82/27.46 | | |
% 157.82/27.46 | | | Case 1:
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | (79) all_54_1 = e1
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | COMBINE_EQS: (17), (79) imply:
% 157.82/27.46 | | | | (80) all_52_4 = e1
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | REDUCE: (24), (80) imply:
% 157.82/27.46 | | | | (81) ~ (all_52_12 = e1)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | SIMP: (81) implies:
% 157.82/27.46 | | | | (82) ~ (all_52_12 = e1)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | REDUCE: (47), (80) imply:
% 157.82/27.46 | | | | (83) ~ (e3 = e1)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | SIMP: (83) implies:
% 157.82/27.46 | | | | (84) ~ (e3 = e1)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | REDUCE: (22), (80) imply:
% 157.82/27.46 | | | | (85) ~ (e2 = e1)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | SIMP: (85) implies:
% 157.82/27.46 | | | | (86) ~ (e2 = e1)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | REDUCE: (40), (80) imply:
% 157.82/27.46 | | | | (87) ~ (e1 = e0)
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | BETA: splitting (23) gives:
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | Case 1:
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | (88) all_54_3 = e3
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | COMBINE_EQS: (50), (88) imply:
% 157.82/27.46 | | | | | (89) all_52_12 = e3
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | REDUCE: (1), (89) imply:
% 157.82/27.46 | | | | | (90) $false
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | CLOSE: (90) is inconsistent.
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | Case 2:
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | (91) ~ (all_54_3 = e3)
% 157.82/27.46 | | | | | (92) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | BETA: splitting (5) gives:
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | | Case 1:
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | (93) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 157.82/27.46 | | | | | | e2) = e1)
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | BETA: splitting (93) gives:
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | Case 1:
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | (94) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | ALPHA: (94) implies:
% 157.82/27.46 | | | | | | | (95) all_58_1 = e1
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | BETA: splitting (92) gives:
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | Case 1:
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | | (96) all_54_3 = e2
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | | COMBINE_EQS: (50), (96) imply:
% 157.82/27.46 | | | | | | | | (97) all_52_12 = e2
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | | REDUCE: (8), (97) imply:
% 157.82/27.46 | | | | | | | | (98) $false
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | | CLOSE: (98) is inconsistent.
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | Case 2:
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | | (99) ~ (all_54_3 = e2)
% 157.82/27.46 | | | | | | | | (100) all_54_3 = e1 | all_54_3 = e0
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | | BETA: splitting (57) gives:
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | | Case 1:
% 157.82/27.46 | | | | | | | | |
% 157.82/27.46 | | | | | | | | | (101) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 157.82/27.46 | | | | | | | | | op(e3, e2) = e3)
% 157.82/27.46 | | | | | | | | |
% 157.82/27.46 | | | | | | | | | BETA: splitting (101) gives:
% 157.82/27.46 | | | | | | | | |
% 157.82/27.46 | | | | | | | | | Case 1:
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | (102) all_58_0 = e3 & op(e3, e3) = e3
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | ALPHA: (102) implies:
% 157.82/27.46 | | | | | | | | | | (103) all_58_0 = e3
% 157.82/27.46 | | | | | | | | | | (104) op(e3, e3) = e3
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | BETA: splitting (29) gives:
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | Case 1:
% 157.82/27.46 | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | (105) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.82/27.46 | | | | | | | | | | | & op(e2, e3) = e1)
% 157.82/27.46 | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | REF_CLOSE: (36), (63), (84), (86), (103), (105) are
% 157.82/27.46 | | | | | | | | | | | inconsistent by sub-proof #809.
% 157.82/27.46 | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | Case 2:
% 157.82/27.46 | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | (106) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 157.82/27.46 | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 157.82/27.46 | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | BETA: splitting (106) gives:
% 157.82/27.46 | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | Case 1:
% 157.82/27.46 | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | (107) all_58_6 = e1 & op(e1, e3) = e1
% 157.82/27.46 | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | ALPHA: (107) implies:
% 157.82/27.46 | | | | | | | | | | | | (108) all_58_6 = e1
% 157.82/27.46 | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | BETA: splitting (62) gives:
% 157.82/27.46 | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | Case 1:
% 157.82/27.46 | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | (109) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 157.82/27.46 | | | | | | | | | | | | | & op(e2, e3) = e0)
% 157.82/27.46 | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | BETA: splitting (109) gives:
% 157.82/27.46 | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | Case 1:
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | (110) all_58_0 = e0 & op(e3, e3) = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | ALPHA: (110) implies:
% 157.82/27.46 | | | | | | | | | | | | | | (111) all_58_0 = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12),
% 157.82/27.46 | | | | | | | | | | | | | | (13), (14), (15), (16), (18), (20), (21), (25),
% 157.82/27.46 | | | | | | | | | | | | | | (26), (27), (28), (29), (30), (31), (32), (33),
% 157.82/27.46 | | | | | | | | | | | | | | (34), (35), (36), (37), (38), (41), (42), (43),
% 157.82/27.46 | | | | | | | | | | | | | | (44), (45), (46), (47), (48), (49), (50), (52),
% 157.82/27.46 | | | | | | | | | | | | | | (53), (55), (56), (57), (58), (60), (61), (62),
% 157.82/27.46 | | | | | | | | | | | | | | (63), (66), (67), (68), (82), (84), (86), (87),
% 157.82/27.46 | | | | | | | | | | | | | | (95), (100), (104), (111) are inconsistent by
% 157.82/27.46 | | | | | | | | | | | | | | sub-proof #404.
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | Case 2:
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | (112) all_58_2 = e0 & op(e2, e3) = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | ALPHA: (112) implies:
% 157.82/27.46 | | | | | | | | | | | | | | (113) op(e2, e3) = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | REF_CLOSE: (32), (36), (63), (113) are inconsistent by
% 157.82/27.46 | | | | | | | | | | | | | | sub-proof #1156.
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | End of split
% 157.82/27.46 | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | Case 2:
% 157.82/27.46 | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | (114) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 157.82/27.46 | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 157.82/27.46 | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | BETA: splitting (114) gives:
% 157.82/27.46 | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | Case 1:
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | (115) all_58_6 = e0 & op(e1, e3) = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | ALPHA: (115) implies:
% 157.82/27.46 | | | | | | | | | | | | | | (116) all_58_6 = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | COMBINE_EQS: (108), (116) imply:
% 157.82/27.46 | | | | | | | | | | | | | | (117) e1 = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | COMBINE_EQS: (95), (117) imply:
% 157.82/27.46 | | | | | | | | | | | | | | (118) all_58_1 = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.82/27.46 | | | | | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (20),
% 157.82/27.46 | | | | | | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 157.82/27.46 | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (35), (36), (37),
% 157.82/27.46 | | | | | | | | | | | | | | (38), (40), (41), (42), (43), (44), (45), (46),
% 157.82/27.46 | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (54),
% 157.82/27.46 | | | | | | | | | | | | | | (55), (56), (57), (58), (59), (61), (62), (63),
% 157.82/27.46 | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (73), (84), (86),
% 157.82/27.46 | | | | | | | | | | | | | | (87), (118) are inconsistent by sub-proof #400.
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | Case 2:
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | (119) all_58_12 = e0 & op(e0, e3) = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | ALPHA: (119) implies:
% 157.82/27.46 | | | | | | | | | | | | | | (120) all_58_12 = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | COMBINE_EQS: (13), (120) imply:
% 157.82/27.46 | | | | | | | | | | | | | | (121) e3 = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | COMBINE_EQS: (103), (121) imply:
% 157.82/27.46 | | | | | | | | | | | | | | (122) all_58_0 = e0
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12),
% 157.82/27.46 | | | | | | | | | | | | | | (13), (14), (15), (16), (18), (20), (21), (25),
% 157.82/27.46 | | | | | | | | | | | | | | (26), (27), (28), (29), (30), (31), (32), (33),
% 157.82/27.46 | | | | | | | | | | | | | | (34), (35), (36), (37), (38), (41), (42), (43),
% 157.82/27.46 | | | | | | | | | | | | | | (44), (45), (46), (47), (48), (49), (50), (52),
% 157.82/27.46 | | | | | | | | | | | | | | (53), (55), (56), (57), (58), (60), (61), (62),
% 157.82/27.46 | | | | | | | | | | | | | | (63), (66), (67), (68), (82), (84), (86), (87),
% 157.82/27.46 | | | | | | | | | | | | | | (95), (100), (104), (122) are inconsistent by
% 157.82/27.46 | | | | | | | | | | | | | | sub-proof #404.
% 157.82/27.46 | | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | | End of split
% 157.82/27.46 | | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | End of split
% 157.82/27.46 | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | Case 2:
% 157.82/27.46 | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | (123) all_58_12 = e1 & op(e0, e3) = e1
% 157.82/27.46 | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | | REF_CLOSE: (13), (84), (123) are inconsistent by sub-proof
% 157.82/27.46 | | | | | | | | | | | | #1388.
% 157.82/27.46 | | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | | End of split
% 157.82/27.46 | | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | End of split
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | Case 2:
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | (124) all_58_1 = e3 & op(e3, e2) = e3
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | ALPHA: (124) implies:
% 157.82/27.46 | | | | | | | | | | (125) op(e3, e2) = e3
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | | REF_CLOSE: (18), (47), (63), (125) are inconsistent by
% 157.82/27.46 | | | | | | | | | | sub-proof #1540.
% 157.82/27.46 | | | | | | | | | |
% 157.82/27.46 | | | | | | | | | End of split
% 157.82/27.46 | | | | | | | | |
% 157.82/27.46 | | | | | | | | Case 2:
% 157.82/27.46 | | | | | | | | |
% 157.82/27.46 | | | | | | | | | (126) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 157.82/27.46 | | | | | | | | | op(e3, e0) = e3)
% 157.82/27.46 | | | | | | | | |
% 157.82/27.46 | | | | | | | | | REF_CLOSE: (4), (7), (9), (10), (11), (16), (20), (26), (27),
% 157.82/27.46 | | | | | | | | | (28), (29), (30), (31), (32), (35), (36), (37),
% 157.82/27.46 | | | | | | | | | (38), (39), (41), (44), (45), (46), (48), (52),
% 157.82/27.46 | | | | | | | | | (53), (56), (58), (61), (62), (63), (66), (67),
% 157.82/27.46 | | | | | | | | | (68), (84), (86), (87), (126) are inconsistent by
% 157.82/27.46 | | | | | | | | | sub-proof #397.
% 157.82/27.46 | | | | | | | | |
% 157.82/27.46 | | | | | | | | End of split
% 157.82/27.46 | | | | | | | |
% 157.82/27.46 | | | | | | | End of split
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | Case 2:
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | (127) all_58_3 = e1 & op(e2, e2) = e1
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | | REF_CLOSE: (52), (84), (127) are inconsistent by sub-proof #912.
% 157.82/27.46 | | | | | | |
% 157.82/27.46 | | | | | | End of split
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | Case 2:
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | (128) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 157.82/27.46 | | | | | | op(e0, e2) = e1)
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | | REF_CLOSE: (2), (14), (86), (87), (128) are inconsistent by
% 157.82/27.46 | | | | | | sub-proof #858.
% 157.82/27.46 | | | | | |
% 157.82/27.46 | | | | | End of split
% 157.82/27.46 | | | | |
% 157.82/27.46 | | | | End of split
% 157.82/27.46 | | | |
% 157.82/27.46 | | | Case 2:
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | (129) all_54_1 = e0
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | COMBINE_EQS: (17), (129) imply:
% 157.82/27.46 | | | | (130) all_52_4 = e0
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | REDUCE: (40), (130) imply:
% 157.82/27.46 | | | | (131) $false
% 157.82/27.46 | | | |
% 157.82/27.46 | | | | CLOSE: (131) is inconsistent.
% 157.82/27.46 | | | |
% 157.82/27.46 | | | End of split
% 157.82/27.46 | | |
% 157.82/27.46 | | End of split
% 157.82/27.46 | |
% 157.82/27.46 | End of split
% 157.82/27.46 |
% 157.82/27.46 End of proof
% 157.82/27.46
% 157.82/27.46 Sub-proof #397 shows that the following formulas are inconsistent:
% 157.82/27.46 ----------------------------------------------------------------
% 157.82/27.46 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.46 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.46 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.46 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.46 (3) ~ (all_52_7 = e3)
% 157.82/27.46 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.82/27.46 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.46 (5) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.46 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.46 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.46 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.46 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.46 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.46 (8) op(e2, e3) = all_52_1
% 157.82/27.46 (9) ~ (all_52_13 = e3)
% 157.82/27.46 (10) ~ (e3 = e0)
% 157.82/27.46 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.46 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.46 (12) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.46 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.46 (13) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.46 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.46 e2)
% 157.82/27.46 (14) ~ (e2 = e0)
% 157.82/27.46 (15) op(e2, e0) = all_52_13
% 157.82/27.46 (16) op(e2, e3) = e2
% 157.82/27.46 (17) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.46 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.46 (18) ~ (e3 = e1)
% 157.82/27.46 (19) op(e1, e2) = all_52_6
% 157.82/27.46 (20) all_58_9 = e0
% 157.82/27.46 (21) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.46 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.46 (22) op(e0, e0) = e2
% 157.82/27.46 (23) all_58_4 = e2
% 157.82/27.46 (24) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.46 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.46 (25) op(e0, e2) = e0
% 157.82/27.46 (26) ~ (e2 = e1)
% 157.82/27.46 (27) ~ (e1 = e0)
% 157.82/27.46 (28) all_58_3 = e3
% 157.82/27.46 (29) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.46 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.46 e3)
% 157.82/27.46 (30) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.46 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.46 (31) op(e0, e2) = all_52_7
% 157.82/27.46 (32) ~ (all_52_6 = e3)
% 157.82/27.47 (33) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.47 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.47 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.47 (35) ~ (e3 = e2)
% 157.82/27.47 (36) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.47 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.47 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.82/27.47 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.82/27.47 (37) all_58_11 = e3
% 157.82/27.47 (38) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.47
% 157.82/27.47 Begin of proof
% 157.82/27.47 |
% 157.82/27.47 | BETA: splitting (38) gives:
% 157.82/27.47 |
% 157.82/27.47 | Case 1:
% 157.82/27.47 | |
% 157.82/27.47 | | (39) all_58_4 = e3 & op(e3, e1) = e3
% 157.82/27.47 | |
% 157.82/27.47 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.82/27.47 | | (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 157.82/27.47 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 157.82/27.47 | | (36), (37), (39) are inconsistent by sub-proof #644.
% 157.82/27.47 | |
% 157.82/27.47 | Case 2:
% 157.82/27.47 | |
% 157.82/27.47 | | (40) all_58_9 = e3 & op(e3, e0) = e3
% 157.82/27.47 | |
% 157.82/27.47 | | ALPHA: (40) implies:
% 157.82/27.47 | | (41) all_58_9 = e3
% 157.82/27.47 | |
% 157.82/27.47 | | REF_CLOSE: (10), (20), (41) are inconsistent by sub-proof #1315.
% 157.82/27.47 | |
% 157.82/27.47 | End of split
% 157.82/27.47 |
% 157.82/27.47 End of proof
% 157.82/27.47
% 157.82/27.47 Sub-proof #398 shows that the following formulas are inconsistent:
% 157.82/27.47 ----------------------------------------------------------------
% 157.82/27.47 (1) ~ (all_52_13 = e3)
% 157.82/27.47 (2) ~ (e3 = e0)
% 157.82/27.47 (3) op(e2, e0) = all_52_13
% 157.82/27.47 (4) all_58_9 = e0
% 157.82/27.47 (5) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 157.82/27.47 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.47
% 157.82/27.47 Begin of proof
% 157.82/27.47 |
% 157.82/27.47 | BETA: splitting (5) gives:
% 157.82/27.47 |
% 157.82/27.47 | Case 1:
% 157.82/27.47 | |
% 157.82/27.47 | | (7) all_58_9 = e3 & op(e3, e0) = e3
% 157.82/27.47 | |
% 157.82/27.47 | | ALPHA: (7) implies:
% 157.82/27.47 | | (8) all_58_9 = e3
% 157.82/27.47 | |
% 157.82/27.47 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #1315.
% 157.82/27.47 | |
% 157.82/27.47 | Case 2:
% 157.82/27.47 | |
% 157.82/27.47 | | (9) all_58_10 = e3 & op(e2, e0) = e3
% 157.82/27.47 | |
% 157.82/27.47 | | ALPHA: (9) implies:
% 157.82/27.47 | | (10) op(e2, e0) = e3
% 157.82/27.47 | |
% 157.82/27.47 | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #1364.
% 157.82/27.47 | |
% 157.82/27.47 | End of split
% 157.82/27.47 |
% 157.82/27.47 End of proof
% 157.82/27.47
% 157.82/27.47 Sub-proof #399 shows that the following formulas are inconsistent:
% 157.82/27.47 ----------------------------------------------------------------
% 157.82/27.47 (1) ~ (all_52_12 = e3)
% 157.82/27.47 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.47 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.47 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.47 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.47 (4) ~ (all_52_14 = e2)
% 157.82/27.47 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.47 (6) all_58_1 = e0
% 157.82/27.47 (7) ~ (all_52_12 = e2)
% 157.82/27.47 (8) ~ (all_52_7 = e3)
% 157.82/27.47 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.82/27.47 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.47 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.47 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.47 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.47 (12) all_58_12 = e3
% 157.82/27.47 (13) all_58_7 = e2
% 157.82/27.47 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.47 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.47 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.47 (16) all_54_1 = all_52_4
% 157.82/27.47 (17) op(e3, e2) = all_52_4
% 157.82/27.47 (18) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.47 (19) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.47 (20) ~ (all_52_12 = all_52_13)
% 157.82/27.47 (21) ~ (all_52_4 = e2)
% 157.82/27.47 (22) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.47 (23) ~ (all_52_4 = all_52_12)
% 157.82/27.47 (24) op(e2, e1) = all_52_9
% 157.82/27.47 (25) op(e2, e3) = all_52_1
% 157.82/27.47 (26) ~ (all_52_13 = e3)
% 157.82/27.47 (27) ~ (e3 = e0)
% 157.82/27.47 (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.47 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.47 (29) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.47 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.47 (30) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.47 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.47 e2)
% 157.82/27.47 (31) ~ (e2 = e0)
% 157.82/27.47 (32) ~ (all_52_9 = e3)
% 157.82/27.47 (33) op(e2, e0) = all_52_13
% 157.82/27.47 (34) op(e2, e3) = e2
% 157.82/27.47 (35) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.47 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.47 (36) ~ (e3 = e1)
% 157.82/27.47 (37) op(e1, e2) = all_52_6
% 157.82/27.47 (38) ~ (all_52_4 = e0)
% 157.82/27.47 (39) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.47 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.47 (40) all_54_7 = all_52_13
% 157.82/27.47 (41) ~ (all_52_13 = e2)
% 157.82/27.47 (42) op(e0, e0) = e2
% 157.82/27.47 (43) all_58_4 = e2
% 157.82/27.47 (44) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.47 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.47 (45) ~ (all_52_4 = e3)
% 157.82/27.47 (46) op(e0, e2) = e0
% 157.82/27.47 (47) all_58_15 = e2
% 157.82/27.47 (48) ~ (e2 = e1)
% 157.82/27.47 (49) all_54_3 = all_52_12
% 157.82/27.47 (50) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.47 (51) ~ (e1 = e0)
% 157.82/27.47 (52) all_58_3 = e3
% 157.82/27.47 (53) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.47 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.47 e3)
% 157.82/27.47 (54) ~ (all_52_12 = all_52_14)
% 157.82/27.47 (55) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.47 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.47 (56) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.47 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.47 (57) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.47 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.47 (58) op(e0, e2) = all_52_7
% 157.82/27.47 (59) op(e1, e0) = all_52_14
% 157.82/27.47 (60) ~ (all_52_6 = e3)
% 157.82/27.47 (61) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.47 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.47 (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.47 (63) all_54_11 = all_52_14
% 157.82/27.47 (64) ~ (all_52_13 = all_52_14)
% 157.82/27.47 (65) ~ (e3 = e2)
% 157.82/27.47 (66) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.47 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.47 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.82/27.47 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.82/27.47
% 157.82/27.47 Begin of proof
% 157.82/27.47 |
% 157.82/27.47 | BETA: splitting (10) gives:
% 157.82/27.47 |
% 157.82/27.47 | Case 1:
% 157.82/27.47 | |
% 157.82/27.47 | | (67) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 157.82/27.47 | | e3)
% 157.82/27.47 | |
% 157.82/27.47 | | BETA: splitting (67) gives:
% 157.82/27.47 | |
% 157.82/27.47 | | Case 1:
% 157.82/27.47 | | |
% 157.82/27.47 | | | (68) all_58_9 = e3 & op(e3, e0) = e3
% 157.82/27.47 | | |
% 157.82/27.47 | | | ALPHA: (68) implies:
% 157.82/27.47 | | | (69) all_58_9 = e3
% 157.82/27.47 | | |
% 157.82/27.47 | | | BETA: splitting (18) gives:
% 157.82/27.47 | | |
% 157.82/27.47 | | | Case 1:
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | (70) all_54_1 = e3
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | COMBINE_EQS: (16), (70) imply:
% 157.82/27.47 | | | | (71) all_52_4 = e3
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | REDUCE: (45), (71) imply:
% 157.82/27.47 | | | | (72) $false
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | CLOSE: (72) is inconsistent.
% 157.82/27.47 | | | |
% 157.82/27.47 | | | Case 2:
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | (73) ~ (all_54_1 = e3)
% 157.82/27.47 | | | | (74) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (11), (12), (13), (14), (15),
% 157.82/27.47 | | | | (16), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 157.82/27.47 | | | | (31), (32), (34), (36), (38), (40), (41), (43), (45), (47),
% 157.82/27.47 | | | | (48), (49), (50), (51), (52), (54), (55), (59), (61), (62),
% 157.82/27.47 | | | | (63), (64), (65), (66), (69), (74) are inconsistent by
% 157.82/27.47 | | | | sub-proof #402.
% 157.82/27.47 | | | |
% 157.82/27.47 | | | End of split
% 157.82/27.47 | | |
% 157.82/27.47 | | Case 2:
% 157.82/27.47 | | |
% 157.82/27.47 | | | (75) all_58_10 = e3 & op(e2, e0) = e3
% 157.82/27.47 | | |
% 157.82/27.47 | | | ALPHA: (75) implies:
% 157.82/27.47 | | | (76) op(e2, e0) = e3
% 157.82/27.47 | | |
% 157.82/27.47 | | | REF_CLOSE: (26), (33), (62), (76) are inconsistent by sub-proof #1364.
% 157.82/27.47 | | |
% 157.82/27.47 | | End of split
% 157.82/27.47 | |
% 157.82/27.47 | Case 2:
% 157.82/27.47 | |
% 157.82/27.47 | | (77) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.47 | | e3)
% 157.82/27.47 | |
% 157.82/27.47 | | BETA: splitting (77) gives:
% 157.82/27.47 | |
% 157.82/27.47 | | Case 1:
% 157.82/27.47 | | |
% 157.82/27.47 | | | (78) all_58_11 = e3 & op(e1, e0) = e3
% 157.82/27.47 | | |
% 157.82/27.47 | | | ALPHA: (78) implies:
% 157.82/27.47 | | | (79) all_58_11 = e3
% 157.82/27.47 | | |
% 157.82/27.47 | | | BETA: splitting (18) gives:
% 157.82/27.47 | | |
% 157.82/27.47 | | | Case 1:
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | (80) all_54_1 = e3
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | COMBINE_EQS: (16), (80) imply:
% 157.82/27.47 | | | | (81) all_52_4 = e3
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | REDUCE: (45), (81) imply:
% 157.82/27.47 | | | | (82) $false
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | CLOSE: (82) is inconsistent.
% 157.82/27.47 | | | |
% 157.82/27.47 | | | Case 2:
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | (83) ~ (all_54_1 = e3)
% 157.82/27.47 | | | | (84) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.82/27.47 | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21), (22),
% 157.82/27.47 | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 157.82/27.47 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 157.82/27.47 | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 157.82/27.47 | | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 157.82/27.47 | | | | (63), (64), (65), (66), (79), (84) are inconsistent by
% 157.82/27.47 | | | | sub-proof #400.
% 157.82/27.47 | | | |
% 157.82/27.47 | | | End of split
% 157.82/27.47 | | |
% 157.82/27.47 | | Case 2:
% 157.82/27.47 | | |
% 157.82/27.47 | | | (85) all_58_15 = e3 & op(e0, e0) = e3
% 157.82/27.47 | | |
% 157.82/27.47 | | | ALPHA: (85) implies:
% 157.82/27.47 | | | (86) op(e0, e0) = e3
% 157.82/27.47 | | |
% 157.82/27.47 | | | REF_CLOSE: (42), (62), (65), (86) are inconsistent by sub-proof #1382.
% 157.82/27.47 | | |
% 157.82/27.47 | | End of split
% 157.82/27.47 | |
% 157.82/27.47 | End of split
% 157.82/27.47 |
% 157.82/27.47 End of proof
% 157.82/27.47
% 157.82/27.47 Sub-proof #400 shows that the following formulas are inconsistent:
% 157.82/27.47 ----------------------------------------------------------------
% 157.82/27.47 (1) ~ (all_52_12 = e3)
% 157.82/27.47 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.47 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.47 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.47 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.47 (4) ~ (all_52_14 = e2)
% 157.82/27.47 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.47 (6) all_58_1 = e0
% 157.82/27.47 (7) ~ (all_52_12 = e2)
% 157.82/27.47 (8) ~ (all_52_7 = e3)
% 157.82/27.47 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.82/27.47 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.47 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.47 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.47 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.47 (12) all_58_12 = e3
% 157.82/27.47 (13) all_58_7 = e2
% 157.82/27.47 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.47 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.47 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.47 (16) all_54_1 = all_52_4
% 157.82/27.47 (17) op(e3, e2) = all_52_4
% 157.82/27.47 (18) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.47 (19) ~ (all_52_12 = all_52_13)
% 157.82/27.47 (20) ~ (all_52_4 = e2)
% 157.82/27.47 (21) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.47 (22) ~ (all_52_4 = all_52_12)
% 157.82/27.47 (23) op(e2, e1) = all_52_9
% 157.82/27.47 (24) op(e2, e3) = all_52_1
% 157.82/27.47 (25) ~ (all_52_13 = e3)
% 157.82/27.47 (26) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.47 (27) ~ (e3 = e0)
% 157.82/27.47 (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.47 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.47 (29) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.47 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.47 (30) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.47 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.47 e2)
% 157.82/27.47 (31) ~ (e2 = e0)
% 157.82/27.47 (32) ~ (all_52_9 = e3)
% 157.82/27.47 (33) op(e2, e0) = all_52_13
% 157.82/27.47 (34) op(e2, e3) = e2
% 157.82/27.47 (35) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.47 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.47 (36) ~ (e3 = e1)
% 157.82/27.47 (37) op(e1, e2) = all_52_6
% 157.82/27.47 (38) ~ (all_52_4 = e0)
% 157.82/27.47 (39) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.47 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.47 (40) all_54_7 = all_52_13
% 157.82/27.47 (41) ~ (all_52_13 = e2)
% 157.82/27.47 (42) op(e0, e0) = e2
% 157.82/27.47 (43) all_58_4 = e2
% 157.82/27.47 (44) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.47 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.47 (45) ~ (all_52_4 = e3)
% 157.82/27.47 (46) op(e0, e2) = e0
% 157.82/27.47 (47) all_58_15 = e2
% 157.82/27.47 (48) ~ (e2 = e1)
% 157.82/27.47 (49) all_54_3 = all_52_12
% 157.82/27.47 (50) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.47 (51) ~ (e1 = e0)
% 157.82/27.47 (52) all_58_3 = e3
% 157.82/27.47 (53) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.47 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.47 e3)
% 157.82/27.47 (54) ~ (all_52_12 = all_52_14)
% 157.82/27.47 (55) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.47 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.47 (56) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.47 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.47 (57) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.47 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.47 (58) op(e0, e2) = all_52_7
% 157.82/27.47 (59) op(e1, e0) = all_52_14
% 157.82/27.47 (60) ~ (all_52_6 = e3)
% 157.82/27.47 (61) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.47 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.47 (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.47 (63) all_54_11 = all_52_14
% 157.82/27.47 (64) ~ (all_52_13 = all_52_14)
% 157.82/27.47 (65) ~ (e3 = e2)
% 157.82/27.47 (66) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.47 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.47 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.82/27.47 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.82/27.47 (67) all_58_11 = e3
% 157.82/27.47
% 157.82/27.47 Begin of proof
% 157.82/27.47 |
% 157.82/27.47 | BETA: splitting (3) gives:
% 157.82/27.47 |
% 157.82/27.47 | Case 1:
% 157.82/27.47 | |
% 157.82/27.47 | | (68) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 157.82/27.47 | | e1)
% 157.82/27.47 | |
% 157.82/27.47 | | REF_CLOSE: (6), (36), (51), (52), (68) are inconsistent by sub-proof #419.
% 157.82/27.47 | |
% 157.82/27.47 | Case 2:
% 157.82/27.47 | |
% 157.82/27.47 | | (69) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 157.82/27.47 | | e1)
% 157.82/27.47 | |
% 157.82/27.47 | | BETA: splitting (69) gives:
% 157.82/27.47 | |
% 157.82/27.47 | | Case 1:
% 157.82/27.47 | | |
% 157.82/27.47 | | | (70) all_58_7 = e1 & op(e1, e2) = e1
% 157.82/27.47 | | |
% 157.82/27.47 | | | REF_CLOSE: (13), (48), (70) are inconsistent by sub-proof #1045.
% 157.82/27.47 | | |
% 157.82/27.47 | | Case 2:
% 157.82/27.47 | | |
% 157.82/27.47 | | | (71) all_58_13 = e1 & op(e0, e2) = e1
% 157.82/27.47 | | |
% 157.82/27.47 | | | ALPHA: (71) implies:
% 157.82/27.47 | | | (72) all_58_13 = e1
% 157.82/27.47 | | |
% 157.82/27.47 | | | BETA: splitting (57) gives:
% 157.82/27.47 | | |
% 157.82/27.47 | | | Case 1:
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | (73) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 157.82/27.47 | | | | = e3)
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | BETA: splitting (73) gives:
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | Case 1:
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | (74) all_58_0 = e3 & op(e3, e3) = e3
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | ALPHA: (74) implies:
% 157.82/27.47 | | | | | (75) all_58_0 = e3
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | BETA: splitting (28) gives:
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | Case 1:
% 157.82/27.47 | | | | | |
% 157.82/27.47 | | | | | | (76) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 157.82/27.47 | | | | | | e3) = e1)
% 157.82/27.47 | | | | | |
% 157.82/27.47 | | | | | | REF_CLOSE: (34), (36), (48), (62), (75), (76) are inconsistent by
% 157.82/27.47 | | | | | | sub-proof #809.
% 157.82/27.47 | | | | | |
% 157.82/27.47 | | | | | Case 2:
% 157.82/27.47 | | | | | |
% 157.82/27.47 | | | | | | (77) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 157.82/27.47 | | | | | | e3) = e1)
% 157.82/27.47 | | | | | |
% 157.82/27.47 | | | | | | BETA: splitting (77) gives:
% 157.82/27.47 | | | | | |
% 157.82/27.47 | | | | | | Case 1:
% 157.82/27.47 | | | | | | |
% 157.82/27.47 | | | | | | | (78) all_58_6 = e1 & op(e1, e3) = e1
% 157.82/27.47 | | | | | | |
% 157.82/27.47 | | | | | | | ALPHA: (78) implies:
% 157.82/27.47 | | | | | | | (79) all_58_6 = e1
% 157.82/27.47 | | | | | | |
% 157.82/27.47 | | | | | | | BETA: splitting (61) gives:
% 157.82/27.47 | | | | | | |
% 157.82/27.47 | | | | | | | Case 1:
% 157.82/27.47 | | | | | | | |
% 157.82/27.47 | | | | | | | | (80) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 157.82/27.47 | | | | | | | | op(e2, e3) = e0)
% 157.82/27.47 | | | | | | | |
% 157.82/27.47 | | | | | | | | BETA: splitting (80) gives:
% 157.82/27.47 | | | | | | | |
% 157.82/27.47 | | | | | | | | Case 1:
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | (81) all_58_0 = e0 & op(e3, e3) = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | ALPHA: (81) implies:
% 157.82/27.47 | | | | | | | | | (82) all_58_0 = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (10), (12), (15), (17),
% 157.82/27.47 | | | | | | | | | (18), (24), (25), (27), (28), (29), (30), (31),
% 157.82/27.47 | | | | | | | | | (33), (34), (35), (36), (37), (39), (42), (43),
% 157.82/27.47 | | | | | | | | | (44), (45), (46), (48), (51), (52), (53), (55),
% 157.82/27.47 | | | | | | | | | (56), (57), (58), (60), (61), (62), (65), (66),
% 157.82/27.47 | | | | | | | | | (67), (82) are inconsistent by sub-proof #401.
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | Case 2:
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | (83) all_58_2 = e0 & op(e2, e3) = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | ALPHA: (83) implies:
% 157.82/27.47 | | | | | | | | | (84) op(e2, e3) = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | REF_CLOSE: (31), (34), (62), (84) are inconsistent by
% 157.82/27.47 | | | | | | | | | sub-proof #1156.
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | End of split
% 157.82/27.47 | | | | | | | |
% 157.82/27.47 | | | | | | | Case 2:
% 157.82/27.47 | | | | | | | |
% 157.82/27.47 | | | | | | | | (85) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 157.82/27.47 | | | | | | | | op(e0, e3) = e0)
% 157.82/27.47 | | | | | | | |
% 157.82/27.47 | | | | | | | | BETA: splitting (85) gives:
% 157.82/27.47 | | | | | | | |
% 157.82/27.47 | | | | | | | | Case 1:
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | (86) all_58_6 = e0 & op(e1, e3) = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | ALPHA: (86) implies:
% 157.82/27.47 | | | | | | | | | (87) all_58_6 = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | COMBINE_EQS: (79), (87) imply:
% 157.82/27.47 | | | | | | | | | (88) e1 = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | COMBINE_EQS: (72), (88) imply:
% 157.82/27.47 | | | | | | | | | (89) all_58_13 = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | REF_CLOSE: (3), (6), (13), (36), (48), (51), (52), (89) are
% 157.82/27.47 | | | | | | | | | inconsistent by sub-proof #857.
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | Case 2:
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | (90) all_58_12 = e0 & op(e0, e3) = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | ALPHA: (90) implies:
% 157.82/27.47 | | | | | | | | | (91) all_58_12 = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | COMBINE_EQS: (12), (91) imply:
% 157.82/27.47 | | | | | | | | | (92) e3 = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | COMBINE_EQS: (75), (92) imply:
% 157.82/27.47 | | | | | | | | | (93) all_58_0 = e0
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (10), (12), (15), (17),
% 157.82/27.47 | | | | | | | | | (18), (24), (25), (27), (28), (29), (30), (31),
% 157.82/27.47 | | | | | | | | | (33), (34), (35), (36), (37), (39), (42), (43),
% 157.82/27.47 | | | | | | | | | (44), (45), (46), (48), (51), (52), (53), (55),
% 157.82/27.47 | | | | | | | | | (56), (57), (58), (60), (61), (62), (65), (66),
% 157.82/27.47 | | | | | | | | | (67), (93) are inconsistent by sub-proof #401.
% 157.82/27.47 | | | | | | | | |
% 157.82/27.47 | | | | | | | | End of split
% 157.82/27.47 | | | | | | | |
% 157.82/27.47 | | | | | | | End of split
% 157.82/27.47 | | | | | | |
% 157.82/27.47 | | | | | | Case 2:
% 157.82/27.47 | | | | | | |
% 157.82/27.47 | | | | | | | (94) all_58_12 = e1 & op(e0, e3) = e1
% 157.82/27.47 | | | | | | |
% 157.82/27.47 | | | | | | | REF_CLOSE: (12), (36), (94) are inconsistent by sub-proof #1388.
% 157.82/27.47 | | | | | | |
% 157.82/27.47 | | | | | | End of split
% 157.82/27.47 | | | | | |
% 157.82/27.47 | | | | | End of split
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | Case 2:
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | (95) all_58_1 = e3 & op(e3, e2) = e3
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | ALPHA: (95) implies:
% 157.82/27.47 | | | | | (96) op(e3, e2) = e3
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | REF_CLOSE: (17), (45), (62), (96) are inconsistent by sub-proof #1540.
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | End of split
% 157.82/27.47 | | | |
% 157.82/27.47 | | | Case 2:
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | (97) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 157.82/27.47 | | | | = e3)
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | BETA: splitting (97) gives:
% 157.82/27.47 | | | |
% 157.82/27.47 | | | | Case 1:
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | (98) all_58_4 = e3 & op(e3, e1) = e3
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | REF_CLOSE: (2), (5), (8), (9), (10), (15), (18), (24), (25), (27),
% 157.82/27.47 | | | | | (28), (29), (30), (31), (33), (34), (35), (36), (37), (39),
% 157.82/27.47 | | | | | (42), (43), (44), (46), (48), (51), (52), (53), (56), (58),
% 157.82/27.47 | | | | | (60), (61), (62), (65), (66), (67), (98) are inconsistent
% 157.82/27.47 | | | | | by sub-proof #644.
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | Case 2:
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | (99) all_58_9 = e3 & op(e3, e0) = e3
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | ALPHA: (99) implies:
% 157.82/27.47 | | | | | (100) all_58_9 = e3
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (11), (12), (13), (14), (15),
% 157.82/27.47 | | | | | (16), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 157.82/27.47 | | | | | (28), (31), (32), (34), (36), (38), (40), (41), (43), (45),
% 157.82/27.47 | | | | | (47), (48), (49), (50), (51), (52), (54), (55), (59), (61),
% 157.82/27.47 | | | | | (62), (63), (64), (65), (66), (100) are inconsistent by
% 157.82/27.47 | | | | | sub-proof #402.
% 157.82/27.47 | | | | |
% 157.82/27.47 | | | | End of split
% 157.82/27.47 | | | |
% 157.82/27.47 | | | End of split
% 157.82/27.47 | | |
% 157.82/27.47 | | End of split
% 157.82/27.47 | |
% 157.82/27.47 | End of split
% 157.82/27.47 |
% 157.82/27.47 End of proof
% 157.82/27.47
% 157.82/27.47 Sub-proof #401 shows that the following formulas are inconsistent:
% 157.82/27.47 ----------------------------------------------------------------
% 157.82/27.47 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.47 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.47 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.47 (3) all_58_1 = e0
% 157.82/27.47 (4) ~ (all_52_7 = e3)
% 157.82/27.47 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.82/27.47 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.47 (6) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.47 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.47 (7) all_58_12 = e3
% 157.82/27.47 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.47 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.47 (9) op(e3, e2) = all_52_4
% 157.82/27.48 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.48 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.48 (11) op(e2, e3) = all_52_1
% 157.82/27.48 (12) ~ (all_52_13 = e3)
% 157.82/27.48 (13) ~ (e3 = e0)
% 157.82/27.48 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.48 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.48 (15) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.48 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.48 (16) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.48 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.48 e2)
% 157.82/27.48 (17) ~ (e2 = e0)
% 157.82/27.48 (18) op(e2, e0) = all_52_13
% 157.82/27.48 (19) op(e2, e3) = e2
% 157.82/27.48 (20) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.48 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.48 (21) ~ (e3 = e1)
% 157.82/27.48 (22) op(e1, e2) = all_52_6
% 157.82/27.48 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.48 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.48 (24) op(e0, e0) = e2
% 157.82/27.48 (25) all_58_4 = e2
% 157.82/27.48 (26) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.48 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.48 (27) ~ (all_52_4 = e3)
% 157.82/27.48 (28) op(e0, e2) = e0
% 157.82/27.48 (29) ~ (e2 = e1)
% 157.82/27.48 (30) ~ (e1 = e0)
% 157.82/27.48 (31) all_58_3 = e3
% 157.82/27.48 (32) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.48 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.48 e3)
% 157.82/27.48 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.48 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.48 (34) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.48 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.48 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.48 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.48 (36) op(e0, e2) = all_52_7
% 157.82/27.48 (37) all_58_0 = e0
% 157.82/27.48 (38) ~ (all_52_6 = e3)
% 157.82/27.48 (39) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.48 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.48 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.48 (41) ~ (e3 = e2)
% 157.82/27.48 (42) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.48 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.48 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.82/27.48 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.82/27.48 (43) all_58_11 = e3
% 157.82/27.48
% 157.82/27.48 Begin of proof
% 157.82/27.48 |
% 157.82/27.48 | BETA: splitting (35) gives:
% 157.82/27.48 |
% 157.82/27.48 | Case 1:
% 157.82/27.48 | |
% 157.82/27.48 | | (44) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 157.82/27.48 | | e3)
% 157.82/27.48 | |
% 157.82/27.48 | | REF_CLOSE: (9), (13), (27), (37), (40), (44) are inconsistent by sub-proof
% 157.82/27.48 | | #645.
% 157.82/27.48 | |
% 157.82/27.48 | Case 2:
% 157.82/27.48 | |
% 157.82/27.48 | | (45) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 157.82/27.48 | | e3)
% 157.82/27.48 | |
% 157.82/27.48 | | BETA: splitting (45) gives:
% 157.82/27.48 | |
% 157.82/27.48 | | Case 1:
% 157.82/27.48 | | |
% 157.82/27.48 | | | (46) all_58_4 = e3 & op(e3, e1) = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 157.82/27.48 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 157.82/27.48 | | | (25), (26), (28), (29), (30), (31), (32), (34), (36), (38),
% 157.82/27.48 | | | (39), (40), (41), (42), (43), (46) are inconsistent by
% 157.82/27.48 | | | sub-proof #644.
% 157.82/27.48 | | |
% 157.82/27.48 | | Case 2:
% 157.82/27.48 | | |
% 157.82/27.48 | | | (47) all_58_9 = e3 & op(e3, e0) = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | ALPHA: (47) implies:
% 157.82/27.48 | | | (48) all_58_9 = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | REF_CLOSE: (3), (7), (14), (19), (21), (25), (29), (30), (33), (37), (40),
% 157.82/27.48 | | | (48) are inconsistent by sub-proof #498.
% 157.82/27.48 | | |
% 157.82/27.48 | | End of split
% 157.82/27.48 | |
% 157.82/27.48 | End of split
% 157.82/27.48 |
% 157.82/27.48 End of proof
% 157.82/27.48
% 157.82/27.48 Sub-proof #402 shows that the following formulas are inconsistent:
% 157.82/27.48 ----------------------------------------------------------------
% 157.82/27.48 (1) ~ (all_52_12 = e3)
% 157.82/27.48 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.48 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.48 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.48 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.48 (4) ~ (all_52_14 = e2)
% 157.82/27.48 (5) all_58_1 = e0
% 157.82/27.48 (6) ~ (all_52_12 = e2)
% 157.82/27.48 (7) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.48 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.48 (8) all_58_12 = e3
% 157.82/27.48 (9) all_58_7 = e2
% 157.82/27.48 (10) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.48 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.48 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.48 (12) all_54_1 = all_52_4
% 157.82/27.48 (13) ~ (all_52_12 = all_52_13)
% 157.82/27.48 (14) ~ (all_52_4 = e2)
% 157.82/27.48 (15) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.48 (16) ~ (all_52_4 = all_52_12)
% 157.82/27.48 (17) op(e2, e1) = all_52_9
% 157.82/27.48 (18) op(e2, e3) = all_52_1
% 157.82/27.48 (19) ~ (all_52_13 = e3)
% 157.82/27.48 (20) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.48 (21) ~ (e3 = e0)
% 157.82/27.48 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.48 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.48 (23) ~ (e2 = e0)
% 157.82/27.48 (24) ~ (all_52_9 = e3)
% 157.82/27.48 (25) all_58_9 = e3
% 157.82/27.48 (26) op(e2, e3) = e2
% 157.82/27.48 (27) ~ (e3 = e1)
% 157.82/27.48 (28) ~ (all_52_4 = e0)
% 157.82/27.48 (29) all_54_7 = all_52_13
% 157.82/27.48 (30) ~ (all_52_13 = e2)
% 157.82/27.48 (31) all_58_4 = e2
% 157.82/27.48 (32) ~ (all_52_4 = e3)
% 157.82/27.48 (33) all_58_15 = e2
% 157.82/27.48 (34) ~ (e2 = e1)
% 157.82/27.48 (35) all_54_3 = all_52_12
% 157.82/27.48 (36) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.48 (37) ~ (e1 = e0)
% 157.82/27.48 (38) all_58_3 = e3
% 157.82/27.48 (39) ~ (all_52_12 = all_52_14)
% 157.82/27.48 (40) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.48 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.48 (41) op(e1, e0) = all_52_14
% 157.82/27.48 (42) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.48 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.48 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.48 (44) all_54_11 = all_52_14
% 157.82/27.48 (45) ~ (all_52_13 = all_52_14)
% 157.82/27.48 (46) ~ (e3 = e2)
% 157.82/27.48 (47) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.48 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.48 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.82/27.48 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.82/27.48
% 157.82/27.48 Begin of proof
% 157.82/27.48 |
% 157.82/27.48 | BETA: splitting (7) gives:
% 157.82/27.48 |
% 157.82/27.48 | Case 1:
% 157.82/27.48 | |
% 157.82/27.48 | | (48) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 157.82/27.48 | | e3)
% 157.82/27.48 | |
% 157.82/27.48 | | BETA: splitting (48) gives:
% 157.82/27.48 | |
% 157.82/27.48 | | Case 1:
% 157.82/27.48 | | |
% 157.82/27.48 | | | (49) all_58_4 = e3 & op(e3, e1) = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | ALPHA: (49) implies:
% 157.82/27.48 | | | (50) all_58_4 = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | COMBINE_EQS: (31), (50) imply:
% 157.82/27.48 | | | (51) e3 = e2
% 157.82/27.48 | | |
% 157.82/27.48 | | | SIMP: (51) implies:
% 157.82/27.48 | | | (52) e3 = e2
% 157.82/27.48 | | |
% 157.82/27.48 | | | COMBINE_EQS: (8), (52) imply:
% 157.82/27.48 | | | (53) all_58_12 = e2
% 157.82/27.48 | | |
% 157.82/27.48 | | | REF_CLOSE: (11), (18), (21), (22), (23), (26), (27), (34), (37), (42),
% 157.82/27.48 | | | (43), (46), (53) are inconsistent by sub-proof #1062.
% 157.82/27.48 | | |
% 157.82/27.48 | | Case 2:
% 157.82/27.48 | | |
% 157.82/27.48 | | | (54) all_58_5 = e3 & op(e2, e1) = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | ALPHA: (54) implies:
% 157.82/27.48 | | | (55) op(e2, e1) = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | REF_CLOSE: (17), (24), (43), (55) are inconsistent by sub-proof #1196.
% 157.82/27.48 | | |
% 157.82/27.48 | | End of split
% 157.82/27.48 | |
% 157.82/27.48 | Case 2:
% 157.82/27.48 | |
% 157.82/27.48 | | (56) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 157.82/27.48 | | e3)
% 157.82/27.48 | |
% 157.82/27.48 | | BETA: splitting (56) gives:
% 157.82/27.48 | |
% 157.82/27.48 | | Case 1:
% 157.82/27.48 | | |
% 157.82/27.48 | | | (57) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | ALPHA: (57) implies:
% 157.82/27.48 | | | (58) all_58_8 = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14),
% 157.82/27.48 | | | (15), (16), (19), (20), (21), (22), (23), (25), (26), (27),
% 157.82/27.48 | | | (28), (29), (30), (31), (32), (34), (35), (36), (37), (38),
% 157.82/27.48 | | | (39), (40), (41), (42), (43), (44), (45), (58) are inconsistent
% 157.82/27.48 | | | by sub-proof #416.
% 157.82/27.48 | | |
% 157.82/27.48 | | Case 2:
% 157.82/27.48 | | |
% 157.82/27.48 | | | (59) all_58_14 = e3 & op(e0, e1) = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | ALPHA: (59) implies:
% 157.82/27.48 | | | (60) all_58_14 = e3
% 157.82/27.48 | | |
% 157.82/27.48 | | | REF_CLOSE: (3), (5), (8), (9), (21), (23), (27), (33), (34), (37), (38),
% 157.82/27.48 | | | (47), (60) are inconsistent by sub-proof #425.
% 157.82/27.48 | | |
% 157.82/27.48 | | End of split
% 157.82/27.48 | |
% 157.82/27.48 | End of split
% 157.82/27.48 |
% 157.82/27.48 End of proof
% 157.82/27.48
% 157.82/27.48 Sub-proof #403 shows that the following formulas are inconsistent:
% 157.82/27.48 ----------------------------------------------------------------
% 157.82/27.48 (1) ~ (all_52_12 = e3)
% 157.82/27.48 (2) all_58_13 = e0
% 157.82/27.48 (3) op(e3, e0) = all_52_12
% 157.82/27.48 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.48 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.48 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.48 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.48 (6) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.48 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.48 (7) ~ (all_52_12 = e2)
% 157.82/27.48 (8) ~ (all_52_7 = e3)
% 157.82/27.48 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.82/27.48 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.48 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.48 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.48 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.48 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.48 (12) all_58_12 = e3
% 157.82/27.48 (13) all_58_7 = e2
% 157.82/27.48 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.48 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.48 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.48 (16) all_54_1 = all_52_4
% 157.82/27.48 (17) op(e3, e2) = all_52_4
% 157.82/27.48 (18) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.48 (19) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.48 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.48 (20) ~ (all_52_12 = all_52_13)
% 157.82/27.48 (21) ~ (all_52_4 = e2)
% 157.82/27.48 (22) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.48 (23) ~ (all_52_4 = all_52_12)
% 157.82/27.48 (24) op(e2, e1) = all_52_9
% 157.82/27.48 (25) op(e2, e3) = all_52_1
% 157.82/27.48 (26) ~ (all_52_13 = e3)
% 157.82/27.48 (27) ~ (e3 = e0)
% 157.82/27.48 (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.48 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.48 (29) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.48 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.48 (30) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.48 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.48 e2)
% 157.82/27.48 (31) ~ (e2 = e0)
% 157.82/27.48 (32) ~ (all_52_9 = e3)
% 157.82/27.48 (33) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.48 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.48 (34) op(e2, e0) = all_52_13
% 157.82/27.48 (35) op(e2, e3) = e2
% 157.82/27.48 (36) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.48 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.48 (37) op(e1, e2) = all_52_6
% 157.82/27.48 (38) ~ (all_52_4 = e0)
% 157.82/27.48 (39) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.48 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.48 (40) all_54_7 = all_52_13
% 157.82/27.48 (41) ~ (all_52_13 = e2)
% 157.82/27.48 (42) op(e0, e0) = e2
% 157.82/27.48 (43) all_58_4 = e2
% 157.82/27.48 (44) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.48 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.48 (45) ~ (all_52_4 = e3)
% 157.82/27.48 (46) op(e0, e2) = e0
% 157.82/27.48 (47) all_58_15 = e2
% 157.82/27.48 (48) op(e3, e3) = e3
% 157.82/27.48 (49) all_54_3 = all_52_12
% 157.82/27.48 (50) all_58_3 = e3
% 157.82/27.48 (51) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.48 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.48 e3)
% 157.82/27.48 (52) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.48 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.48 (53) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.48 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.48 (54) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.48 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.48 (55) op(e0, e2) = all_52_7
% 157.82/27.48 (56) op(e3, e3) = all_22_1
% 157.82/27.48 (57) all_58_0 = e0
% 157.82/27.48 (58) ~ (all_52_6 = e3)
% 157.82/27.48 (59) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.48 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.48 (60) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.48 (61) ~ (e3 = e2)
% 157.82/27.48 (62) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.48 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.48 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.82/27.48 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.82/27.48 (63) all_58_11 = e3
% 157.82/27.48
% 157.82/27.48 Begin of proof
% 157.82/27.48 |
% 157.82/27.48 | BETA: splitting (18) gives:
% 157.82/27.48 |
% 157.82/27.48 | Case 1:
% 157.82/27.48 | |
% 157.82/27.48 | | (64) all_54_1 = e3
% 157.82/27.48 | |
% 157.82/27.48 | | COMBINE_EQS: (16), (64) imply:
% 157.82/27.48 | | (65) all_52_4 = e3
% 157.82/27.48 | |
% 157.82/27.48 | | REDUCE: (45), (65) imply:
% 157.82/27.48 | | (66) $false
% 157.82/27.48 | |
% 157.82/27.48 | | CLOSE: (66) is inconsistent.
% 157.82/27.48 | |
% 157.82/27.48 | Case 2:
% 157.82/27.48 | |
% 157.82/27.48 | | (67) ~ (all_54_1 = e3)
% 157.82/27.48 | | (68) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.48 | |
% 157.82/27.48 | | BETA: splitting (68) gives:
% 157.82/27.48 | |
% 157.82/27.48 | | Case 1:
% 157.82/27.48 | | |
% 157.82/27.48 | | | (69) all_54_1 = e2
% 157.82/27.48 | | |
% 157.82/27.48 | | | COMBINE_EQS: (16), (69) imply:
% 157.82/27.48 | | | (70) all_52_4 = e2
% 157.82/27.48 | | |
% 157.82/27.48 | | | REDUCE: (21), (70) imply:
% 157.82/27.48 | | | (71) $false
% 157.82/27.48 | | |
% 157.82/27.48 | | | CLOSE: (71) is inconsistent.
% 157.82/27.48 | | |
% 157.82/27.48 | | Case 2:
% 157.82/27.48 | | |
% 157.82/27.48 | | | (72) ~ (all_54_1 = e2)
% 157.82/27.48 | | | (73) all_54_1 = e1 | all_54_1 = e0
% 157.82/27.48 | | |
% 157.82/27.48 | | | BETA: splitting (73) gives:
% 157.82/27.48 | | |
% 157.82/27.48 | | | Case 1:
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | (74) all_54_1 = e1
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | COMBINE_EQS: (16), (74) imply:
% 157.82/27.48 | | | | (75) all_52_4 = e1
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | REDUCE: (23), (75) imply:
% 157.82/27.48 | | | | (76) ~ (all_52_12 = e1)
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | SIMP: (76) implies:
% 157.82/27.48 | | | | (77) ~ (all_52_12 = e1)
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | REDUCE: (45), (75) imply:
% 157.82/27.48 | | | | (78) ~ (e3 = e1)
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | SIMP: (78) implies:
% 157.82/27.48 | | | | (79) ~ (e3 = e1)
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | REDUCE: (21), (75) imply:
% 157.82/27.48 | | | | (80) ~ (e2 = e1)
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | SIMP: (80) implies:
% 157.82/27.48 | | | | (81) ~ (e2 = e1)
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | REDUCE: (38), (75) imply:
% 157.82/27.48 | | | | (82) ~ (e1 = e0)
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | BETA: splitting (22) gives:
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | Case 1:
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | | (83) all_54_3 = e3
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | | COMBINE_EQS: (49), (83) imply:
% 157.82/27.48 | | | | | (84) all_52_12 = e3
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | | REDUCE: (1), (84) imply:
% 157.82/27.48 | | | | | (85) $false
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | | CLOSE: (85) is inconsistent.
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | Case 2:
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | | (86) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | | BETA: splitting (5) gives:
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | | Case 1:
% 157.82/27.48 | | | | | |
% 157.82/27.48 | | | | | | (87) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 157.82/27.48 | | | | | | e2) = e1)
% 157.82/27.48 | | | | | |
% 157.82/27.48 | | | | | | BETA: splitting (87) gives:
% 157.82/27.48 | | | | | |
% 157.82/27.48 | | | | | | Case 1:
% 157.82/27.48 | | | | | | |
% 157.82/27.48 | | | | | | | (88) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.48 | | | | | | |
% 157.82/27.48 | | | | | | | ALPHA: (88) implies:
% 157.82/27.48 | | | | | | | (89) all_58_1 = e1
% 157.82/27.48 | | | | | | |
% 157.82/27.48 | | | | | | | BETA: splitting (86) gives:
% 157.82/27.48 | | | | | | |
% 157.82/27.48 | | | | | | | Case 1:
% 157.82/27.48 | | | | | | | |
% 157.82/27.48 | | | | | | | | (90) all_54_3 = e2
% 157.82/27.48 | | | | | | | |
% 157.82/27.48 | | | | | | | | COMBINE_EQS: (49), (90) imply:
% 157.82/27.48 | | | | | | | | (91) all_52_12 = e2
% 157.82/27.48 | | | | | | | |
% 157.82/27.48 | | | | | | | | REDUCE: (7), (91) imply:
% 157.82/27.48 | | | | | | | | (92) $false
% 157.82/27.48 | | | | | | | |
% 157.82/27.48 | | | | | | | | CLOSE: (92) is inconsistent.
% 157.82/27.48 | | | | | | | |
% 157.82/27.48 | | | | | | | Case 2:
% 157.82/27.48 | | | | | | | |
% 157.82/27.48 | | | | | | | | (93) all_54_3 = e1 | all_54_3 = e0
% 157.82/27.48 | | | | | | | |
% 157.82/27.48 | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 157.82/27.48 | | | | | | | | (13), (14), (15), (17), (19), (20), (24), (25), (26),
% 157.82/27.48 | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 157.82/27.48 | | | | | | | | (36), (37), (39), (40), (41), (42), (43), (44), (45),
% 157.82/27.48 | | | | | | | | (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 157.82/27.48 | | | | | | | | (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 157.82/27.48 | | | | | | | | (77), (79), (81), (82), (89), (93) are inconsistent
% 157.82/27.48 | | | | | | | | by sub-proof #404.
% 157.82/27.48 | | | | | | | |
% 157.82/27.48 | | | | | | | End of split
% 157.82/27.48 | | | | | | |
% 157.82/27.48 | | | | | | Case 2:
% 157.82/27.48 | | | | | | |
% 157.82/27.48 | | | | | | | (94) all_58_3 = e1 & op(e2, e2) = e1
% 157.82/27.48 | | | | | | |
% 157.82/27.48 | | | | | | | REF_CLOSE: (50), (79), (94) are inconsistent by sub-proof #912.
% 157.82/27.48 | | | | | | |
% 157.82/27.48 | | | | | | End of split
% 157.82/27.48 | | | | | |
% 157.82/27.48 | | | | | Case 2:
% 157.82/27.48 | | | | | |
% 157.82/27.48 | | | | | | (95) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 157.82/27.48 | | | | | | e2) = e1)
% 157.82/27.48 | | | | | |
% 157.82/27.48 | | | | | | REF_CLOSE: (2), (13), (81), (82), (95) are inconsistent by sub-proof
% 157.82/27.48 | | | | | | #858.
% 157.82/27.48 | | | | | |
% 157.82/27.48 | | | | | End of split
% 157.82/27.48 | | | | |
% 157.82/27.48 | | | | End of split
% 157.82/27.48 | | | |
% 157.82/27.48 | | | Case 2:
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | (96) all_54_1 = e0
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | COMBINE_EQS: (16), (96) imply:
% 157.82/27.48 | | | | (97) all_52_4 = e0
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | REDUCE: (38), (97) imply:
% 157.82/27.48 | | | | (98) $false
% 157.82/27.48 | | | |
% 157.82/27.48 | | | | CLOSE: (98) is inconsistent.
% 157.82/27.48 | | | |
% 157.82/27.48 | | | End of split
% 157.82/27.48 | | |
% 157.82/27.48 | | End of split
% 157.82/27.48 | |
% 157.82/27.48 | End of split
% 157.82/27.48 |
% 157.82/27.48 End of proof
% 157.82/27.48
% 157.82/27.48 Sub-proof #404 shows that the following formulas are inconsistent:
% 157.82/27.48 ----------------------------------------------------------------
% 157.82/27.48 (1) all_58_13 = e0
% 157.82/27.48 (2) op(e3, e0) = all_52_12
% 157.82/27.48 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.48 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.48 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.48 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.48 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.48 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.48 (6) ~ (all_52_7 = e3)
% 157.82/27.48 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.82/27.48 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.48 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.48 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.48 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.48 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.48 (10) all_58_12 = e3
% 157.82/27.48 (11) all_58_7 = e2
% 157.82/27.48 (12) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.48 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.48 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.48 (14) op(e3, e2) = all_52_4
% 157.82/27.48 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.48 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.48 (16) ~ (all_52_12 = all_52_13)
% 157.82/27.48 (17) op(e2, e1) = all_52_9
% 157.82/27.48 (18) op(e2, e3) = all_52_1
% 157.82/27.48 (19) ~ (all_52_13 = e3)
% 157.82/27.48 (20) all_54_3 = e1 | all_54_3 = e0
% 157.82/27.48 (21) ~ (e3 = e0)
% 157.82/27.48 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.48 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.48 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.48 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.48 (24) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.48 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.48 e2)
% 157.82/27.48 (25) ~ (e2 = e0)
% 157.82/27.48 (26) ~ (all_52_9 = e3)
% 157.82/27.48 (27) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.48 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.48 (28) op(e2, e0) = all_52_13
% 157.82/27.48 (29) op(e2, e3) = e2
% 157.82/27.48 (30) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.48 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.48 (31) ~ (e3 = e1)
% 157.82/27.48 (32) op(e1, e2) = all_52_6
% 157.82/27.48 (33) all_58_1 = e1
% 157.82/27.48 (34) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.48 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.48 (35) all_54_7 = all_52_13
% 157.82/27.48 (36) ~ (all_52_13 = e2)
% 157.82/27.48 (37) op(e0, e0) = e2
% 157.82/27.48 (38) all_58_4 = e2
% 157.82/27.49 (39) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.49 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.49 (40) ~ (all_52_4 = e3)
% 157.82/27.49 (41) op(e0, e2) = e0
% 157.82/27.49 (42) all_58_15 = e2
% 157.82/27.49 (43) ~ (e2 = e1)
% 157.82/27.49 (44) op(e3, e3) = e3
% 157.82/27.49 (45) all_54_3 = all_52_12
% 157.82/27.49 (46) ~ (e1 = e0)
% 157.82/27.49 (47) all_58_3 = e3
% 157.82/27.49 (48) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.49 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.49 e3)
% 157.82/27.49 (49) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.49 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.49 (50) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.49 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.49 (51) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.49 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.49 (52) op(e0, e2) = all_52_7
% 157.82/27.49 (53) op(e3, e3) = all_22_1
% 157.82/27.49 (54) all_58_0 = e0
% 157.82/27.49 (55) ~ (all_52_6 = e3)
% 157.82/27.49 (56) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.49 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.49 (57) ~ (all_52_12 = e1)
% 157.82/27.49 (58) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.49 (59) ~ (e3 = e2)
% 157.82/27.49 (60) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.49 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.49 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.82/27.49 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.82/27.49 (61) all_58_11 = e3
% 157.82/27.49
% 157.82/27.49 Begin of proof
% 157.82/27.49 |
% 157.82/27.49 | BETA: splitting (51) gives:
% 157.82/27.49 |
% 157.82/27.49 | Case 1:
% 157.82/27.49 | |
% 157.82/27.49 | | (62) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 157.82/27.49 | | e3)
% 157.82/27.49 | |
% 157.82/27.49 | | REF_CLOSE: (14), (21), (40), (54), (58), (62) are inconsistent by sub-proof
% 157.82/27.49 | | #645.
% 157.82/27.49 | |
% 157.82/27.49 | Case 2:
% 157.82/27.49 | |
% 157.82/27.49 | | (63) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 157.82/27.49 | | e3)
% 157.82/27.49 | |
% 157.82/27.49 | | BETA: splitting (63) gives:
% 157.82/27.49 | |
% 157.82/27.49 | | Case 1:
% 157.82/27.49 | | |
% 157.82/27.49 | | | (64) all_58_4 = e3 & op(e3, e1) = e3
% 157.82/27.49 | | |
% 157.82/27.49 | | | REF_CLOSE: (3), (5), (6), (7), (8), (13), (15), (18), (19), (21), (22),
% 157.82/27.49 | | | (23), (24), (25), (28), (29), (30), (31), (32), (34), (37),
% 157.82/27.49 | | | (38), (39), (41), (43), (46), (47), (48), (50), (52), (55),
% 157.82/27.49 | | | (56), (58), (59), (60), (61), (64) are inconsistent by
% 157.82/27.49 | | | sub-proof #644.
% 157.82/27.49 | | |
% 157.82/27.49 | | Case 2:
% 157.82/27.49 | | |
% 157.82/27.49 | | | (65) all_58_9 = e3 & op(e3, e0) = e3
% 157.82/27.49 | | |
% 157.82/27.49 | | | ALPHA: (65) implies:
% 157.82/27.49 | | | (66) all_58_9 = e3
% 157.82/27.49 | | | (67) op(e3, e0) = e3
% 157.82/27.49 | | |
% 157.82/27.49 | | | BETA: splitting (60) gives:
% 157.82/27.49 | | |
% 157.82/27.49 | | | Case 1:
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | (68) all_58_15 = e0 & op(e0, e0) = e0
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | REF_CLOSE: (25), (42), (68) are inconsistent by sub-proof #885.
% 157.82/27.49 | | | |
% 157.82/27.49 | | | Case 2:
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | (69) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 157.82/27.49 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 157.82/27.49 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 157.82/27.49 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | ALPHA: (69) implies:
% 157.82/27.49 | | | | (70) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 157.82/27.49 | | | | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | BETA: splitting (22) gives:
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | Case 1:
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 157.82/27.49 | | | | | e3) = e1)
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | BETA: splitting (71) gives:
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | Case 1:
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | (72) all_58_0 = e1 & op(e3, e3) = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | ALPHA: (72) implies:
% 157.82/27.49 | | | | | | (73) all_58_0 = e1
% 157.82/27.49 | | | | | | (74) op(e3, e3) = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | COMBINE_EQS: (54), (73) imply:
% 157.82/27.49 | | | | | | (75) e1 = e0
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | SIMP: (75) implies:
% 157.82/27.49 | | | | | | (76) e1 = e0
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | COMBINE_EQS: (33), (76) imply:
% 157.82/27.49 | | | | | | (77) all_58_1 = e0
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | BETA: splitting (4) gives:
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | Case 1:
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | (78) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 157.82/27.49 | | | | | | | op(e2, e2) = e1)
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | BETA: splitting (78) gives:
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | Case 1:
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | (79) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (13), (14), (15),
% 157.82/27.49 | | | | | | | | (18), (19), (21), (22), (23), (24), (25), (28), (29),
% 157.82/27.49 | | | | | | | | (30), (31), (32), (34), (37), (38), (39), (40), (41),
% 157.82/27.49 | | | | | | | | (43), (46), (47), (48), (49), (50), (51), (52), (54),
% 157.82/27.49 | | | | | | | | (55), (56), (58), (59), (60), (61), (77) are
% 157.82/27.49 | | | | | | | | inconsistent by sub-proof #639.
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | Case 2:
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | (80) all_58_3 = e1 & op(e2, e2) = e1
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | REF_CLOSE: (31), (47), (80) are inconsistent by sub-proof #912.
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | End of split
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | Case 2:
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | (81) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 157.82/27.49 | | | | | | | op(e0, e2) = e1)
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | REF_CLOSE: (2), (4), (11), (12), (16), (19), (20), (35), (36),
% 157.82/27.49 | | | | | | | (38), (43), (44), (45), (47), (49), (53), (57), (58),
% 157.82/27.49 | | | | | | | (66), (67), (73), (74), (77), (81) are inconsistent by
% 157.82/27.49 | | | | | | | sub-proof #405.
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | End of split
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | Case 2:
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | (82) all_58_2 = e1 & op(e2, e3) = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | ALPHA: (82) implies:
% 157.82/27.49 | | | | | | (83) op(e2, e3) = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | REF_CLOSE: (29), (43), (58), (83) are inconsistent by sub-proof
% 157.82/27.49 | | | | | | #1430.
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | End of split
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | Case 2:
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | (84) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 157.82/27.49 | | | | | e3) = e1)
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | BETA: splitting (84) gives:
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | Case 1:
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | (85) all_58_6 = e1 & op(e1, e3) = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | ALPHA: (85) implies:
% 157.82/27.49 | | | | | | (86) all_58_6 = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | BETA: splitting (27) gives:
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | Case 1:
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | (87) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 157.82/27.49 | | | | | | | op(e1, e2) = e0)
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | REF_CLOSE: (10), (11), (22), (25), (29), (31), (43), (46), (54),
% 157.82/27.49 | | | | | | | (58), (87) are inconsistent by sub-proof #715.
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | Case 2:
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | (88) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 157.82/27.49 | | | | | | | op(e1, e0) = e0)
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | BETA: splitting (88) gives:
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | | Case 1:
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | (89) all_58_8 = e0 & op(e1, e1) = e0
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | ALPHA: (89) implies:
% 157.82/27.49 | | | | | | | | (90) all_58_8 = e0
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | BETA: splitting (9) gives:
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | Case 1:
% 157.82/27.49 | | | | | | | | |
% 157.82/27.49 | | | | | | | | | (91) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 157.82/27.49 | | | | | | | | | op(e2, e1) = e3)
% 157.82/27.49 | | | | | | | | |
% 157.82/27.49 | | | | | | | | | BETA: splitting (91) gives:
% 157.82/27.49 | | | | | | | | |
% 157.82/27.49 | | | | | | | | | Case 1:
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | (92) all_58_4 = e3 & op(e3, e1) = e3
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | ALPHA: (92) implies:
% 157.82/27.49 | | | | | | | | | | (93) all_58_4 = e3
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | COMBINE_EQS: (38), (93) imply:
% 157.82/27.49 | | | | | | | | | | (94) e3 = e2
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | SIMP: (94) implies:
% 157.82/27.49 | | | | | | | | | | (95) e3 = e2
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | COMBINE_EQS: (61), (95) imply:
% 157.82/27.49 | | | | | | | | | | (96) all_58_11 = e2
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | REF_CLOSE: (5), (21), (25), (31), (42), (43), (46), (66),
% 157.82/27.49 | | | | | | | | | | (70), (96) are inconsistent by sub-proof #1454.
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | Case 2:
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | (97) all_58_5 = e3 & op(e2, e1) = e3
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | ALPHA: (97) implies:
% 157.82/27.49 | | | | | | | | | | (98) op(e2, e1) = e3
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | REF_CLOSE: (17), (26), (58), (98) are inconsistent by
% 157.82/27.49 | | | | | | | | | | sub-proof #1196.
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | End of split
% 157.82/27.49 | | | | | | | | |
% 157.82/27.49 | | | | | | | | Case 2:
% 157.82/27.49 | | | | | | | | |
% 157.82/27.49 | | | | | | | | | (99) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 157.82/27.49 | | | | | | | | | op(e0, e1) = e3)
% 157.82/27.49 | | | | | | | | |
% 157.82/27.49 | | | | | | | | | BETA: splitting (99) gives:
% 157.82/27.49 | | | | | | | | |
% 157.82/27.49 | | | | | | | | | Case 1:
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | (100) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | ALPHA: (100) implies:
% 157.82/27.49 | | | | | | | | | | (101) all_58_8 = e3
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | REF_CLOSE: (21), (90), (101) are inconsistent by sub-proof
% 157.82/27.49 | | | | | | | | | | #781.
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | Case 2:
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | (102) all_58_14 = e3 & op(e0, e1) = e3
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | ALPHA: (102) implies:
% 157.82/27.49 | | | | | | | | | | (103) all_58_14 = e3
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | | REF_CLOSE: (1), (4), (5), (11), (15), (21), (25), (29), (31),
% 157.82/27.49 | | | | | | | | | | (32), (33), (34), (37), (38), (39), (43), (46),
% 157.82/27.49 | | | | | | | | | | (47), (55), (58), (66), (86), (90), (103) are
% 157.82/27.49 | | | | | | | | | | inconsistent by sub-proof #411.
% 157.82/27.49 | | | | | | | | | |
% 157.82/27.49 | | | | | | | | | End of split
% 157.82/27.49 | | | | | | | | |
% 157.82/27.49 | | | | | | | | End of split
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | Case 2:
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | (104) all_58_11 = e0 & op(e1, e0) = e0
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | | REF_CLOSE: (21), (61), (104) are inconsistent by sub-proof
% 157.82/27.49 | | | | | | | | #1083.
% 157.82/27.49 | | | | | | | |
% 157.82/27.49 | | | | | | | End of split
% 157.82/27.49 | | | | | | |
% 157.82/27.49 | | | | | | End of split
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | Case 2:
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | (105) all_58_12 = e1 & op(e0, e3) = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | REF_CLOSE: (10), (31), (105) are inconsistent by sub-proof #1388.
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | End of split
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | End of split
% 157.82/27.49 | | | |
% 157.82/27.49 | | | End of split
% 157.82/27.49 | | |
% 157.82/27.49 | | End of split
% 157.82/27.49 | |
% 157.82/27.49 | End of split
% 157.82/27.49 |
% 157.82/27.49 End of proof
% 157.82/27.49
% 157.82/27.49 Sub-proof #405 shows that the following formulas are inconsistent:
% 157.82/27.49 ----------------------------------------------------------------
% 157.82/27.49 (1) op(e3, e0) = all_52_12
% 157.82/27.49 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.49 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.49 (3) all_58_1 = e0
% 157.82/27.49 (4) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.49 (5) all_58_7 = e2
% 157.82/27.49 (6) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.49 (7) all_58_0 = e1
% 157.82/27.49 (8) ~ (all_52_12 = all_52_13)
% 157.82/27.49 (9) ~ (all_52_13 = e3)
% 157.82/27.49 (10) all_54_3 = e1 | all_54_3 = e0
% 157.82/27.49 (11) all_58_9 = e3
% 157.82/27.49 (12) all_54_7 = all_52_13
% 157.82/27.49 (13) op(e3, e3) = e1
% 157.82/27.49 (14) ~ (all_52_13 = e2)
% 157.82/27.49 (15) all_58_4 = e2
% 157.82/27.49 (16) ~ (e2 = e1)
% 157.82/27.49 (17) op(e3, e3) = e3
% 157.82/27.49 (18) all_54_3 = all_52_12
% 157.82/27.49 (19) all_58_3 = e3
% 157.82/27.49 (20) op(e3, e0) = e3
% 157.82/27.49 (21) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.49 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.49 (22) op(e3, e3) = all_22_1
% 157.82/27.49 (23) ~ (all_52_12 = e1)
% 157.82/27.49 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.49
% 157.82/27.49 Begin of proof
% 157.82/27.49 |
% 157.82/27.49 | BETA: splitting (4) gives:
% 157.82/27.49 |
% 157.82/27.49 | Case 1:
% 157.82/27.49 | |
% 157.82/27.49 | | (25) all_58_7 = e1 & op(e1, e2) = e1
% 157.82/27.49 | |
% 157.82/27.49 | | REF_CLOSE: (5), (16), (25) are inconsistent by sub-proof #1045.
% 157.82/27.49 | |
% 157.82/27.49 | Case 2:
% 157.82/27.49 | |
% 157.82/27.49 | | (26) all_58_13 = e1 & op(e0, e2) = e1
% 157.82/27.49 | |
% 157.82/27.49 | | ALPHA: (26) implies:
% 157.82/27.49 | | (27) all_58_13 = e1
% 157.82/27.49 | |
% 157.82/27.49 | | BETA: splitting (10) gives:
% 157.82/27.49 | |
% 157.82/27.49 | | Case 1:
% 157.82/27.49 | | |
% 157.82/27.49 | | | (28) all_54_3 = e1
% 157.82/27.49 | | |
% 157.82/27.49 | | | COMBINE_EQS: (18), (28) imply:
% 157.82/27.49 | | | (29) all_52_12 = e1
% 157.82/27.49 | | |
% 157.82/27.49 | | | REDUCE: (23), (29) imply:
% 157.82/27.49 | | | (30) $false
% 157.82/27.49 | | |
% 157.82/27.49 | | | CLOSE: (30) is inconsistent.
% 157.82/27.49 | | |
% 157.82/27.49 | | Case 2:
% 157.82/27.49 | | |
% 157.82/27.49 | | | (31) all_54_3 = e0
% 157.82/27.49 | | |
% 157.82/27.49 | | | COMBINE_EQS: (18), (31) imply:
% 157.82/27.49 | | | (32) all_52_12 = e0
% 157.82/27.49 | | |
% 157.82/27.49 | | | REDUCE: (8), (32) imply:
% 157.82/27.49 | | | (33) ~ (all_52_13 = e0)
% 157.82/27.49 | | |
% 157.82/27.49 | | | SIMP: (33) implies:
% 157.82/27.49 | | | (34) ~ (all_52_13 = e0)
% 157.82/27.49 | | |
% 157.82/27.49 | | | REDUCE: (1), (32) imply:
% 157.82/27.49 | | | (35) op(e3, e0) = e0
% 157.82/27.49 | | |
% 157.82/27.49 | | | BETA: splitting (6) gives:
% 157.82/27.49 | | |
% 157.82/27.49 | | | Case 1:
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | (36) all_54_7 = e3
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | COMBINE_EQS: (12), (36) imply:
% 157.82/27.49 | | | | (37) all_52_13 = e3
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | REDUCE: (9), (37) imply:
% 157.82/27.49 | | | | (38) $false
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | CLOSE: (38) is inconsistent.
% 157.82/27.49 | | | |
% 157.82/27.49 | | | Case 2:
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | (39) ~ (all_54_7 = e3)
% 157.82/27.49 | | | | (40) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | BETA: splitting (40) gives:
% 157.82/27.49 | | | |
% 157.82/27.49 | | | | Case 1:
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | (41) all_54_7 = e2
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | COMBINE_EQS: (12), (41) imply:
% 157.82/27.49 | | | | | (42) all_52_13 = e2
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | REDUCE: (14), (42) imply:
% 157.82/27.49 | | | | | (43) $false
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | CLOSE: (43) is inconsistent.
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | Case 2:
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | (44) ~ (all_54_7 = e2)
% 157.82/27.49 | | | | | (45) all_54_7 = e1 | all_54_7 = e0
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | BETA: splitting (45) gives:
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | | Case 1:
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | (46) all_54_7 = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | COMBINE_EQS: (12), (46) imply:
% 157.82/27.49 | | | | | | (47) all_52_13 = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | REDUCE: (9), (47) imply:
% 157.82/27.49 | | | | | | (48) ~ (e3 = e1)
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | SIMP: (48) implies:
% 157.82/27.49 | | | | | | (49) ~ (e3 = e1)
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | REDUCE: (14), (47) imply:
% 157.82/27.49 | | | | | | (50) ~ (e2 = e1)
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | REDUCE: (34), (47) imply:
% 157.82/27.49 | | | | | | (51) ~ (e1 = e0)
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | GROUND_INST: instantiating (24) with e0, e3, e0, e3, simplifying
% 157.82/27.49 | | | | | | with (20), (35) gives:
% 157.82/27.49 | | | | | | (52) e3 = e0
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | GROUND_INST: instantiating (24) with e3, all_22_1, e3, e3,
% 157.82/27.49 | | | | | | simplifying with (17), (22) gives:
% 157.82/27.49 | | | | | | (53) all_22_1 = e3
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | GROUND_INST: instantiating (24) with e1, all_22_1, e3, e3,
% 157.82/27.49 | | | | | | simplifying with (13), (22) gives:
% 157.82/27.49 | | | | | | (54) all_22_1 = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | COMBINE_EQS: (53), (54) imply:
% 157.82/27.49 | | | | | | (55) e3 = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | SIMP: (55) implies:
% 157.82/27.49 | | | | | | (56) e3 = e1
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | COMBINE_EQS: (52), (56) imply:
% 157.82/27.49 | | | | | | (57) e1 = e0
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | COMBINE_EQS: (7), (57) imply:
% 157.82/27.49 | | | | | | (58) all_58_0 = e0
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | REF_CLOSE: (2), (3), (5), (11), (15), (16), (19), (21), (27), (49),
% 157.82/27.49 | | | | | | (51), (58) are inconsistent by sub-proof #641.
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | Case 2:
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | (59) all_54_7 = e0
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | COMBINE_EQS: (12), (59) imply:
% 157.82/27.49 | | | | | | (60) all_52_13 = e0
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | REDUCE: (34), (60) imply:
% 157.82/27.49 | | | | | | (61) $false
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | | CLOSE: (61) is inconsistent.
% 157.82/27.49 | | | | | |
% 157.82/27.49 | | | | | End of split
% 157.82/27.49 | | | | |
% 157.82/27.49 | | | | End of split
% 157.82/27.49 | | | |
% 157.82/27.49 | | | End of split
% 157.82/27.49 | | |
% 157.82/27.49 | | End of split
% 157.82/27.49 | |
% 157.82/27.49 | End of split
% 157.82/27.49 |
% 157.82/27.49 End of proof
% 157.82/27.49
% 157.82/27.49 Sub-proof #406 shows that the following formulas are inconsistent:
% 157.82/27.49 ----------------------------------------------------------------
% 157.82/27.49 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.82/27.49 (2) ~ (all_52_12 = e3)
% 157.82/27.49 (3) all_58_13 = e0
% 157.82/27.49 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.49 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.49 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.49 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.49 (6) ~ (all_52_14 = e2)
% 157.82/27.49 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.49 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.49 (8) ~ (all_52_12 = e2)
% 157.82/27.49 (9) op(e1, e1) = all_6_2
% 157.82/27.49 (10) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.49 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.49 (11) all_54_10 = all_6_2
% 157.82/27.49 (12) ~ (all_52_2 = all_52_3)
% 157.82/27.49 (13) all_58_12 = e3
% 157.82/27.49 (14) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.82/27.49 (15) all_58_7 = e2
% 157.82/27.49 (16) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.49 (17) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.82/27.49 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.49 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.49 (19) all_54_1 = all_52_4
% 157.82/27.49 (20) ~ (all_52_3 = e0)
% 157.82/27.49 (21) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.49 (22) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.49 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.49 (23) ~ (all_52_12 = all_52_13)
% 157.82/27.49 (24) ~ (all_52_4 = e2)
% 157.82/27.49 (25) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.49 (26) ~ (all_52_4 = all_52_12)
% 157.82/27.49 (27) op(e2, e1) = all_52_9
% 157.82/27.49 (28) op(e2, e3) = all_52_1
% 157.82/27.49 (29) ~ (all_52_13 = e3)
% 157.82/27.49 (30) ~ (all_52_3 = e3)
% 157.82/27.49 (31) ~ (all_52_2 = all_6_2)
% 157.82/27.49 (32) ~ (e3 = e0)
% 157.82/27.49 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.49 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.49 (34) ~ (e2 = e0)
% 157.82/27.49 (35) ~ (all_52_9 = e3)
% 157.82/27.49 (36) op(e3, e3) = e0
% 157.82/27.49 (37) ~ (all_52_11 = all_6_2)
% 157.82/27.49 (38) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.49 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.49 (39) ~ (all_52_3 = e2)
% 157.82/27.49 (40) all_58_9 = e3
% 157.82/27.49 (41) op(e2, e3) = e2
% 157.82/27.49 (42) ~ (e3 = e1)
% 157.82/27.49 (43) op(e1, e2) = all_52_6
% 157.82/27.49 (44) ~ (all_52_4 = e0)
% 157.82/27.49 (45) ~ (all_52_11 = e2)
% 157.82/27.49 (46) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.49 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.49 (47) ~ (all_52_9 = all_6_2)
% 157.82/27.49 (48) all_54_8 = all_52_2
% 157.82/27.49 (49) all_54_7 = all_52_13
% 157.82/27.49 (50) ~ (all_52_2 = e3)
% 157.82/27.49 (51) ~ (all_52_13 = e2)
% 157.82/27.49 (52) op(e0, e0) = e2
% 157.82/27.49 (53) all_58_4 = e2
% 157.82/27.49 (54) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.49 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.49 (55) ~ (all_52_4 = e3)
% 157.82/27.49 (56) all_54_6 = all_52_9
% 157.82/27.49 (57) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.82/27.49 (58) ~ (e2 = e1)
% 157.82/27.49 (59) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.82/27.49 (60) op(e3, e3) = e3
% 157.82/27.49 (61) all_54_3 = all_52_12
% 157.82/27.49 (62) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.49 (63) ~ (e1 = e0)
% 157.82/27.49 (64) ~ (all_52_2 = e2)
% 157.82/27.49 (65) all_58_3 = e3
% 157.82/27.49 (66) ~ (all_6_2 = e2)
% 157.82/27.49 (67) all_56_14 = all_6_2
% 157.82/27.49 (68) ~ (all_52_12 = all_52_14)
% 157.82/27.49 (69) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.49 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.49 (70) ~ (all_52_9 = e2)
% 157.82/27.49 (71) all_54_14 = all_52_11
% 157.82/27.49 (72) op(e1, e0) = all_52_14
% 157.82/27.49 (73) op(e3, e3) = all_22_1
% 157.82/27.49 (74) all_58_0 = e0
% 157.82/27.49 (75) ~ (all_52_6 = e3)
% 157.82/27.49 (76) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.49 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.49 (77) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.49 (78) ~ (all_52_3 = all_52_11)
% 157.82/27.49 (79) all_54_11 = all_52_14
% 157.82/27.49 (80) ~ (all_52_13 = all_52_14)
% 157.82/27.49 (81) ~ (e3 = e2)
% 157.82/27.49 (82) ~ (all_52_11 = e0)
% 157.82/27.49 (83) all_54_12 = all_52_3
% 157.82/27.49 (84) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.82/27.49
% 157.82/27.49 Begin of proof
% 157.82/27.49 |
% 157.82/27.49 | BETA: splitting (21) gives:
% 157.82/27.49 |
% 157.82/27.49 | Case 1:
% 157.82/27.49 | |
% 157.82/27.49 | | (85) all_54_1 = e3
% 157.82/27.49 | |
% 157.82/27.49 | | COMBINE_EQS: (19), (85) imply:
% 157.82/27.49 | | (86) all_52_4 = e3
% 157.82/27.49 | |
% 157.82/27.49 | | REDUCE: (55), (86) imply:
% 157.82/27.49 | | (87) $false
% 157.82/27.49 | |
% 157.82/27.49 | | CLOSE: (87) is inconsistent.
% 157.82/27.49 | |
% 157.82/27.49 | Case 2:
% 157.82/27.49 | |
% 157.82/27.49 | | (88) ~ (all_54_1 = e3)
% 157.82/27.49 | | (89) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.49 | |
% 157.82/27.49 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.82/27.49 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 157.82/27.49 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 157.82/27.49 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 157.82/27.49 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 157.82/27.49 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 157.82/27.49 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 157.82/27.49 | | (80), (81), (82), (83), (84), (89) are inconsistent by sub-proof
% 157.82/27.49 | | #407.
% 157.82/27.49 | |
% 157.82/27.49 | End of split
% 157.82/27.49 |
% 157.82/27.49 End of proof
% 157.82/27.49
% 157.82/27.49 Sub-proof #407 shows that the following formulas are inconsistent:
% 157.82/27.49 ----------------------------------------------------------------
% 157.82/27.49 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.82/27.49 (2) ~ (all_52_12 = e3)
% 157.82/27.49 (3) all_58_13 = e0
% 157.82/27.49 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.49 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.49 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.49 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.49 (6) ~ (all_52_14 = e2)
% 157.82/27.49 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.49 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.49 (8) ~ (all_52_12 = e2)
% 157.82/27.49 (9) op(e1, e1) = all_6_2
% 157.82/27.49 (10) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.49 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.49 (11) all_54_10 = all_6_2
% 157.82/27.49 (12) ~ (all_52_2 = all_52_3)
% 157.82/27.49 (13) all_58_12 = e3
% 157.82/27.49 (14) ~ (all_56_14 = e3) | (all_56_6 = e1 & op(e1, e3) = e1)
% 157.82/27.49 (15) all_58_7 = e2
% 157.82/27.49 (16) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.49 (17) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.82/27.49 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.49 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.49 (19) all_54_1 = all_52_4
% 157.82/27.49 (20) ~ (all_52_3 = e0)
% 157.82/27.49 (21) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.49 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.49 (22) ~ (all_52_12 = all_52_13)
% 157.82/27.49 (23) ~ (all_52_4 = e2)
% 157.82/27.49 (24) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.49 (25) ~ (all_52_4 = all_52_12)
% 157.82/27.49 (26) op(e2, e1) = all_52_9
% 157.82/27.49 (27) op(e2, e3) = all_52_1
% 157.82/27.49 (28) ~ (all_52_13 = e3)
% 157.82/27.49 (29) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.49 (30) ~ (all_52_3 = e3)
% 157.82/27.49 (31) ~ (all_52_2 = all_6_2)
% 157.82/27.49 (32) ~ (e3 = e0)
% 157.82/27.49 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.49 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.49 (34) ~ (e2 = e0)
% 157.82/27.49 (35) ~ (all_52_9 = e3)
% 157.82/27.49 (36) op(e3, e3) = e0
% 157.82/27.49 (37) ~ (all_52_11 = all_6_2)
% 157.82/27.49 (38) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.49 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.49 (39) ~ (all_52_3 = e2)
% 157.82/27.49 (40) all_58_9 = e3
% 157.82/27.49 (41) op(e2, e3) = e2
% 157.82/27.49 (42) ~ (e3 = e1)
% 157.82/27.49 (43) op(e1, e2) = all_52_6
% 157.82/27.49 (44) ~ (all_52_4 = e0)
% 157.82/27.50 (45) ~ (all_52_11 = e2)
% 157.82/27.50 (46) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.50 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.50 (47) ~ (all_52_9 = all_6_2)
% 157.82/27.50 (48) all_54_8 = all_52_2
% 157.82/27.50 (49) all_54_7 = all_52_13
% 157.82/27.50 (50) ~ (all_52_2 = e3)
% 157.82/27.50 (51) ~ (all_52_13 = e2)
% 157.82/27.50 (52) op(e0, e0) = e2
% 157.82/27.50 (53) all_58_4 = e2
% 157.82/27.50 (54) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.50 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.50 (55) ~ (all_52_4 = e3)
% 157.82/27.50 (56) all_54_6 = all_52_9
% 157.82/27.50 (57) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.82/27.50 (58) ~ (e2 = e1)
% 157.82/27.50 (59) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.82/27.50 (60) op(e3, e3) = e3
% 157.82/27.50 (61) all_54_3 = all_52_12
% 157.82/27.50 (62) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.50 (63) ~ (e1 = e0)
% 157.82/27.50 (64) ~ (all_52_2 = e2)
% 157.82/27.50 (65) all_58_3 = e3
% 157.82/27.50 (66) ~ (all_6_2 = e2)
% 157.82/27.50 (67) all_56_14 = all_6_2
% 157.82/27.50 (68) ~ (all_52_12 = all_52_14)
% 157.82/27.50 (69) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.50 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.50 (70) ~ (all_52_9 = e2)
% 157.82/27.50 (71) all_54_14 = all_52_11
% 157.82/27.50 (72) op(e1, e0) = all_52_14
% 157.82/27.50 (73) op(e3, e3) = all_22_1
% 157.82/27.50 (74) all_58_0 = e0
% 157.82/27.50 (75) ~ (all_52_6 = e3)
% 157.82/27.50 (76) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.50 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.50 (77) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.50 (78) ~ (all_52_3 = all_52_11)
% 157.82/27.50 (79) all_54_11 = all_52_14
% 157.82/27.50 (80) ~ (all_52_13 = all_52_14)
% 157.82/27.50 (81) ~ (e3 = e2)
% 157.82/27.50 (82) ~ (all_52_11 = e0)
% 157.82/27.50 (83) all_54_12 = all_52_3
% 157.82/27.50 (84) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.82/27.50
% 157.82/27.50 Begin of proof
% 157.82/27.50 |
% 157.82/27.50 | BETA: splitting (33) gives:
% 157.82/27.50 |
% 157.82/27.50 | Case 1:
% 157.82/27.50 | |
% 157.82/27.50 | | (85) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 157.82/27.50 | | e1)
% 157.82/27.50 | |
% 157.82/27.50 | | REF_CLOSE: (41), (58), (63), (74), (77), (85) are inconsistent by sub-proof
% 157.82/27.50 | | #1160.
% 157.82/27.50 | |
% 157.82/27.50 | Case 2:
% 157.82/27.50 | |
% 157.82/27.50 | | (86) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 157.82/27.50 | | e1)
% 157.82/27.50 | |
% 157.82/27.50 | | BETA: splitting (86) gives:
% 157.82/27.50 | |
% 157.82/27.50 | | Case 1:
% 157.82/27.50 | | |
% 157.82/27.50 | | | (87) all_58_6 = e1 & op(e1, e3) = e1
% 157.82/27.50 | | |
% 157.82/27.50 | | | ALPHA: (87) implies:
% 157.82/27.50 | | | (88) all_58_6 = e1
% 157.82/27.50 | | |
% 157.82/27.50 | | | BETA: splitting (57) gives:
% 157.82/27.50 | | |
% 157.82/27.50 | | | Case 1:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | (89) all_54_12 = e2
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | COMBINE_EQS: (83), (89) imply:
% 157.82/27.50 | | | | (90) all_52_3 = e2
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | REDUCE: (39), (90) imply:
% 157.82/27.50 | | | | (91) $false
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | CLOSE: (91) is inconsistent.
% 157.82/27.50 | | | |
% 157.82/27.50 | | | Case 2:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | (92) ~ (all_54_12 = e2)
% 157.82/27.50 | | | | (93) all_54_12 = e1 | all_54_12 = e0
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | BETA: splitting (93) gives:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | Case 1:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (94) all_54_12 = e1
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | COMBINE_EQS: (83), (94) imply:
% 157.82/27.50 | | | | | (95) all_52_3 = e1
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REDUCE: (12), (95) imply:
% 157.82/27.50 | | | | | (96) ~ (all_52_2 = e1)
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REDUCE: (78), (95) imply:
% 157.82/27.50 | | | | | (97) ~ (all_52_11 = e1)
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | SIMP: (97) implies:
% 157.82/27.50 | | | | | (98) ~ (all_52_11 = e1)
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REDUCE: (30), (95) imply:
% 157.82/27.50 | | | | | (99) ~ (e3 = e1)
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REDUCE: (39), (95) imply:
% 157.82/27.50 | | | | | (100) ~ (e2 = e1)
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | BETA: splitting (14) gives:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | Case 1:
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | (101) ~ (all_56_14 = e3)
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | REDUCE: (67), (101) imply:
% 157.82/27.50 | | | | | | (102) ~ (all_6_2 = e3)
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | BETA: splitting (10) gives:
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | Case 1:
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | (103) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 157.82/27.50 | | | | | | | op(e2, e1) = e3)
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | BETA: splitting (103) gives:
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | (104) all_58_4 = e3 & op(e3, e1) = e3
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | ALPHA: (104) implies:
% 157.82/27.50 | | | | | | | | (105) all_58_4 = e3
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | COMBINE_EQS: (53), (105) imply:
% 157.82/27.50 | | | | | | | | (106) e3 = e2
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | REF_CLOSE: (13), (18), (27), (32), (41), (42), (74), (77), (81),
% 157.82/27.50 | | | | | | | | (88), (106) are inconsistent by sub-proof #698.
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | (107) all_58_5 = e3 & op(e2, e1) = e3
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | ALPHA: (107) implies:
% 157.82/27.50 | | | | | | | | (108) op(e2, e1) = e3
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | REF_CLOSE: (26), (35), (77), (108) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | #1196.
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | End of split
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | Case 2:
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | (109) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 157.82/27.50 | | | | | | | op(e0, e1) = e3)
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | BETA: splitting (109) gives:
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | (110) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | ALPHA: (110) implies:
% 157.82/27.50 | | | | | | | | (111) all_58_8 = e3
% 157.82/27.50 | | | | | | | | (112) op(e1, e1) = e3
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | BETA: splitting (17) gives:
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | (113) all_54_8 = e3
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | REF_CLOSE: (48), (50), (113) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | #1425.
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | (114) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | BETA: splitting (114) gives:
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | (115) all_54_8 = e2
% 157.82/27.50 | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | REF_CLOSE: (48), (64), (115) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | | #1231.
% 157.82/27.50 | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | (116) all_54_8 = e1 | all_54_8 = e0
% 157.82/27.50 | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | BETA: splitting (116) gives:
% 157.82/27.50 | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | (117) all_54_8 = e1
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | REF_CLOSE: (48), (96), (117) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | | | #1379.
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | (118) all_54_8 = e0
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | COMBINE_EQS: (48), (118) imply:
% 157.82/27.50 | | | | | | | | | | | (119) all_52_2 = e0
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | SIMP: (119) implies:
% 157.82/27.50 | | | | | | | | | | | (120) all_52_2 = e0
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | REDUCE: (31), (120) imply:
% 157.82/27.50 | | | | | | | | | | | (121) ~ (all_6_2 = e0)
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | SIMP: (121) implies:
% 157.82/27.50 | | | | | | | | | | | (122) ~ (all_6_2 = e0)
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | REDUCE: (96), (120) imply:
% 157.82/27.50 | | | | | | | | | | | (123) ~ (e1 = e0)
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | BETA: splitting (59) gives:
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | (124) all_54_10 = e3
% 157.82/27.50 | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | REF_CLOSE: (11), (102), (124) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | | | | #1531.
% 157.82/27.50 | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | (125) ~ (all_54_10 = e3)
% 157.82/27.50 | | | | | | | | | | | | (126) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 157.82/27.50 | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | BETA: splitting (126) gives:
% 157.82/27.50 | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | (127) all_54_10 = e2
% 157.82/27.50 | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | REF_CLOSE: (11), (66), (127) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | | | | | #1530.
% 157.82/27.50 | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | (128) ~ (all_54_10 = e2)
% 157.82/27.50 | | | | | | | | | | | | | (129) all_54_10 = e1 | all_54_10 = e0
% 157.82/27.50 | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | BETA: splitting (5) gives:
% 157.82/27.50 | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | (130) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 157.82/27.50 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.82/27.50 | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 157.82/27.50 | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | (131) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 157.82/27.50 | | | | | | | | | | | | | | | (132) all_58_1 = e1
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | (133) all_54_10 = e1
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (133) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | (134) all_6_2 = e1
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | SIMP: (134) implies:
% 157.82/27.50 | | | | | | | | | | | | | | | | (135) all_6_2 = e1
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | REDUCE: (47), (135) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | (136) ~ (all_52_9 = e1)
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | REDUCE: (9), (135) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | (137) op(e1, e1) = e1
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | (138) all_54_6 = e3
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (138) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | (139) all_52_9 = e3
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | REDUCE: (35), (139) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | (140) $false
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | (141) ~ (all_54_6 = e3)
% 157.82/27.50 | | | | | | | | | | | | | | | | | (142) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | (143) all_54_6 = e2
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (143) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | (144) all_52_9 = e2
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | REDUCE: (70), (144) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | (145) $false
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent.
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | (146) ~ (all_54_6 = e2)
% 157.82/27.50 | | | | | | | | | | | | | | | | | | (147) all_54_6 = e1 | all_54_6 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (148) all_54_6 = e1
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (136), (148) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | #562.
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (149) all_54_6 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (149) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (150) all_52_9 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | SIMP: (150) implies:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (151) all_52_9 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | REDUCE: (35), (151) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (152) ~ (e3 = e0)
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | REDUCE: (70), (151) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (153) ~ (e2 = e0)
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (77) with e1, e3, e1, e1,
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | simplifying with (112), (137) gives:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (154) e3 = e1
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (77) with e3, all_22_1, e3, e3,
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | simplifying with (60), (73) gives:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (155) all_22_1 = e3
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (77) with e0, all_22_1, e3, e3,
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | simplifying with (36), (73) gives:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (156) all_22_1 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (156) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (157) e3 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | SIMP: (157) implies:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (158) e3 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (158) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (159) e1 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (160) e1 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (160) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (161) all_58_1 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (13), (15), (16), (19),
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (22), (23), (24), (25), (28), (29), (32), (33),
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (34), (40), (41), (42), (44), (49), (51), (53),
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (55), (58), (61), (62), (63), (65), (68), (69),
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | (72), (76), (77), (79), (80), (111), (161) are
% 157.82/27.50 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #416.
% 157.82/27.50 | | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | (162) all_54_10 = e0
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (122), (162) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | | | | | | | | #1528.
% 157.82/27.50 | | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | (163) all_58_3 = e1 & op(e2, e2) = e1
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | REF_CLOSE: (42), (65), (163) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | | | | | | | #912.
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | (164) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 157.82/27.50 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.82/27.50 | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 157.82/27.50 | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | (165) all_58_7 = e1 & op(e1, e2) = e1
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | REF_CLOSE: (15), (58), (165) are inconsistent by sub-proof
% 157.82/27.50 | | | | | | | | | | | | | | | #1045.
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | (166) all_58_13 = e1 & op(e0, e2) = e1
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 157.82/27.50 | | | | | | | | | | | | | | | (167) all_58_13 = e1
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | COMBINE_EQS: (3), (167) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | (168) e1 = e0
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | SIMP: (168) implies:
% 157.82/27.50 | | | | | | | | | | | | | | | (169) e1 = e0
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | COMBINE_EQS: (88), (169) imply:
% 157.82/27.50 | | | | | | | | | | | | | | | (170) all_58_6 = e0
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | | REF_CLOSE: (13), (33), (41), (42), (58), (63), (74), (77),
% 157.82/27.50 | | | | | | | | | | | | | | | (170) are inconsistent by sub-proof #733.
% 157.82/27.50 | | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | | |
% 157.82/27.50 | | | | | | | | | End of split
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | End of split
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | (171) all_58_14 = e3 & op(e0, e1) = e3
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | ALPHA: (171) implies:
% 157.82/27.50 | | | | | | | | (172) all_58_14 = e3
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | REF_CLOSE: (3), (5), (7), (15), (21), (32), (34), (38), (40),
% 157.82/27.50 | | | | | | | | (41), (42), (43), (46), (52), (53), (54), (58), (63),
% 157.82/27.50 | | | | | | | | (65), (75), (77), (88), (172) are inconsistent by
% 157.82/27.50 | | | | | | | | sub-proof #409.
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | End of split
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | End of split
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | Case 2:
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | (173) all_56_14 = e3
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | COMBINE_EQS: (67), (173) imply:
% 157.82/27.50 | | | | | | (174) all_6_2 = e3
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | SIMP: (174) implies:
% 157.82/27.50 | | | | | | (175) all_6_2 = e3
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | REF_CLOSE: (37), (45), (71), (82), (84), (98), (175) are
% 157.82/27.50 | | | | | | inconsistent by sub-proof #408.
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | End of split
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | Case 2:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (176) all_54_12 = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | COMBINE_EQS: (83), (176) imply:
% 157.82/27.50 | | | | | (177) all_52_3 = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REDUCE: (20), (177) imply:
% 157.82/27.50 | | | | | (178) $false
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | CLOSE: (178) is inconsistent.
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | End of split
% 157.82/27.50 | | | |
% 157.82/27.50 | | | End of split
% 157.82/27.50 | | |
% 157.82/27.50 | | Case 2:
% 157.82/27.50 | | |
% 157.82/27.50 | | | (179) all_58_12 = e1 & op(e0, e3) = e1
% 157.82/27.50 | | |
% 157.82/27.50 | | | ALPHA: (179) implies:
% 157.82/27.50 | | | (180) all_58_12 = e1
% 157.82/27.50 | | |
% 157.82/27.50 | | | REF_CLOSE: (13), (42), (180) are inconsistent by sub-proof #1516.
% 157.82/27.50 | | |
% 157.82/27.50 | | End of split
% 157.82/27.50 | |
% 157.82/27.50 | End of split
% 157.82/27.50 |
% 157.82/27.50 End of proof
% 157.82/27.50
% 157.82/27.50 Sub-proof #408 shows that the following formulas are inconsistent:
% 157.82/27.50 ----------------------------------------------------------------
% 157.82/27.50 (1) ~ (all_52_11 = all_6_2)
% 157.82/27.50 (2) ~ (all_52_11 = e2)
% 157.82/27.50 (3) all_6_2 = e3
% 157.82/27.50 (4) ~ (all_52_11 = e1)
% 157.82/27.50 (5) all_54_14 = all_52_11
% 157.82/27.50 (6) ~ (all_52_11 = e0)
% 157.82/27.50 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.82/27.50
% 157.82/27.50 Begin of proof
% 157.82/27.50 |
% 157.82/27.50 | REDUCE: (1), (3) imply:
% 157.82/27.50 | (8) ~ (all_52_11 = e3)
% 157.82/27.50 |
% 157.82/27.50 | BETA: splitting (7) gives:
% 157.82/27.50 |
% 157.82/27.50 | Case 1:
% 157.82/27.50 | |
% 157.82/27.50 | | (9) all_54_14 = e3
% 157.82/27.50 | |
% 157.82/27.50 | | REF_CLOSE: (5), (8), (9) are inconsistent by sub-proof #1413.
% 157.82/27.50 | |
% 157.82/27.50 | Case 2:
% 157.82/27.50 | |
% 157.82/27.50 | | (10) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.82/27.50 | |
% 157.82/27.50 | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1149.
% 157.82/27.50 | |
% 157.82/27.50 | End of split
% 157.82/27.50 |
% 157.82/27.50 End of proof
% 157.82/27.50
% 157.82/27.50 Sub-proof #409 shows that the following formulas are inconsistent:
% 157.82/27.50 ----------------------------------------------------------------
% 157.82/27.50 (1) all_58_13 = e0
% 157.82/27.50 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.50 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.50 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.50 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.50 (4) all_58_14 = e3
% 157.82/27.50 (5) all_58_7 = e2
% 157.82/27.50 (6) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.50 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.50 (7) all_58_6 = e1
% 157.82/27.50 (8) ~ (e3 = e0)
% 157.82/27.50 (9) ~ (e2 = e0)
% 157.82/27.50 (10) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.50 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.50 (11) all_58_9 = e3
% 157.82/27.50 (12) op(e2, e3) = e2
% 157.82/27.50 (13) ~ (e3 = e1)
% 157.82/27.50 (14) op(e1, e2) = all_52_6
% 157.82/27.50 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.50 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.50 (16) op(e0, e0) = e2
% 157.82/27.50 (17) all_58_4 = e2
% 157.82/27.50 (18) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.50 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.50 (19) ~ (e2 = e1)
% 157.82/27.50 (20) ~ (e1 = e0)
% 157.82/27.50 (21) all_58_3 = e3
% 157.82/27.50 (22) ~ (all_52_6 = e3)
% 157.82/27.50 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.50
% 157.82/27.50 Begin of proof
% 157.82/27.50 |
% 157.82/27.50 | BETA: splitting (2) gives:
% 157.82/27.50 |
% 157.82/27.50 | Case 1:
% 157.82/27.50 | |
% 157.82/27.50 | | (24) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 157.82/27.50 | | e1)
% 157.82/27.50 | |
% 157.82/27.50 | | BETA: splitting (24) gives:
% 157.82/27.50 | |
% 157.82/27.50 | | Case 1:
% 157.82/27.50 | | |
% 157.82/27.50 | | | (25) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.50 | | |
% 157.82/27.50 | | | ALPHA: (25) implies:
% 157.82/27.50 | | | (26) all_58_1 = e1
% 157.82/27.50 | | |
% 157.82/27.50 | | | BETA: splitting (10) gives:
% 157.82/27.50 | | |
% 157.82/27.50 | | | Case 1:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | (27) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 157.82/27.50 | | | | = e0)
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | BETA: splitting (27) gives:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | Case 1:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (28) all_58_6 = e0 & op(e1, e3) = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | ALPHA: (28) implies:
% 157.82/27.50 | | | | | (29) all_58_6 = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | COMBINE_EQS: (7), (29) imply:
% 157.82/27.50 | | | | | (30) e1 = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | COMBINE_EQS: (26), (30) imply:
% 157.82/27.50 | | | | | (31) all_58_1 = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REF_CLOSE: (1), (2), (5), (13), (19), (20), (21), (31) are
% 157.82/27.50 | | | | | inconsistent by sub-proof #857.
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | Case 2:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (32) all_58_7 = e0 & op(e1, e2) = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | ALPHA: (32) implies:
% 157.82/27.50 | | | | | (33) all_58_7 = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REF_CLOSE: (5), (9), (33) are inconsistent by sub-proof #1086.
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | End of split
% 157.82/27.50 | | | |
% 157.82/27.50 | | | Case 2:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | (34) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.82/27.50 | | | | = e0)
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | BETA: splitting (34) gives:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | Case 1:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (35) all_58_8 = e0 & op(e1, e1) = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | ALPHA: (35) implies:
% 157.82/27.50 | | | | | (36) all_58_8 = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 157.82/27.50 | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.82/27.50 | | | | | (23), (26), (36) are inconsistent by sub-proof #411.
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | Case 2:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (37) all_58_11 = e0 & op(e1, e0) = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | ALPHA: (37) implies:
% 157.82/27.50 | | | | | (38) all_58_11 = e0
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 157.82/27.50 | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 157.82/27.50 | | | | | (23), (26), (38) are inconsistent by sub-proof #410.
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | End of split
% 157.82/27.50 | | | |
% 157.82/27.50 | | | End of split
% 157.82/27.50 | | |
% 157.82/27.50 | | Case 2:
% 157.82/27.50 | | |
% 157.82/27.50 | | | (39) all_58_3 = e1 & op(e2, e2) = e1
% 157.82/27.50 | | |
% 157.82/27.50 | | | REF_CLOSE: (13), (21), (39) are inconsistent by sub-proof #912.
% 157.82/27.50 | | |
% 157.82/27.50 | | End of split
% 157.82/27.50 | |
% 157.82/27.50 | Case 2:
% 157.82/27.50 | |
% 157.82/27.50 | | (40) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 157.82/27.50 | | e1)
% 157.82/27.50 | |
% 157.82/27.50 | | REF_CLOSE: (1), (5), (19), (20), (40) are inconsistent by sub-proof #858.
% 157.82/27.50 | |
% 157.82/27.50 | End of split
% 157.82/27.50 |
% 157.82/27.50 End of proof
% 157.82/27.50
% 157.82/27.50 Sub-proof #410 shows that the following formulas are inconsistent:
% 157.82/27.50 ----------------------------------------------------------------
% 157.82/27.50 (1) all_58_13 = e0
% 157.82/27.50 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.50 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.50 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.50 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.50 (4) all_58_14 = e3
% 157.82/27.50 (5) all_58_7 = e2
% 157.82/27.50 (6) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.50 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.50 (7) all_58_6 = e1
% 157.82/27.50 (8) ~ (e3 = e0)
% 157.82/27.50 (9) ~ (e2 = e0)
% 157.82/27.50 (10) all_58_9 = e3
% 157.82/27.50 (11) op(e2, e3) = e2
% 157.82/27.50 (12) ~ (e3 = e1)
% 157.82/27.50 (13) op(e1, e2) = all_52_6
% 157.82/27.50 (14) all_58_1 = e1
% 157.82/27.50 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.50 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.50 (16) op(e0, e0) = e2
% 157.82/27.50 (17) all_58_4 = e2
% 157.82/27.50 (18) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.50 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.50 (19) ~ (e2 = e1)
% 157.82/27.50 (20) ~ (e1 = e0)
% 157.82/27.50 (21) all_58_3 = e3
% 157.82/27.50 (22) all_58_11 = e0
% 157.82/27.50 (23) ~ (all_52_6 = e3)
% 157.82/27.50 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.50
% 157.82/27.50 Begin of proof
% 157.82/27.50 |
% 157.82/27.50 | BETA: splitting (6) gives:
% 157.82/27.50 |
% 157.82/27.50 | Case 1:
% 157.82/27.50 | |
% 157.82/27.50 | | (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 157.82/27.50 | | e3)
% 157.82/27.50 | |
% 157.82/27.50 | | REF_CLOSE: (7), (12), (13), (23), (24), (25) are inconsistent by sub-proof
% 157.82/27.50 | | #718.
% 157.82/27.50 | |
% 157.82/27.50 | Case 2:
% 157.82/27.50 | |
% 157.82/27.50 | | (26) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 157.82/27.50 | | e3)
% 157.82/27.50 | |
% 157.82/27.50 | | BETA: splitting (26) gives:
% 157.82/27.50 | |
% 157.82/27.50 | | Case 1:
% 157.82/27.50 | | |
% 157.82/27.50 | | | (27) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.50 | | |
% 157.82/27.50 | | | ALPHA: (27) implies:
% 157.82/27.50 | | | (28) all_58_8 = e3
% 157.82/27.50 | | |
% 157.82/27.50 | | | BETA: splitting (18) gives:
% 157.82/27.50 | | |
% 157.82/27.50 | | | Case 1:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | (29) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 157.82/27.50 | | | | = e1)
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | BETA: splitting (29) gives:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | Case 1:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (30) all_58_4 = e1 & op(e3, e1) = e1
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REF_CLOSE: (17), (19), (30) are inconsistent by sub-proof #1476.
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | Case 2:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (31) all_58_5 = e1 & op(e2, e1) = e1
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | ALPHA: (31) implies:
% 157.82/27.50 | | | | | (32) all_58_5 = e1
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | BETA: splitting (15) gives:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | Case 1:
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | (33) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2,
% 157.82/27.50 | | | | | | e2) = e0)
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | REF_CLOSE: (8), (9), (11), (21), (24), (33) are inconsistent by
% 157.82/27.50 | | | | | | sub-proof #909.
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | Case 2:
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | (34) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2,
% 157.82/27.50 | | | | | | e0) = e0)
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | BETA: splitting (34) gives:
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | | Case 1:
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | (35) all_58_5 = e0 & op(e2, e1) = e0
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | REF_CLOSE: (1), (2), (5), (12), (14), (19), (20), (21), (32), (35)
% 157.82/27.50 | | | | | | | are inconsistent by sub-proof #415.
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | Case 2:
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | (36) all_58_10 = e0 & op(e2, e0) = e0
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | ALPHA: (36) implies:
% 157.82/27.50 | | | | | | | (37) all_58_10 = e0
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | BETA: splitting (3) gives:
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | (38) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 157.82/27.50 | | | | | | | | op(e2, e0) = e1)
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | REF_CLOSE: (1), (2), (5), (10), (12), (14), (19), (20), (21),
% 157.82/27.50 | | | | | | | | (37), (38) are inconsistent by sub-proof #414.
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | (39) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 157.82/27.50 | | | | | | | | op(e0, e0) = e1)
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | BETA: splitting (39) gives:
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | | Case 1:
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | (40) all_58_11 = e1 & op(e1, e0) = e1
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | ALPHA: (40) implies:
% 157.82/27.50 | | | | | | | | | (41) all_58_11 = e1
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | COMBINE_EQS: (22), (41) imply:
% 157.82/27.50 | | | | | | | | | (42) e1 = e0
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | SIMP: (42) implies:
% 157.82/27.50 | | | | | | | | | (43) e1 = e0
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | COMBINE_EQS: (14), (43) imply:
% 157.82/27.50 | | | | | | | | | (44) all_58_1 = e0
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | REF_CLOSE: (1), (2), (5), (12), (19), (20), (21), (44) are
% 157.82/27.50 | | | | | | | | | inconsistent by sub-proof #857.
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | Case 2:
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | (45) all_58_15 = e1 & op(e0, e0) = e1
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | ALPHA: (45) implies:
% 157.82/27.50 | | | | | | | | | (46) op(e0, e0) = e1
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | | REF_CLOSE: (16), (19), (24), (46) are inconsistent by
% 157.82/27.50 | | | | | | | | | sub-proof #1386.
% 157.82/27.50 | | | | | | | | |
% 157.82/27.50 | | | | | | | | End of split
% 157.82/27.50 | | | | | | | |
% 157.82/27.50 | | | | | | | End of split
% 157.82/27.50 | | | | | | |
% 157.82/27.50 | | | | | | End of split
% 157.82/27.50 | | | | | |
% 157.82/27.50 | | | | | End of split
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | End of split
% 157.82/27.50 | | | |
% 157.82/27.50 | | | Case 2:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | (47) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 157.82/27.50 | | | | = e1)
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | BETA: splitting (47) gives:
% 157.82/27.50 | | | |
% 157.82/27.50 | | | | Case 1:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (48) all_58_8 = e1 & op(e1, e1) = e1
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REF_CLOSE: (12), (28), (48) are inconsistent by sub-proof #959.
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | Case 2:
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | (49) all_58_14 = e1 & op(e0, e1) = e1
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | | REF_CLOSE: (4), (12), (49) are inconsistent by sub-proof #844.
% 157.82/27.50 | | | | |
% 157.82/27.50 | | | | End of split
% 157.82/27.50 | | | |
% 157.82/27.50 | | | End of split
% 157.82/27.50 | | |
% 157.82/27.50 | | Case 2:
% 157.82/27.50 | | |
% 157.82/27.50 | | | (50) all_58_11 = e3 & op(e1, e0) = e3
% 157.82/27.50 | | |
% 157.82/27.50 | | | ALPHA: (50) implies:
% 157.82/27.50 | | | (51) all_58_11 = e3
% 157.82/27.50 | | |
% 157.82/27.50 | | | REF_CLOSE: (8), (22), (51) are inconsistent by sub-proof #1216.
% 157.82/27.51 | | |
% 157.82/27.51 | | End of split
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #411 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) all_58_13 = e0
% 157.82/27.51 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.51 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.51 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.51 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.51 (4) all_58_14 = e3
% 157.82/27.51 (5) all_58_7 = e2
% 157.82/27.51 (6) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.51 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.51 (7) all_58_6 = e1
% 157.82/27.51 (8) ~ (e3 = e0)
% 157.82/27.51 (9) ~ (e2 = e0)
% 157.82/27.51 (10) all_58_9 = e3
% 157.82/27.51 (11) op(e2, e3) = e2
% 157.82/27.51 (12) ~ (e3 = e1)
% 157.82/27.51 (13) op(e1, e2) = all_52_6
% 157.82/27.51 (14) all_58_1 = e1
% 157.82/27.51 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.51 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.51 (16) op(e0, e0) = e2
% 157.82/27.51 (17) all_58_4 = e2
% 157.82/27.51 (18) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.51 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.51 (19) ~ (e2 = e1)
% 157.82/27.51 (20) ~ (e1 = e0)
% 157.82/27.51 (21) all_58_3 = e3
% 157.82/27.51 (22) ~ (all_52_6 = e3)
% 157.82/27.51 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.51 (24) all_58_8 = e0
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | BETA: splitting (18) gives:
% 157.82/27.51 |
% 157.82/27.51 | Case 1:
% 157.82/27.51 | |
% 157.82/27.51 | | (25) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 157.82/27.51 | | e1)
% 157.82/27.51 | |
% 157.82/27.51 | | BETA: splitting (25) gives:
% 157.82/27.51 | |
% 157.82/27.51 | | Case 1:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (26) all_58_4 = e1 & op(e3, e1) = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | REF_CLOSE: (17), (19), (26) are inconsistent by sub-proof #1476.
% 157.82/27.51 | | |
% 157.82/27.51 | | Case 2:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (27) all_58_5 = e1 & op(e2, e1) = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | ALPHA: (27) implies:
% 157.82/27.51 | | | (28) all_58_5 = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | BETA: splitting (6) gives:
% 157.82/27.51 | | |
% 157.82/27.51 | | | Case 1:
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | (29) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 157.82/27.51 | | | | = e3)
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | REF_CLOSE: (7), (12), (13), (22), (23), (29) are inconsistent by
% 157.82/27.51 | | | | sub-proof #718.
% 157.82/27.51 | | | |
% 157.82/27.51 | | | Case 2:
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | (30) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 157.82/27.51 | | | | = e3)
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | BETA: splitting (30) gives:
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | Case 1:
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | (31) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | ALPHA: (31) implies:
% 157.82/27.51 | | | | | (32) all_58_8 = e3
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | REF_CLOSE: (8), (24), (32) are inconsistent by sub-proof #781.
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | Case 2:
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | (33) all_58_11 = e3 & op(e1, e0) = e3
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | ALPHA: (33) implies:
% 157.82/27.51 | | | | | (34) all_58_11 = e3
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (11), (12), (14), (15),
% 157.82/27.51 | | | | | (16), (19), (20), (21), (23), (28), (34) are inconsistent
% 157.82/27.51 | | | | | by sub-proof #412.
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | End of split
% 157.82/27.51 | | | |
% 157.82/27.51 | | | End of split
% 157.82/27.51 | | |
% 157.82/27.51 | | End of split
% 157.82/27.51 | |
% 157.82/27.51 | Case 2:
% 157.82/27.51 | |
% 157.82/27.51 | | (35) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 157.82/27.51 | | e1)
% 157.82/27.51 | |
% 157.82/27.51 | | BETA: splitting (35) gives:
% 157.82/27.51 | |
% 157.82/27.51 | | Case 1:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (36) all_58_8 = e1 & op(e1, e1) = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | REF_CLOSE: (1), (2), (5), (12), (14), (19), (20), (21), (24), (36) are
% 157.82/27.51 | | | inconsistent by sub-proof #436.
% 157.82/27.51 | | |
% 157.82/27.51 | | Case 2:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (37) all_58_14 = e1 & op(e0, e1) = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | REF_CLOSE: (4), (12), (37) are inconsistent by sub-proof #844.
% 157.82/27.51 | | |
% 157.82/27.51 | | End of split
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #412 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) all_58_13 = e0
% 157.82/27.51 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.51 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.51 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.51 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.51 (4) all_58_7 = e2
% 157.82/27.51 (5) ~ (e3 = e0)
% 157.82/27.51 (6) ~ (e2 = e0)
% 157.82/27.51 (7) all_58_9 = e3
% 157.82/27.51 (8) op(e2, e3) = e2
% 157.82/27.51 (9) ~ (e3 = e1)
% 157.82/27.51 (10) all_58_5 = e1
% 157.82/27.51 (11) all_58_1 = e1
% 157.82/27.51 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.51 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.51 (13) op(e0, e0) = e2
% 157.82/27.51 (14) ~ (e2 = e1)
% 157.82/27.51 (15) ~ (e1 = e0)
% 157.82/27.51 (16) all_58_3 = e3
% 157.82/27.51 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.51 (18) all_58_11 = e3
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | BETA: splitting (12) gives:
% 157.82/27.51 |
% 157.82/27.51 | Case 1:
% 157.82/27.51 | |
% 157.82/27.51 | | (19) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 157.82/27.51 | | e0)
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (5), (6), (8), (16), (17), (19) are inconsistent by sub-proof
% 157.82/27.51 | | #909.
% 157.82/27.51 | |
% 157.82/27.51 | Case 2:
% 157.82/27.51 | |
% 157.82/27.51 | | (20) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 157.82/27.51 | | e0)
% 157.82/27.51 | |
% 157.82/27.51 | | BETA: splitting (20) gives:
% 157.82/27.51 | |
% 157.82/27.51 | | Case 1:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (21) all_58_5 = e0 & op(e2, e1) = e0
% 157.82/27.51 | | |
% 157.82/27.51 | | | REF_CLOSE: (1), (2), (4), (9), (10), (11), (14), (15), (16), (21) are
% 157.82/27.51 | | | inconsistent by sub-proof #415.
% 157.82/27.51 | | |
% 157.82/27.51 | | Case 2:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (22) all_58_10 = e0 & op(e2, e0) = e0
% 157.82/27.51 | | |
% 157.82/27.51 | | | ALPHA: (22) implies:
% 157.82/27.51 | | | (23) all_58_10 = e0
% 157.82/27.51 | | |
% 157.82/27.51 | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (11), (13), (14), (15), (16),
% 157.82/27.51 | | | (17), (18), (23) are inconsistent by sub-proof #413.
% 157.82/27.51 | | |
% 157.82/27.51 | | End of split
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #413 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) all_58_13 = e0
% 157.82/27.51 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.51 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.51 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.51 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.51 (4) all_58_7 = e2
% 157.82/27.51 (5) all_58_9 = e3
% 157.82/27.51 (6) ~ (e3 = e1)
% 157.82/27.51 (7) all_58_1 = e1
% 157.82/27.51 (8) op(e0, e0) = e2
% 157.82/27.51 (9) ~ (e2 = e1)
% 157.82/27.51 (10) ~ (e1 = e0)
% 157.82/27.51 (11) all_58_3 = e3
% 157.82/27.51 (12) all_58_10 = e0
% 157.82/27.51 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.51 (14) all_58_11 = e3
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | BETA: splitting (3) gives:
% 157.82/27.51 |
% 157.82/27.51 | Case 1:
% 157.82/27.51 | |
% 157.82/27.51 | | (15) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 157.82/27.51 | | e1)
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (15) are
% 157.82/27.51 | | inconsistent by sub-proof #414.
% 157.82/27.51 | |
% 157.82/27.51 | Case 2:
% 157.82/27.51 | |
% 157.82/27.51 | | (16) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.82/27.51 | | e1)
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (6), (8), (9), (13), (14), (16) are inconsistent by sub-proof
% 157.82/27.51 | | #609.
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #414 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) all_58_13 = e0
% 157.82/27.51 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.51 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.51 (3) all_58_7 = e2
% 157.82/27.51 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.82/27.51 (5) all_58_9 = e3
% 157.82/27.51 (6) ~ (e3 = e1)
% 157.82/27.51 (7) all_58_1 = e1
% 157.82/27.51 (8) ~ (e2 = e1)
% 157.82/27.51 (9) ~ (e1 = e0)
% 157.82/27.51 (10) all_58_3 = e3
% 157.82/27.51 (11) all_58_10 = e0
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | BETA: splitting (4) gives:
% 157.82/27.51 |
% 157.82/27.51 | Case 1:
% 157.82/27.51 | |
% 157.82/27.51 | | (12) all_58_9 = e1 & op(e3, e0) = e1
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #1078.
% 157.82/27.51 | |
% 157.82/27.51 | Case 2:
% 157.82/27.51 | |
% 157.82/27.51 | | (13) all_58_10 = e1 & op(e2, e0) = e1
% 157.82/27.51 | |
% 157.82/27.51 | | ALPHA: (13) implies:
% 157.82/27.51 | | (14) all_58_10 = e1
% 157.82/27.51 | |
% 157.82/27.51 | | COMBINE_EQS: (11), (14) imply:
% 157.82/27.51 | | (15) e1 = e0
% 157.82/27.51 | |
% 157.82/27.51 | | SIMP: (15) implies:
% 157.82/27.51 | | (16) e1 = e0
% 157.82/27.51 | |
% 157.82/27.51 | | COMBINE_EQS: (7), (16) imply:
% 157.82/27.51 | | (17) all_58_1 = e0
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (17) are inconsistent by
% 157.82/27.51 | | sub-proof #857.
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #415 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) all_58_5 = e0 & op(e2, e1) = e0
% 157.82/27.51 (2) all_58_13 = e0
% 157.82/27.51 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.51 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.51 (4) all_58_7 = e2
% 157.82/27.51 (5) ~ (e3 = e1)
% 157.82/27.51 (6) all_58_5 = e1
% 157.82/27.51 (7) all_58_1 = e1
% 157.82/27.51 (8) ~ (e2 = e1)
% 157.82/27.51 (9) ~ (e1 = e0)
% 157.82/27.51 (10) all_58_3 = e3
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | ALPHA: (1) implies:
% 157.82/27.51 | (11) all_58_5 = e0
% 157.82/27.51 |
% 157.82/27.51 | COMBINE_EQS: (6), (11) imply:
% 157.82/27.51 | (12) e1 = e0
% 157.82/27.51 |
% 157.82/27.51 | COMBINE_EQS: (7), (12) imply:
% 157.82/27.51 | (13) all_58_1 = e0
% 157.82/27.51 |
% 157.82/27.51 | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (13) are inconsistent by
% 157.82/27.51 | sub-proof #857.
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #416 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) ~ (all_52_12 = e3)
% 157.82/27.51 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.51 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.51 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.51 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.51 (4) ~ (all_52_14 = e2)
% 157.82/27.51 (5) all_58_1 = e0
% 157.82/27.51 (6) ~ (all_52_12 = e2)
% 157.82/27.51 (7) all_58_12 = e3
% 157.82/27.51 (8) all_58_7 = e2
% 157.82/27.51 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.51 (10) all_58_8 = e3
% 157.82/27.51 (11) all_54_1 = all_52_4
% 157.82/27.51 (12) ~ (all_52_12 = all_52_13)
% 157.82/27.51 (13) ~ (all_52_4 = e2)
% 157.82/27.51 (14) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.51 (15) ~ (all_52_4 = all_52_12)
% 157.82/27.51 (16) ~ (all_52_13 = e3)
% 157.82/27.51 (17) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.51 (18) ~ (e3 = e0)
% 157.82/27.51 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.51 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.51 (20) ~ (e2 = e0)
% 157.82/27.51 (21) all_58_9 = e3
% 157.82/27.51 (22) op(e2, e3) = e2
% 157.82/27.51 (23) ~ (e3 = e1)
% 157.82/27.51 (24) ~ (all_52_4 = e0)
% 157.82/27.51 (25) all_54_7 = all_52_13
% 157.82/27.51 (26) ~ (all_52_13 = e2)
% 157.82/27.51 (27) all_58_4 = e2
% 157.82/27.51 (28) ~ (all_52_4 = e3)
% 157.82/27.51 (29) ~ (e2 = e1)
% 157.82/27.51 (30) all_54_3 = all_52_12
% 157.82/27.51 (31) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.51 (32) ~ (e1 = e0)
% 157.82/27.51 (33) all_58_3 = e3
% 157.82/27.51 (34) ~ (all_52_12 = all_52_14)
% 157.82/27.51 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.51 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.51 (36) op(e1, e0) = all_52_14
% 157.82/27.51 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.51 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.51 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.51 (39) all_54_11 = all_52_14
% 157.82/27.51 (40) ~ (all_52_13 = all_52_14)
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | BETA: splitting (3) gives:
% 157.82/27.51 |
% 157.82/27.51 | Case 1:
% 157.82/27.51 | |
% 157.82/27.51 | | (41) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 157.82/27.51 | | e1)
% 157.82/27.51 | |
% 157.82/27.51 | | BETA: splitting (41) gives:
% 157.82/27.51 | |
% 157.82/27.51 | | Case 1:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (42) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | REF_CLOSE: (5), (32), (42) are inconsistent by sub-proof #1424.
% 157.82/27.51 | | |
% 157.82/27.51 | | Case 2:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (43) all_58_3 = e1 & op(e2, e2) = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | REF_CLOSE: (23), (33), (43) are inconsistent by sub-proof #912.
% 157.82/27.51 | | |
% 157.82/27.51 | | End of split
% 157.82/27.51 | |
% 157.82/27.51 | Case 2:
% 157.82/27.51 | |
% 157.82/27.51 | | (44) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 157.82/27.51 | | e1)
% 157.82/27.51 | |
% 157.82/27.51 | | BETA: splitting (44) gives:
% 157.82/27.51 | |
% 157.82/27.51 | | Case 1:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (45) all_58_7 = e1 & op(e1, e2) = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | ALPHA: (45) implies:
% 157.82/27.51 | | | (46) all_58_7 = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | REF_CLOSE: (8), (29), (46) are inconsistent by sub-proof #721.
% 157.82/27.51 | | |
% 157.82/27.51 | | Case 2:
% 157.82/27.51 | | |
% 157.82/27.51 | | | (47) all_58_13 = e1 & op(e0, e2) = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | ALPHA: (47) implies:
% 157.82/27.51 | | | (48) all_58_13 = e1
% 157.82/27.51 | | |
% 157.82/27.51 | | | BETA: splitting (17) gives:
% 157.82/27.51 | | |
% 157.82/27.51 | | | Case 1:
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | (49) all_54_1 = e2
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | COMBINE_EQS: (11), (49) imply:
% 157.82/27.51 | | | | (50) all_52_4 = e2
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | REDUCE: (13), (50) imply:
% 157.82/27.51 | | | | (51) $false
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | CLOSE: (51) is inconsistent.
% 157.82/27.51 | | | |
% 157.82/27.51 | | | Case 2:
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | (52) ~ (all_54_1 = e2)
% 157.82/27.51 | | | | (53) all_54_1 = e1 | all_54_1 = e0
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | BETA: splitting (53) gives:
% 157.82/27.51 | | | |
% 157.82/27.51 | | | | Case 1:
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | (54) all_54_1 = e1
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | COMBINE_EQS: (11), (54) imply:
% 157.82/27.51 | | | | | (55) all_52_4 = e1
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | REDUCE: (15), (55) imply:
% 157.82/27.51 | | | | | (56) ~ (all_52_12 = e1)
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | SIMP: (56) implies:
% 157.82/27.51 | | | | | (57) ~ (all_52_12 = e1)
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | REDUCE: (28), (55) imply:
% 157.82/27.51 | | | | | (58) ~ (e3 = e1)
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | REDUCE: (13), (55) imply:
% 157.82/27.51 | | | | | (59) ~ (e2 = e1)
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | BETA: splitting (35) gives:
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | Case 1:
% 157.82/27.51 | | | | | |
% 157.82/27.51 | | | | | | (60) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3,
% 157.82/27.51 | | | | | | e2) = e1)
% 157.82/27.51 | | | | | |
% 157.82/27.51 | | | | | | BETA: splitting (60) gives:
% 157.82/27.51 | | | | | |
% 157.82/27.51 | | | | | | Case 1:
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | (61) all_58_0 = e1 & op(e3, e3) = e1
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | ALPHA: (61) implies:
% 157.82/27.51 | | | | | | | (62) all_58_0 = e1
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | BETA: splitting (2) gives:
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | Case 1:
% 157.82/27.51 | | | | | | | |
% 157.82/27.51 | | | | | | | | (63) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 157.82/27.51 | | | | | | | | op(e1, e2) = e1)
% 157.82/27.51 | | | | | | | |
% 157.82/27.51 | | | | | | | | BETA: splitting (63) gives:
% 157.82/27.51 | | | | | | | |
% 157.82/27.51 | | | | | | | | Case 1:
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | (64) all_58_6 = e1 & op(e1, e3) = e1
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | ALPHA: (64) implies:
% 157.82/27.51 | | | | | | | | | (65) all_58_6 = e1
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | BETA: splitting (37) gives:
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | Case 1:
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | (66) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 157.82/27.51 | | | | | | | | | | op(e2, e3) = e0)
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | BETA: splitting (66) gives:
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | Case 1:
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | (67) all_58_0 = e0 & op(e3, e3) = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | ALPHA: (67) implies:
% 157.82/27.51 | | | | | | | | | | | (68) all_58_0 = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | REF_CLOSE: (5), (7), (19), (21), (22), (23), (27), (29),
% 157.82/27.51 | | | | | | | | | | | (32), (35), (38), (65), (68) are inconsistent by
% 157.82/27.51 | | | | | | | | | | | sub-proof #502.
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | Case 2:
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | (69) all_58_2 = e0 & op(e2, e3) = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | ALPHA: (69) implies:
% 157.82/27.51 | | | | | | | | | | | (70) op(e2, e3) = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | REF_CLOSE: (20), (22), (38), (70) are inconsistent by
% 157.82/27.51 | | | | | | | | | | | sub-proof #1156.
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | End of split
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | Case 2:
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | (71) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0
% 157.82/27.51 | | | | | | | | | | & op(e0, e3) = e0)
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | BETA: splitting (71) gives:
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | Case 1:
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | (72) all_58_6 = e0 & op(e1, e3) = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | ALPHA: (72) implies:
% 157.82/27.51 | | | | | | | | | | | (73) all_58_6 = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | COMBINE_EQS: (65), (73) imply:
% 157.82/27.51 | | | | | | | | | | | (74) e1 = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | COMBINE_EQS: (62), (74) imply:
% 157.82/27.51 | | | | | | | | | | | (75) all_58_0 = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | REF_CLOSE: (7), (19), (22), (23), (29), (32), (38), (73),
% 157.82/27.51 | | | | | | | | | | | (75) are inconsistent by sub-proof #733.
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | Case 2:
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | (76) all_58_12 = e0 & op(e0, e3) = e0
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | | REF_CLOSE: (7), (18), (76) are inconsistent by sub-proof
% 157.82/27.51 | | | | | | | | | | | #1505.
% 157.82/27.51 | | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | End of split
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | End of split
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | Case 2:
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | (77) all_58_7 = e1 & op(e1, e2) = e1
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | REF_CLOSE: (8), (29), (77) are inconsistent by sub-proof
% 157.82/27.51 | | | | | | | | | #1045.
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | End of split
% 157.82/27.51 | | | | | | | |
% 157.82/27.51 | | | | | | | Case 2:
% 157.82/27.51 | | | | | | | |
% 157.82/27.51 | | | | | | | | (78) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 157.82/27.51 | | | | | | | | op(e1, e0) = e1)
% 157.82/27.51 | | | | | | | |
% 157.82/27.51 | | | | | | | | BETA: splitting (78) gives:
% 157.82/27.51 | | | | | | | |
% 157.82/27.51 | | | | | | | | Case 1:
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | (79) all_58_8 = e1 & op(e1, e1) = e1
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | REF_CLOSE: (10), (23), (79) are inconsistent by sub-proof
% 157.82/27.51 | | | | | | | | | #959.
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | Case 2:
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | (80) all_58_11 = e1 & op(e1, e0) = e1
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | ALPHA: (80) implies:
% 157.82/27.51 | | | | | | | | | (81) op(e1, e0) = e1
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | BETA: splitting (14) gives:
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | | Case 1:
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | (82) all_54_3 = e3
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | COMBINE_EQS: (30), (82) imply:
% 157.82/27.51 | | | | | | | | | | (83) all_52_12 = e3
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | REDUCE: (1), (83) imply:
% 157.82/27.51 | | | | | | | | | | (84) $false
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | CLOSE: (84) is inconsistent.
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | Case 2:
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | (85) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | | REF_CLOSE: (4), (6), (9), (12), (16), (25), (26), (30), (31),
% 157.82/27.51 | | | | | | | | | | (34), (36), (38), (39), (40), (57), (81), (85) are
% 157.82/27.51 | | | | | | | | | | inconsistent by sub-proof #417.
% 157.82/27.51 | | | | | | | | | |
% 157.82/27.51 | | | | | | | | | End of split
% 157.82/27.51 | | | | | | | | |
% 157.82/27.51 | | | | | | | | End of split
% 157.82/27.51 | | | | | | | |
% 157.82/27.51 | | | | | | | End of split
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | Case 2:
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | (86) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | REF_CLOSE: (3), (5), (8), (23), (29), (32), (33), (48), (86) are
% 157.82/27.51 | | | | | | | inconsistent by sub-proof #643.
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | End of split
% 157.82/27.51 | | | | | |
% 157.82/27.51 | | | | | Case 2:
% 157.82/27.51 | | | | | |
% 157.82/27.51 | | | | | | (87) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3,
% 157.82/27.51 | | | | | | e0) = e1)
% 157.82/27.51 | | | | | |
% 157.82/27.51 | | | | | | BETA: splitting (87) gives:
% 157.82/27.51 | | | | | |
% 157.82/27.51 | | | | | | Case 1:
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | (88) all_58_4 = e1 & op(e3, e1) = e1
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | REF_CLOSE: (27), (29), (88) are inconsistent by sub-proof #1476.
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | Case 2:
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | (89) all_58_9 = e1 & op(e3, e0) = e1
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | | REF_CLOSE: (21), (23), (89) are inconsistent by sub-proof #1078.
% 157.82/27.51 | | | | | | |
% 157.82/27.51 | | | | | | End of split
% 157.82/27.51 | | | | | |
% 157.82/27.51 | | | | | End of split
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | Case 2:
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | (90) all_54_1 = e0
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | COMBINE_EQS: (11), (90) imply:
% 157.82/27.51 | | | | | (91) all_52_4 = e0
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | REDUCE: (24), (91) imply:
% 157.82/27.51 | | | | | (92) $false
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | | CLOSE: (92) is inconsistent.
% 157.82/27.51 | | | | |
% 157.82/27.51 | | | | End of split
% 157.82/27.51 | | | |
% 157.82/27.51 | | | End of split
% 157.82/27.51 | | |
% 157.82/27.51 | | End of split
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #417 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) ~ (all_52_14 = e2)
% 157.82/27.51 (2) ~ (all_52_12 = e2)
% 157.82/27.51 (3) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.51 (4) ~ (all_52_12 = all_52_13)
% 157.82/27.51 (5) ~ (all_52_13 = e3)
% 157.82/27.51 (6) all_54_7 = all_52_13
% 157.82/27.51 (7) op(e1, e0) = e1
% 157.82/27.51 (8) ~ (all_52_13 = e2)
% 157.82/27.51 (9) all_54_3 = all_52_12
% 157.82/27.51 (10) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.51 (11) ~ (all_52_12 = all_52_14)
% 157.82/27.51 (12) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 157.82/27.51 (13) op(e1, e0) = all_52_14
% 157.82/27.51 (14) ~ (all_52_12 = e1)
% 157.82/27.51 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.51 (16) all_54_11 = all_52_14
% 157.82/27.51 (17) ~ (all_52_13 = all_52_14)
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | BETA: splitting (12) gives:
% 157.82/27.51 |
% 157.82/27.51 | Case 1:
% 157.82/27.51 | |
% 157.82/27.51 | | (18) all_54_3 = e2
% 157.82/27.51 | |
% 157.82/27.51 | | COMBINE_EQS: (9), (18) imply:
% 157.82/27.51 | | (19) all_52_12 = e2
% 157.82/27.51 | |
% 157.82/27.51 | | REDUCE: (2), (19) imply:
% 157.82/27.51 | | (20) $false
% 157.82/27.51 | |
% 157.82/27.51 | | CLOSE: (20) is inconsistent.
% 157.82/27.51 | |
% 157.82/27.51 | Case 2:
% 157.82/27.51 | |
% 157.82/27.51 | | (21) all_54_3 = e1 | all_54_3 = e0
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 157.82/27.51 | | (15), (16), (17), (21) are inconsistent by sub-proof #418.
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #418 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) ~ (all_52_14 = e2)
% 157.82/27.51 (2) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.51 (3) ~ (all_52_12 = all_52_13)
% 157.82/27.51 (4) ~ (all_52_13 = e3)
% 157.82/27.51 (5) all_54_3 = e1 | all_54_3 = e0
% 157.82/27.51 (6) all_54_7 = all_52_13
% 157.82/27.51 (7) op(e1, e0) = e1
% 157.82/27.51 (8) ~ (all_52_13 = e2)
% 157.82/27.51 (9) all_54_3 = all_52_12
% 157.82/27.51 (10) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.51 (11) ~ (all_52_12 = all_52_14)
% 157.82/27.51 (12) op(e1, e0) = all_52_14
% 157.82/27.51 (13) ~ (all_52_12 = e1)
% 157.82/27.51 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.51 (15) all_54_11 = all_52_14
% 157.82/27.51 (16) ~ (all_52_13 = all_52_14)
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | BETA: splitting (5) gives:
% 157.82/27.51 |
% 157.82/27.51 | Case 1:
% 157.82/27.51 | |
% 157.82/27.51 | | (17) all_54_3 = e1
% 157.82/27.51 | |
% 157.82/27.51 | | COMBINE_EQS: (9), (17) imply:
% 157.82/27.51 | | (18) all_52_12 = e1
% 157.82/27.51 | |
% 157.82/27.51 | | REDUCE: (13), (18) imply:
% 157.82/27.51 | | (19) $false
% 157.82/27.51 | |
% 157.82/27.51 | | CLOSE: (19) is inconsistent.
% 157.82/27.51 | |
% 157.82/27.51 | Case 2:
% 157.82/27.51 | |
% 157.82/27.51 | | (20) all_54_3 = e0
% 157.82/27.51 | |
% 157.82/27.51 | | COMBINE_EQS: (9), (20) imply:
% 157.82/27.51 | | (21) all_52_12 = e0
% 157.82/27.51 | |
% 157.82/27.51 | | REDUCE: (3), (21) imply:
% 157.82/27.51 | | (22) ~ (all_52_13 = e0)
% 157.82/27.51 | |
% 157.82/27.51 | | SIMP: (22) implies:
% 157.82/27.51 | | (23) ~ (all_52_13 = e0)
% 157.82/27.51 | |
% 157.82/27.51 | | REDUCE: (11), (21) imply:
% 157.82/27.51 | | (24) ~ (all_52_14 = e0)
% 157.82/27.51 | |
% 157.82/27.51 | | SIMP: (24) implies:
% 157.82/27.51 | | (25) ~ (all_52_14 = e0)
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (12), (14), (15), (16), (23),
% 157.82/27.51 | | (25) are inconsistent by sub-proof #680.
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #419 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) all_58_1 = e0
% 157.82/27.51 (2) ~ (e3 = e1)
% 157.82/27.51 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 157.82/27.51 (4) ~ (e1 = e0)
% 157.82/27.51 (5) all_58_3 = e3
% 157.82/27.51
% 157.82/27.51 Begin of proof
% 157.82/27.51 |
% 157.82/27.51 | BETA: splitting (3) gives:
% 157.82/27.51 |
% 157.82/27.51 | Case 1:
% 157.82/27.51 | |
% 157.82/27.51 | | (6) all_58_1 = e1 & op(e3, e2) = e1
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #1424.
% 157.82/27.51 | |
% 157.82/27.51 | Case 2:
% 157.82/27.51 | |
% 157.82/27.51 | | (7) all_58_3 = e1 & op(e2, e2) = e1
% 157.82/27.51 | |
% 157.82/27.51 | | ALPHA: (7) implies:
% 157.82/27.51 | | (8) all_58_3 = e1
% 157.82/27.51 | |
% 157.82/27.51 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #841.
% 157.82/27.51 | |
% 157.82/27.51 | End of split
% 157.82/27.51 |
% 157.82/27.51 End of proof
% 157.82/27.51
% 157.82/27.51 Sub-proof #420 shows that the following formulas are inconsistent:
% 157.82/27.51 ----------------------------------------------------------------
% 157.82/27.51 (1) op(e1, e1) = e3
% 157.82/27.51 (2) op(e1, e1) = all_32_1
% 157.82/27.51 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.82/27.51 (4) all_56_14 = e3
% 157.82/27.51 (5) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.82/27.51 (6) ~ (all_52_3 = e1)
% 157.82/27.51 (7) op(e3, e1) = e3
% 157.82/27.51 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.51 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.52 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.52 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.52 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.52 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.52 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.82/27.52 (12) all_54_13 = all_52_7
% 157.82/27.52 (13) op(e1, e1) = all_6_2
% 157.82/27.52 (14) ~ (all_52_7 = e3)
% 157.82/27.52 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.52 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.82/27.52 e1)
% 157.82/27.52 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.52 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.52 (17) ~ (all_52_6 = all_52_14)
% 157.82/27.52 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.52 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.52 (19) ~ (all_52_11 = e3)
% 157.82/27.52 (20) ~ (all_52_2 = all_52_3)
% 157.82/27.52 (21) ~ (all_52_4 = all_52_6)
% 157.82/27.52 (22) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.52 (23) ~ (all_52_7 = all_52_11)
% 157.82/27.52 (24) op(e1, e2) = all_14_0
% 157.82/27.52 (25) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.82/27.52 (26) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.52 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.52 (27) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.82/27.52 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.82/27.52 (28) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.82/27.52 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.82/27.52 (29) ~ (all_52_14 = e3)
% 157.82/27.52 (30) all_54_1 = all_52_4
% 157.82/27.52 (31) op(e3, e2) = all_52_4
% 157.82/27.52 (32) ~ (all_4_2 = e2)
% 157.82/27.52 (33) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.52 (34) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.52 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.52 (35) op(e2, e1) = all_52_9
% 157.82/27.52 (36) op(e2, e3) = all_52_1
% 157.82/27.52 (37) ~ (all_52_13 = e3)
% 157.82/27.52 (38) all_54_2 = all_52_8
% 157.82/27.52 (39) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.82/27.52 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.82/27.52 (40) ~ (all_52_8 = all_52_9)
% 157.82/27.52 (41) ~ (e3 = e0)
% 157.82/27.52 (42) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.52 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.52 (43) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.52 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.52 (44) ~ (all_52_9 = all_52_13)
% 157.82/27.52 (45) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.52 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.52 e2)
% 157.82/27.52 (46) ~ (e2 = e0)
% 157.82/27.52 (47) ~ (all_52_9 = e3)
% 157.82/27.52 (48) ~ (all_52_2 = all_52_6)
% 157.82/27.52 (49) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.52 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.52 (50) ~ (all_52_3 = e2)
% 157.82/27.52 (51) op(e1, e3) = all_52_2
% 157.82/27.52 (52) op(e2, e0) = all_52_13
% 157.82/27.52 (53) op(e2, e3) = e2
% 157.82/27.52 (54) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.52 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.52 (55) ~ (e3 = e1)
% 157.82/27.52 (56) all_56_12 = e1
% 157.82/27.52 (57) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.82/27.52 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.82/27.52 (58) op(e1, e2) = all_52_6
% 157.82/27.52 (59) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 157.82/27.52 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3,
% 157.82/27.52 e3) = all_28_1 & $i(all_28_1))
% 157.82/27.52 (60) ~ (all_4_2 = e1)
% 157.82/27.52 (61) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.82/27.52 (62) ~ (all_52_3 = all_4_2)
% 157.82/27.52 (63) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.52 (64) op(e0, e0) = all_4_2
% 157.82/27.52 (65) all_54_8 = all_52_2
% 157.82/27.52 (66) all_54_7 = all_52_13
% 157.82/27.52 (67) ~ (all_52_2 = e3)
% 157.82/27.52 (68) op(e3, e3) = e1
% 157.82/27.52 (69) ~ (all_52_13 = e2)
% 157.82/27.52 (70) all_56_15 = all_4_2
% 157.82/27.52 (71) ~ (all_52_4 = e1)
% 157.82/27.52 (72) ~ (all_52_9 = all_52_11)
% 157.82/27.52 (73) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 157.82/27.52 (74) ~ (all_52_13 = all_4_2)
% 157.82/27.52 (75) ~ (all_52_2 = e1)
% 157.82/27.52 (76) ~ (all_52_2 = all_52_14)
% 157.82/27.52 (77) ~ (all_52_6 = all_52_7)
% 157.82/27.52 (78) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.52 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.52 (79) ~ (all_52_4 = e3)
% 157.82/27.52 (80) all_54_6 = all_52_9
% 157.82/27.52 (81) ~ (e2 = e1)
% 157.82/27.52 (82) ~ (all_52_4 = all_52_7)
% 157.82/27.52 (83) ~ (all_52_8 = all_52_11)
% 157.82/27.52 (84) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.52 (85) ~ (e1 = e0)
% 157.82/27.52 (86) ~ (all_52_2 = e2)
% 157.82/27.52 (87) all_58_3 = e3
% 157.82/27.52 (88) op(e3, e1) = all_52_8
% 157.82/27.52 (89) ~ (all_6_2 = e2)
% 157.82/27.52 (90) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.52 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.52 e3)
% 157.82/27.52 (91) all_56_13 = e3
% 157.82/27.52 (92) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.52 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.52 (93) ~ (all_52_9 = e2)
% 157.82/27.52 (94) ~ (all_52_8 = e3)
% 157.82/27.52 (95) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.52 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.52 (96) all_54_14 = all_52_11
% 157.82/27.52 (97) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.82/27.52 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 157.82/27.52 e3) = all_22_1 & $i(all_22_1))
% 157.82/27.52 (98) ~ (all_52_7 = all_4_2)
% 157.82/27.52 (99) op(e1, e3) = e1
% 157.82/27.52 (100) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.52 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.52 (101) op(e0, e2) = all_52_7
% 157.82/27.52 (102) op(e1, e0) = all_52_14
% 157.82/27.52 (103) all_54_15 = all_4_2
% 157.82/27.52 (104) ~ (all_52_8 = e1)
% 157.82/27.52 (105) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.82/27.52 (106) ~ (all_52_6 = e3)
% 157.82/27.52 (107) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.52 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.52 (108) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.52 (109) ~ (all_52_3 = all_52_11)
% 157.82/27.52 (110) ~ (all_52_11 = all_4_2)
% 157.82/27.52 (111) all_54_11 = all_52_14
% 157.82/27.52 (112) ~ (all_52_13 = all_52_14)
% 157.82/27.52 (113) ~ (e3 = e2)
% 157.82/27.52 (114) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.82/27.52 (115) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.82/27.52 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.52 (116) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.82/27.52 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.82/27.52 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.82/27.52 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.82/27.52 e0)))
% 157.82/27.52 (117) all_54_9 = all_52_6
% 157.82/27.52 (118) ~ (all_52_4 = all_52_8)
% 157.82/27.52 (119) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.82/27.52 (120) all_54_12 = all_52_3
% 157.82/27.52 (121) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.82/27.52 (122) ~ (all_52_14 = all_4_2)
% 157.82/27.52 (123) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.82/27.52 (124) ~ (all_52_3 = all_52_7)
% 157.82/27.52
% 157.82/27.52 Begin of proof
% 157.82/27.52 |
% 157.82/27.52 | BETA: splitting (59) gives:
% 157.82/27.52 |
% 157.82/27.52 | Case 1:
% 157.82/27.52 | |
% 157.82/27.52 | | (125) ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 157.82/27.52 | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 157.82/27.52 | |
% 157.82/27.52 | | ALPHA: (125) implies:
% 157.82/27.52 | | (126) op(e3, e3) = all_28_1
% 157.82/27.52 | |
% 157.82/27.52 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.82/27.52 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.82/27.52 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 157.82/27.52 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.82/27.52 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 157.82/27.52 | | (57), (58), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 157.82/27.52 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 157.82/27.52 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 157.82/27.52 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 157.82/27.52 | | (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 157.82/27.52 | | (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 157.82/27.52 | | (119), (120), (121), (122), (123), (124), (126) are inconsistent
% 157.82/27.52 | | by sub-proof #421.
% 157.82/27.52 | |
% 157.82/27.52 | Case 2:
% 157.82/27.52 | |
% 157.82/27.52 | | (127) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1)
% 157.82/27.52 | |
% 157.82/27.52 | | ALPHA: (127) implies:
% 157.82/27.52 | | (128) op(e3, e3) = all_28_1
% 157.82/27.52 | |
% 157.82/27.52 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.82/27.52 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.82/27.52 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 157.82/27.52 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.82/27.52 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 157.82/27.52 | | (57), (58), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 157.82/27.52 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 157.82/27.52 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 157.82/27.52 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 157.82/27.52 | | (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 157.82/27.52 | | (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 157.82/27.52 | | (119), (120), (121), (122), (123), (124), (128) are inconsistent
% 157.82/27.52 | | by sub-proof #421.
% 157.82/27.52 | |
% 157.82/27.52 | End of split
% 157.82/27.52 |
% 157.82/27.52 End of proof
% 157.82/27.52
% 157.82/27.52 Sub-proof #421 shows that the following formulas are inconsistent:
% 157.82/27.52 ----------------------------------------------------------------
% 157.82/27.52 (1) op(e1, e1) = e3
% 157.82/27.52 (2) op(e1, e1) = all_32_1
% 157.82/27.52 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.82/27.52 (4) all_56_14 = e3
% 157.82/27.52 (5) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.82/27.52 (6) ~ (all_52_3 = e1)
% 157.82/27.52 (7) op(e3, e1) = e3
% 157.82/27.52 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.52 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.52 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.52 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.52 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.52 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.52 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.82/27.52 (12) all_54_13 = all_52_7
% 157.82/27.52 (13) op(e1, e1) = all_6_2
% 157.82/27.52 (14) ~ (all_52_7 = e3)
% 157.82/27.52 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.52 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.82/27.52 e1)
% 157.82/27.52 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.52 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.52 (17) ~ (all_52_6 = all_52_14)
% 157.82/27.52 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.52 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.52 (19) ~ (all_52_11 = e3)
% 157.82/27.52 (20) ~ (all_52_2 = all_52_3)
% 157.82/27.52 (21) ~ (all_52_4 = all_52_6)
% 157.82/27.52 (22) op(e3, e3) = all_28_1
% 157.82/27.52 (23) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.52 (24) ~ (all_52_7 = all_52_11)
% 157.82/27.52 (25) op(e1, e2) = all_14_0
% 157.82/27.52 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.82/27.52 (27) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.52 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.52 (28) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.82/27.52 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.82/27.52 (29) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.82/27.52 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.82/27.52 (30) ~ (all_52_14 = e3)
% 157.82/27.52 (31) all_54_1 = all_52_4
% 157.82/27.52 (32) op(e3, e2) = all_52_4
% 157.82/27.52 (33) ~ (all_4_2 = e2)
% 157.82/27.52 (34) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.52 (35) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.52 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.52 (36) op(e2, e1) = all_52_9
% 157.82/27.52 (37) op(e2, e3) = all_52_1
% 157.82/27.52 (38) ~ (all_52_13 = e3)
% 157.82/27.52 (39) all_54_2 = all_52_8
% 157.82/27.52 (40) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.82/27.52 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.82/27.52 (41) ~ (all_52_8 = all_52_9)
% 157.82/27.52 (42) ~ (e3 = e0)
% 157.82/27.52 (43) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.52 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.52 (44) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.52 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.52 (45) ~ (all_52_9 = all_52_13)
% 157.82/27.52 (46) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.52 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.52 e2)
% 157.82/27.52 (47) ~ (e2 = e0)
% 157.82/27.52 (48) ~ (all_52_9 = e3)
% 157.82/27.52 (49) ~ (all_52_2 = all_52_6)
% 157.82/27.52 (50) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.52 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.52 (51) ~ (all_52_3 = e2)
% 157.82/27.52 (52) op(e1, e3) = all_52_2
% 157.82/27.52 (53) op(e2, e0) = all_52_13
% 157.82/27.52 (54) op(e2, e3) = e2
% 157.82/27.52 (55) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.52 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.52 (56) ~ (e3 = e1)
% 157.82/27.52 (57) all_56_12 = e1
% 157.82/27.52 (58) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.82/27.52 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.82/27.52 (59) op(e1, e2) = all_52_6
% 157.82/27.52 (60) ~ (all_4_2 = e1)
% 157.82/27.52 (61) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.82/27.52 (62) ~ (all_52_3 = all_4_2)
% 157.82/27.52 (63) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.52 (64) op(e0, e0) = all_4_2
% 157.82/27.52 (65) all_54_8 = all_52_2
% 157.82/27.52 (66) all_54_7 = all_52_13
% 157.82/27.52 (67) ~ (all_52_2 = e3)
% 157.82/27.52 (68) op(e3, e3) = e1
% 157.82/27.52 (69) ~ (all_52_13 = e2)
% 157.82/27.52 (70) all_56_15 = all_4_2
% 157.82/27.52 (71) ~ (all_52_4 = e1)
% 157.82/27.52 (72) ~ (all_52_9 = all_52_11)
% 157.82/27.52 (73) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 157.82/27.52 (74) ~ (all_52_13 = all_4_2)
% 157.82/27.52 (75) ~ (all_52_2 = e1)
% 157.82/27.52 (76) ~ (all_52_2 = all_52_14)
% 157.82/27.52 (77) ~ (all_52_6 = all_52_7)
% 157.82/27.52 (78) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.52 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.52 (79) ~ (all_52_4 = e3)
% 157.82/27.52 (80) all_54_6 = all_52_9
% 157.82/27.52 (81) ~ (e2 = e1)
% 157.82/27.52 (82) ~ (all_52_4 = all_52_7)
% 157.82/27.52 (83) ~ (all_52_8 = all_52_11)
% 157.82/27.52 (84) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.52 (85) ~ (e1 = e0)
% 157.82/27.52 (86) ~ (all_52_2 = e2)
% 157.82/27.52 (87) all_58_3 = e3
% 157.82/27.52 (88) op(e3, e1) = all_52_8
% 157.82/27.52 (89) ~ (all_6_2 = e2)
% 157.82/27.52 (90) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.52 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.52 e3)
% 157.82/27.52 (91) all_56_13 = e3
% 157.82/27.52 (92) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.52 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.52 (93) ~ (all_52_9 = e2)
% 157.82/27.52 (94) ~ (all_52_8 = e3)
% 157.82/27.52 (95) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.52 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.52 (96) all_54_14 = all_52_11
% 157.82/27.52 (97) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.82/27.52 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 157.82/27.52 e3) = all_22_1 & $i(all_22_1))
% 157.82/27.52 (98) ~ (all_52_7 = all_4_2)
% 157.82/27.52 (99) op(e1, e3) = e1
% 157.82/27.52 (100) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.52 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.52 (101) op(e0, e2) = all_52_7
% 157.82/27.52 (102) op(e1, e0) = all_52_14
% 157.82/27.52 (103) all_54_15 = all_4_2
% 157.82/27.52 (104) ~ (all_52_8 = e1)
% 157.82/27.52 (105) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.82/27.52 (106) ~ (all_52_6 = e3)
% 157.82/27.52 (107) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.52 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.52 (108) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.52 (109) ~ (all_52_3 = all_52_11)
% 157.82/27.52 (110) ~ (all_52_11 = all_4_2)
% 157.82/27.52 (111) all_54_11 = all_52_14
% 157.82/27.52 (112) ~ (all_52_13 = all_52_14)
% 157.82/27.52 (113) ~ (e3 = e2)
% 157.82/27.52 (114) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.82/27.52 (115) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.82/27.52 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.52 (116) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.82/27.52 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.82/27.52 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.82/27.52 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.82/27.52 e0)))
% 157.82/27.52 (117) all_54_9 = all_52_6
% 157.82/27.52 (118) ~ (all_52_4 = all_52_8)
% 157.82/27.52 (119) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.82/27.52 (120) all_54_12 = all_52_3
% 157.82/27.52 (121) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.82/27.52 (122) ~ (all_52_14 = all_4_2)
% 157.82/27.52 (123) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.82/27.52 (124) ~ (all_52_3 = all_52_7)
% 157.82/27.52
% 157.82/27.52 Begin of proof
% 157.82/27.52 |
% 157.82/27.52 | BETA: splitting (97) gives:
% 157.82/27.52 |
% 157.82/27.52 | Case 1:
% 157.82/27.52 | |
% 157.82/27.52 | | (125) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 157.82/27.52 | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 157.82/27.52 | |
% 157.82/27.52 | | ALPHA: (125) implies:
% 157.82/27.52 | | (126) op(e3, e3) = all_22_1
% 157.82/27.52 | |
% 157.82/27.52 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.82/27.52 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.82/27.52 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 157.82/27.52 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.82/27.52 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 157.82/27.52 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 157.82/27.52 | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 157.82/27.52 | | (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 157.82/27.52 | | (90), (91), (92), (93), (94), (95), (96), (98), (99), (100),
% 157.82/27.52 | | (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 157.82/27.52 | | (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 157.82/27.52 | | (119), (120), (121), (122), (123), (124), (126) are inconsistent
% 157.82/27.52 | | by sub-proof #422.
% 157.82/27.52 | |
% 157.82/27.52 | Case 2:
% 157.82/27.52 | |
% 157.82/27.52 | | (127) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 157.82/27.52 | |
% 157.82/27.52 | | ALPHA: (127) implies:
% 157.82/27.52 | | (128) op(e3, e3) = all_22_1
% 157.82/27.52 | |
% 157.82/27.52 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 157.82/27.52 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 157.82/27.52 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 157.82/27.52 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.82/27.52 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 157.82/27.52 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 157.82/27.52 | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 157.82/27.52 | | (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 157.82/27.52 | | (90), (91), (92), (93), (94), (95), (96), (98), (99), (100),
% 157.82/27.52 | | (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 157.82/27.52 | | (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 157.82/27.52 | | (119), (120), (121), (122), (123), (124), (128) are inconsistent
% 157.82/27.52 | | by sub-proof #422.
% 157.82/27.52 | |
% 157.82/27.52 | End of split
% 157.82/27.52 |
% 157.82/27.52 End of proof
% 157.82/27.52
% 157.82/27.52 Sub-proof #422 shows that the following formulas are inconsistent:
% 157.82/27.52 ----------------------------------------------------------------
% 157.82/27.52 (1) op(e1, e1) = e3
% 157.82/27.52 (2) op(e1, e1) = all_32_1
% 157.82/27.52 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 157.82/27.52 (4) all_56_14 = e3
% 157.82/27.52 (5) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.82/27.52 (6) ~ (all_52_3 = e1)
% 157.82/27.52 (7) op(e3, e1) = e3
% 157.82/27.52 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.82/27.52 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.82/27.52 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.52 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.53 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 157.82/27.53 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.82/27.53 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.82/27.53 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.82/27.53 (12) all_54_13 = all_52_7
% 157.82/27.53 (13) op(e1, e1) = all_6_2
% 157.82/27.53 (14) ~ (all_52_7 = e3)
% 157.82/27.53 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.82/27.53 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.82/27.53 e1)
% 157.82/27.53 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 157.82/27.53 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 157.82/27.53 (17) ~ (all_52_6 = all_52_14)
% 157.82/27.53 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 157.82/27.53 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 157.82/27.53 (19) ~ (all_52_11 = e3)
% 157.82/27.53 (20) ~ (all_52_2 = all_52_3)
% 157.82/27.53 (21) ~ (all_52_4 = all_52_6)
% 157.82/27.53 (22) op(e3, e3) = all_28_1
% 157.82/27.53 (23) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.82/27.53 (24) ~ (all_52_7 = all_52_11)
% 157.82/27.53 (25) op(e1, e2) = all_14_0
% 157.82/27.53 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 157.82/27.53 (27) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.82/27.53 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.82/27.53 (28) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.82/27.53 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.82/27.53 (29) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.82/27.53 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.82/27.53 (30) ~ (all_52_14 = e3)
% 157.82/27.53 (31) all_54_1 = all_52_4
% 157.82/27.53 (32) op(e3, e2) = all_52_4
% 157.82/27.53 (33) ~ (all_4_2 = e2)
% 157.82/27.53 (34) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 157.82/27.53 (35) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 157.82/27.53 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 157.82/27.53 (36) op(e2, e1) = all_52_9
% 157.82/27.53 (37) op(e2, e3) = all_52_1
% 157.82/27.53 (38) ~ (all_52_13 = e3)
% 157.82/27.53 (39) all_54_2 = all_52_8
% 157.82/27.53 (40) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.82/27.53 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.82/27.53 (41) ~ (all_52_8 = all_52_9)
% 157.82/27.53 (42) ~ (e3 = e0)
% 157.82/27.53 (43) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.82/27.53 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.82/27.53 (44) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 157.82/27.53 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 157.82/27.53 (45) ~ (all_52_9 = all_52_13)
% 157.82/27.53 (46) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.53 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.82/27.53 e2)
% 157.82/27.53 (47) ~ (e2 = e0)
% 157.82/27.53 (48) ~ (all_52_9 = e3)
% 157.82/27.53 (49) ~ (all_52_2 = all_52_6)
% 157.82/27.53 (50) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 157.82/27.53 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.82/27.53 (51) ~ (all_52_3 = e2)
% 157.82/27.53 (52) op(e1, e3) = all_52_2
% 157.82/27.53 (53) op(e2, e0) = all_52_13
% 157.82/27.53 (54) op(e2, e3) = e2
% 157.82/27.53 (55) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.53 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.82/27.53 (56) ~ (e3 = e1)
% 157.82/27.53 (57) all_56_12 = e1
% 157.82/27.53 (58) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.82/27.53 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.82/27.53 (59) op(e1, e2) = all_52_6
% 157.82/27.53 (60) ~ (all_4_2 = e1)
% 157.82/27.53 (61) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.82/27.53 (62) ~ (all_52_3 = all_4_2)
% 157.82/27.53 (63) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.82/27.53 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.82/27.53 (64) op(e0, e0) = all_4_2
% 157.82/27.53 (65) all_54_8 = all_52_2
% 157.82/27.53 (66) all_54_7 = all_52_13
% 157.82/27.53 (67) ~ (all_52_2 = e3)
% 157.82/27.53 (68) op(e3, e3) = e1
% 157.82/27.53 (69) ~ (all_52_13 = e2)
% 157.82/27.53 (70) all_56_15 = all_4_2
% 157.82/27.53 (71) ~ (all_52_4 = e1)
% 157.82/27.53 (72) ~ (all_52_9 = all_52_11)
% 157.82/27.53 (73) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 157.82/27.53 (74) ~ (all_52_13 = all_4_2)
% 157.82/27.53 (75) ~ (all_52_2 = e1)
% 157.82/27.53 (76) ~ (all_52_2 = all_52_14)
% 157.82/27.53 (77) ~ (all_52_6 = all_52_7)
% 157.82/27.53 (78) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 157.82/27.53 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 157.82/27.53 (79) ~ (all_52_4 = e3)
% 157.82/27.53 (80) all_54_6 = all_52_9
% 157.82/27.53 (81) ~ (e2 = e1)
% 157.82/27.53 (82) ~ (all_52_4 = all_52_7)
% 157.82/27.53 (83) ~ (all_52_8 = all_52_11)
% 157.82/27.53 (84) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 157.82/27.53 (85) ~ (e1 = e0)
% 157.82/27.53 (86) ~ (all_52_2 = e2)
% 157.82/27.53 (87) all_58_3 = e3
% 157.82/27.53 (88) op(e3, e1) = all_52_8
% 157.82/27.53 (89) ~ (all_6_2 = e2)
% 157.82/27.53 (90) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.82/27.53 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.82/27.53 e3)
% 157.82/27.53 (91) all_56_13 = e3
% 157.82/27.53 (92) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.82/27.53 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.82/27.53 (93) ~ (all_52_9 = e2)
% 157.82/27.53 (94) ~ (all_52_8 = e3)
% 157.82/27.53 (95) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 157.82/27.53 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.82/27.53 (96) all_54_14 = all_52_11
% 157.82/27.53 (97) ~ (all_52_7 = all_4_2)
% 157.82/27.53 (98) op(e1, e3) = e1
% 157.82/27.53 (99) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.82/27.53 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.82/27.53 (100) op(e0, e2) = all_52_7
% 157.82/27.53 (101) op(e1, e0) = all_52_14
% 157.82/27.53 (102) op(e3, e3) = all_22_1
% 157.82/27.53 (103) all_54_15 = all_4_2
% 157.82/27.53 (104) ~ (all_52_8 = e1)
% 157.82/27.53 (105) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.82/27.53 (106) ~ (all_52_6 = e3)
% 157.82/27.53 (107) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.82/27.53 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.82/27.53 (108) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.82/27.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.82/27.53 (109) ~ (all_52_3 = all_52_11)
% 157.82/27.53 (110) ~ (all_52_11 = all_4_2)
% 157.82/27.53 (111) all_54_11 = all_52_14
% 157.82/27.53 (112) ~ (all_52_13 = all_52_14)
% 157.82/27.53 (113) ~ (e3 = e2)
% 157.82/27.53 (114) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 157.82/27.53 (115) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.82/27.53 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.82/27.53 (116) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 157.82/27.53 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 157.82/27.53 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.82/27.53 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 157.82/27.53 e0)))
% 157.82/27.53 (117) all_54_9 = all_52_6
% 157.82/27.53 (118) ~ (all_52_4 = all_52_8)
% 157.82/27.53 (119) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 157.82/27.53 (120) all_54_12 = all_52_3
% 157.82/27.53 (121) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.82/27.53 (122) ~ (all_52_14 = all_4_2)
% 157.82/27.53 (123) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.82/27.53 (124) ~ (all_52_3 = all_52_7)
% 157.82/27.53
% 157.82/27.53 Begin of proof
% 157.82/27.53 |
% 157.82/27.53 | BETA: splitting (18) gives:
% 157.82/27.53 |
% 157.82/27.53 | Case 1:
% 157.82/27.53 | |
% 157.82/27.53 | | (125) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 157.82/27.53 | | e3)
% 157.82/27.53 | |
% 157.82/27.53 | | BETA: splitting (125) gives:
% 157.82/27.53 | |
% 157.82/27.53 | | Case 1:
% 157.82/27.53 | | |
% 157.82/27.53 | | | (126) all_58_4 = e3 & op(e3, e1) = e3
% 157.82/27.53 | | |
% 157.82/27.53 | | | ALPHA: (126) implies:
% 157.82/27.53 | | | (127) all_58_4 = e3
% 157.82/27.53 | | |
% 157.82/27.53 | | | BETA: splitting (35) gives:
% 157.82/27.53 | | |
% 157.82/27.53 | | | Case 1:
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | (128) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 157.82/27.53 | | | | = e3)
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | BETA: splitting (128) gives:
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | Case 1:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | (129) all_58_6 = e3 & op(e1, e3) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | ALPHA: (129) implies:
% 157.82/27.53 | | | | | (130) all_58_6 = e3
% 157.82/27.53 | | | | | (131) op(e1, e3) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.82/27.53 | | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21), (22),
% 157.82/27.53 | | | | | (23), (24), (26), (27), (28), (29), (30), (31), (32), (33),
% 157.82/27.53 | | | | | (34), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.82/27.53 | | | | | (46), (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 157.82/27.53 | | | | | (57), (58), (60), (61), (62), (63), (64), (65), (66), (67),
% 157.82/27.53 | | | | | (68), (69), (70), (72), (74), (75), (77), (78), (79), (80),
% 157.82/27.53 | | | | | (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 157.82/27.53 | | | | | (91), (92), (93), (94), (96), (97), (98), (100), (101),
% 157.82/27.53 | | | | | (102), (103), (104), (105), (106), (107), (108), (109),
% 157.82/27.53 | | | | | (110), (111), (112), (113), (114), (115), (116), (117),
% 157.82/27.53 | | | | | (119), (120), (121), (122), (123), (124), (127), (130),
% 157.82/27.53 | | | | | (131) are inconsistent by sub-proof #535.
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | Case 2:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | (132) all_58_7 = e3 & op(e1, e2) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | REF_CLOSE: (59), (106), (108), (132) are inconsistent by sub-proof
% 157.82/27.53 | | | | | #1184.
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | End of split
% 157.82/27.53 | | | |
% 157.82/27.53 | | | Case 2:
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | (133) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 157.82/27.53 | | | | e0) = e3)
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | BETA: splitting (133) gives:
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | Case 1:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | (134) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | ALPHA: (134) implies:
% 157.82/27.53 | | | | | (135) all_58_8 = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | REF_CLOSE: (3), (4), (5), (8), (9), (10), (11), (12), (13), (14),
% 157.82/27.53 | | | | | (15), (16), (17), (19), (21), (22), (23), (24), (25), (26),
% 157.82/27.53 | | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (37),
% 157.82/27.53 | | | | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 157.82/27.53 | | | | | (48), (49), (50), (53), (54), (55), (56), (57), (58), (59),
% 157.82/27.53 | | | | | (60), (61), (63), (64), (65), (66), (67), (68), (69), (70),
% 157.82/27.53 | | | | | (71), (72), (74), (75), (76), (77), (78), (79), (80), (81),
% 157.82/27.53 | | | | | (83), (84), (85), (86), (87), (89), (90), (91), (92), (93),
% 157.82/27.53 | | | | | (94), (96), (97), (98), (99), (100), (102), (104), (105),
% 157.82/27.53 | | | | | (106), (107), (108), (111), (112), (113), (115), (116),
% 157.82/27.53 | | | | | (117), (118), (121), (122), (123), (135) are inconsistent
% 157.82/27.53 | | | | | by sub-proof #480.
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | Case 2:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | (136) all_58_11 = e3 & op(e1, e0) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | ALPHA: (136) implies:
% 157.82/27.53 | | | | | (137) all_58_11 = e3
% 157.82/27.53 | | | | | (138) op(e1, e0) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.82/27.53 | | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21), (22),
% 157.82/27.53 | | | | | (23), (24), (26), (27), (28), (29), (30), (31), (32), (33),
% 157.82/27.53 | | | | | (34), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.82/27.53 | | | | | (46), (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 157.82/27.53 | | | | | (57), (58), (60), (61), (62), (63), (64), (65), (66), (67),
% 157.82/27.53 | | | | | (68), (69), (70), (72), (74), (75), (77), (78), (79), (80),
% 157.82/27.53 | | | | | (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 157.82/27.53 | | | | | (91), (92), (93), (94), (95), (96), (97), (98), (100),
% 157.82/27.53 | | | | | (101), (102), (103), (104), (105), (106), (107), (108),
% 157.82/27.53 | | | | | (109), (110), (111), (112), (113), (114), (115), (116),
% 157.82/27.53 | | | | | (117), (119), (120), (121), (122), (123), (124), (127),
% 157.82/27.53 | | | | | (137), (138) are inconsistent by sub-proof #464.
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | End of split
% 157.82/27.53 | | | |
% 157.82/27.53 | | | End of split
% 157.82/27.53 | | |
% 157.82/27.53 | | Case 2:
% 157.82/27.53 | | |
% 157.82/27.53 | | | (139) all_58_5 = e3 & op(e2, e1) = e3
% 157.82/27.53 | | |
% 157.82/27.53 | | | ALPHA: (139) implies:
% 157.82/27.53 | | | (140) op(e2, e1) = e3
% 157.82/27.53 | | |
% 157.82/27.53 | | | REF_CLOSE: (36), (48), (108), (140) are inconsistent by sub-proof #1196.
% 157.82/27.53 | | |
% 157.82/27.53 | | End of split
% 157.82/27.53 | |
% 157.82/27.53 | Case 2:
% 157.82/27.53 | |
% 157.82/27.53 | | (141) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 157.82/27.53 | | e3)
% 157.82/27.53 | |
% 157.82/27.53 | | BETA: splitting (141) gives:
% 157.82/27.53 | |
% 157.82/27.53 | | Case 1:
% 157.82/27.53 | | |
% 157.82/27.53 | | | (142) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.53 | | |
% 157.82/27.53 | | | ALPHA: (142) implies:
% 157.82/27.53 | | | (143) all_58_8 = e3
% 157.82/27.53 | | |
% 157.82/27.53 | | | REF_CLOSE: (3), (4), (5), (8), (9), (10), (11), (12), (13), (14), (15),
% 157.82/27.53 | | | (16), (17), (19), (21), (22), (23), (24), (25), (26), (27),
% 157.82/27.53 | | | (28), (29), (30), (31), (32), (33), (34), (35), (37), (38),
% 157.82/27.53 | | | (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 157.82/27.53 | | | (49), (50), (53), (54), (55), (56), (57), (58), (59), (60),
% 157.82/27.53 | | | (61), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 157.82/27.53 | | | (72), (74), (75), (76), (77), (78), (79), (80), (81), (83),
% 157.82/27.53 | | | (84), (85), (86), (87), (89), (90), (91), (92), (93), (94),
% 157.82/27.53 | | | (96), (97), (98), (99), (100), (102), (104), (105), (106),
% 157.82/27.53 | | | (107), (108), (111), (112), (113), (115), (116), (117), (118),
% 157.82/27.53 | | | (121), (122), (123), (143) are inconsistent by sub-proof #480.
% 157.82/27.53 | | |
% 157.82/27.53 | | Case 2:
% 157.82/27.53 | | |
% 157.82/27.53 | | | (144) all_58_14 = e3 & op(e0, e1) = e3
% 157.82/27.53 | | |
% 157.82/27.53 | | | ALPHA: (144) implies:
% 157.82/27.53 | | | (145) all_58_14 = e3
% 157.82/27.53 | | |
% 157.82/27.53 | | | BETA: splitting (35) gives:
% 157.82/27.53 | | |
% 157.82/27.53 | | | Case 1:
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | (146) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 157.82/27.53 | | | | = e3)
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | BETA: splitting (146) gives:
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | Case 1:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | (147) all_58_6 = e3 & op(e1, e3) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | ALPHA: (147) implies:
% 157.82/27.53 | | | | | (148) all_58_6 = e3
% 157.82/27.53 | | | | | (149) op(e1, e3) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 157.82/27.53 | | | | | (13), (14), (15), (16), (17), (19), (22), (23), (24), (25),
% 157.82/27.53 | | | | | (26), (27), (28), (29), (30), (32), (33), (37), (38), (39),
% 157.82/27.53 | | | | | (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 157.82/27.53 | | | | | (50), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 157.82/27.53 | | | | | (61), (63), (64), (65), (66), (67), (68), (69), (70), (72),
% 157.82/27.53 | | | | | (73), (74), (75), (77), (78), (79), (80), (81), (83), (84),
% 157.82/27.53 | | | | | (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 157.82/27.53 | | | | | (96), (97), (99), (100), (102), (103), (104), (105), (106),
% 157.82/27.53 | | | | | (107), (108), (111), (112), (113), (114), (115), (116),
% 157.82/27.53 | | | | | (117), (121), (122), (123), (145), (148), (149) are
% 157.82/27.53 | | | | | inconsistent by sub-proof #438.
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | Case 2:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | (150) all_58_7 = e3 & op(e1, e2) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | REF_CLOSE: (59), (106), (108), (150) are inconsistent by sub-proof
% 157.82/27.53 | | | | | #1184.
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | End of split
% 157.82/27.53 | | | |
% 157.82/27.53 | | | Case 2:
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | (151) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 157.82/27.53 | | | | e0) = e3)
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | BETA: splitting (151) gives:
% 157.82/27.53 | | | |
% 157.82/27.53 | | | | Case 1:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | (152) all_58_8 = e3 & op(e1, e1) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | ALPHA: (152) implies:
% 157.82/27.53 | | | | | (153) all_58_8 = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | REF_CLOSE: (11), (13), (28), (42), (47), (54), (56), (58), (63), (78),
% 157.82/27.53 | | | | | (81), (85), (87), (89), (108), (113), (145), (153) are
% 157.82/27.53 | | | | | inconsistent by sub-proof #780.
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | Case 2:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | (154) all_58_11 = e3 & op(e1, e0) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | ALPHA: (154) implies:
% 157.82/27.53 | | | | | (155) all_58_11 = e3
% 157.82/27.53 | | | | | (156) op(e1, e0) = e3
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | BETA: splitting (27) gives:
% 157.82/27.53 | | | | |
% 157.82/27.53 | | | | | Case 1:
% 157.82/27.53 | | | | | |
% 157.82/27.53 | | | | | | (157) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2,
% 157.82/27.53 | | | | | | e3) = e3)
% 157.82/27.53 | | | | | |
% 157.82/27.53 | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (13),
% 157.82/27.53 | | | | | | (14), (15), (19), (23), (24), (27), (28), (29), (37),
% 157.82/27.53 | | | | | | (38), (39), (40), (41), (42), (43), (45), (46), (47),
% 157.82/27.53 | | | | | | (48), (54), (55), (56), (57), (58), (61), (63), (66),
% 157.82/27.53 | | | | | | (69), (70), (72), (74), (80), (81), (83), (85), (87),
% 157.82/27.53 | | | | | | (88), (89), (90), (91), (92), (93), (94), (96), (97),
% 157.82/27.53 | | | | | | (100), (104), (105), (107), (108), (113), (115), (116),
% 157.82/27.53 | | | | | | (121), (123), (145), (155), (156), (157) are inconsistent
% 157.82/27.53 | | | | | | by sub-proof #429.
% 157.82/27.53 | | | | | |
% 157.82/27.53 | | | | | Case 2:
% 157.82/27.53 | | | | | |
% 157.82/27.53 | | | | | | (158) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 157.82/27.53 | | | | | | op(e0, e3) = e3)
% 157.82/27.53 | | | | | |
% 157.82/27.53 | | | | | | BETA: splitting (158) gives:
% 157.82/27.53 | | | | | |
% 157.82/27.53 | | | | | | Case 1:
% 157.82/27.53 | | | | | | |
% 157.82/27.53 | | | | | | | (159) all_58_6 = e3 & op(e1, e3) = e3
% 157.82/27.53 | | | | | | |
% 157.82/27.53 | | | | | | | ALPHA: (159) implies:
% 157.92/27.53 | | | | | | | (160) all_58_6 = e3
% 157.92/27.53 | | | | | | | (161) op(e1, e3) = e3
% 157.92/27.53 | | | | | | |
% 157.92/27.53 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 157.92/27.53 | | | | | | | (12), (13), (14), (15), (16), (17), (19), (22), (23),
% 157.92/27.53 | | | | | | | (24), (25), (26), (27), (28), (29), (30), (32), (33),
% 157.92/27.53 | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.92/27.53 | | | | | | | (46), (47), (48), (49), (50), (52), (53), (54), (55),
% 157.92/27.53 | | | | | | | (56), (57), (58), (59), (60), (61), (63), (64), (65),
% 157.92/27.53 | | | | | | | (66), (67), (68), (69), (70), (72), (73), (74), (75),
% 157.92/27.53 | | | | | | | (77), (78), (79), (80), (81), (83), (84), (85), (86),
% 157.92/27.53 | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), (96),
% 157.92/27.53 | | | | | | | (97), (99), (100), (102), (103), (104), (105), (106),
% 157.92/27.53 | | | | | | | (107), (108), (111), (112), (113), (114), (115), (116),
% 157.92/27.53 | | | | | | | (117), (121), (122), (123), (145), (160), (161) are
% 157.92/27.53 | | | | | | | inconsistent by sub-proof #438.
% 157.92/27.53 | | | | | | |
% 157.92/27.53 | | | | | | Case 2:
% 157.92/27.53 | | | | | | |
% 157.92/27.53 | | | | | | | (162) all_58_12 = e3 & op(e0, e3) = e3
% 157.92/27.53 | | | | | | |
% 157.92/27.53 | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (13),
% 157.92/27.53 | | | | | | | (14), (15), (19), (23), (24), (27), (28), (29), (32),
% 157.92/27.53 | | | | | | | (33), (37), (38), (39), (40), (41), (42), (43), (45),
% 157.92/27.53 | | | | | | | (46), (47), (48), (54), (55), (56), (57), (58), (60),
% 157.92/27.53 | | | | | | | (61), (63), (66), (69), (70), (72), (74), (79), (80),
% 157.92/27.53 | | | | | | | (81), (83), (85), (87), (88), (89), (90), (91), (92),
% 157.92/27.53 | | | | | | | (93), (94), (96), (97), (98), (99), (100), (104),
% 157.92/27.53 | | | | | | | (105), (107), (108), (113), (115), (116), (121), (123),
% 157.92/27.53 | | | | | | | (145), (155), (156), (162) are inconsistent by
% 157.92/27.53 | | | | | | | sub-proof #423.
% 157.92/27.53 | | | | | | |
% 157.92/27.53 | | | | | | End of split
% 157.92/27.53 | | | | | |
% 157.92/27.53 | | | | | End of split
% 157.92/27.53 | | | | |
% 157.92/27.53 | | | | End of split
% 157.92/27.53 | | | |
% 157.92/27.53 | | | End of split
% 157.92/27.53 | | |
% 157.92/27.53 | | End of split
% 157.92/27.53 | |
% 157.92/27.53 | End of split
% 157.92/27.53 |
% 157.92/27.53 End of proof
% 157.92/27.53
% 157.92/27.53 Sub-proof #423 shows that the following formulas are inconsistent:
% 157.92/27.53 ----------------------------------------------------------------
% 157.92/27.53 (1) op(e1, e1) = e3
% 157.92/27.53 (2) op(e1, e1) = all_32_1
% 157.92/27.53 (3) all_56_14 = e3
% 157.92/27.53 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.92/27.53 (5) op(e3, e1) = e3
% 157.92/27.53 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.92/27.53 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.92/27.53 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.53 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.53 (8) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.53 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.92/27.53 (9) all_58_14 = e3
% 157.92/27.53 (10) all_54_13 = all_52_7
% 157.92/27.53 (11) op(e1, e1) = all_6_2
% 157.92/27.53 (12) ~ (all_52_7 = e3)
% 157.92/27.53 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.53 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.92/27.53 e1)
% 157.92/27.53 (14) ~ (all_52_11 = e3)
% 157.92/27.53 (15) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.92/27.53 (16) ~ (all_52_7 = all_52_11)
% 157.92/27.53 (17) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.92/27.53 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.92/27.53 (18) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.92/27.53 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.92/27.53 (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.92/27.53 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.92/27.53 (20) op(e3, e2) = all_52_4
% 157.92/27.53 (21) ~ (all_4_2 = e2)
% 157.92/27.53 (22) op(e2, e3) = all_52_1
% 157.92/27.53 (23) ~ (all_52_13 = e3)
% 157.92/27.53 (24) all_54_2 = all_52_8
% 157.92/27.53 (25) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.92/27.53 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.92/27.53 (26) ~ (all_52_8 = all_52_9)
% 157.92/27.53 (27) ~ (e3 = e0)
% 157.92/27.53 (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.92/27.53 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.92/27.53 (29) ~ (all_52_9 = all_52_13)
% 157.92/27.53 (30) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.92/27.53 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.92/27.53 e2)
% 157.92/27.53 (31) ~ (e2 = e0)
% 157.92/27.53 (32) ~ (all_52_9 = e3)
% 157.92/27.53 (33) op(e2, e3) = e2
% 157.92/27.53 (34) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.53 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.92/27.53 (35) ~ (e3 = e1)
% 157.92/27.53 (36) all_56_12 = e1
% 157.92/27.53 (37) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.92/27.53 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.92/27.53 (38) ~ (all_4_2 = e1)
% 157.92/27.53 (39) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.92/27.53 (40) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.53 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.92/27.53 (41) all_54_7 = all_52_13
% 157.92/27.53 (42) ~ (all_52_13 = e2)
% 157.92/27.53 (43) all_56_15 = all_4_2
% 157.92/27.53 (44) ~ (all_52_9 = all_52_11)
% 157.92/27.53 (45) ~ (all_52_13 = all_4_2)
% 157.92/27.53 (46) ~ (all_52_4 = e3)
% 157.92/27.53 (47) all_54_6 = all_52_9
% 157.92/27.53 (48) ~ (e2 = e1)
% 157.92/27.53 (49) ~ (all_52_8 = all_52_11)
% 157.92/27.53 (50) ~ (e1 = e0)
% 157.92/27.53 (51) all_58_3 = e3
% 157.92/27.53 (52) op(e3, e1) = all_52_8
% 157.92/27.53 (53) ~ (all_6_2 = e2)
% 157.92/27.54 (54) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.92/27.54 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.92/27.54 e3)
% 157.92/27.54 (55) all_56_13 = e3
% 157.92/27.54 (56) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.92/27.54 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.92/27.54 (57) ~ (all_52_9 = e2)
% 157.92/27.54 (58) ~ (all_52_8 = e3)
% 157.92/27.54 (59) all_54_14 = all_52_11
% 157.92/27.54 (60) ~ (all_52_7 = all_4_2)
% 157.92/27.54 (61) op(e1, e3) = e1
% 157.92/27.54 (62) op(e1, e0) = e3
% 157.92/27.54 (63) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 157.92/27.54 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 157.92/27.54 (64) op(e0, e2) = all_52_7
% 157.92/27.54 (65) all_58_12 = e3 & op(e0, e3) = e3
% 157.92/27.54 (66) ~ (all_52_8 = e1)
% 157.92/27.54 (67) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.92/27.54 (68) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.54 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.54 (69) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.54 (70) ~ (e3 = e2)
% 157.92/27.54 (71) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.92/27.54 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.54 (72) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.54 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.92/27.54 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.54 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.92/27.54 (73) all_58_11 = e3
% 157.92/27.54 (74) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.92/27.54 (75) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.92/27.54
% 157.92/27.54 Begin of proof
% 157.92/27.54 |
% 157.92/27.54 | ALPHA: (65) implies:
% 157.92/27.54 | (76) all_58_12 = e3
% 157.92/27.54 |
% 157.92/27.54 | BETA: splitting (56) gives:
% 157.92/27.54 |
% 157.92/27.54 | Case 1:
% 157.92/27.54 | |
% 157.92/27.54 | | (77) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 157.92/27.54 | | e1)
% 157.92/27.54 | |
% 157.92/27.54 | | BETA: splitting (77) gives:
% 157.92/27.54 | |
% 157.92/27.54 | | Case 1:
% 157.92/27.54 | | |
% 157.92/27.54 | | | (78) all_58_0 = e1 & op(e3, e3) = e1
% 157.92/27.54 | | |
% 157.92/27.54 | | | ALPHA: (78) implies:
% 157.92/27.54 | | | (79) all_58_0 = e1
% 157.92/27.54 | | |
% 157.92/27.54 | | | BETA: splitting (68) gives:
% 157.92/27.54 | | |
% 157.92/27.54 | | | Case 1:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | (80) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 157.92/27.54 | | | | = e0)
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | REF_CLOSE: (31), (33), (50), (69), (79), (80) are inconsistent by
% 157.92/27.54 | | | | sub-proof #534.
% 157.92/27.54 | | | |
% 157.92/27.54 | | | Case 2:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | (81) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 157.92/27.54 | | | | = e0)
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | BETA: splitting (81) gives:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | Case 1:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | (82) all_58_6 = e0 & op(e1, e3) = e0
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | ALPHA: (82) implies:
% 157.92/27.54 | | | | | (83) all_58_6 = e0
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | REF_CLOSE: (3), (4), (14), (15), (17), (21), (22), (23), (24), (26),
% 157.92/27.54 | | | | | (27), (28), (29), (32), (33), (35), (36), (38), (39), (41),
% 157.92/27.54 | | | | | (42), (43), (44), (45), (47), (48), (49), (50), (55), (57),
% 157.92/27.54 | | | | | (58), (59), (61), (66), (68), (69), (70), (74), (75), (76),
% 157.92/27.54 | | | | | (79), (83) are inconsistent by sub-proof #478.
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | Case 2:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | (84) all_58_12 = e0 & op(e0, e3) = e0
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | ALPHA: (84) implies:
% 157.92/27.54 | | | | | (85) all_58_12 = e0
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | REF_CLOSE: (27), (76), (85) are inconsistent by sub-proof #1463.
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | End of split
% 157.92/27.54 | | | |
% 157.92/27.54 | | | End of split
% 157.92/27.54 | | |
% 157.92/27.54 | | Case 2:
% 157.92/27.54 | | |
% 157.92/27.54 | | | (86) all_58_1 = e1 & op(e3, e2) = e1
% 157.92/27.54 | | |
% 157.92/27.54 | | | ALPHA: (86) implies:
% 157.92/27.54 | | | (87) all_58_1 = e1
% 157.92/27.54 | | |
% 157.92/27.54 | | | BETA: splitting (30) gives:
% 157.92/27.54 | | |
% 157.92/27.54 | | | Case 1:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | (88) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 157.92/27.54 | | | | e2) = e2)
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | BETA: splitting (88) gives:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | Case 1:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | (89) all_58_12 = e2 & op(e0, e3) = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | ALPHA: (89) implies:
% 157.92/27.54 | | | | | (90) all_58_12 = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | REF_CLOSE: (17), (22), (27), (28), (31), (33), (35), (48), (50), (68),
% 157.92/27.54 | | | | | (69), (70), (90) are inconsistent by sub-proof #1062.
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | Case 2:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | (91) all_58_13 = e2 & op(e0, e2) = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | REF_CLOSE: (11), (17), (22), (25), (27), (28), (31), (33), (34), (35),
% 157.92/27.54 | | | | | (48), (50), (51), (53), (64), (68), (69), (70), (73), (76),
% 157.92/27.54 | | | | | (87), (91) are inconsistent by sub-proof #716.
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | End of split
% 157.92/27.54 | | | |
% 157.92/27.54 | | | Case 2:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | (92) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 157.92/27.54 | | | | e0) = e2)
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | BETA: splitting (92) gives:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | Case 1:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | (93) all_58_14 = e2 & op(e0, e1) = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | ALPHA: (93) implies:
% 157.92/27.54 | | | | | (94) all_58_14 = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | COMBINE_EQS: (9), (94) imply:
% 157.92/27.54 | | | | | (95) e3 = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | COMBINE_EQS: (76), (95) imply:
% 157.92/27.54 | | | | | (96) all_58_12 = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | REF_CLOSE: (17), (22), (27), (28), (31), (33), (35), (48), (50), (68),
% 157.92/27.54 | | | | | (69), (70), (96) are inconsistent by sub-proof #1062.
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | Case 2:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | (97) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | REF_CLOSE: (3), (4), (8), (9), (10), (11), (12), (13), (14), (15),
% 157.92/27.54 | | | | | (16), (17), (18), (22), (23), (24), (25), (26), (27), (28),
% 157.92/27.54 | | | | | (29), (31), (32), (33), (34), (35), (36), (39), (40), (41),
% 157.92/27.54 | | | | | (42), (43), (44), (45), (47), (48), (49), (50), (51), (53),
% 157.92/27.54 | | | | | (54), (55), (57), (58), (59), (60), (64), (66), (67), (68),
% 157.92/27.54 | | | | | (69), (70), (72), (73), (74), (75), (87), (97) are
% 157.92/27.54 | | | | | inconsistent by sub-proof #437.
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | End of split
% 157.92/27.54 | | | |
% 157.92/27.54 | | | End of split
% 157.92/27.54 | | |
% 157.92/27.54 | | End of split
% 157.92/27.54 | |
% 157.92/27.54 | Case 2:
% 157.92/27.54 | |
% 157.92/27.54 | | (98) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 157.92/27.54 | | e1)
% 157.92/27.54 | |
% 157.92/27.54 | | BETA: splitting (98) gives:
% 157.92/27.54 | |
% 157.92/27.54 | | Case 1:
% 157.92/27.54 | | |
% 157.92/27.54 | | | (99) all_58_4 = e1 & op(e3, e1) = e1
% 157.92/27.54 | | |
% 157.92/27.54 | | | ALPHA: (99) implies:
% 157.92/27.54 | | | (100) all_58_4 = e1
% 157.92/27.54 | | |
% 157.92/27.54 | | | REF_CLOSE: (8), (9), (11), (18), (27), (31), (33), (35), (40), (48), (50),
% 157.92/27.54 | | | (51), (53), (69), (70), (100) are inconsistent by sub-proof
% 157.92/27.54 | | | #850.
% 157.92/27.54 | | |
% 157.92/27.54 | | Case 2:
% 157.92/27.54 | | |
% 157.92/27.54 | | | (101) all_58_9 = e1 & op(e3, e0) = e1
% 157.92/27.54 | | |
% 157.92/27.54 | | | ALPHA: (101) implies:
% 157.92/27.54 | | | (102) all_58_9 = e1
% 157.92/27.54 | | |
% 157.92/27.54 | | | BETA: splitting (19) gives:
% 157.92/27.54 | | |
% 157.92/27.54 | | | Case 1:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | (103) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 157.92/27.54 | | | | e0) = e2)
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | REF_CLOSE: (8), (27), (31), (33), (35), (40), (48), (50), (51), (69),
% 157.92/27.54 | | | | (102), (103) are inconsistent by sub-proof #686.
% 157.92/27.54 | | | |
% 157.92/27.54 | | | Case 2:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | (104) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 157.92/27.54 | | | | e0) = e2)
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | BETA: splitting (104) gives:
% 157.92/27.54 | | | |
% 157.92/27.54 | | | | Case 1:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | (105) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | REF_CLOSE: (17), (22), (27), (28), (31), (33), (35), (48), (50), (68),
% 157.92/27.54 | | | | | (69), (70), (73), (76), (105) are inconsistent by sub-proof
% 157.92/27.54 | | | | | #428.
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | Case 2:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | (106) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | ALPHA: (106) implies:
% 157.92/27.54 | | | | | (107) all_58_15 = e2
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | BETA: splitting (72) gives:
% 157.92/27.54 | | | | |
% 157.92/27.54 | | | | | Case 1:
% 157.92/27.54 | | | | | |
% 157.92/27.54 | | | | | | (108) all_58_15 = e0 & op(e0, e0) = e0
% 157.92/27.54 | | | | | |
% 157.92/27.54 | | | | | | REF_CLOSE: (31), (107), (108) are inconsistent by sub-proof #885.
% 157.92/27.54 | | | | | |
% 157.92/27.54 | | | | | Case 2:
% 157.92/27.54 | | | | | |
% 157.92/27.54 | | | | | | (109) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 157.92/27.54 | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0))
% 157.92/27.54 | | | | | | & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.54 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.92/27.54 | | | | | |
% 157.92/27.54 | | | | | | ALPHA: (109) implies:
% 157.92/27.54 | | | | | | (110) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 157.92/27.54 | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.92/27.54 | | | | | |
% 157.92/27.54 | | | | | | BETA: splitting (68) gives:
% 157.92/27.54 | | | | | |
% 157.92/27.54 | | | | | | Case 1:
% 157.92/27.54 | | | | | | |
% 157.92/27.54 | | | | | | | (111) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 157.92/27.54 | | | | | | | op(e2, e3) = e0)
% 157.92/27.54 | | | | | | |
% 157.92/27.54 | | | | | | | BETA: splitting (111) gives:
% 157.92/27.54 | | | | | | |
% 157.92/27.54 | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | |
% 157.92/27.54 | | | | | | | | (112) all_58_0 = e0 & op(e3, e3) = e0
% 157.92/27.54 | | | | | | | |
% 157.92/27.54 | | | | | | | | ALPHA: (112) implies:
% 157.92/27.54 | | | | | | | | (113) all_58_0 = e0
% 157.92/27.54 | | | | | | | |
% 157.92/27.54 | | | | | | | | BETA: splitting (8) gives:
% 157.92/27.54 | | | | | | | |
% 157.92/27.54 | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | |
% 157.92/27.54 | | | | | | | | | (114) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 157.92/27.54 | | | | | | | | | op(e2, e2) = e1)
% 157.92/27.54 | | | | | | | | |
% 157.92/27.54 | | | | | | | | | REF_CLOSE: (33), (35), (48), (51), (69), (114) are
% 157.92/27.54 | | | | | | | | | inconsistent by sub-proof #840.
% 157.92/27.54 | | | | | | | | |
% 157.92/27.54 | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | |
% 157.92/27.54 | | | | | | | | | (115) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 157.92/27.54 | | | | | | | | | op(e2, e0) = e1)
% 157.92/27.54 | | | | | | | | |
% 157.92/27.54 | | | | | | | | | BETA: splitting (115) gives:
% 157.92/27.54 | | | | | | | | |
% 157.92/27.54 | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | (116) all_58_5 = e1 & op(e2, e1) = e1
% 157.92/27.54 | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | ALPHA: (116) implies:
% 157.92/27.54 | | | | | | | | | | (117) all_58_5 = e1
% 157.92/27.54 | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | BETA: splitting (37) gives:
% 157.92/27.54 | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | (118) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 157.92/27.54 | | | | | | | | | | | & op(e2, e1) = e0)
% 157.92/27.54 | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (18), (27), (31), (33), (35),
% 157.92/27.54 | | | | | | | | | | | (40), (48), (50), (51), (53), (69), (70), (117),
% 157.92/27.54 | | | | | | | | | | | (118) are inconsistent by sub-proof #782.
% 157.92/27.54 | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | (119) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 157.92/27.54 | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 157.92/27.54 | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | BETA: splitting (119) gives:
% 157.92/27.54 | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | (120) all_58_8 = e0 & op(e1, e1) = e0
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | ALPHA: (120) implies:
% 157.92/27.54 | | | | | | | | | | | | (121) op(e1, e1) = e0
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | BETA: splitting (25) gives:
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | (122) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 157.92/27.54 | | | | | | | | | | | | | & op(e1, e2) = e2)
% 157.92/27.54 | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | BETA: splitting (122) gives:
% 157.92/27.54 | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | (123) all_58_6 = e2 & op(e1, e3) = e2
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | ALPHA: (123) implies:
% 157.92/27.54 | | | | | | | | | | | | | | (124) all_58_6 = e2
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | REF_CLOSE: (17), (22), (27), (28), (31), (33), (35), (48),
% 157.92/27.54 | | | | | | | | | | | | | | (50), (68), (69), (70), (124) are inconsistent by
% 157.92/27.54 | | | | | | | | | | | | | | sub-proof #1152.
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | (125) all_58_7 = e2 & op(e1, e2) = e2
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | ALPHA: (125) implies:
% 157.92/27.54 | | | | | | | | | | | | | | (126) all_58_7 = e2
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | (127) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 157.92/27.54 | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 157.92/27.54 | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | (128) all_58_0 = e1 & op(e3, e3) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | (129) all_58_0 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | (130) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (131) all_58_1 = e1 & op(e3, e2) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (132) all_58_1 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | (133) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (134) all_58_1 = e0 & op(e3, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (135) all_58_1 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (135) imply:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (136) e1 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (10), (12), (14), (15), (16), (17),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (22), (23), (24), (26), (27), (28), (29), (31),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (32), (33), (34), (35), (36), (39), (41), (42),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (47), (48), (49), (50), (51),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (55), (57), (58), (59), (60), (64), (66), (67),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (69), (70), (74), (75), (76), (113), (126), (132)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #469.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (137) all_58_3 = e0 & op(e2, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (51), (137) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | #910.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | (138) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (139) all_58_7 = e0 & op(e1, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (140) all_58_7 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (126), (140) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | #1086.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (141) all_58_13 = e0 & op(e0, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (142) op(e0, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (13), (14), (15), (17), (18), (22), (23), (24),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (26), (27), (28), (29), (30), (31), (32), (33),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (35), (36), (39), (40), (41), (42), (43), (44),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (45), (47), (48), (49), (50), (51), (52), (53),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (54), (55), (57), (58), (59), (64), (66), (68),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (69), (70), (72), (74), (75), (76), (121), (142)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #426.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (143) all_58_3 = e1 & op(e2, e2) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (144) all_58_3 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (51), (144) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | #841.
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | (145) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 157.92/27.54 | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (146) all_58_7 = e1 & op(e1, e2) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (126), (146) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | #1045.
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (147) all_58_13 = e1 & op(e0, e2) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (148) all_58_13 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | (149) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (150) all_58_1 = e0 & op(e3, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (17), (22), (27), (28), (30), (31),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (33), (35), (48), (50), (51), (68), (69), (70),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (72), (76), (126), (148), (150) are inconsistent
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | by sub-proof #424.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (151) all_58_3 = e0 & op(e2, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (51), (151) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | #756.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | (152) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (153) all_58_7 = e0 & op(e1, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (126), (153) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | #1468.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (154) all_58_13 = e0 & op(e0, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (155) all_58_13 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (156) op(e0, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (155) imply:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (157) e1 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (10), (12), (14), (15), (16), (17),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (22), (23), (24), (26), (27), (28), (29), (32),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (33), (35), (36), (39), (41), (42), (43), (44),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (45), (47), (48), (49), (50), (55), (57), (58),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (59), (60), (64), (66), (67), (69), (70), (74),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (75), (76), (113), (156) are inconsistent by
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | sub-proof #471.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | (158) all_58_2 = e1 & op(e2, e3) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | (159) op(e2, e3) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (48), (69), (159) are inconsistent by
% 157.92/27.54 | | | | | | | | | | | | | | | | sub-proof #1430.
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | (160) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 157.92/27.54 | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 157.92/27.54 | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 157.92/27.54 | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | (161) all_58_6 = e1 & op(e1, e3) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | (162) all_58_6 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | (163) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (164) all_58_1 = e1 & op(e3, e2) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (165) all_58_1 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | (166) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (167) all_58_1 = e0 & op(e3, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (168) all_58_1 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (168) imply:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (169) e1 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (169) imply:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (170) all_58_6 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (14), (15), (17), (21), (22), (23),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (24), (26), (27), (28), (29), (32), (33), (35),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (36), (38), (39), (41), (42), (43), (44), (45),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (55), (57), (58), (59),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (61), (66), (68), (69), (70), (74), (75), (76),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (170) are inconsistent by sub-proof #477.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (171) all_58_3 = e0 & op(e2, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (51), (171) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | #756.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | (172) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (173) all_58_7 = e0 & op(e1, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (174) all_58_7 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (126), (174) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | #1086.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (175) all_58_13 = e0 & op(e0, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (176) op(e0, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (13), (14), (15), (17), (18), (22), (23), (24),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (26), (27), (28), (29), (30), (31), (32), (33),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (35), (36), (39), (40), (41), (42), (43), (44),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (45), (47), (48), (49), (50), (51), (52), (53),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (54), (55), (57), (58), (59), (64), (66), (68),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (69), (70), (72), (74), (75), (76), (121), (176)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #426.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (177) all_58_3 = e1 & op(e2, e2) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (51), (177) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | #912.
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | (178) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 157.92/27.54 | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (179) all_58_7 = e1 & op(e1, e2) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (126), (179) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | #1045.
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (180) all_58_13 = e1 & op(e0, e2) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | (181) all_58_13 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | (182) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (183) all_58_1 = e0 & op(e3, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (17), (22), (27), (28), (30), (31),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (33), (35), (48), (50), (51), (68), (69), (70),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (72), (76), (126), (181), (183) are inconsistent
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | by sub-proof #424.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (184) all_58_3 = e0 & op(e2, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (51), (184) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | #910.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | (185) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (186) all_58_7 = e0 & op(e1, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (126), (186) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | #1468.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (187) all_58_13 = e0 & op(e0, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (188) op(e0, e2) = e0
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (13), (14), (15), (17), (18), (22), (23), (24),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (26), (27), (28), (29), (30), (31), (32), (33),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (35), (36), (39), (40), (41), (42), (43), (44),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (45), (47), (48), (49), (50), (51), (52), (53),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (54), (55), (57), (58), (59), (64), (66), (68),
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | (69), (70), (72), (74), (75), (76), (121), (188)
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #426.
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | (189) all_58_12 = e1 & op(e0, e3) = e1
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 157.92/27.54 | | | | | | | | | | | | | | | | (190) all_58_12 = e1
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (76), (190) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | | | | | #1516.
% 157.92/27.54 | | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | (191) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 157.92/27.54 | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 157.92/27.54 | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | BETA: splitting (191) gives:
% 157.92/27.54 | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | Case 1:
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | (192) all_58_8 = e2 & op(e1, e1) = e2
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | REF_CLOSE: (11), (53), (69), (192) are inconsistent by
% 157.92/27.54 | | | | | | | | | | | | | | sub-proof #1440.
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | (193) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | | REF_CLOSE: (17), (22), (27), (28), (31), (33), (35), (48),
% 157.92/27.54 | | | | | | | | | | | | | | (50), (68), (69), (70), (73), (76), (193) are
% 157.92/27.54 | | | | | | | | | | | | | | inconsistent by sub-proof #428.
% 157.92/27.54 | | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | Case 2:
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | (194) all_58_14 = e0 & op(e0, e1) = e0
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | ALPHA: (194) implies:
% 157.92/27.54 | | | | | | | | | | | | (195) all_58_14 = e0
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | | REF_CLOSE: (9), (27), (195) are inconsistent by sub-proof
% 157.92/27.54 | | | | | | | | | | | | #1444.
% 157.92/27.54 | | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | | End of split
% 157.92/27.54 | | | | | | | | | | |
% 157.92/27.54 | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | (196) all_58_10 = e1 & op(e2, e0) = e1
% 157.92/27.55 | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | ALPHA: (196) implies:
% 157.92/27.55 | | | | | | | | | | (197) all_58_10 = e1
% 157.92/27.55 | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | BETA: splitting (63) gives:
% 157.92/27.55 | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | (198) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 157.92/27.55 | | | | | | | | | | | & op(e3, e2) = e3)
% 157.92/27.55 | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | BETA: splitting (198) gives:
% 157.92/27.55 | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | (199) all_58_0 = e3 & op(e3, e3) = e3
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | ALPHA: (199) implies:
% 157.92/27.55 | | | | | | | | | | | | (200) all_58_0 = e3
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 157.92/27.55 | | | | | | | | | | | | (12), (13), (14), (15), (17), (18), (19), (22),
% 157.92/27.55 | | | | | | | | | | | | (23), (24), (25), (26), (27), (28), (29), (31),
% 157.92/27.55 | | | | | | | | | | | | (32), (33), (34), (35), (36), (37), (39), (40),
% 157.92/27.55 | | | | | | | | | | | | (41), (42), (43), (44), (45), (47), (48), (49),
% 157.92/27.55 | | | | | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (57),
% 157.92/27.55 | | | | | | | | | | | | (58), (59), (62), (64), (66), (68), (69), (70),
% 157.92/27.55 | | | | | | | | | | | | (71), (72), (73), (74), (75), (102), (110), (200)
% 157.92/27.55 | | | | | | | | | | | | are inconsistent by sub-proof #430.
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | (201) all_58_1 = e3 & op(e3, e2) = e3
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | ALPHA: (201) implies:
% 157.92/27.55 | | | | | | | | | | | | (202) op(e3, e2) = e3
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | REF_CLOSE: (20), (46), (69), (202) are inconsistent by
% 157.92/27.55 | | | | | | | | | | | | sub-proof #1540.
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | (203) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 157.92/27.55 | | | | | | | | | | | & op(e3, e0) = e3)
% 157.92/27.55 | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | BETA: splitting (203) gives:
% 157.92/27.55 | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | (204) all_58_4 = e3 & op(e3, e1) = e3
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | ALPHA: (204) implies:
% 157.92/27.55 | | | | | | | | | | | | (205) all_58_4 = e3
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | BETA: splitting (72) gives:
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | (206) all_58_15 = e0 & op(e0, e0) = e0
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | ALPHA: (206) implies:
% 157.92/27.55 | | | | | | | | | | | | | (207) all_58_15 = e0
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | REF_CLOSE: (8), (17), (19), (22), (27), (28), (31), (33),
% 157.92/27.55 | | | | | | | | | | | | | (35), (40), (48), (50), (51), (69), (70), (73),
% 157.92/27.55 | | | | | | | | | | | | | (76), (102), (113), (207) are inconsistent by
% 157.92/27.55 | | | | | | | | | | | | | sub-proof #691.
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | ALPHA: (109) implies:
% 157.92/27.55 | | | | | | | | | | | | | (208) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 157.92/27.55 | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 157.92/27.55 | | | | | | | | | | | | | e1) = e0)
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | BETA: splitting (40) gives:
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | (209) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 157.92/27.55 | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.92/27.55 | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | REF_CLOSE: (27), (31), (33), (51), (69), (209) are
% 157.92/27.55 | | | | | | | | | | | | | | inconsistent by sub-proof #755.
% 157.92/27.55 | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | (210) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 157.92/27.55 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 157.92/27.55 | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 157.92/27.55 | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | (211) all_58_5 = e0 & op(e2, e1) = e0
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 157.92/27.55 | | | | | | | | | | | | | | | (212) all_58_5 = e0
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | (213) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.92/27.55 | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.92/27.55 | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 157.92/27.55 | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | (214) all_58_9 = e2 & op(e3, e0) = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 157.92/27.55 | | | | | | | | | | | | | | | | | (215) all_58_9 = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (27), (31), (33), (35), (48), (50), (51),
% 157.92/27.55 | | | | | | | | | | | | | | | | | (69), (73), (110), (212), (215) are inconsistent
% 157.92/27.55 | | | | | | | | | | | | | | | | | by sub-proof #837.
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | (216) all_58_10 = e2 & op(e2, e0) = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 157.92/27.55 | | | | | | | | | | | | | | | | | (217) all_58_10 = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (27), (31), (33), (35), (40), (48), (50),
% 157.92/27.55 | | | | | | | | | | | | | | | | | (51), (69), (217) are inconsistent by sub-proof
% 157.92/27.55 | | | | | | | | | | | | | | | | | #906.
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 157.92/27.55 | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | (218) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (22), (27), (28), (33), (35), (48), (50),
% 157.92/27.55 | | | | | | | | | | | | | | | | | (69), (70), (73), (76), (113), (218) are
% 157.92/27.55 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #692.
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 157.92/27.55 | | | | | | | | | | | | | | | | | (219) op(e0, e0) = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | (220) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 157.92/27.55 | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 157.92/27.55 | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.55 | | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | (221) all_58_4 = e2 & op(e3, e1) = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (22), (27), (28), (33), (35), (48), (50),
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | (69), (70), (76), (113), (205), (221) are
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #587.
% 157.92/27.55 | | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | (222) all_58_5 = e2 & op(e2, e1) = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | (223) all_58_5 = e2
% 157.92/27.55 | | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (31), (33), (40), (50), (51), (69), (197),
% 157.92/27.55 | | | | | | | | | | | | | | | | | | | (223) are inconsistent by sub-proof #899.
% 157.92/27.55 | | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | (224) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 157.92/27.55 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 157.92/27.55 | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (27), (31), (35), (48), (50), (53),
% 157.92/27.55 | | | | | | | | | | | | | | | | | | (69), (76), (208), (219), (224) are inconsistent
% 157.92/27.55 | | | | | | | | | | | | | | | | | | by sub-proof #506.
% 157.92/27.55 | | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | (225) all_58_10 = e0 & op(e2, e0) = e0
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 157.92/27.55 | | | | | | | | | | | | | | | (226) all_58_10 = e0
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | | REF_CLOSE: (50), (197), (226) are inconsistent by sub-proof
% 157.92/27.55 | | | | | | | | | | | | | | | #1279.
% 157.92/27.55 | | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | (227) all_58_9 = e3 & op(e3, e0) = e3
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | | REF_CLOSE: (35), (102), (227) are inconsistent by sub-proof
% 157.92/27.55 | | | | | | | | | | | | #934.
% 157.92/27.55 | | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | | |
% 157.92/27.55 | | | | | | | | | End of split
% 157.92/27.55 | | | | | | | | |
% 157.92/27.55 | | | | | | | | End of split
% 157.92/27.55 | | | | | | | |
% 157.92/27.55 | | | | | | | Case 2:
% 157.92/27.55 | | | | | | | |
% 157.92/27.55 | | | | | | | | (228) all_58_2 = e0 & op(e2, e3) = e0
% 157.92/27.55 | | | | | | | |
% 157.92/27.55 | | | | | | | | ALPHA: (228) implies:
% 157.92/27.55 | | | | | | | | (229) op(e2, e3) = e0
% 157.92/27.55 | | | | | | | |
% 157.92/27.55 | | | | | | | | REF_CLOSE: (31), (33), (69), (229) are inconsistent by sub-proof
% 157.92/27.55 | | | | | | | | #1156.
% 157.92/27.55 | | | | | | | |
% 157.92/27.55 | | | | | | | End of split
% 157.92/27.55 | | | | | | |
% 157.92/27.55 | | | | | | Case 2:
% 157.92/27.55 | | | | | | |
% 157.92/27.55 | | | | | | | (230) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 157.92/27.55 | | | | | | | op(e0, e3) = e0)
% 157.92/27.55 | | | | | | |
% 157.92/27.55 | | | | | | | REF_CLOSE: (3), (4), (14), (15), (17), (21), (22), (23), (24),
% 157.92/27.55 | | | | | | | (26), (27), (28), (29), (32), (33), (35), (36), (38),
% 157.92/27.55 | | | | | | | (39), (41), (42), (43), (44), (45), (47), (48), (49),
% 157.92/27.55 | | | | | | | (50), (55), (57), (58), (59), (61), (66), (68), (69),
% 157.92/27.55 | | | | | | | (70), (74), (75), (76), (230) are inconsistent by
% 157.92/27.55 | | | | | | | sub-proof #467.
% 157.92/27.55 | | | | | | |
% 157.92/27.55 | | | | | | End of split
% 157.92/27.55 | | | | | |
% 157.92/27.55 | | | | | End of split
% 157.92/27.55 | | | | |
% 157.92/27.55 | | | | End of split
% 157.92/27.55 | | | |
% 157.92/27.55 | | | End of split
% 157.92/27.55 | | |
% 157.92/27.55 | | End of split
% 157.92/27.55 | |
% 157.92/27.55 | End of split
% 157.92/27.55 |
% 157.92/27.55 End of proof
% 157.92/27.55
% 157.92/27.55 Sub-proof #424 shows that the following formulas are inconsistent:
% 157.92/27.55 ----------------------------------------------------------------
% 157.92/27.55 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.55 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.55 (2) all_58_14 = e3
% 157.92/27.55 (3) all_58_12 = e3
% 157.92/27.55 (4) all_58_7 = e2
% 157.92/27.55 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.92/27.55 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.92/27.55 (6) op(e2, e3) = all_52_1
% 157.92/27.55 (7) all_58_13 = e1
% 157.92/27.55 (8) ~ (e3 = e0)
% 157.92/27.55 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.92/27.55 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.92/27.55 (10) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.92/27.55 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.92/27.55 e2)
% 157.92/27.55 (11) ~ (e2 = e0)
% 157.92/27.55 (12) op(e2, e3) = e2
% 157.92/27.55 (13) ~ (e3 = e1)
% 157.92/27.55 (14) ~ (e2 = e1)
% 157.92/27.55 (15) ~ (e1 = e0)
% 157.92/27.55 (16) all_58_3 = e3
% 157.92/27.55 (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.55 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.55 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.55 (19) ~ (e3 = e2)
% 157.92/27.55 (20) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.55 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.92/27.55 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.55 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.92/27.55 (21) all_58_1 = e0 & op(e3, e2) = e0
% 157.92/27.55
% 157.92/27.55 Begin of proof
% 157.92/27.55 |
% 157.92/27.55 | ALPHA: (21) implies:
% 157.92/27.55 | (22) all_58_1 = e0
% 157.92/27.55 |
% 157.92/27.55 | BETA: splitting (10) gives:
% 157.92/27.55 |
% 157.92/27.55 | Case 1:
% 157.92/27.55 | |
% 157.92/27.55 | | (23) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 157.92/27.55 | | e2)
% 157.92/27.55 | |
% 157.92/27.55 | | REF_CLOSE: (5), (6), (7), (8), (9), (11), (12), (13), (14), (15), (17),
% 157.92/27.55 | | (18), (19), (23) are inconsistent by sub-proof #806.
% 157.92/27.55 | |
% 157.92/27.55 | Case 2:
% 157.92/27.55 | |
% 157.92/27.55 | | (24) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.92/27.55 | | e2)
% 157.92/27.55 | |
% 157.92/27.55 | | BETA: splitting (24) gives:
% 157.92/27.55 | |
% 157.92/27.55 | | Case 1:
% 157.92/27.55 | | |
% 157.92/27.55 | | | (25) all_58_14 = e2 & op(e0, e1) = e2
% 157.92/27.55 | | |
% 157.92/27.55 | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (11), (12), (13), (14), (15),
% 157.92/27.55 | | | (17), (18), (19), (25) are inconsistent by sub-proof #427.
% 157.92/27.55 | | |
% 157.92/27.55 | | Case 2:
% 157.92/27.55 | | |
% 157.92/27.55 | | | (26) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.55 | | |
% 157.92/27.55 | | | ALPHA: (26) implies:
% 157.92/27.55 | | | (27) all_58_15 = e2
% 157.92/27.55 | | |
% 157.92/27.55 | | | REF_CLOSE: (1), (2), (3), (4), (8), (11), (13), (14), (15), (16), (20),
% 157.92/27.55 | | | (22), (27) are inconsistent by sub-proof #425.
% 157.92/27.55 | | |
% 157.92/27.55 | | End of split
% 157.92/27.55 | |
% 157.92/27.55 | End of split
% 157.92/27.55 |
% 157.92/27.55 End of proof
% 157.92/27.55
% 157.92/27.55 Sub-proof #425 shows that the following formulas are inconsistent:
% 157.92/27.55 ----------------------------------------------------------------
% 157.92/27.55 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.55 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.55 (2) all_58_1 = e0
% 157.92/27.55 (3) all_58_14 = e3
% 157.92/27.55 (4) all_58_12 = e3
% 157.92/27.55 (5) all_58_7 = e2
% 157.92/27.55 (6) ~ (e3 = e0)
% 157.92/27.55 (7) ~ (e2 = e0)
% 157.92/27.55 (8) ~ (e3 = e1)
% 157.92/27.55 (9) all_58_15 = e2
% 157.92/27.55 (10) ~ (e2 = e1)
% 157.92/27.55 (11) ~ (e1 = e0)
% 157.92/27.55 (12) all_58_3 = e3
% 157.92/27.55 (13) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.55 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.92/27.55 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.55 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.92/27.55
% 157.92/27.55 Begin of proof
% 157.92/27.55 |
% 157.92/27.55 | BETA: splitting (13) gives:
% 157.92/27.55 |
% 157.92/27.55 | Case 1:
% 157.92/27.55 | |
% 157.92/27.55 | | (14) all_58_15 = e0 & op(e0, e0) = e0
% 157.92/27.55 | |
% 157.92/27.55 | | REF_CLOSE: (7), (9), (14) are inconsistent by sub-proof #885.
% 157.92/27.55 | |
% 157.92/27.55 | Case 2:
% 157.92/27.55 | |
% 157.92/27.55 | | (15) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 157.92/27.55 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 157.92/27.55 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 157.92/27.55 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 157.92/27.55 | |
% 157.92/27.55 | | ALPHA: (15) implies:
% 157.92/27.55 | | (16) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 157.92/27.55 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.92/27.55 | |
% 157.92/27.55 | | BETA: splitting (16) gives:
% 157.92/27.55 | |
% 157.92/27.55 | | Case 1:
% 157.92/27.55 | | |
% 157.92/27.55 | | | (17) all_58_12 = e0 & op(e0, e3) = e0
% 157.92/27.55 | | |
% 157.92/27.55 | | | REF_CLOSE: (4), (6), (17) are inconsistent by sub-proof #1505.
% 157.92/27.55 | | |
% 157.92/27.55 | | Case 2:
% 157.92/27.55 | | |
% 157.92/27.55 | | | (18) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 157.92/27.55 | | | = e0)
% 157.92/27.55 | | |
% 157.92/27.55 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (11), (12), (18) are
% 157.92/27.55 | | | inconsistent by sub-proof #649.
% 157.92/27.55 | | |
% 157.92/27.55 | | End of split
% 157.92/27.55 | |
% 157.92/27.55 | End of split
% 157.92/27.55 |
% 157.92/27.55 End of proof
% 157.92/27.55
% 157.92/27.55 Sub-proof #426 shows that the following formulas are inconsistent:
% 157.92/27.55 ----------------------------------------------------------------
% 157.92/27.55 (1) op(e1, e1) = e3
% 157.92/27.55 (2) op(e1, e1) = all_32_1
% 157.92/27.55 (3) all_56_14 = e3
% 157.92/27.55 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.92/27.55 (5) op(e3, e1) = e3
% 157.92/27.55 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.55 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.92/27.55 (7) all_58_14 = e3
% 157.92/27.55 (8) op(e1, e1) = all_6_2
% 157.92/27.55 (9) ~ (all_52_7 = e3)
% 157.92/27.55 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.55 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.92/27.55 e1)
% 157.92/27.55 (11) ~ (all_52_11 = e3)
% 157.92/27.55 (12) all_58_12 = e3
% 157.92/27.55 (13) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.92/27.55 (14) op(e1, e1) = e0
% 157.92/27.55 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.92/27.55 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.92/27.55 (16) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.92/27.55 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.92/27.55 (17) op(e2, e3) = all_52_1
% 157.92/27.55 (18) ~ (all_52_13 = e3)
% 157.92/27.55 (19) all_54_2 = all_52_8
% 157.92/27.55 (20) ~ (all_52_8 = all_52_9)
% 157.92/27.55 (21) ~ (e3 = e0)
% 157.92/27.55 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.92/27.55 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.92/27.55 (23) ~ (all_52_9 = all_52_13)
% 157.92/27.55 (24) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.92/27.55 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.92/27.55 e2)
% 157.92/27.55 (25) ~ (e2 = e0)
% 157.92/27.55 (26) ~ (all_52_9 = e3)
% 157.92/27.55 (27) op(e2, e3) = e2
% 157.92/27.55 (28) ~ (e3 = e1)
% 157.92/27.55 (29) all_56_12 = e1
% 157.92/27.55 (30) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.92/27.55 (31) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.55 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.92/27.55 (32) all_54_7 = all_52_13
% 157.92/27.55 (33) ~ (all_52_13 = e2)
% 157.92/27.55 (34) all_56_15 = all_4_2
% 157.92/27.55 (35) ~ (all_52_9 = all_52_11)
% 157.92/27.55 (36) ~ (all_52_13 = all_4_2)
% 157.92/27.55 (37) all_54_6 = all_52_9
% 157.92/27.55 (38) op(e0, e2) = e0
% 157.92/27.55 (39) ~ (e2 = e1)
% 157.92/27.55 (40) ~ (all_52_8 = all_52_11)
% 157.92/27.55 (41) ~ (e1 = e0)
% 157.92/27.55 (42) all_58_3 = e3
% 157.92/27.55 (43) op(e3, e1) = all_52_8
% 157.92/27.55 (44) ~ (all_6_2 = e2)
% 157.92/27.55 (45) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.92/27.55 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.92/27.55 e3)
% 157.92/27.55 (46) all_56_13 = e3
% 157.92/27.55 (47) ~ (all_52_9 = e2)
% 157.92/27.55 (48) ~ (all_52_8 = e3)
% 157.92/27.55 (49) all_54_14 = all_52_11
% 157.92/27.55 (50) op(e0, e2) = all_52_7
% 157.92/27.55 (51) ~ (all_52_8 = e1)
% 157.92/27.55 (52) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.55 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.55 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.55 (54) ~ (e3 = e2)
% 157.92/27.55 (55) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.55 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.92/27.55 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.55 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.92/27.55 (56) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.92/27.55 (57) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.92/27.55
% 157.92/27.55 Begin of proof
% 157.92/27.55 |
% 157.92/27.55 | BETA: splitting (57) gives:
% 157.92/27.55 |
% 157.92/27.55 | Case 1:
% 157.92/27.55 | |
% 157.92/27.55 | | (58) all_56_12 = e3
% 157.92/27.55 | |
% 157.92/27.55 | | COMBINE_EQS: (29), (58) imply:
% 157.92/27.55 | | (59) e3 = e1
% 157.92/27.55 | |
% 157.92/27.55 | | REDUCE: (28), (59) imply:
% 157.92/27.55 | | (60) $false
% 157.92/27.55 | |
% 157.92/27.55 | | CLOSE: (60) is inconsistent.
% 157.92/27.55 | |
% 157.92/27.55 | Case 2:
% 157.92/27.55 | |
% 157.92/27.55 | | (61) ~ (all_56_12 = e3)
% 157.92/27.55 | | (62) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.92/27.55 | |
% 157.92/27.55 | | REDUCE: (29), (61) imply:
% 157.92/27.55 | | (63) ~ (e3 = e1)
% 157.92/27.55 | |
% 157.92/27.55 | | BETA: splitting (24) gives:
% 157.92/27.55 | |
% 157.92/27.55 | | Case 1:
% 157.92/27.55 | | |
% 157.92/27.55 | | | (64) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2)
% 157.92/27.55 | | | = e2)
% 157.92/27.55 | | |
% 157.92/27.55 | | | REF_CLOSE: (15), (17), (21), (22), (25), (27), (28), (38), (39), (41),
% 157.92/27.55 | | | (50), (52), (53), (54), (64) are inconsistent by sub-proof
% 157.92/27.55 | | | #1039.
% 157.92/27.55 | | |
% 157.92/27.55 | | Case 2:
% 157.92/27.55 | | |
% 157.92/27.55 | | | (65) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0)
% 157.92/27.55 | | | = e2)
% 157.92/27.55 | | |
% 157.92/27.55 | | | BETA: splitting (65) gives:
% 157.92/27.55 | | |
% 157.92/27.55 | | | Case 1:
% 157.92/27.55 | | | |
% 157.92/27.55 | | | | (66) all_58_14 = e2 & op(e0, e1) = e2
% 157.92/27.55 | | | |
% 157.92/27.55 | | | | REF_CLOSE: (7), (12), (15), (17), (21), (22), (25), (27), (28), (39),
% 157.92/27.55 | | | | (41), (52), (53), (54), (66) are inconsistent by sub-proof
% 157.92/27.55 | | | | #427.
% 157.92/27.55 | | | |
% 157.92/27.55 | | | Case 2:
% 157.92/27.55 | | | |
% 157.92/27.55 | | | | (67) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.55 | | | |
% 157.92/27.55 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 157.92/27.55 | | | | (13), (14), (16), (18), (19), (20), (21), (23), (25), (26),
% 157.92/27.55 | | | | (27), (28), (30), (31), (32), (33), (34), (35), (36), (37),
% 157.92/27.55 | | | | (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 157.92/27.55 | | | | (49), (50), (51), (53), (54), (55), (56), (62), (67) are
% 157.92/27.55 | | | | inconsistent by sub-proof #432.
% 157.92/27.55 | | | |
% 157.92/27.55 | | | End of split
% 157.92/27.55 | | |
% 157.92/27.55 | | End of split
% 157.92/27.55 | |
% 157.92/27.55 | End of split
% 157.92/27.55 |
% 157.92/27.55 End of proof
% 157.92/27.55
% 157.92/27.55 Sub-proof #427 shows that the following formulas are inconsistent:
% 157.92/27.55 ----------------------------------------------------------------
% 157.92/27.55 (1) all_58_14 = e3
% 157.92/27.55 (2) all_58_12 = e3
% 157.92/27.55 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.92/27.55 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.92/27.55 (4) op(e2, e3) = all_52_1
% 157.92/27.55 (5) ~ (e3 = e0)
% 157.92/27.55 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.92/27.55 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.92/27.55 (7) ~ (e2 = e0)
% 157.92/27.55 (8) op(e2, e3) = e2
% 157.92/27.55 (9) ~ (e3 = e1)
% 157.92/27.55 (10) ~ (e2 = e1)
% 157.92/27.55 (11) ~ (e1 = e0)
% 157.92/27.55 (12) all_58_14 = e2 & op(e0, e1) = e2
% 157.92/27.55 (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.55 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.55 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.55 (15) ~ (e3 = e2)
% 157.92/27.55
% 157.92/27.55 Begin of proof
% 157.92/27.55 |
% 157.92/27.55 | ALPHA: (12) implies:
% 157.92/27.55 | (16) all_58_14 = e2
% 157.92/27.55 |
% 157.92/27.55 | COMBINE_EQS: (1), (16) imply:
% 157.92/27.55 | (17) e3 = e2
% 157.92/27.55 |
% 157.92/27.55 | SIMP: (17) implies:
% 157.92/27.55 | (18) e3 = e2
% 157.92/27.55 |
% 157.92/27.55 | COMBINE_EQS: (2), (18) imply:
% 157.92/27.55 | (19) all_58_12 = e2
% 157.92/27.55 |
% 157.92/27.55 | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 157.92/27.55 | (19) are inconsistent by sub-proof #1062.
% 157.92/27.55 |
% 157.92/27.55 End of proof
% 157.92/27.55
% 157.92/27.55 Sub-proof #428 shows that the following formulas are inconsistent:
% 157.92/27.55 ----------------------------------------------------------------
% 157.92/27.55 (1) all_58_12 = e3
% 157.92/27.55 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.92/27.55 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.92/27.55 (3) op(e2, e3) = all_52_1
% 157.92/27.55 (4) ~ (e3 = e0)
% 157.92/27.55 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.92/27.55 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.92/27.55 (6) ~ (e2 = e0)
% 157.92/27.55 (7) op(e2, e3) = e2
% 157.92/27.55 (8) ~ (e3 = e1)
% 157.92/27.55 (9) ~ (e2 = e1)
% 157.92/27.55 (10) ~ (e1 = e0)
% 157.92/27.55 (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.55 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.55 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.55 (13) ~ (e3 = e2)
% 157.92/27.55 (14) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.55 (15) all_58_11 = e3
% 157.92/27.55
% 157.92/27.55 Begin of proof
% 157.92/27.55 |
% 157.92/27.55 | ALPHA: (14) implies:
% 157.92/27.55 | (16) all_58_11 = e2
% 157.92/27.55 |
% 157.92/27.55 | COMBINE_EQS: (15), (16) imply:
% 157.92/27.55 | (17) e3 = e2
% 157.92/27.55 |
% 157.92/27.55 | SIMP: (17) implies:
% 157.92/27.55 | (18) e3 = e2
% 157.92/27.55 |
% 157.92/27.55 | COMBINE_EQS: (1), (18) imply:
% 157.92/27.55 | (19) all_58_12 = e2
% 157.92/27.55 |
% 157.92/27.55 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 157.92/27.55 | (19) are inconsistent by sub-proof #1062.
% 157.92/27.55 |
% 157.92/27.55 End of proof
% 157.92/27.55
% 157.92/27.55 Sub-proof #429 shows that the following formulas are inconsistent:
% 157.92/27.55 ----------------------------------------------------------------
% 157.92/27.55 (1) op(e1, e1) = e3
% 157.92/27.55 (2) op(e1, e1) = all_32_1
% 157.92/27.55 (3) all_56_14 = e3
% 157.92/27.55 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.92/27.55 (5) op(e3, e1) = e3
% 157.92/27.55 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.92/27.55 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.92/27.55 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.55 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.55 (8) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.55 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.92/27.55 (9) all_58_14 = e3
% 157.92/27.55 (10) all_54_13 = all_52_7
% 157.92/27.55 (11) op(e1, e1) = all_6_2
% 157.92/27.55 (12) ~ (all_52_7 = e3)
% 157.92/27.55 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.55 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.92/27.55 e1)
% 157.92/27.55 (14) ~ (all_52_11 = e3)
% 157.92/27.55 (15) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.92/27.55 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 157.92/27.55 (17) ~ (all_52_7 = all_52_11)
% 157.92/27.55 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.92/27.55 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.92/27.55 (19) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.92/27.55 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.92/27.56 (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.92/27.56 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.92/27.56 (21) op(e2, e3) = all_52_1
% 157.92/27.56 (22) ~ (all_52_13 = e3)
% 157.92/27.56 (23) all_54_2 = all_52_8
% 157.92/27.56 (24) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.92/27.56 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.92/27.56 (25) ~ (all_52_8 = all_52_9)
% 157.92/27.56 (26) ~ (e3 = e0)
% 157.92/27.56 (27) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.92/27.56 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.92/27.56 (28) ~ (all_52_9 = all_52_13)
% 157.92/27.56 (29) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 157.92/27.56 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 157.92/27.56 e2)
% 157.92/27.56 (30) ~ (e2 = e0)
% 157.92/27.56 (31) ~ (all_52_9 = e3)
% 157.92/27.56 (32) op(e2, e3) = e2
% 157.92/27.56 (33) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.56 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.92/27.56 (34) ~ (e3 = e1)
% 157.92/27.56 (35) all_56_12 = e1
% 157.92/27.56 (36) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.92/27.56 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.92/27.56 (37) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.92/27.56 (38) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.56 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.92/27.56 (39) all_54_7 = all_52_13
% 157.92/27.56 (40) ~ (all_52_13 = e2)
% 157.92/27.56 (41) all_56_15 = all_4_2
% 157.92/27.56 (42) ~ (all_52_9 = all_52_11)
% 157.92/27.56 (43) ~ (all_52_13 = all_4_2)
% 157.92/27.56 (44) all_54_6 = all_52_9
% 157.92/27.56 (45) ~ (e2 = e1)
% 157.92/27.56 (46) ~ (all_52_8 = all_52_11)
% 157.92/27.56 (47) ~ (e1 = e0)
% 157.92/27.56 (48) all_58_3 = e3
% 157.92/27.56 (49) op(e3, e1) = all_52_8
% 157.92/27.56 (50) ~ (all_6_2 = e2)
% 157.92/27.56 (51) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.92/27.56 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.92/27.56 e3)
% 157.92/27.56 (52) all_56_13 = e3
% 157.92/27.56 (53) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.92/27.56 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.92/27.56 (54) ~ (all_52_9 = e2)
% 157.92/27.56 (55) ~ (all_52_8 = e3)
% 157.92/27.56 (56) all_54_14 = all_52_11
% 157.92/27.56 (57) ~ (all_52_7 = all_4_2)
% 157.92/27.56 (58) op(e1, e0) = e3
% 157.92/27.56 (59) op(e0, e2) = all_52_7
% 157.92/27.56 (60) ~ (all_52_8 = e1)
% 157.92/27.56 (61) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.92/27.56 (62) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.56 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.56 (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.56 (64) ~ (e3 = e2)
% 157.92/27.56 (65) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.92/27.56 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.56 (66) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.56 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.92/27.56 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.56 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.92/27.56 (67) all_58_11 = e3
% 157.92/27.56 (68) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.92/27.56 (69) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.92/27.56
% 157.92/27.56 Begin of proof
% 157.92/27.56 |
% 157.92/27.56 | BETA: splitting (16) gives:
% 157.92/27.56 |
% 157.92/27.56 | Case 1:
% 157.92/27.56 | |
% 157.92/27.56 | | (70) all_58_0 = e3 & op(e3, e3) = e3
% 157.92/27.56 | |
% 157.92/27.56 | | ALPHA: (70) implies:
% 157.92/27.56 | | (71) all_58_0 = e3
% 157.92/27.56 | |
% 157.92/27.56 | | BETA: splitting (53) gives:
% 157.92/27.56 | |
% 157.92/27.56 | | Case 1:
% 157.92/27.56 | | |
% 157.92/27.56 | | | (72) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 157.92/27.56 | | | e1)
% 157.92/27.56 | | |
% 157.92/27.56 | | | BETA: splitting (72) gives:
% 157.92/27.56 | | |
% 157.92/27.56 | | | Case 1:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | (73) all_58_0 = e1 & op(e3, e3) = e1
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | REF_CLOSE: (34), (71), (73) are inconsistent by sub-proof #1487.
% 157.92/27.56 | | | |
% 157.92/27.56 | | | Case 2:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | (74) all_58_1 = e1 & op(e3, e2) = e1
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | ALPHA: (74) implies:
% 157.92/27.56 | | | | (75) all_58_1 = e1
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | BETA: splitting (20) gives:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | Case 1:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | (76) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 157.92/27.56 | | | | | e0) = e2)
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | BETA: splitting (76) gives:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | Case 1:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | (77) all_58_9 = e2 & op(e3, e0) = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | ALPHA: (77) implies:
% 157.92/27.56 | | | | | | (78) all_58_9 = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | BETA: splitting (29) gives:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | Case 1:
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | (79) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 157.92/27.56 | | | | | | | op(e0, e2) = e2)
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | BETA: splitting (79) gives:
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | (80) all_58_12 = e2 & op(e0, e3) = e2
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | ALPHA: (80) implies:
% 157.92/27.56 | | | | | | | | (81) all_58_12 = e2
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | REF_CLOSE: (18), (21), (26), (27), (30), (32), (34), (45), (47),
% 157.92/27.56 | | | | | | | | (62), (63), (64), (81) are inconsistent by sub-proof
% 157.92/27.56 | | | | | | | | #1062.
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | (82) all_58_13 = e2 & op(e0, e2) = e2
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | ALPHA: (82) implies:
% 157.92/27.56 | | | | | | | | (83) all_58_13 = e2
% 157.92/27.56 | | | | | | | | (84) op(e0, e2) = e2
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | REF_CLOSE: (7), (8), (9), (11), (18), (19), (21), (24), (26),
% 157.92/27.56 | | | | | | | | (27), (30), (32), (33), (34), (38), (45), (47), (48),
% 157.92/27.56 | | | | | | | | (50), (59), (62), (63), (64), (65), (67), (71), (75),
% 157.92/27.56 | | | | | | | | (78), (83), (84) are inconsistent by sub-proof #851.
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | End of split
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | Case 2:
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | (85) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 157.92/27.56 | | | | | | | op(e0, e0) = e2)
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | BETA: splitting (85) gives:
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | (86) all_58_14 = e2 & op(e0, e1) = e2
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | REF_CLOSE: (9), (64), (86) are inconsistent by sub-proof #1439.
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | (87) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | REF_CLOSE: (3), (4), (8), (9), (10), (11), (12), (13), (14),
% 157.92/27.56 | | | | | | | | (15), (17), (18), (19), (21), (22), (23), (24), (25),
% 157.92/27.56 | | | | | | | | (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 157.92/27.56 | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 157.92/27.56 | | | | | | | | (46), (47), (48), (50), (51), (52), (54), (55), (56),
% 157.92/27.56 | | | | | | | | (57), (59), (60), (61), (62), (63), (64), (66), (67),
% 157.92/27.56 | | | | | | | | (68), (69), (75), (87) are inconsistent by sub-proof
% 157.92/27.56 | | | | | | | | #437.
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | End of split
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | End of split
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | Case 2:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | (88) all_58_10 = e2 & op(e2, e0) = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | ALPHA: (88) implies:
% 157.92/27.56 | | | | | | (89) all_58_10 = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | REF_CLOSE: (8), (26), (30), (32), (34), (38), (45), (47), (48),
% 157.92/27.56 | | | | | | (63), (89) are inconsistent by sub-proof #906.
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | End of split
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | Case 2:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | (90) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 157.92/27.56 | | | | | e0) = e2)
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | BETA: splitting (90) gives:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | Case 1:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | (91) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | ALPHA: (91) implies:
% 157.92/27.56 | | | | | | (92) all_58_11 = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | REF_CLOSE: (64), (67), (92) are inconsistent by sub-proof #1049.
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | Case 2:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | (93) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | REF_CLOSE: (3), (4), (8), (9), (10), (11), (12), (13), (14), (15),
% 157.92/27.56 | | | | | | (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 157.92/27.56 | | | | | | (27), (28), (30), (31), (32), (33), (34), (35), (37),
% 157.92/27.56 | | | | | | (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 157.92/27.56 | | | | | | (47), (48), (50), (51), (52), (54), (55), (56), (57),
% 157.92/27.56 | | | | | | (59), (60), (61), (62), (63), (64), (66), (67), (68),
% 157.92/27.56 | | | | | | (69), (75), (93) are inconsistent by sub-proof #437.
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | End of split
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | End of split
% 157.92/27.56 | | | |
% 157.92/27.56 | | | End of split
% 157.92/27.56 | | |
% 157.92/27.56 | | Case 2:
% 157.92/27.56 | | |
% 157.92/27.56 | | | (94) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 157.92/27.56 | | | e1)
% 157.92/27.56 | | |
% 157.92/27.56 | | | BETA: splitting (94) gives:
% 157.92/27.56 | | |
% 157.92/27.56 | | | Case 1:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | (95) all_58_4 = e1 & op(e3, e1) = e1
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | ALPHA: (95) implies:
% 157.92/27.56 | | | | (96) all_58_4 = e1
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | REF_CLOSE: (8), (9), (11), (19), (26), (30), (32), (34), (38), (45),
% 157.92/27.56 | | | | (47), (48), (50), (63), (64), (96) are inconsistent by
% 157.92/27.56 | | | | sub-proof #850.
% 157.92/27.56 | | | |
% 157.92/27.56 | | | Case 2:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | (97) all_58_9 = e1 & op(e3, e0) = e1
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | ALPHA: (97) implies:
% 157.92/27.56 | | | | (98) all_58_9 = e1
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | BETA: splitting (20) gives:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | Case 1:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | (99) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 157.92/27.56 | | | | | e0) = e2)
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | REF_CLOSE: (8), (26), (30), (32), (34), (38), (45), (47), (48), (63),
% 157.92/27.56 | | | | | (98), (99) are inconsistent by sub-proof #693.
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | Case 2:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | (100) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 157.92/27.56 | | | | | e0) = e2)
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | BETA: splitting (100) gives:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | Case 1:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | (101) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | ALPHA: (101) implies:
% 157.92/27.56 | | | | | | (102) all_58_11 = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | REF_CLOSE: (64), (67), (102) are inconsistent by sub-proof #1049.
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | Case 2:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | (103) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | ALPHA: (103) implies:
% 157.92/27.56 | | | | | | (104) all_58_15 = e2
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | BETA: splitting (66) gives:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | Case 1:
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | (105) all_58_15 = e0 & op(e0, e0) = e0
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | REF_CLOSE: (30), (104), (105) are inconsistent by sub-proof #885.
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | Case 2:
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | (106) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 157.92/27.56 | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 157.92/27.56 | | | | | | | e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 157.92/27.56 | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 157.92/27.56 | | | | | | | op(e0, e1) = e0))
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | ALPHA: (106) implies:
% 157.92/27.56 | | | | | | | (107) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 157.92/27.56 | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 157.92/27.56 | | | | | | | (12), (13), (14), (15), (18), (19), (20), (21), (22),
% 157.92/27.56 | | | | | | | (23), (24), (25), (26), (27), (28), (30), (31), (32),
% 157.92/27.56 | | | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 157.92/27.56 | | | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 157.92/27.56 | | | | | | | (51), (52), (53), (54), (55), (56), (58), (59), (60),
% 157.92/27.56 | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69), (71),
% 157.92/27.56 | | | | | | | (98), (107) are inconsistent by sub-proof #430.
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | End of split
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | End of split
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | End of split
% 157.92/27.56 | | | |
% 157.92/27.56 | | | End of split
% 157.92/27.56 | | |
% 157.92/27.56 | | End of split
% 157.92/27.56 | |
% 157.92/27.56 | Case 2:
% 157.92/27.56 | |
% 157.92/27.56 | | (108) all_58_2 = e3 & op(e2, e3) = e3
% 157.92/27.56 | |
% 157.92/27.56 | | ALPHA: (108) implies:
% 157.92/27.56 | | (109) op(e2, e3) = e3
% 157.92/27.56 | |
% 157.92/27.56 | | REF_CLOSE: (21), (32), (63), (64), (109) are inconsistent by sub-proof
% 157.92/27.56 | | #1159.
% 157.92/27.56 | |
% 157.92/27.56 | End of split
% 157.92/27.56 |
% 157.92/27.56 End of proof
% 157.92/27.56
% 157.92/27.56 Sub-proof #430 shows that the following formulas are inconsistent:
% 157.92/27.56 ----------------------------------------------------------------
% 157.92/27.56 (1) op(e1, e1) = e3
% 157.92/27.56 (2) op(e1, e1) = all_32_1
% 157.92/27.56 (3) all_56_14 = e3
% 157.92/27.56 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.92/27.56 (5) op(e3, e1) = e3
% 157.92/27.56 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.92/27.56 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.92/27.56 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.56 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.56 (8) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.56 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.92/27.56 (9) all_58_14 = e3
% 157.92/27.56 (10) op(e1, e1) = all_6_2
% 157.92/27.56 (11) ~ (all_52_7 = e3)
% 157.92/27.56 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.56 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.92/27.56 e1)
% 157.92/27.56 (13) ~ (all_52_11 = e3)
% 157.92/27.56 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.92/27.56 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.92/27.56 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.92/27.56 (16) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.92/27.56 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.92/27.56 (17) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 157.92/27.56 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 157.92/27.56 (18) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 157.92/27.56 (all_58_11 = e0 & op(e1, e0) = e0)
% 157.92/27.56 (19) op(e2, e3) = all_52_1
% 157.92/27.56 (20) ~ (all_52_13 = e3)
% 157.92/27.56 (21) all_54_2 = all_52_8
% 157.92/27.56 (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.92/27.56 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.92/27.56 (23) ~ (all_52_8 = all_52_9)
% 157.92/27.56 (24) ~ (e3 = e0)
% 157.92/27.56 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.92/27.56 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.92/27.56 (26) ~ (all_52_9 = all_52_13)
% 157.92/27.56 (27) ~ (e2 = e0)
% 157.92/27.56 (28) ~ (all_52_9 = e3)
% 157.92/27.56 (29) op(e2, e3) = e2
% 157.92/27.56 (30) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.56 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.92/27.56 (31) ~ (e3 = e1)
% 157.92/27.56 (32) all_56_12 = e1
% 157.92/27.56 (33) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 157.92/27.56 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 157.92/27.56 (34) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.92/27.56 (35) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.56 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.92/27.56 (36) all_54_7 = all_52_13
% 157.92/27.56 (37) ~ (all_52_13 = e2)
% 157.92/27.56 (38) all_56_15 = all_4_2
% 157.92/27.56 (39) ~ (all_52_9 = all_52_11)
% 157.92/27.56 (40) ~ (all_52_13 = all_4_2)
% 157.92/27.56 (41) all_58_0 = e3
% 157.92/27.56 (42) all_54_6 = all_52_9
% 157.92/27.56 (43) ~ (e2 = e1)
% 157.92/27.56 (44) ~ (all_52_8 = all_52_11)
% 157.92/27.56 (45) ~ (e1 = e0)
% 157.92/27.56 (46) all_58_3 = e3
% 157.92/27.56 (47) all_58_9 = e1
% 157.92/27.56 (48) op(e3, e1) = all_52_8
% 157.92/27.56 (49) ~ (all_6_2 = e2)
% 157.92/27.56 (50) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.92/27.56 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.92/27.56 e3)
% 157.92/27.56 (51) all_56_13 = e3
% 157.92/27.56 (52) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 157.92/27.56 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 157.92/27.56 (53) ~ (all_52_9 = e2)
% 157.92/27.56 (54) ~ (all_52_8 = e3)
% 157.92/27.56 (55) all_54_14 = all_52_11
% 157.92/27.56 (56) op(e1, e0) = e3
% 157.92/27.56 (57) op(e0, e2) = all_52_7
% 157.92/27.56 (58) ~ (all_52_8 = e1)
% 157.92/27.56 (59) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.56 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.56 (60) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.56 (61) ~ (e3 = e2)
% 157.92/27.56 (62) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 157.92/27.56 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.56 (63) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.56 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.92/27.56 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.56 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.92/27.56 (64) all_58_11 = e3
% 157.92/27.56 (65) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.92/27.56 (66) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.92/27.56
% 157.92/27.56 Begin of proof
% 157.92/27.56 |
% 157.92/27.56 | BETA: splitting (18) gives:
% 157.92/27.56 |
% 157.92/27.56 | Case 1:
% 157.92/27.56 | |
% 157.92/27.56 | | (67) all_58_9 = e0 & op(e3, e0) = e0
% 157.92/27.56 | |
% 157.92/27.56 | | REF_CLOSE: (45), (47), (67) are inconsistent by sub-proof #1202.
% 157.92/27.56 | |
% 157.92/27.56 | Case 2:
% 157.92/27.56 | |
% 157.92/27.56 | | (68) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 157.92/27.56 | | e0)
% 157.92/27.56 | |
% 157.92/27.56 | | BETA: splitting (68) gives:
% 157.92/27.56 | |
% 157.92/27.56 | | Case 1:
% 157.92/27.56 | | |
% 157.92/27.56 | | | (69) all_58_10 = e0 & op(e2, e0) = e0
% 157.92/27.56 | | |
% 157.92/27.56 | | | ALPHA: (69) implies:
% 157.92/27.56 | | | (70) all_58_10 = e0
% 157.92/27.56 | | |
% 157.92/27.56 | | | BETA: splitting (8) gives:
% 157.92/27.56 | | |
% 157.92/27.56 | | | Case 1:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | (71) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 157.92/27.56 | | | | = e1)
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | REF_CLOSE: (29), (31), (43), (46), (60), (71) are inconsistent by
% 157.92/27.56 | | | | sub-proof #840.
% 157.92/27.56 | | | |
% 157.92/27.56 | | | Case 2:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | (72) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 157.92/27.56 | | | | = e1)
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | BETA: splitting (72) gives:
% 157.92/27.56 | | | |
% 157.92/27.56 | | | | Case 1:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | (73) all_58_5 = e1 & op(e2, e1) = e1
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | ALPHA: (73) implies:
% 157.92/27.56 | | | | | (74) all_58_5 = e1
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | BETA: splitting (33) gives:
% 157.92/27.56 | | | | |
% 157.92/27.56 | | | | | Case 1:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | (75) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 157.92/27.56 | | | | | | e1) = e0)
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | REF_CLOSE: (8), (9), (10), (16), (24), (27), (29), (31), (35), (43),
% 157.92/27.56 | | | | | | (45), (46), (49), (60), (61), (74), (75) are inconsistent
% 157.92/27.56 | | | | | | by sub-proof #652.
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | Case 2:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | (76) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 157.92/27.56 | | | | | | e1) = e0)
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | BETA: splitting (76) gives:
% 157.92/27.56 | | | | | |
% 157.92/27.56 | | | | | | Case 1:
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | (77) all_58_8 = e0 & op(e1, e1) = e0
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | ALPHA: (77) implies:
% 157.92/27.56 | | | | | | | (78) all_58_8 = e0
% 157.92/27.56 | | | | | | | (79) op(e1, e1) = e0
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | BETA: splitting (22) gives:
% 157.92/27.56 | | | | | | |
% 157.92/27.56 | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | (80) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 157.92/27.56 | | | | | | | | op(e1, e2) = e2)
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | BETA: splitting (80) gives:
% 157.92/27.56 | | | | | | | |
% 157.92/27.56 | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | |
% 157.92/27.56 | | | | | | | | | (81) all_58_6 = e2 & op(e1, e3) = e2
% 157.92/27.56 | | | | | | | | |
% 157.92/27.56 | | | | | | | | | ALPHA: (81) implies:
% 157.92/27.56 | | | | | | | | | (82) all_58_6 = e2
% 157.92/27.56 | | | | | | | | |
% 157.92/27.56 | | | | | | | | | REF_CLOSE: (15), (19), (24), (25), (27), (29), (31), (43),
% 157.92/27.56 | | | | | | | | | (45), (59), (60), (61), (82) are inconsistent by
% 157.92/27.56 | | | | | | | | | sub-proof #1152.
% 157.92/27.56 | | | | | | | | |
% 157.92/27.56 | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | |
% 157.92/27.56 | | | | | | | | | (83) all_58_7 = e2 & op(e1, e2) = e2
% 157.92/27.56 | | | | | | | | |
% 157.92/27.56 | | | | | | | | | ALPHA: (83) implies:
% 157.92/27.56 | | | | | | | | | (84) all_58_7 = e2
% 157.92/27.56 | | | | | | | | |
% 157.92/27.56 | | | | | | | | | BETA: splitting (66) gives:
% 157.92/27.56 | | | | | | | | |
% 157.92/27.56 | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | (85) all_56_12 = e3
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | COMBINE_EQS: (32), (85) imply:
% 157.92/27.56 | | | | | | | | | | (86) e3 = e1
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | REDUCE: (31), (86) imply:
% 157.92/27.56 | | | | | | | | | | (87) $false
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | CLOSE: (87) is inconsistent.
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | (88) ~ (all_56_12 = e3)
% 157.92/27.56 | | | | | | | | | | (89) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | REDUCE: (32), (88) imply:
% 157.92/27.56 | | | | | | | | | | (90) ~ (e3 = e1)
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | BETA: splitting (17) gives:
% 157.92/27.56 | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | (91) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 157.92/27.56 | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 157.92/27.56 | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | BETA: splitting (91) gives:
% 157.92/27.56 | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | (92) all_58_9 = e2 & op(e3, e0) = e2
% 157.92/27.56 | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | ALPHA: (92) implies:
% 157.92/27.56 | | | | | | | | | | | | (93) all_58_9 = e2
% 157.92/27.56 | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | BETA: splitting (52) gives:
% 157.92/27.56 | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | (94) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 157.92/27.56 | | | | | | | | | | | | | & op(e3, e2) = e1)
% 157.92/27.56 | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | BETA: splitting (94) gives:
% 157.92/27.56 | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | (95) all_58_0 = e1 & op(e3, e3) = e1
% 157.92/27.56 | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | REF_CLOSE: (31), (41), (95) are inconsistent by sub-proof
% 157.92/27.56 | | | | | | | | | | | | | | #1487.
% 157.92/27.56 | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | (96) all_58_1 = e1 & op(e3, e2) = e1
% 157.92/27.56 | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | ALPHA: (96) implies:
% 157.92/27.56 | | | | | | | | | | | | | | (97) all_58_1 = e1
% 157.92/27.56 | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 157.92/27.56 | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | (98) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 157.92/27.56 | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 157.92/27.56 | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 157.92/27.56 | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | (99) all_58_1 = e0 & op(e3, e2) = e0
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (97), (99) are inconsistent by sub-proof
% 157.92/27.56 | | | | | | | | | | | | | | | | #1327.
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | (100) all_58_3 = e0 & op(e2, e2) = e0
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | REF_CLOSE: (24), (46), (100) are inconsistent by sub-proof
% 157.92/27.56 | | | | | | | | | | | | | | | | #910.
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | End of split
% 157.92/27.56 | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | (101) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 157.92/27.56 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 157.92/27.56 | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 157.92/27.56 | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | (102) all_58_7 = e0 & op(e1, e2) = e0
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 157.92/27.56 | | | | | | | | | | | | | | | | (103) all_58_7 = e0
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (84), (103) are inconsistent by sub-proof
% 157.92/27.56 | | | | | | | | | | | | | | | | #1086.
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | (104) all_58_13 = e0 & op(e0, e2) = e0
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 157.92/27.56 | | | | | | | | | | | | | | | | (105) all_58_13 = e0
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 157.92/27.56 | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (16), (24), (27), (29), (31),
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (35), (41), (43), (45), (46), (49), (60), (61),
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (62), (84), (93), (105) are inconsistent by
% 157.92/27.56 | | | | | | | | | | | | | | | | | | sub-proof #853.
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (106) all_58_10 = e2 & op(e2, e0) = e2
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (107) all_58_10 = e2
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (29), (35), (45), (46), (60), (74),
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (107) are inconsistent by sub-proof #907.
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | End of split
% 157.92/27.56 | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | (108) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.92/27.56 | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.92/27.56 | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 157.92/27.56 | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | Case 1:
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (109) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (109) are inconsistent by sub-proof
% 157.92/27.56 | | | | | | | | | | | | | | | | | | #852.
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (110) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (111) op(e0, e0) = e2
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (12), (24), (27), (29), (31), (41),
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (43), (45), (46), (56), (59), (60), (78), (84),
% 157.92/27.56 | | | | | | | | | | | | | | | | | | (97), (105), (111) are inconsistent by sub-proof
% 157.92/27.56 | | | | | | | | | | | | | | | | | | #433.
% 157.92/27.56 | | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | | End of split
% 157.92/27.56 | | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | | End of split
% 157.92/27.56 | | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | | End of split
% 157.92/27.56 | | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | | End of split
% 157.92/27.56 | | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | End of split
% 157.92/27.56 | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | (112) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 157.92/27.56 | | | | | | | | | | | | | & op(e3, e0) = e1)
% 157.92/27.56 | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10), (16), (24), (27), (29), (31),
% 157.92/27.56 | | | | | | | | | | | | | (35), (43), (45), (46), (49), (60), (61), (93),
% 157.92/27.56 | | | | | | | | | | | | | (112) are inconsistent by sub-proof #555.
% 157.92/27.56 | | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | End of split
% 157.92/27.56 | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | Case 2:
% 157.92/27.56 | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | (113) all_58_10 = e2 & op(e2, e0) = e2
% 157.92/27.56 | | | | | | | | | | | |
% 157.92/27.56 | | | | | | | | | | | | ALPHA: (113) implies:
% 157.92/27.57 | | | | | | | | | | | | (114) all_58_10 = e2
% 157.92/27.57 | | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | | REF_CLOSE: (24), (27), (29), (35), (45), (46), (60), (74),
% 157.92/27.57 | | | | | | | | | | | | (114) are inconsistent by sub-proof #907.
% 157.92/27.57 | | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | End of split
% 157.92/27.57 | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | Case 2:
% 157.92/27.57 | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | (115) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 157.92/27.57 | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 157.92/27.57 | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | BETA: splitting (115) gives:
% 157.92/27.57 | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | Case 1:
% 157.92/27.57 | | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | | (116) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.57 | | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | | REF_CLOSE: (61), (64), (116) are inconsistent by sub-proof
% 157.92/27.57 | | | | | | | | | | | | #852.
% 157.92/27.57 | | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | Case 2:
% 157.92/27.57 | | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | | (117) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.57 | | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11),
% 157.92/27.57 | | | | | | | | | | | | (12), (13), (14), (16), (20), (21), (23), (24),
% 157.92/27.57 | | | | | | | | | | | | (26), (27), (28), (29), (31), (34), (35), (36),
% 157.92/27.57 | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 157.92/27.57 | | | | | | | | | | | | (46), (48), (49), (50), (51), (53), (54), (55),
% 157.92/27.57 | | | | | | | | | | | | (57), (58), (60), (61), (63), (65), (79), (89),
% 157.92/27.57 | | | | | | | | | | | | (117) are inconsistent by sub-proof #432.
% 157.92/27.57 | | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | | End of split
% 157.92/27.57 | | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | End of split
% 157.92/27.57 | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | End of split
% 157.92/27.57 | | | | | | | | |
% 157.92/27.57 | | | | | | | | End of split
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | Case 2:
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | (118) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 157.92/27.57 | | | | | | | | op(e1, e0) = e2)
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | REF_CLOSE: (10), (49), (60), (61), (64), (118) are inconsistent
% 157.92/27.57 | | | | | | | | by sub-proof #431.
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | End of split
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | Case 2:
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | | (119) all_58_14 = e0 & op(e0, e1) = e0
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | | ALPHA: (119) implies:
% 157.92/27.57 | | | | | | | (120) all_58_14 = e0
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | | REF_CLOSE: (9), (24), (120) are inconsistent by sub-proof #1444.
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | End of split
% 157.92/27.57 | | | | | |
% 157.92/27.57 | | | | | End of split
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | Case 2:
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | (121) all_58_10 = e1 & op(e2, e0) = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | REF_CLOSE: (45), (70), (121) are inconsistent by sub-proof #1373.
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | End of split
% 157.92/27.57 | | | |
% 157.92/27.57 | | | End of split
% 157.92/27.57 | | |
% 157.92/27.57 | | Case 2:
% 157.92/27.57 | | |
% 157.92/27.57 | | | (122) all_58_11 = e0 & op(e1, e0) = e0
% 157.92/27.57 | | |
% 157.92/27.57 | | | ALPHA: (122) implies:
% 157.92/27.57 | | | (123) all_58_11 = e0
% 157.92/27.57 | | |
% 157.92/27.57 | | | REF_CLOSE: (24), (64), (123) are inconsistent by sub-proof #1216.
% 157.92/27.57 | | |
% 157.92/27.57 | | End of split
% 157.92/27.57 | |
% 157.92/27.57 | End of split
% 157.92/27.57 |
% 157.92/27.57 End of proof
% 157.92/27.57
% 157.92/27.57 Sub-proof #431 shows that the following formulas are inconsistent:
% 157.92/27.57 ----------------------------------------------------------------
% 157.92/27.57 (1) op(e1, e1) = all_6_2
% 157.92/27.57 (2) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.92/27.57 (3) ~ (all_6_2 = e2)
% 157.92/27.57 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.57 (5) ~ (e3 = e2)
% 157.92/27.57 (6) all_58_11 = e3
% 157.92/27.57
% 157.92/27.57 Begin of proof
% 157.92/27.57 |
% 157.92/27.57 | BETA: splitting (2) gives:
% 157.92/27.57 |
% 157.92/27.57 | Case 1:
% 157.92/27.57 | |
% 157.92/27.57 | | (7) all_58_8 = e2 & op(e1, e1) = e2
% 157.92/27.57 | |
% 157.92/27.57 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #1440.
% 157.92/27.57 | |
% 157.92/27.57 | Case 2:
% 157.92/27.57 | |
% 157.92/27.57 | | (8) all_58_11 = e2 & op(e1, e0) = e2
% 157.92/27.57 | |
% 157.92/27.57 | | ALPHA: (8) implies:
% 157.92/27.57 | | (9) all_58_11 = e2
% 157.92/27.57 | |
% 157.92/27.57 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #1049.
% 157.92/27.57 | |
% 157.92/27.57 | End of split
% 157.92/27.57 |
% 157.92/27.57 End of proof
% 157.92/27.57
% 157.92/27.57 Sub-proof #432 shows that the following formulas are inconsistent:
% 157.92/27.57 ----------------------------------------------------------------
% 157.92/27.57 (1) op(e1, e1) = e3
% 157.92/27.57 (2) op(e1, e1) = all_32_1
% 157.92/27.57 (3) all_56_14 = e3
% 157.92/27.57 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.92/27.57 (5) op(e3, e1) = e3
% 157.92/27.57 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.57 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.92/27.57 (7) all_58_14 = e3
% 157.92/27.57 (8) op(e1, e1) = all_6_2
% 157.92/27.57 (9) ~ (all_52_7 = e3)
% 157.92/27.57 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.57 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.92/27.57 e1)
% 157.92/27.57 (11) ~ (all_52_11 = e3)
% 157.92/27.57 (12) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.92/27.57 (13) op(e1, e1) = e0
% 157.92/27.57 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.92/27.57 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.92/27.57 (15) ~ (all_52_13 = e3)
% 157.92/27.57 (16) all_54_2 = all_52_8
% 157.92/27.57 (17) ~ (all_52_8 = all_52_9)
% 157.92/27.57 (18) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.92/27.57 (19) ~ (e3 = e0)
% 157.92/27.57 (20) ~ (all_52_9 = all_52_13)
% 157.92/27.57 (21) ~ (e2 = e0)
% 157.92/27.57 (22) ~ (all_52_9 = e3)
% 157.92/27.57 (23) op(e2, e3) = e2
% 157.92/27.57 (24) ~ (e3 = e1)
% 157.92/27.57 (25) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.92/27.57 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.92/27.57 (27) all_54_7 = all_52_13
% 157.92/27.57 (28) ~ (all_52_13 = e2)
% 157.92/27.57 (29) all_56_15 = all_4_2
% 157.92/27.57 (30) ~ (all_52_9 = all_52_11)
% 157.92/27.57 (31) ~ (all_52_13 = all_4_2)
% 157.92/27.57 (32) all_54_6 = all_52_9
% 157.92/27.57 (33) ~ (e2 = e1)
% 157.92/27.57 (34) ~ (all_52_8 = all_52_11)
% 157.92/27.57 (35) ~ (e1 = e0)
% 157.92/27.57 (36) all_58_3 = e3
% 157.92/27.57 (37) op(e3, e1) = all_52_8
% 157.92/27.57 (38) ~ (all_6_2 = e2)
% 157.92/27.57 (39) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.92/27.57 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.92/27.57 e3)
% 157.92/27.57 (40) all_56_13 = e3
% 157.92/27.57 (41) ~ (all_52_9 = e2)
% 157.92/27.57 (42) ~ (all_52_8 = e3)
% 157.92/27.57 (43) all_54_14 = all_52_11
% 157.92/27.57 (44) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.57 (45) op(e0, e2) = all_52_7
% 157.92/27.57 (46) ~ (all_52_8 = e1)
% 157.92/27.57 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.57 (48) ~ (e3 = e2)
% 157.92/27.57 (49) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.57 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.92/27.57 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.57 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.92/27.57 (50) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.92/27.57
% 157.92/27.57 Begin of proof
% 157.92/27.57 |
% 157.92/27.57 | ALPHA: (44) implies:
% 157.92/27.57 | (51) all_58_15 = e2
% 157.92/27.57 | (52) op(e0, e0) = e2
% 157.92/27.57 |
% 157.92/27.57 | BETA: splitting (14) gives:
% 157.92/27.57 |
% 157.92/27.57 | Case 1:
% 157.92/27.57 | |
% 157.92/27.57 | | (53) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 157.92/27.57 | | e2)
% 157.92/27.57 | |
% 157.92/27.57 | | BETA: splitting (53) gives:
% 157.92/27.57 | |
% 157.92/27.57 | | Case 1:
% 157.92/27.57 | | |
% 157.92/27.57 | | | (54) all_58_4 = e2 & op(e3, e1) = e2
% 157.92/27.57 | | |
% 157.92/27.57 | | | ALPHA: (54) implies:
% 157.92/27.57 | | | (55) all_58_4 = e2
% 157.92/27.57 | | |
% 157.92/27.57 | | | BETA: splitting (18) gives:
% 157.92/27.57 | | |
% 157.92/27.57 | | | Case 1:
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | (56) all_56_13 = e2
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | COMBINE_EQS: (40), (56) imply:
% 157.92/27.57 | | | | (57) e3 = e2
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | COMBINE_EQS: (7), (57) imply:
% 157.92/27.57 | | | | (58) all_58_14 = e2
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | REF_CLOSE: (9), (10), (19), (21), (24), (33), (35), (39), (45), (47),
% 157.92/27.57 | | | | (48), (49), (51), (52), (58) are inconsistent by sub-proof
% 157.92/27.57 | | | | #1380.
% 157.92/27.57 | | | |
% 157.92/27.57 | | | Case 2:
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | (59) all_56_14 = e1 | all_56_15 = e0
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | BETA: splitting (59) gives:
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | Case 1:
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | (60) all_56_14 = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | COMBINE_EQS: (3), (60) imply:
% 157.92/27.57 | | | | | (61) e3 = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | REDUCE: (24), (61) imply:
% 157.92/27.57 | | | | | (62) $false
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | CLOSE: (62) is inconsistent.
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | Case 2:
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | (63) all_56_15 = e0
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | COMBINE_EQS: (29), (63) imply:
% 157.92/27.57 | | | | | (64) all_4_2 = e0
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | REDUCE: (31), (64) imply:
% 157.92/27.57 | | | | | (65) ~ (all_52_13 = e0)
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | BETA: splitting (12) gives:
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | Case 1:
% 157.92/27.57 | | | | | |
% 157.92/27.57 | | | | | | (66) all_54_7 = e3
% 157.92/27.57 | | | | | |
% 157.92/27.57 | | | | | | REF_CLOSE: (15), (27), (66) are inconsistent by sub-proof #1428.
% 157.92/27.57 | | | | | |
% 157.92/27.57 | | | | | Case 2:
% 157.92/27.57 | | | | | |
% 157.92/27.57 | | | | | | (67) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.92/27.57 | | | | | |
% 157.92/27.57 | | | | | | BETA: splitting (67) gives:
% 157.92/27.57 | | | | | |
% 157.92/27.57 | | | | | | Case 1:
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | | (68) all_54_7 = e2
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | | REF_CLOSE: (27), (28), (68) are inconsistent by sub-proof #1427.
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | Case 2:
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | | (69) all_54_7 = e1 | all_54_7 = e0
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | | BETA: splitting (69) gives:
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | | Case 1:
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | (70) all_54_7 = e1
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | COMBINE_EQS: (27), (70) imply:
% 157.92/27.57 | | | | | | | | (71) all_52_13 = e1
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | SIMP: (71) implies:
% 157.92/27.57 | | | | | | | | (72) all_52_13 = e1
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | REDUCE: (20), (72) imply:
% 157.92/27.57 | | | | | | | | (73) ~ (all_52_9 = e1)
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | BETA: splitting (4) gives:
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | Case 1:
% 157.92/27.57 | | | | | | | | |
% 157.92/27.57 | | | | | | | | | (74) all_54_6 = e3
% 157.92/27.57 | | | | | | | | |
% 157.92/27.57 | | | | | | | | | REF_CLOSE: (22), (32), (74) are inconsistent by sub-proof
% 157.92/27.57 | | | | | | | | | #1193.
% 157.92/27.57 | | | | | | | | |
% 157.92/27.57 | | | | | | | | Case 2:
% 157.92/27.57 | | | | | | | | |
% 157.92/27.57 | | | | | | | | | (75) ~ (all_54_6 = e3)
% 157.92/27.57 | | | | | | | | | (76) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.92/27.57 | | | | | | | | |
% 157.92/27.57 | | | | | | | | | BETA: splitting (76) gives:
% 157.92/27.57 | | | | | | | | |
% 157.92/27.57 | | | | | | | | | Case 1:
% 157.92/27.57 | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | (77) all_54_6 = e2
% 157.92/27.57 | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | REF_CLOSE: (32), (41), (77) are inconsistent by sub-proof
% 157.92/27.57 | | | | | | | | | | #1192.
% 157.92/27.57 | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | Case 2:
% 157.92/27.57 | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | (78) all_54_6 = e1 | all_54_6 = e0
% 157.92/27.57 | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (11), (13), (14),
% 157.92/27.57 | | | | | | | | | | (16), (17), (22), (23), (25), (26), (30), (32),
% 157.92/27.57 | | | | | | | | | | (34), (36), (37), (38), (42), (43), (46), (47),
% 157.92/27.57 | | | | | | | | | | (50), (55), (73), (78) are inconsistent by
% 157.92/27.57 | | | | | | | | | | sub-proof #455.
% 157.92/27.57 | | | | | | | | | |
% 157.92/27.57 | | | | | | | | | End of split
% 157.92/27.57 | | | | | | | | |
% 157.92/27.57 | | | | | | | | End of split
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | Case 2:
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | (79) all_54_7 = e0
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | | REF_CLOSE: (27), (65), (79) are inconsistent by sub-proof #1112.
% 157.92/27.57 | | | | | | | |
% 157.92/27.57 | | | | | | | End of split
% 157.92/27.57 | | | | | | |
% 157.92/27.57 | | | | | | End of split
% 157.92/27.57 | | | | | |
% 157.92/27.57 | | | | | End of split
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | End of split
% 157.92/27.57 | | | |
% 157.92/27.57 | | | End of split
% 157.92/27.57 | | |
% 157.92/27.57 | | Case 2:
% 157.92/27.57 | | |
% 157.92/27.57 | | | (80) all_58_5 = e2 & op(e2, e1) = e2
% 157.92/27.57 | | |
% 157.92/27.57 | | | ALPHA: (80) implies:
% 157.92/27.57 | | | (81) all_58_5 = e2
% 157.92/27.57 | | |
% 157.92/27.57 | | | REF_CLOSE: (6), (19), (21), (23), (24), (26), (33), (35), (36), (47), (81)
% 157.92/27.57 | | | are inconsistent by sub-proof #898.
% 157.92/27.57 | | |
% 157.92/27.57 | | End of split
% 157.92/27.57 | |
% 157.92/27.57 | Case 2:
% 157.92/27.57 | |
% 157.92/27.57 | | (82) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 157.92/27.57 | | e2)
% 157.92/27.57 | |
% 157.92/27.57 | | REF_CLOSE: (8), (9), (10), (19), (21), (24), (33), (35), (38), (39), (45),
% 157.92/27.57 | | (47), (48), (49), (51), (52), (82) are inconsistent by sub-proof
% 157.92/27.57 | | #891.
% 157.92/27.57 | |
% 157.92/27.57 | End of split
% 157.92/27.57 |
% 157.92/27.57 End of proof
% 157.92/27.57
% 157.92/27.57 Sub-proof #433 shows that the following formulas are inconsistent:
% 157.92/27.57 ----------------------------------------------------------------
% 157.92/27.57 (1) all_58_13 = e0
% 157.92/27.57 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 157.92/27.57 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 157.92/27.57 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.57 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.57 (4) all_58_14 = e3
% 157.92/27.57 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.92/27.57 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.92/27.57 (6) all_58_7 = e2
% 157.92/27.57 (7) ~ (e3 = e0)
% 157.92/27.57 (8) ~ (e2 = e0)
% 157.92/27.57 (9) op(e2, e3) = e2
% 157.92/27.57 (10) ~ (e3 = e1)
% 157.92/27.57 (11) all_58_1 = e1
% 157.92/27.57 (12) op(e0, e0) = e2
% 157.92/27.57 (13) all_58_0 = e3
% 157.92/27.57 (14) ~ (e2 = e1)
% 157.92/27.57 (15) ~ (e1 = e0)
% 157.92/27.57 (16) all_58_3 = e3
% 157.92/27.57 (17) op(e1, e0) = e3
% 157.92/27.57 (18) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.57 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.57 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.57 (20) all_58_8 = e0
% 157.92/27.57
% 157.92/27.57 Begin of proof
% 157.92/27.57 |
% 157.92/27.57 | BETA: splitting (18) gives:
% 157.92/27.57 |
% 157.92/27.57 | Case 1:
% 157.92/27.57 | |
% 157.92/27.57 | | (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 157.92/27.57 | | e0)
% 157.92/27.57 | |
% 157.92/27.57 | | REF_CLOSE: (7), (8), (9), (13), (19), (21) are inconsistent by sub-proof
% 157.92/27.57 | | #615.
% 157.92/27.57 | |
% 157.92/27.57 | Case 2:
% 157.92/27.57 | |
% 157.92/27.57 | | (22) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 157.92/27.57 | | e0)
% 157.92/27.57 | |
% 157.92/27.57 | | BETA: splitting (22) gives:
% 157.92/27.57 | |
% 157.92/27.57 | | Case 1:
% 157.92/27.57 | | |
% 157.92/27.57 | | | (23) all_58_6 = e0 & op(e1, e3) = e0
% 157.92/27.57 | | |
% 157.92/27.57 | | | ALPHA: (23) implies:
% 157.92/27.57 | | | (24) all_58_6 = e0
% 157.92/27.57 | | |
% 157.92/27.57 | | | BETA: splitting (2) gives:
% 157.92/27.57 | | |
% 157.92/27.57 | | | Case 1:
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | (25) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 157.92/27.57 | | | | = e1)
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | BETA: splitting (25) gives:
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | Case 1:
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | (26) all_58_6 = e1 & op(e1, e3) = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | ALPHA: (26) implies:
% 157.92/27.57 | | | | | (27) all_58_6 = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | COMBINE_EQS: (24), (27) imply:
% 157.92/27.57 | | | | | (28) e1 = e0
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | COMBINE_EQS: (11), (28) imply:
% 157.92/27.57 | | | | | (29) all_58_1 = e0
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | REF_CLOSE: (1), (3), (6), (10), (14), (15), (16), (29) are
% 157.92/27.57 | | | | | inconsistent by sub-proof #857.
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | Case 2:
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | (30) all_58_7 = e1 & op(e1, e2) = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | ALPHA: (30) implies:
% 157.92/27.57 | | | | | (31) all_58_7 = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | REF_CLOSE: (6), (14), (31) are inconsistent by sub-proof #721.
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | End of split
% 157.92/27.57 | | | |
% 157.92/27.57 | | | Case 2:
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | (32) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 157.92/27.57 | | | | = e1)
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | BETA: splitting (32) gives:
% 157.92/27.57 | | | |
% 157.92/27.57 | | | | Case 1:
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | (33) all_58_8 = e1 & op(e1, e1) = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | REF_CLOSE: (1), (3), (6), (10), (11), (14), (15), (16), (20), (33) are
% 157.92/27.57 | | | | | inconsistent by sub-proof #436.
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | Case 2:
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | (34) all_58_11 = e1 & op(e1, e0) = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | ALPHA: (34) implies:
% 157.92/27.57 | | | | | (35) op(e1, e0) = e1
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | | REF_CLOSE: (10), (17), (19), (35) are inconsistent by sub-proof #1275.
% 157.92/27.57 | | | | |
% 157.92/27.57 | | | | End of split
% 157.92/27.57 | | | |
% 157.92/27.57 | | | End of split
% 157.92/27.57 | | |
% 157.92/27.57 | | Case 2:
% 157.92/27.57 | | |
% 157.92/27.57 | | | (36) all_58_12 = e0 & op(e0, e3) = e0
% 157.92/27.57 | | |
% 157.92/27.57 | | | REF_CLOSE: (1), (3), (4), (5), (6), (10), (11), (12), (14), (15), (16),
% 157.92/27.57 | | | (19), (36) are inconsistent by sub-proof #434.
% 157.92/27.57 | | |
% 157.92/27.57 | | End of split
% 157.92/27.57 | |
% 157.92/27.57 | End of split
% 157.92/27.57 |
% 157.92/27.57 End of proof
% 157.92/27.57
% 157.92/27.57 Sub-proof #434 shows that the following formulas are inconsistent:
% 157.92/27.57 ----------------------------------------------------------------
% 157.92/27.57 (1) all_58_13 = e0
% 157.92/27.57 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.57 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.57 (3) all_58_14 = e3
% 157.92/27.57 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.92/27.57 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.92/27.57 (5) all_58_7 = e2
% 157.92/27.57 (6) all_58_12 = e0 & op(e0, e3) = e0
% 157.92/27.57 (7) ~ (e3 = e1)
% 157.92/27.57 (8) all_58_1 = e1
% 157.92/27.57 (9) op(e0, e0) = e2
% 157.92/27.57 (10) ~ (e2 = e1)
% 157.92/27.57 (11) ~ (e1 = e0)
% 157.92/27.57 (12) all_58_3 = e3
% 157.92/27.57 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.57
% 157.92/27.57 Begin of proof
% 157.92/27.57 |
% 157.92/27.57 | ALPHA: (6) implies:
% 157.92/27.57 | (14) all_58_12 = e0
% 157.92/27.57 |
% 157.92/27.57 | BETA: splitting (4) gives:
% 157.92/27.57 |
% 157.92/27.57 | Case 1:
% 157.92/27.57 | |
% 157.92/27.57 | | (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 157.92/27.57 | | e1)
% 157.92/27.57 | |
% 157.92/27.57 | | BETA: splitting (15) gives:
% 157.92/27.57 | |
% 157.92/27.57 | | Case 1:
% 157.92/27.57 | | |
% 157.92/27.57 | | | (16) all_58_12 = e1 & op(e0, e3) = e1
% 157.92/27.57 | | |
% 157.92/27.57 | | | ALPHA: (16) implies:
% 157.92/27.57 | | | (17) all_58_12 = e1
% 157.92/27.57 | | |
% 157.92/27.57 | | | COMBINE_EQS: (14), (17) imply:
% 157.92/27.57 | | | (18) e1 = e0
% 157.92/27.57 | | |
% 157.92/27.57 | | | SIMP: (18) implies:
% 157.92/27.57 | | | (19) e1 = e0
% 157.92/27.57 | | |
% 157.92/27.57 | | | COMBINE_EQS: (8), (19) imply:
% 157.92/27.57 | | | (20) all_58_1 = e0
% 157.92/27.57 | | |
% 157.92/27.57 | | | REF_CLOSE: (1), (2), (5), (7), (10), (11), (12), (20) are inconsistent by
% 157.92/27.57 | | | sub-proof #857.
% 157.92/27.57 | | |
% 157.92/27.57 | | Case 2:
% 157.92/27.57 | | |
% 157.92/27.57 | | | (21) all_58_13 = e1 & op(e0, e2) = e1
% 157.92/27.57 | | |
% 157.92/27.57 | | | ALPHA: (21) implies:
% 157.92/27.57 | | | (22) all_58_13 = e1
% 157.92/27.57 | | |
% 157.92/27.57 | | | REF_CLOSE: (1), (2), (5), (7), (8), (10), (11), (12), (22) are
% 157.92/27.57 | | | inconsistent by sub-proof #690.
% 157.92/27.57 | | |
% 157.92/27.57 | | End of split
% 157.92/27.57 | |
% 157.92/27.57 | Case 2:
% 157.92/27.57 | |
% 157.92/27.57 | | (23) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 157.92/27.57 | | e1)
% 157.92/27.57 | |
% 157.92/27.57 | | REF_CLOSE: (3), (7), (9), (10), (13), (23) are inconsistent by sub-proof
% 157.92/27.57 | | #435.
% 157.92/27.57 | |
% 157.92/27.57 | End of split
% 157.92/27.57 |
% 157.92/27.57 End of proof
% 157.92/27.57
% 157.92/27.57 Sub-proof #435 shows that the following formulas are inconsistent:
% 157.92/27.57 ----------------------------------------------------------------
% 157.92/27.57 (1) all_58_14 = e3
% 157.92/27.57 (2) ~ (e3 = e1)
% 157.92/27.57 (3) op(e0, e0) = e2
% 157.92/27.57 (4) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.92/27.57 (5) ~ (e2 = e1)
% 157.92/27.57 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.57
% 157.92/27.57 Begin of proof
% 157.92/27.57 |
% 157.92/27.57 | BETA: splitting (4) gives:
% 157.92/27.57 |
% 157.92/27.57 | Case 1:
% 157.92/27.57 | |
% 157.92/27.57 | | (7) all_58_14 = e1 & op(e0, e1) = e1
% 157.92/27.57 | |
% 157.92/27.57 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #844.
% 157.92/27.57 | |
% 157.92/27.57 | Case 2:
% 157.92/27.57 | |
% 157.92/27.57 | | (8) all_58_15 = e1 & op(e0, e0) = e1
% 157.92/27.57 | |
% 157.92/27.57 | | ALPHA: (8) implies:
% 157.92/27.57 | | (9) op(e0, e0) = e1
% 157.92/27.57 | |
% 157.92/27.57 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #1386.
% 157.92/27.57 | |
% 157.92/27.57 | End of split
% 157.92/27.57 |
% 157.92/27.57 End of proof
% 157.92/27.57
% 157.92/27.57 Sub-proof #436 shows that the following formulas are inconsistent:
% 157.92/27.57 ----------------------------------------------------------------
% 157.92/27.57 (1) all_58_13 = e0
% 157.92/27.57 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.57 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 157.92/27.57 (3) all_58_7 = e2
% 157.92/27.57 (4) all_58_8 = e1 & op(e1, e1) = e1
% 157.92/27.57 (5) ~ (e3 = e1)
% 157.92/27.57 (6) all_58_1 = e1
% 157.92/27.57 (7) ~ (e2 = e1)
% 157.92/27.57 (8) ~ (e1 = e0)
% 157.92/27.57 (9) all_58_3 = e3
% 157.92/27.57 (10) all_58_8 = e0
% 157.92/27.57
% 157.92/27.57 Begin of proof
% 157.92/27.57 |
% 157.92/27.57 | ALPHA: (4) implies:
% 157.92/27.57 | (11) all_58_8 = e1
% 157.92/27.57 |
% 157.92/27.57 | COMBINE_EQS: (10), (11) imply:
% 157.92/27.57 | (12) e1 = e0
% 157.92/27.57 |
% 157.92/27.57 | SIMP: (12) implies:
% 157.92/27.57 | (13) e1 = e0
% 157.92/27.57 |
% 157.92/27.57 | COMBINE_EQS: (6), (13) imply:
% 157.92/27.57 | (14) all_58_1 = e0
% 157.92/27.57 |
% 157.92/27.57 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (14) are inconsistent by
% 157.92/27.57 | sub-proof #857.
% 157.92/27.57 |
% 157.92/27.57 End of proof
% 157.92/27.57
% 157.92/27.57 Sub-proof #437 shows that the following formulas are inconsistent:
% 157.92/27.57 ----------------------------------------------------------------
% 157.92/27.57 (1) all_56_14 = e3
% 157.92/27.57 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 157.92/27.57 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 157.92/27.57 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 157.92/27.57 (4) all_58_14 = e3
% 157.92/27.57 (5) all_54_13 = all_52_7
% 157.92/27.57 (6) op(e1, e1) = all_6_2
% 157.92/27.57 (7) ~ (all_52_7 = e3)
% 157.92/27.57 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 157.92/27.57 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 157.92/27.57 (9) ~ (all_52_11 = e3)
% 157.92/27.57 (10) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 157.92/27.57 (11) ~ (all_52_7 = all_52_11)
% 157.92/27.57 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 157.92/27.57 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 157.92/27.57 (13) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 157.92/27.57 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 157.92/27.57 (14) op(e2, e3) = all_52_1
% 157.92/27.57 (15) ~ (all_52_13 = e3)
% 157.92/27.57 (16) all_54_2 = all_52_8
% 157.92/27.57 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 157.92/27.57 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 157.92/27.57 (18) ~ (all_52_8 = all_52_9)
% 157.92/27.57 (19) ~ (e3 = e0)
% 157.92/27.57 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 157.92/27.57 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 157.92/27.57 (21) ~ (all_52_9 = all_52_13)
% 157.92/27.57 (22) ~ (e2 = e0)
% 157.92/27.57 (23) ~ (all_52_9 = e3)
% 157.92/27.57 (24) op(e2, e3) = e2
% 157.92/27.57 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.57 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 157.92/27.57 (26) ~ (e3 = e1)
% 157.92/27.57 (27) all_56_12 = e1
% 157.92/27.57 (28) all_58_1 = e1
% 157.92/27.57 (29) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 157.92/27.57 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 157.92/27.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 157.92/27.57 (31) all_54_7 = all_52_13
% 157.92/27.57 (32) ~ (all_52_13 = e2)
% 157.92/27.57 (33) all_56_15 = all_4_2
% 157.92/27.57 (34) ~ (all_52_9 = all_52_11)
% 157.92/27.57 (35) ~ (all_52_13 = all_4_2)
% 157.92/27.57 (36) all_54_6 = all_52_9
% 157.92/27.57 (37) ~ (e2 = e1)
% 157.92/27.57 (38) ~ (all_52_8 = all_52_11)
% 157.92/27.57 (39) ~ (e1 = e0)
% 157.92/27.57 (40) all_58_3 = e3
% 157.92/27.57 (41) ~ (all_6_2 = e2)
% 157.92/27.57 (42) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 157.92/27.57 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 157.92/27.57 e3)
% 157.92/27.57 (43) all_56_13 = e3
% 157.92/27.57 (44) ~ (all_52_9 = e2)
% 157.92/27.57 (45) ~ (all_52_8 = e3)
% 157.92/27.57 (46) all_54_14 = all_52_11
% 157.92/27.57 (47) ~ (all_52_7 = all_4_2)
% 157.92/27.57 (48) all_58_15 = e2 & op(e0, e0) = e2
% 157.92/27.57 (49) op(e0, e2) = all_52_7
% 157.92/27.57 (50) ~ (all_52_8 = e1)
% 157.92/27.57 (51) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 157.92/27.57 (52) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 157.92/27.57 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 157.92/27.57 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 157.92/27.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 157.92/27.57 (54) ~ (e3 = e2)
% 157.92/27.57 (55) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 157.92/27.57 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 157.92/27.57 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 157.92/27.57 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 157.92/27.57 (56) all_58_11 = e3
% 157.92/27.57 (57) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 157.92/27.58 (58) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 157.92/27.58
% 157.92/27.58 Begin of proof
% 157.92/27.58 |
% 157.92/27.58 | ALPHA: (48) implies:
% 157.92/27.58 | (59) all_58_15 = e2
% 157.92/27.58 | (60) op(e0, e0) = e2
% 157.92/27.58 |
% 157.92/27.58 | BETA: splitting (13) gives:
% 157.92/27.58 |
% 157.92/27.58 | Case 1:
% 157.92/27.58 | |
% 158.02/27.58 | | (61) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 158.02/27.58 | | e2)
% 158.02/27.58 | |
% 158.02/27.58 | | BETA: splitting (61) gives:
% 158.02/27.58 | |
% 158.02/27.58 | | Case 1:
% 158.02/27.58 | | |
% 158.02/27.58 | | | (62) all_58_4 = e2 & op(e3, e1) = e2
% 158.02/27.58 | | |
% 158.02/27.58 | | | ALPHA: (62) implies:
% 158.02/27.58 | | | (63) all_58_4 = e2
% 158.02/27.58 | | |
% 158.02/27.58 | | | BETA: splitting (58) gives:
% 158.02/27.58 | | |
% 158.02/27.58 | | | Case 1:
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | (64) all_56_12 = e3
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | COMBINE_EQS: (27), (64) imply:
% 158.02/27.58 | | | | (65) e3 = e1
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | REDUCE: (26), (65) imply:
% 158.02/27.58 | | | | (66) $false
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | CLOSE: (66) is inconsistent.
% 158.02/27.58 | | | |
% 158.02/27.58 | | | Case 2:
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | (67) ~ (all_56_12 = e3)
% 158.02/27.58 | | | | (68) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | REDUCE: (27), (67) imply:
% 158.02/27.58 | | | | (69) ~ (e3 = e1)
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | BETA: splitting (68) gives:
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | Case 1:
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | (70) all_56_13 = e2
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | COMBINE_EQS: (43), (70) imply:
% 158.02/27.58 | | | | | (71) e3 = e2
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | SIMP: (71) implies:
% 158.02/27.58 | | | | | (72) e3 = e2
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | COMBINE_EQS: (4), (72) imply:
% 158.02/27.58 | | | | | (73) all_58_14 = e2
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | REF_CLOSE: (7), (8), (19), (22), (26), (37), (39), (42), (49), (53),
% 158.02/27.58 | | | | | (54), (55), (59), (60), (73) are inconsistent by sub-proof
% 158.02/27.58 | | | | | #1380.
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | Case 2:
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | (74) ~ (all_56_13 = e2)
% 158.02/27.58 | | | | | (75) all_56_14 = e1 | all_56_15 = e0
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | BETA: splitting (25) gives:
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | Case 1:
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | (76) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 158.02/27.58 | | | | | | e2) = e0)
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | BETA: splitting (76) gives:
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | Case 1:
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | (77) all_58_1 = e0 & op(e3, e2) = e0
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | REF_CLOSE: (28), (39), (77) are inconsistent by sub-proof #1327.
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | Case 2:
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | (78) all_58_3 = e0 & op(e2, e2) = e0
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | REF_CLOSE: (19), (40), (78) are inconsistent by sub-proof #910.
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | End of split
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | Case 2:
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | (79) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 158.02/27.58 | | | | | | e2) = e0)
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | BETA: splitting (79) gives:
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | Case 1:
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | (80) all_58_7 = e0 & op(e1, e2) = e0
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | ALPHA: (80) implies:
% 158.02/27.58 | | | | | | | (81) all_58_7 = e0
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (12), (13), (14), (17), (19),
% 158.02/27.58 | | | | | | | (20), (22), (24), (26), (30), (37), (39), (40), (41),
% 158.02/27.58 | | | | | | | (42), (49), (52), (53), (54), (55), (56), (59), (60),
% 158.02/27.58 | | | | | | | (63), (81) are inconsistent by sub-proof #635.
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | Case 2:
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | (82) all_58_13 = e0 & op(e0, e2) = e0
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | ALPHA: (82) implies:
% 158.02/27.58 | | | | | | | (83) op(e0, e2) = e0
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | REF_CLOSE: (1), (2), (5), (7), (9), (10), (11), (15), (16), (18),
% 158.02/27.58 | | | | | | | (21), (23), (26), (29), (31), (32), (33), (34), (35),
% 158.02/27.58 | | | | | | | (36), (38), (44), (45), (46), (47), (49), (50), (51),
% 158.02/27.58 | | | | | | | (53), (57), (75), (83) are inconsistent by sub-proof
% 158.02/27.58 | | | | | | | #472.
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | End of split
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | End of split
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | End of split
% 158.02/27.58 | | | |
% 158.02/27.58 | | | End of split
% 158.02/27.58 | | |
% 158.02/27.58 | | Case 2:
% 158.02/27.58 | | |
% 158.02/27.58 | | | (84) all_58_5 = e2 & op(e2, e1) = e2
% 158.02/27.58 | | |
% 158.02/27.58 | | | ALPHA: (84) implies:
% 158.02/27.58 | | | (85) all_58_5 = e2
% 158.02/27.58 | | |
% 158.02/27.58 | | | REF_CLOSE: (3), (19), (22), (24), (26), (30), (37), (39), (40), (53), (85)
% 158.02/27.58 | | | are inconsistent by sub-proof #898.
% 158.02/27.58 | | |
% 158.02/27.58 | | End of split
% 158.02/27.58 | |
% 158.02/27.58 | Case 2:
% 158.02/27.58 | |
% 158.02/27.58 | | (86) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 158.02/27.58 | | e2)
% 158.02/27.58 | |
% 158.02/27.58 | | REF_CLOSE: (6), (7), (8), (19), (22), (26), (37), (39), (41), (42), (49),
% 158.02/27.58 | | (53), (54), (55), (59), (60), (86) are inconsistent by sub-proof
% 158.02/27.58 | | #891.
% 158.02/27.58 | |
% 158.02/27.58 | End of split
% 158.02/27.58 |
% 158.02/27.58 End of proof
% 158.02/27.58
% 158.02/27.58 Sub-proof #438 shows that the following formulas are inconsistent:
% 158.02/27.58 ----------------------------------------------------------------
% 158.02/27.58 (1) op(e1, e3) = e3
% 158.02/27.58 (2) op(e1, e1) = e3
% 158.02/27.58 (3) op(e1, e1) = all_32_1
% 158.02/27.58 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.02/27.58 (5) all_56_14 = e3
% 158.02/27.58 (6) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.02/27.58 (7) op(e3, e1) = e3
% 158.02/27.58 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.02/27.58 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.02/27.58 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.58 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.58 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.02/27.58 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.02/27.58 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.58 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.02/27.58 (12) all_58_14 = e3
% 158.02/27.58 (13) all_54_13 = all_52_7
% 158.02/27.58 (14) op(e1, e1) = all_6_2
% 158.02/27.58 (15) ~ (all_52_7 = e3)
% 158.02/27.58 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.58 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.02/27.58 e1)
% 158.02/27.58 (17) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.02/27.58 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.02/27.58 (18) ~ (all_52_6 = all_52_14)
% 158.02/27.58 (19) ~ (all_52_11 = e3)
% 158.02/27.58 (20) op(e3, e3) = all_28_1
% 158.02/27.58 (21) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.02/27.58 (22) ~ (all_52_7 = all_52_11)
% 158.02/27.58 (23) op(e1, e2) = all_14_0
% 158.02/27.58 (24) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.02/27.58 (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.02/27.58 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.02/27.58 (26) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.02/27.58 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.02/27.58 (27) all_58_6 = e3
% 158.02/27.58 (28) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.02/27.58 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.02/27.58 (29) ~ (all_52_14 = e3)
% 158.02/27.58 (30) op(e3, e2) = all_52_4
% 158.02/27.58 (31) ~ (all_4_2 = e2)
% 158.02/27.58 (32) op(e2, e3) = all_52_1
% 158.02/27.58 (33) ~ (all_52_13 = e3)
% 158.02/27.58 (34) all_54_2 = all_52_8
% 158.02/27.58 (35) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.02/27.58 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.02/27.58 (36) ~ (all_52_8 = all_52_9)
% 158.02/27.58 (37) ~ (e3 = e0)
% 158.02/27.58 (38) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.02/27.58 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.02/27.58 (39) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.02/27.58 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.02/27.58 (40) ~ (all_52_9 = all_52_13)
% 158.02/27.58 (41) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.02/27.58 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.02/27.58 e2)
% 158.02/27.58 (42) ~ (e2 = e0)
% 158.02/27.58 (43) ~ (all_52_9 = e3)
% 158.02/27.58 (44) ~ (all_52_2 = all_52_6)
% 158.02/27.58 (45) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.02/27.58 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.02/27.58 (46) op(e1, e3) = all_52_2
% 158.02/27.58 (47) op(e2, e0) = all_52_13
% 158.02/27.58 (48) op(e2, e3) = e2
% 158.02/27.58 (49) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.58 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.02/27.58 (50) ~ (e3 = e1)
% 158.02/27.58 (51) all_56_12 = e1
% 158.02/27.58 (52) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.02/27.58 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.58 (53) op(e1, e2) = all_52_6
% 158.02/27.58 (54) ~ (all_4_2 = e1)
% 158.02/27.58 (55) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.02/27.58 (56) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.58 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.02/27.58 (57) op(e0, e0) = all_4_2
% 158.02/27.58 (58) all_54_8 = all_52_2
% 158.02/27.58 (59) all_54_7 = all_52_13
% 158.02/27.58 (60) ~ (all_52_2 = e3)
% 158.02/27.58 (61) op(e3, e3) = e1
% 158.02/27.58 (62) ~ (all_52_13 = e2)
% 158.02/27.58 (63) all_56_15 = all_4_2
% 158.02/27.58 (64) ~ (all_52_9 = all_52_11)
% 158.02/27.58 (65) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.02/27.58 (66) ~ (all_52_13 = all_4_2)
% 158.02/27.58 (67) ~ (all_52_2 = e1)
% 158.02/27.58 (68) ~ (all_52_6 = all_52_7)
% 158.02/27.58 (69) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.02/27.58 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.02/27.58 (70) ~ (all_52_4 = e3)
% 158.02/27.58 (71) all_54_6 = all_52_9
% 158.02/27.58 (72) ~ (e2 = e1)
% 158.02/27.58 (73) ~ (all_52_8 = all_52_11)
% 158.02/27.58 (74) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.02/27.58 (75) ~ (e1 = e0)
% 158.02/27.58 (76) ~ (all_52_2 = e2)
% 158.02/27.58 (77) all_58_3 = e3
% 158.02/27.58 (78) op(e3, e1) = all_52_8
% 158.02/27.58 (79) ~ (all_6_2 = e2)
% 158.02/27.58 (80) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.02/27.58 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.02/27.58 e3)
% 158.02/27.58 (81) all_56_13 = e3
% 158.02/27.58 (82) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.02/27.58 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.02/27.58 (83) ~ (all_52_9 = e2)
% 158.02/27.58 (84) ~ (all_52_8 = e3)
% 158.02/27.58 (85) all_54_14 = all_52_11
% 158.02/27.58 (86) ~ (all_52_7 = all_4_2)
% 158.02/27.58 (87) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.02/27.58 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.02/27.58 (88) op(e0, e2) = all_52_7
% 158.02/27.58 (89) op(e3, e3) = all_22_1
% 158.02/27.58 (90) all_54_15 = all_4_2
% 158.02/27.58 (91) ~ (all_52_8 = e1)
% 158.02/27.58 (92) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/27.58 (93) ~ (all_52_6 = e3)
% 158.02/27.58 (94) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.02/27.58 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.02/27.58 (95) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.02/27.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.02/27.58 (96) all_54_11 = all_52_14
% 158.02/27.58 (97) ~ (all_52_13 = all_52_14)
% 158.02/27.58 (98) ~ (e3 = e2)
% 158.02/27.58 (99) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.02/27.58 (100) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.02/27.58 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.02/27.58 (101) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 158.02/27.58 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.02/27.58 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 158.02/27.58 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.02/27.58 e0)))
% 158.02/27.58 (102) all_54_9 = all_52_6
% 158.02/27.58 (103) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.02/27.58 (104) ~ (all_52_14 = all_4_2)
% 158.02/27.58 (105) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.02/27.58
% 158.02/27.58 Begin of proof
% 158.02/27.58 |
% 158.02/27.58 | BETA: splitting (94) gives:
% 158.02/27.58 |
% 158.02/27.58 | Case 1:
% 158.02/27.58 | |
% 158.02/27.58 | | (106) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 158.02/27.58 | | e0)
% 158.02/27.58 | |
% 158.02/27.58 | | BETA: splitting (106) gives:
% 158.02/27.58 | |
% 158.02/27.58 | | Case 1:
% 158.02/27.58 | | |
% 158.02/27.58 | | | (107) all_58_0 = e0 & op(e3, e3) = e0
% 158.02/27.58 | | |
% 158.02/27.58 | | | ALPHA: (107) implies:
% 158.02/27.58 | | | (108) all_58_0 = e0
% 158.02/27.58 | | |
% 158.02/27.58 | | | BETA: splitting (24) gives:
% 158.02/27.58 | | |
% 158.02/27.58 | | | Case 1:
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | (109) all_54_8 = e3
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | REF_CLOSE: (58), (60), (109) are inconsistent by sub-proof #1425.
% 158.02/27.58 | | | |
% 158.02/27.58 | | | Case 2:
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | (110) ~ (all_54_8 = e3)
% 158.02/27.58 | | | | (111) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | BETA: splitting (69) gives:
% 158.02/27.58 | | | |
% 158.02/27.58 | | | | Case 1:
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | (112) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 158.02/27.58 | | | | | e1) = e1)
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | BETA: splitting (112) gives:
% 158.02/27.58 | | | | |
% 158.02/27.58 | | | | | Case 1:
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | (113) all_58_4 = e1 & op(e3, e1) = e1
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | ALPHA: (113) implies:
% 158.02/27.58 | | | | | | (114) all_58_4 = e1
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | REF_CLOSE: (11), (12), (14), (26), (37), (42), (48), (50), (56),
% 158.02/27.58 | | | | | | (72), (75), (77), (79), (95), (98), (114) are
% 158.02/27.58 | | | | | | inconsistent by sub-proof #850.
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | Case 2:
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | (115) all_58_5 = e1 & op(e2, e1) = e1
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | ALPHA: (115) implies:
% 158.02/27.58 | | | | | | (116) all_58_5 = e1
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | BETA: splitting (52) gives:
% 158.02/27.58 | | | | | |
% 158.02/27.58 | | | | | | Case 1:
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | (117) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 158.02/27.58 | | | | | | | op(e2, e1) = e0)
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | REF_CLOSE: (11), (12), (14), (26), (37), (42), (48), (50), (56),
% 158.02/27.58 | | | | | | | (72), (75), (77), (79), (95), (98), (116), (117) are
% 158.02/27.58 | | | | | | | inconsistent by sub-proof #652.
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | Case 2:
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | (118) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 158.02/27.58 | | | | | | | op(e0, e1) = e0)
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | BETA: splitting (118) gives:
% 158.02/27.58 | | | | | | |
% 158.02/27.58 | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | |
% 158.02/27.58 | | | | | | | | (119) all_58_8 = e0 & op(e1, e1) = e0
% 158.02/27.58 | | | | | | | |
% 158.02/27.58 | | | | | | | | ALPHA: (119) implies:
% 158.02/27.58 | | | | | | | | (120) all_58_8 = e0
% 158.02/27.58 | | | | | | | |
% 158.02/27.58 | | | | | | | | BETA: splitting (38) gives:
% 158.02/27.58 | | | | | | | |
% 158.02/27.58 | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | |
% 158.02/27.58 | | | | | | | | | (121) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 158.02/27.58 | | | | | | | | | op(e2, e3) = e1)
% 158.02/27.58 | | | | | | | | |
% 158.02/27.58 | | | | | | | | | REF_CLOSE: (48), (72), (75), (95), (108), (121) are
% 158.02/27.58 | | | | | | | | | inconsistent by sub-proof #1160.
% 158.02/27.58 | | | | | | | | |
% 158.02/27.58 | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | |
% 158.02/27.58 | | | | | | | | | (122) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 158.02/27.58 | | | | | | | | | op(e0, e3) = e1)
% 158.02/27.58 | | | | | | | | |
% 158.02/27.58 | | | | | | | | | BETA: splitting (122) gives:
% 158.02/27.58 | | | | | | | | |
% 158.02/27.58 | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | (123) all_58_6 = e1 & op(e1, e3) = e1
% 158.02/27.58 | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | ALPHA: (123) implies:
% 158.02/27.58 | | | | | | | | | | (124) all_58_6 = e1
% 158.02/27.58 | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | REF_CLOSE: (27), (50), (124) are inconsistent by sub-proof
% 158.02/27.58 | | | | | | | | | | #1073.
% 158.02/27.58 | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | (125) all_58_12 = e1 & op(e0, e3) = e1
% 158.02/27.58 | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | ALPHA: (125) implies:
% 158.02/27.58 | | | | | | | | | | (126) all_58_12 = e1
% 158.02/27.58 | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | BETA: splitting (41) gives:
% 158.02/27.58 | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | (127) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 158.02/27.58 | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 158.02/27.58 | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | BETA: splitting (127) gives:
% 158.02/27.58 | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | (128) all_58_12 = e2 & op(e0, e3) = e2
% 158.02/27.58 | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | ALPHA: (128) implies:
% 158.02/27.58 | | | | | | | | | | | | (129) all_58_12 = e2
% 158.02/27.58 | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | REF_CLOSE: (25), (32), (37), (38), (48), (50), (72), (75),
% 158.02/27.58 | | | | | | | | | | | | (95), (98), (108), (129) are inconsistent by
% 158.02/27.58 | | | | | | | | | | | | sub-proof #1066.
% 158.02/27.58 | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | (130) all_58_13 = e2 & op(e0, e2) = e2
% 158.02/27.58 | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | ALPHA: (130) implies:
% 158.02/27.58 | | | | | | | | | | | | (131) all_58_13 = e2
% 158.02/27.58 | | | | | | | | | | | | (132) op(e0, e2) = e2
% 158.02/27.58 | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | BETA: splitting (9) gives:
% 158.02/27.58 | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | (133) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 158.02/27.58 | | | | | | | | | | | | | & op(e2, e2) = e1)
% 158.02/27.58 | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | BETA: splitting (133) gives:
% 158.02/27.58 | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | (134) all_58_1 = e1 & op(e3, e2) = e1
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | ALPHA: (134) implies:
% 158.02/27.58 | | | | | | | | | | | | | | (135) all_58_1 = e1
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | (136) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | (137) all_58_1 = e0 & op(e3, e2) = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 158.02/27.58 | | | | | | | | | | | | | | | | (138) all_58_1 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (138) imply:
% 158.02/27.58 | | | | | | | | | | | | | | | | (139) e1 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (139) imply:
% 158.02/27.58 | | | | | | | | | | | | | | | | (140) all_58_12 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.58 | | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.58 | | | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.58 | | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.58 | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.58 | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.58 | | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.58 | | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.58 | | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.58 | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.58 | | | | | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.58 | | | | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.58 | | | | | | | | | | | | | | | | (103), (104), (105), (111), (140) are inconsistent
% 158.02/27.58 | | | | | | | | | | | | | | | | by sub-proof #444.
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | (141) all_58_3 = e0 & op(e2, e2) = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | REF_CLOSE: (37), (77), (141) are inconsistent by sub-proof
% 158.02/27.58 | | | | | | | | | | | | | | | | #910.
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | End of split
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | (142) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 158.02/27.58 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | (143) all_58_7 = e0 & op(e1, e2) = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 158.02/27.58 | | | | | | | | | | | | | | | | (144) all_58_7 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | (145) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (42), (48), (77), (95), (145) are
% 158.02/27.58 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #909.
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | (146) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 158.02/27.58 | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (147) all_58_5 = e0 & op(e2, e1) = e0
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (148) all_58_5 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (148) imply:
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (149) e1 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (150) e1 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (150) imply:
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (151) all_58_1 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (50), (72), (75), (77), (131), (144), (151)
% 158.02/27.58 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #752.
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (152) all_58_10 = e0 & op(e2, e0) = e0
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (153) all_58_10 = e0
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (14), (25), (27), (32), (35), (37),
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (38), (42), (48), (50), (72), (75), (77), (79),
% 158.02/27.58 | | | | | | | | | | | | | | | | | | (94), (95), (98), (116), (120), (144), (153) are
% 158.02/27.58 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #462.
% 158.02/27.58 | | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | End of split
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | End of split
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | (154) all_58_13 = e0 & op(e0, e2) = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 158.02/27.58 | | | | | | | | | | | | | | | | (155) op(e0, e2) = e0
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (88), (95), (132), (155) are inconsistent by
% 158.02/27.58 | | | | | | | | | | | | | | | | sub-proof #1040.
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | End of split
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | End of split
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | (156) all_58_3 = e1 & op(e2, e2) = e1
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | ALPHA: (156) implies:
% 158.02/27.58 | | | | | | | | | | | | | | (157) all_58_3 = e1
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | REF_CLOSE: (50), (77), (157) are inconsistent by sub-proof
% 158.02/27.58 | | | | | | | | | | | | | | #841.
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | End of split
% 158.02/27.58 | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | Case 2:
% 158.02/27.58 | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | (158) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 158.02/27.58 | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 158.02/27.58 | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | BETA: splitting (158) gives:
% 158.02/27.58 | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | (159) all_58_7 = e1 & op(e1, e2) = e1
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | ALPHA: (159) implies:
% 158.02/27.58 | | | | | | | | | | | | | | (160) all_58_7 = e1
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 158.02/27.58 | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | (161) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 158.02/27.58 | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 158.02/27.58 | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | (162) all_58_4 = e2 & op(e3, e1) = e2
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 158.02/27.58 | | | | | | | | | | | | | | | | (163) all_58_4 = e2
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 158.02/27.58 | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.58 | | | | | | | | | | | | | | | | | (164) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 158.02/27.58 | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 158.02/27.58 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (14), (25), (26), (32), (37), (42),
% 158.02/27.59 | | | | | | | | | | | | | | | | | (48), (50), (56), (72), (75), (77), (79), (95),
% 158.02/27.59 | | | | | | | | | | | | | | | | | (98), (108), (126), (160), (163), (164) are
% 158.02/27.59 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443.
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | (165) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (166) all_58_8 = e2 & op(e1, e1) = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (79), (95), (166) are inconsistent by
% 158.02/27.59 | | | | | | | | | | | | | | | | | | sub-proof #1440.
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (167) all_58_11 = e2 & op(e1, e0) = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (168) all_58_11 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | (169) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (170) all_58_1 = e0 & op(e3, e2) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (171) all_58_1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | (172) all_56_12 = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (51), (172) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | #1191.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | (173) ~ (all_56_12 = e3)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | (174) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (173) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | (175) ~ (e3 = e1)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | (176) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (42), (48), (77), (95), (176) are
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #909.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | (177) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (178) all_58_5 = e0 & op(e2, e1) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (179) all_58_5 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (179) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (180) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (180) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (181) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (181) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (182) all_58_7 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (50), (72), (75), (77), (131), (171), (182)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #752.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (183) all_58_10 = e0 & op(e2, e0) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (184) all_58_10 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | (185) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_58_0 = e1 & op(e3, e3) = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_58_0 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (187) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (188) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (188) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (189) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (189) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_58_5 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (48), (50), (72), (75), (77), (95), (184),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (190) are inconsistent by sub-proof #839.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_58_1 = e1 & op(e3, e2) = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_58_1 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (192) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (193) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (193) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (194) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (194) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_58_5 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (48), (50), (72), (75), (77), (95), (184),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (195) are inconsistent by sub-proof #839.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | (196) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_58_4 = e1 & op(e3, e1) = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_4 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (14), (26), (37), (42), (48), (50),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (56), (72), (75), (77), (79), (95), (98), (198)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #850.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_58_9 = e1 & op(e3, e0) = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_58_9 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_56_13 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (201) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (202) e3 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (202) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_58_6 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (32), (37), (48), (50), (95), (98), (108),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (126), (203) are inconsistent by sub-proof #1125.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (204) ~ (all_56_13 = e2)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_56_14 = e1 | all_56_15 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_15 = e0 & op(e0, e0) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_58_15 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_58_9 = e3 & op(e3, e0) = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_9 = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (200), (210) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1461.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_10 = e3 & op(e2, e0) = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) op(e2, e0) = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (47), (95), (212) are inconsistent by
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1364.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_58_11 = e3 & op(e1, e0) = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_11 = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (27), (32), (37), (48), (50), (95), (98),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (108), (126), (168), (215) are inconsistent by
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #549.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_15 = e3 & op(e0, e0) = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_58_15 = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) op(e0, e0) = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (217) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) e3 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (219) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) e3 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (220) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_6 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (20), (25), (32), (37), (48), (50), (54),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (57), (61), (63), (89), (95), (98), (126), (205),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (221) are inconsistent by sub-proof #573.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (104), (105), (108), (111), (126), (223)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #442.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (224) all_58_3 = e0 & op(e2, e2) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (77), (224) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | #756.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | (225) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (226) all_58_7 = e0 & op(e1, e2) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (227) all_58_7 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (227) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (228) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (229) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (229) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (230) all_58_12 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (103), (104), (105), (111), (230) are inconsistent
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | by sub-proof #444.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (231) all_58_13 = e0 & op(e0, e2) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (232) op(e0, e2) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (88), (95), (132), (232) are inconsistent by
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | sub-proof #1040.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | (233) all_58_5 = e2 & op(e2, e1) = e2
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | (234) all_58_5 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (37), (42), (48), (50), (56), (72), (75),
% 158.02/27.59 | | | | | | | | | | | | | | | | (77), (95), (234) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | #898.
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | (235) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 158.02/27.59 | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 158.02/27.59 | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 158.02/27.59 | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | (236) all_58_8 = e2 & op(e1, e1) = e2
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (79), (95), (236) are inconsistent by
% 158.02/27.59 | | | | | | | | | | | | | | | | sub-proof #1440.
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | (237) all_58_14 = e2 & op(e0, e1) = e2
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (25), (27), (32), (37), (48), (50), (95),
% 158.02/27.59 | | | | | | | | | | | | | | | | (98), (108), (126), (237) are inconsistent by
% 158.02/27.59 | | | | | | | | | | | | | | | | sub-proof #554.
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | (238) all_58_13 = e1 & op(e0, e2) = e1
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | ALPHA: (238) implies:
% 158.02/27.59 | | | | | | | | | | | | | | (239) all_58_13 = e1
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11),
% 158.02/27.59 | | | | | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (21),
% 158.02/27.59 | | | | | | | | | | | | | | (23), (25), (26), (27), (29), (30), (31), (32),
% 158.02/27.59 | | | | | | | | | | | | | | (33), (35), (37), (38), (39), (41), (42), (44),
% 158.02/27.59 | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (53),
% 158.02/27.59 | | | | | | | | | | | | | | (54), (56), (57), (58), (59), (60), (62), (63),
% 158.02/27.59 | | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (72), (74),
% 158.02/27.59 | | | | | | | | | | | | | | (75), (76), (77), (79), (80), (82), (86), (87),
% 158.02/27.59 | | | | | | | | | | | | | | (88), (90), (92), (93), (94), (95), (96), (97),
% 158.02/27.59 | | | | | | | | | | | | | | (98), (99), (101), (102), (104), (108), (111),
% 158.02/27.59 | | | | | | | | | | | | | | (239) are inconsistent by sub-proof #440.
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | (240) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 158.02/27.59 | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 158.02/27.59 | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | BETA: splitting (240) gives:
% 158.02/27.59 | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | (241) all_58_14 = e2 & op(e0, e1) = e2
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | REF_CLOSE: (12), (25), (27), (32), (37), (48), (50), (95),
% 158.02/27.59 | | | | | | | | | | | | (98), (108), (126), (241) are inconsistent by
% 158.02/27.59 | | | | | | | | | | | | sub-proof #554.
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | (242) all_58_15 = e2 & op(e0, e0) = e2
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | ALPHA: (242) implies:
% 158.02/27.59 | | | | | | | | | | | | (243) all_58_15 = e2
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.59 | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.59 | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.59 | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.59 | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.59 | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.59 | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.59 | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.59 | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.59 | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.59 | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.59 | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.59 | | | | | | | | | | | | (103), (104), (105), (108), (111), (126), (243)
% 158.02/27.59 | | | | | | | | | | | | are inconsistent by sub-proof #439.
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | |
% 158.02/27.59 | | | | | | | | End of split
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | | (244) all_58_14 = e0 & op(e0, e1) = e0
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | | ALPHA: (244) implies:
% 158.02/27.59 | | | | | | | | (245) all_58_14 = e0
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | | REF_CLOSE: (12), (37), (245) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | #1444.
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | End of split
% 158.02/27.59 | | | | | | |
% 158.02/27.59 | | | | | | End of split
% 158.02/27.59 | | | | | |
% 158.02/27.59 | | | | | End of split
% 158.02/27.59 | | | | |
% 158.02/27.59 | | | | Case 2:
% 158.02/27.59 | | | | |
% 158.02/27.59 | | | | | (246) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 158.02/27.59 | | | | | e1) = e1)
% 158.02/27.59 | | | | |
% 158.02/27.59 | | | | | BETA: splitting (246) gives:
% 158.02/27.59 | | | | |
% 158.02/27.59 | | | | | Case 1:
% 158.02/27.59 | | | | | |
% 158.02/27.59 | | | | | | (247) all_58_8 = e1 & op(e1, e1) = e1
% 158.02/27.59 | | | | | |
% 158.02/27.59 | | | | | | ALPHA: (247) implies:
% 158.02/27.59 | | | | | | (248) all_58_8 = e1
% 158.02/27.59 | | | | | | (249) op(e1, e1) = e1
% 158.02/27.59 | | | | | |
% 158.02/27.59 | | | | | | BETA: splitting (16) gives:
% 158.02/27.59 | | | | | |
% 158.02/27.59 | | | | | | Case 1:
% 158.02/27.59 | | | | | | |
% 158.02/27.59 | | | | | | | (250) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 158.02/27.59 | | | | | | | op(e0, e2) = e1)
% 158.02/27.59 | | | | | | |
% 158.02/27.59 | | | | | | | BETA: splitting (250) gives:
% 158.02/27.59 | | | | | | |
% 158.02/27.59 | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | | (251) all_58_12 = e1 & op(e0, e3) = e1
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | | ALPHA: (251) implies:
% 158.02/27.59 | | | | | | | | (252) all_58_12 = e1
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | | BETA: splitting (41) gives:
% 158.02/27.59 | | | | | | | |
% 158.02/27.59 | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | |
% 158.02/27.59 | | | | | | | | | (253) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2
% 158.02/27.59 | | | | | | | | | & op(e0, e2) = e2)
% 158.02/27.59 | | | | | | | | |
% 158.02/27.59 | | | | | | | | | BETA: splitting (253) gives:
% 158.02/27.59 | | | | | | | | |
% 158.02/27.59 | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | (254) all_58_12 = e2 & op(e0, e3) = e2
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | ALPHA: (254) implies:
% 158.02/27.59 | | | | | | | | | | (255) all_58_12 = e2
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | REF_CLOSE: (25), (32), (37), (38), (48), (50), (72), (75),
% 158.02/27.59 | | | | | | | | | | (95), (98), (108), (255) are inconsistent by
% 158.02/27.59 | | | | | | | | | | sub-proof #1066.
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | (256) all_58_13 = e2 & op(e0, e2) = e2
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | ALPHA: (256) implies:
% 158.02/27.59 | | | | | | | | | | (257) all_58_13 = e2
% 158.02/27.59 | | | | | | | | | | (258) op(e0, e2) = e2
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | BETA: splitting (26) gives:
% 158.02/27.59 | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | (259) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 158.02/27.59 | | | | | | | | | | | & op(e2, e1) = e2)
% 158.02/27.59 | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | BETA: splitting (259) gives:
% 158.02/27.59 | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | (260) all_58_4 = e2 & op(e3, e1) = e2
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | ALPHA: (260) implies:
% 158.02/27.59 | | | | | | | | | | | | (261) all_58_4 = e2
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | BETA: splitting (52) gives:
% 158.02/27.59 | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | (262) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 158.02/27.59 | | | | | | | | | | | | | & op(e2, e1) = e0)
% 158.02/27.59 | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | BETA: splitting (262) gives:
% 158.02/27.59 | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | (263) all_58_4 = e0 & op(e3, e1) = e0
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | ALPHA: (263) implies:
% 158.02/27.59 | | | | | | | | | | | | | | (264) all_58_4 = e0
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (14), (26), (37), (42), (48), (50),
% 158.02/27.59 | | | | | | | | | | | | | | (56), (72), (75), (77), (79), (95), (98), (264)
% 158.02/27.59 | | | | | | | | | | | | | | are inconsistent by sub-proof #854.
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | (265) all_58_5 = e0 & op(e2, e1) = e0
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | ALPHA: (265) implies:
% 158.02/27.59 | | | | | | | | | | | | | | (266) all_58_5 = e0
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 158.02/27.59 | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | (267) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 158.02/27.59 | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 158.02/27.59 | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | (268) all_58_1 = e1 & op(e3, e2) = e1
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | (269) all_58_1 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | (270) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (50), (72), (77), (95), (270) are
% 158.02/27.59 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | (271) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (272) all_58_5 = e1 & op(e2, e1) = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (273) all_58_5 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (273) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (274) e1 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (274) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (275) all_58_12 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (103), (104), (105), (111), (275) are inconsistent
% 158.02/27.59 | | | | | | | | | | | | | | | | | | by sub-proof #444.
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (276) all_58_10 = e1 & op(e2, e0) = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | (277) all_58_10 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | (278) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (279) all_58_1 = e0 & op(e3, e2) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (48), (50), (72), (75), (77), (95), (266),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (269), (277), (279) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | #823.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (280) all_58_3 = e0 & op(e2, e2) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (77), (280) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | #910.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | (281) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (282) all_58_7 = e0 & op(e1, e2) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | (283) all_58_7 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | (284) all_56_12 = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (51), (284) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | #1191.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | (285) ~ (all_56_12 = e3)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | (286) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (285) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | (287) ~ (e3 = e1)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | (288) all_56_13 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (288) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | (289) e3 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (289) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | (290) all_58_6 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (32), (37), (48), (50), (95), (98), (108),
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | (252), (290) are inconsistent by sub-proof #1125.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | (291) all_56_14 = e1 | all_56_15 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (292) all_56_14 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (292) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (293) e3 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (293) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (294) $false
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (295) all_56_15 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (295) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (296) all_4_2 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (296) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | (297) ~ (all_52_13 = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | (298) all_54_7 = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (59), (298) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | #1428.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | (299) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_54_7 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (62), (300) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | #1427.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_54_7 = e1 | all_54_7 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_54_7 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (302) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_52_13 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (303) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_52_13 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (304) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (305) ~ (all_52_9 = e1)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_54_6 = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (71), (306) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1193.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_54_6 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (83), (308) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1192.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_54_6 = e1 | all_54_6 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_54_6 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (305), (310) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #562.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_54_6 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (311) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_52_9 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (312) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_52_9 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (313) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) ~ (all_52_8 = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (313) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) ~ (all_52_11 = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (315) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) ~ (all_52_11 = e0)
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_54_8 = e2
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (76), (317) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1231.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_54_8 = e1 | all_54_8 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_54_8 = e1
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (67), (319) are inconsistent by sub-proof
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1379.
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_54_8 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (320) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_52_2 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (321) implies:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_52_2 = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (322) imply:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) op(e1, e3) = e0
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_54_2 = e3
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (324) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_52_8 = e3
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (325) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) $false
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (326) is inconsistent.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_54_2 = e2
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (328) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_52_8 = e2
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (329) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) ~ (all_52_11 = e2)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (330) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) ~ (all_52_11 = e2)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_54_14 = e3
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (85), (332) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1413.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) ~ (all_54_14 = e3)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_54_14 = e2
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (331), (335) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1232.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) ~ (all_54_14 = e2)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_54_14 = e1 | all_54_14 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_54_14 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (338) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_52_11 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (339) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_52_11 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (331), (340) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) ~ (e2 = e1)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (95) with e3, all_32_1, e1, e1,
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (2), (3) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_32_1 = e3
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (95) with e1, all_32_1, e1, e1,
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (3), (249) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_32_1 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (95) with e0, e3, e3, e1,
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1), (323) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) e3 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (343) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) e3 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (345) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) e1 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (346) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_58_1 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (50), (72), (75), (77), (257), (283), (347)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #752.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_54_14 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (316), (348) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1400.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_54_2 = e1 | all_54_2 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (91), (314), (349) are inconsistent by
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #561.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_54_7 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (297), (350) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | | #1112.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (351) all_58_13 = e0 & op(e0, e2) = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (351) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (352) op(e0, e2) = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (88), (95), (258), (352) are inconsistent by
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | sub-proof #1040.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | (353) all_58_3 = e1 & op(e2, e2) = e1
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | (354) all_58_3 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | REF_CLOSE: (50), (77), (354) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | | | | | | #841.
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | (355) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 158.02/27.60 | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 158.02/27.60 | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 158.02/27.60 | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | (356) all_58_7 = e1 & op(e1, e2) = e1
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | ALPHA: (356) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | (357) all_58_7 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | (358) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 158.02/27.60 | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (50), (72), (77), (95), (358) are
% 158.02/27.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 158.02/27.60 | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | (359) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 158.02/27.60 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 158.02/27.60 | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | BETA: splitting (359) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (360) all_58_5 = e1 & op(e2, e1) = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | ALPHA: (360) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (361) all_58_5 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (361) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (362) e1 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | SIMP: (362) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (363) e1 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (363) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (364) all_58_12 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (103), (104), (105), (111), (364) are inconsistent
% 158.02/27.60 | | | | | | | | | | | | | | | | | | by sub-proof #444.
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (365) all_58_10 = e1 & op(e2, e0) = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | ALPHA: (365) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | (366) all_58_10 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | (367) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (368) all_58_6 = e0 & op(e1, e3) = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (369) all_58_6 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (37), (369) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | #1321.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (370) all_58_7 = e0 & op(e1, e2) = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (371) all_58_7 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (371) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (372) e1 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | SIMP: (372) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (373) e1 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (373) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (374) all_58_10 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (48), (50), (72), (75), (77), (95), (266),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (374) are inconsistent by sub-proof #839.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | (375) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (375) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (376) all_58_8 = e0 & op(e1, e1) = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (376) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (377) all_58_8 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (377) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (378) e1 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (378) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (379) all_58_10 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (48), (50), (72), (75), (77), (95), (266),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (379) are inconsistent by sub-proof #839.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (380) all_58_11 = e0 & op(e1, e0) = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | (381) all_58_11 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | (382) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (14), (25), (26), (32), (37), (42),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | (48), (50), (56), (72), (75), (77), (79), (95),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | (98), (108), (252), (261), (357), (382) are
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | (383) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (383) gives:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | (384) all_58_8 = e2 & op(e1, e1) = e2
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (79), (95), (384) are inconsistent by
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1440.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | (385) all_58_11 = e2 & op(e1, e0) = e2
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | (386) all_58_11 = e2
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (386) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | (387) e2 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | SIMP: (387) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | (388) e2 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (388) imply:
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | (389) all_58_4 = e0
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (14), (26), (37), (42), (48), (50),
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | (56), (72), (75), (77), (79), (95), (98), (389)
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #854.
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | (390) all_58_13 = e1 & op(e0, e2) = e1
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 158.02/27.60 | | | | | | | | | | | | | | | | (391) all_58_13 = e1
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11),
% 158.02/27.60 | | | | | | | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (21),
% 158.02/27.60 | | | | | | | | | | | | | | | | (23), (25), (26), (27), (29), (30), (31), (32),
% 158.02/27.60 | | | | | | | | | | | | | | | | (33), (35), (37), (38), (39), (41), (42), (44),
% 158.02/27.60 | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (53),
% 158.02/27.60 | | | | | | | | | | | | | | | | (54), (56), (57), (58), (59), (60), (62), (63),
% 158.02/27.60 | | | | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (72), (74),
% 158.02/27.60 | | | | | | | | | | | | | | | | (75), (76), (77), (79), (80), (82), (86), (87),
% 158.02/27.60 | | | | | | | | | | | | | | | | (88), (90), (92), (93), (94), (95), (96), (97),
% 158.02/27.60 | | | | | | | | | | | | | | | | (98), (99), (101), (102), (104), (108), (111),
% 158.02/27.60 | | | | | | | | | | | | | | | | (391) are inconsistent by sub-proof #440.
% 158.02/27.60 | | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | (392) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 158.02/27.60 | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 158.02/27.60 | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | BETA: splitting (392) gives:
% 158.02/27.60 | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | (393) all_58_8 = e0 & op(e1, e1) = e0
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | ALPHA: (393) implies:
% 158.02/27.60 | | | | | | | | | | | | | | (394) all_58_8 = e0
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | COMBINE_EQS: (248), (394) imply:
% 158.02/27.60 | | | | | | | | | | | | | | (395) e1 = e0
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | SIMP: (395) implies:
% 158.02/27.60 | | | | | | | | | | | | | | (396) e1 = e0
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | COMBINE_EQS: (252), (396) imply:
% 158.02/27.60 | | | | | | | | | | | | | | (397) all_58_12 = e0
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.60 | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.60 | | | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.60 | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.60 | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.60 | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.60 | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.60 | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.60 | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.60 | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.60 | | | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.60 | | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.60 | | | | | | | | | | | | | | (103), (104), (105), (111), (397) are inconsistent
% 158.02/27.60 | | | | | | | | | | | | | | by sub-proof #444.
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | (398) all_58_14 = e0 & op(e0, e1) = e0
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | | REF_CLOSE: (12), (37), (398) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | | | | #882.
% 158.02/27.60 | | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | (399) all_58_5 = e2 & op(e2, e1) = e2
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | ALPHA: (399) implies:
% 158.02/27.60 | | | | | | | | | | | | (400) all_58_5 = e2
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | REF_CLOSE: (11), (37), (42), (48), (50), (56), (72), (75),
% 158.02/27.60 | | | | | | | | | | | | (77), (95), (400) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | | #898.
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | (401) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 158.02/27.60 | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | BETA: splitting (401) gives:
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | (402) all_58_8 = e2 & op(e1, e1) = e2
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | REF_CLOSE: (14), (79), (95), (402) are inconsistent by
% 158.02/27.60 | | | | | | | | | | | | sub-proof #1440.
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | (403) all_58_14 = e2 & op(e0, e1) = e2
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | REF_CLOSE: (12), (25), (27), (32), (37), (48), (50), (95),
% 158.02/27.60 | | | | | | | | | | | | (98), (108), (252), (403) are inconsistent by
% 158.02/27.60 | | | | | | | | | | | | sub-proof #554.
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | (404) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2
% 158.02/27.60 | | | | | | | | | & op(e0, e0) = e2)
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | BETA: splitting (404) gives:
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | (405) all_58_14 = e2 & op(e0, e1) = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | ALPHA: (405) implies:
% 158.02/27.60 | | | | | | | | | | (406) all_58_14 = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | COMBINE_EQS: (12), (406) imply:
% 158.02/27.60 | | | | | | | | | | (407) e3 = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | SIMP: (407) implies:
% 158.02/27.60 | | | | | | | | | | (408) e3 = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | COMBINE_EQS: (27), (408) imply:
% 158.02/27.60 | | | | | | | | | | (409) all_58_6 = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | REF_CLOSE: (25), (32), (37), (48), (50), (95), (98), (108),
% 158.02/27.60 | | | | | | | | | | (252), (409) are inconsistent by sub-proof #1125.
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | (410) all_58_15 = e2 & op(e0, e0) = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | ALPHA: (410) implies:
% 158.02/27.60 | | | | | | | | | | (411) all_58_15 = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.60 | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.60 | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.60 | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.60 | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.60 | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.60 | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.60 | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.60 | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.60 | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.60 | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.60 | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.60 | | | | | | | | | | (103), (104), (105), (108), (111), (252), (411)
% 158.02/27.60 | | | | | | | | | | are inconsistent by sub-proof #439.
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | End of split
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | (412) all_58_13 = e1 & op(e0, e2) = e1
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | ALPHA: (412) implies:
% 158.02/27.60 | | | | | | | | (413) all_58_13 = e1
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12),
% 158.02/27.60 | | | | | | | | (13), (14), (15), (16), (17), (18), (21), (23), (25),
% 158.02/27.60 | | | | | | | | (26), (27), (29), (30), (31), (32), (33), (35), (37),
% 158.02/27.60 | | | | | | | | (38), (39), (41), (42), (44), (45), (46), (47), (48),
% 158.02/27.60 | | | | | | | | (49), (50), (52), (53), (54), (56), (57), (58), (59),
% 158.02/27.60 | | | | | | | | (60), (62), (63), (65), (66), (67), (68), (69), (70),
% 158.02/27.60 | | | | | | | | (72), (74), (75), (76), (77), (79), (80), (82), (86),
% 158.02/27.60 | | | | | | | | (87), (88), (90), (92), (93), (94), (95), (96), (97),
% 158.02/27.60 | | | | | | | | (98), (99), (101), (102), (104), (108), (111), (413)
% 158.02/27.60 | | | | | | | | are inconsistent by sub-proof #440.
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | End of split
% 158.02/27.60 | | | | | | |
% 158.02/27.60 | | | | | | Case 2:
% 158.02/27.60 | | | | | | |
% 158.02/27.60 | | | | | | | (414) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 158.02/27.60 | | | | | | | op(e0, e0) = e1)
% 158.02/27.60 | | | | | | |
% 158.02/27.60 | | | | | | | BETA: splitting (414) gives:
% 158.02/27.60 | | | | | | |
% 158.02/27.60 | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | (415) all_58_14 = e1 & op(e0, e1) = e1
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | ALPHA: (415) implies:
% 158.02/27.60 | | | | | | | | (416) all_58_14 = e1
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | REF_CLOSE: (12), (50), (416) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | #1147.
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | (417) all_58_15 = e1 & op(e0, e0) = e1
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | ALPHA: (417) implies:
% 158.02/27.60 | | | | | | | | (418) all_58_15 = e1
% 158.02/27.60 | | | | | | | | (419) op(e0, e0) = e1
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | BETA: splitting (41) gives:
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | (420) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2
% 158.02/27.60 | | | | | | | | | & op(e0, e2) = e2)
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | BETA: splitting (420) gives:
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | (421) all_58_12 = e2 & op(e0, e3) = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | ALPHA: (421) implies:
% 158.02/27.60 | | | | | | | | | | (422) all_58_12 = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | REF_CLOSE: (25), (32), (37), (38), (48), (50), (72), (75),
% 158.02/27.60 | | | | | | | | | | (95), (98), (108), (422) are inconsistent by
% 158.02/27.60 | | | | | | | | | | sub-proof #1066.
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | (423) all_58_13 = e2 & op(e0, e2) = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | ALPHA: (423) implies:
% 158.02/27.60 | | | | | | | | | | (424) op(e0, e2) = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | BETA: splitting (101) gives:
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | (425) all_58_15 = e0 & op(e0, e0) = e0
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | REF_CLOSE: (75), (418), (425) are inconsistent by sub-proof
% 158.02/27.60 | | | | | | | | | | | #1410.
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | (426) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 158.02/27.60 | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.02/27.60 | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 158.02/27.60 | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 158.02/27.60 | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | ALPHA: (426) implies:
% 158.02/27.60 | | | | | | | | | | | (427) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 158.02/27.60 | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 158.02/27.60 | | | | | | | | | | | e1) = e0)
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | BETA: splitting (427) gives:
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | (428) all_58_12 = e0 & op(e0, e3) = e0
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | ALPHA: (428) implies:
% 158.02/27.60 | | | | | | | | | | | | (429) all_58_12 = e0
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.02/27.60 | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.02/27.60 | | | | | | | | | | | | (19), (21), (22), (23), (25), (26), (27), (28),
% 158.02/27.60 | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 158.02/27.60 | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 158.02/27.60 | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.60 | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 158.02/27.60 | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69),
% 158.02/27.60 | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77),
% 158.02/27.60 | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 158.02/27.60 | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (94),
% 158.02/27.60 | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.60 | | | | | | | | | | | | (103), (104), (105), (111), (419), (429) are
% 158.02/27.60 | | | | | | | | | | | | inconsistent by sub-proof #445.
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | (430) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 158.02/27.60 | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | | REF_CLOSE: (12), (37), (42), (88), (95), (424), (430) are
% 158.02/27.60 | | | | | | | | | | | | inconsistent by sub-proof #753.
% 158.02/27.60 | | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | (431) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2
% 158.02/27.60 | | | | | | | | | & op(e0, e0) = e2)
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | BETA: splitting (431) gives:
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | | Case 1:
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | (432) all_58_14 = e2 & op(e0, e1) = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | REF_CLOSE: (12), (25), (27), (32), (37), (38), (48), (50),
% 158.02/27.60 | | | | | | | | | | (72), (75), (95), (98), (108), (432) are
% 158.02/27.60 | | | | | | | | | | inconsistent by sub-proof #441.
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | Case 2:
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | (433) all_58_15 = e2 & op(e0, e0) = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | ALPHA: (433) implies:
% 158.02/27.60 | | | | | | | | | | (434) op(e0, e0) = e2
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | | REF_CLOSE: (72), (95), (419), (434) are inconsistent by
% 158.02/27.60 | | | | | | | | | | sub-proof #1386.
% 158.02/27.60 | | | | | | | | | |
% 158.02/27.60 | | | | | | | | | End of split
% 158.02/27.60 | | | | | | | | |
% 158.02/27.60 | | | | | | | | End of split
% 158.02/27.60 | | | | | | | |
% 158.02/27.60 | | | | | | | End of split
% 158.02/27.60 | | | | | | |
% 158.02/27.60 | | | | | | End of split
% 158.02/27.60 | | | | | |
% 158.02/27.60 | | | | | Case 2:
% 158.02/27.60 | | | | | |
% 158.02/27.60 | | | | | | (435) all_58_14 = e1 & op(e0, e1) = e1
% 158.02/27.60 | | | | | |
% 158.02/27.60 | | | | | | ALPHA: (435) implies:
% 158.02/27.60 | | | | | | (436) all_58_14 = e1
% 158.02/27.60 | | | | | |
% 158.02/27.60 | | | | | | REF_CLOSE: (12), (50), (436) are inconsistent by sub-proof #1147.
% 158.02/27.60 | | | | | |
% 158.02/27.60 | | | | | End of split
% 158.02/27.60 | | | | |
% 158.02/27.60 | | | | End of split
% 158.02/27.60 | | | |
% 158.02/27.60 | | | End of split
% 158.02/27.60 | | |
% 158.02/27.60 | | Case 2:
% 158.02/27.60 | | |
% 158.02/27.60 | | | (437) all_58_2 = e0 & op(e2, e3) = e0
% 158.02/27.60 | | |
% 158.02/27.60 | | | ALPHA: (437) implies:
% 158.02/27.60 | | | (438) op(e2, e3) = e0
% 158.02/27.60 | | |
% 158.02/27.60 | | | REF_CLOSE: (42), (48), (95), (438) are inconsistent by sub-proof #1156.
% 158.02/27.60 | | |
% 158.02/27.60 | | End of split
% 158.02/27.60 | |
% 158.02/27.60 | Case 2:
% 158.02/27.60 | |
% 158.02/27.60 | | (439) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 158.02/27.60 | | e0)
% 158.02/27.60 | |
% 158.02/27.60 | | BETA: splitting (439) gives:
% 158.02/27.60 | |
% 158.02/27.60 | | Case 1:
% 158.02/27.60 | | |
% 158.02/27.60 | | | (440) all_58_6 = e0 & op(e1, e3) = e0
% 158.02/27.60 | | |
% 158.02/27.60 | | | ALPHA: (440) implies:
% 158.02/27.60 | | | (441) all_58_6 = e0
% 158.02/27.60 | | |
% 158.02/27.60 | | | REF_CLOSE: (27), (37), (441) are inconsistent by sub-proof #1321.
% 158.02/27.60 | | |
% 158.02/27.60 | | Case 2:
% 158.02/27.60 | | |
% 158.02/27.60 | | | (442) all_58_12 = e0 & op(e0, e3) = e0
% 158.02/27.60 | | |
% 158.02/27.60 | | | ALPHA: (442) implies:
% 158.02/27.60 | | | (443) all_58_12 = e0
% 158.02/27.60 | | |
% 158.02/27.60 | | | BETA: splitting (24) gives:
% 158.02/27.60 | | |
% 158.02/27.60 | | | Case 1:
% 158.02/27.60 | | | |
% 158.02/27.60 | | | | (444) all_54_8 = e3
% 158.02/27.60 | | | |
% 158.02/27.60 | | | | REF_CLOSE: (58), (60), (444) are inconsistent by sub-proof #1425.
% 158.02/27.60 | | | |
% 158.02/27.60 | | | Case 2:
% 158.02/27.60 | | | |
% 158.02/27.60 | | | | (445) ~ (all_54_8 = e3)
% 158.02/27.60 | | | | (446) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.02/27.60 | | | |
% 158.02/27.60 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 158.02/27.60 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (21), (22),
% 158.02/27.60 | | | | (23), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 158.02/27.60 | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 158.02/27.60 | | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 158.02/27.60 | | | | (54), (55), (56), (57), (58), (59), (60), (62), (63), (64),
% 158.02/27.60 | | | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 158.02/27.60 | | | | (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 158.02/27.60 | | | | (85), (86), (87), (88), (90), (91), (92), (93), (94), (95),
% 158.02/27.60 | | | | (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 158.02/27.60 | | | | (105), (443), (446) are inconsistent by sub-proof #444.
% 158.02/27.60 | | | |
% 158.02/27.60 | | | End of split
% 158.02/27.60 | | |
% 158.02/27.60 | | End of split
% 158.02/27.60 | |
% 158.02/27.60 | End of split
% 158.02/27.60 |
% 158.02/27.60 End of proof
% 158.02/27.60
% 158.02/27.60 Sub-proof #439 shows that the following formulas are inconsistent:
% 158.02/27.60 ----------------------------------------------------------------
% 158.02/27.60 (1) op(e1, e3) = e3
% 158.02/27.60 (2) op(e1, e1) = e3
% 158.02/27.60 (3) op(e1, e1) = all_32_1
% 158.02/27.60 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.02/27.60 (5) all_56_14 = e3
% 158.02/27.60 (6) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.02/27.60 (7) op(e3, e1) = e3
% 158.02/27.60 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.02/27.60 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.02/27.60 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.60 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.60 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.02/27.60 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.02/27.60 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.60 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.02/27.60 (12) all_58_14 = e3
% 158.02/27.60 (13) all_54_13 = all_52_7
% 158.02/27.60 (14) op(e1, e1) = all_6_2
% 158.02/27.60 (15) ~ (all_52_7 = e3)
% 158.02/27.60 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.60 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.02/27.60 e1)
% 158.02/27.60 (17) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.02/27.60 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.02/27.60 (18) ~ (all_52_6 = all_52_14)
% 158.02/27.60 (19) ~ (all_52_11 = e3)
% 158.02/27.60 (20) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.02/27.60 (21) ~ (all_52_7 = all_52_11)
% 158.02/27.60 (22) op(e1, e2) = all_14_0
% 158.02/27.60 (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.02/27.60 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.02/27.60 (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.02/27.60 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.02/27.60 (25) all_58_6 = e3
% 158.02/27.61 (26) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.02/27.61 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.02/27.61 (27) ~ (all_52_14 = e3)
% 158.02/27.61 (28) op(e3, e2) = all_52_4
% 158.02/27.61 (29) ~ (all_4_2 = e2)
% 158.02/27.61 (30) op(e2, e3) = all_52_1
% 158.02/27.61 (31) ~ (all_52_13 = e3)
% 158.02/27.61 (32) all_54_2 = all_52_8
% 158.02/27.61 (33) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.02/27.61 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.02/27.61 (34) ~ (all_52_8 = all_52_9)
% 158.02/27.61 (35) ~ (e3 = e0)
% 158.02/27.61 (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.02/27.61 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.02/27.61 (37) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.02/27.61 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.02/27.61 (38) ~ (all_52_9 = all_52_13)
% 158.02/27.61 (39) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.02/27.61 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.02/27.61 e2)
% 158.02/27.61 (40) ~ (e2 = e0)
% 158.02/27.61 (41) ~ (all_52_9 = e3)
% 158.02/27.61 (42) ~ (all_52_2 = all_52_6)
% 158.02/27.61 (43) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.02/27.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.02/27.61 (44) op(e1, e3) = all_52_2
% 158.02/27.61 (45) op(e2, e0) = all_52_13
% 158.02/27.61 (46) op(e2, e3) = e2
% 158.02/27.61 (47) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.61 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.02/27.61 (48) ~ (e3 = e1)
% 158.02/27.61 (49) all_56_12 = e1
% 158.02/27.61 (50) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.02/27.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.61 (51) op(e1, e2) = all_52_6
% 158.02/27.61 (52) ~ (all_4_2 = e1)
% 158.02/27.61 (53) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.02/27.61 (54) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.02/27.61 (55) op(e0, e0) = all_4_2
% 158.02/27.61 (56) all_54_8 = all_52_2
% 158.02/27.61 (57) all_54_7 = all_52_13
% 158.02/27.61 (58) ~ (all_52_2 = e3)
% 158.02/27.61 (59) ~ (all_52_13 = e2)
% 158.02/27.61 (60) all_56_15 = all_4_2
% 158.02/27.61 (61) ~ (all_52_9 = all_52_11)
% 158.02/27.61 (62) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.02/27.61 (63) ~ (all_52_13 = all_4_2)
% 158.02/27.61 (64) ~ (all_52_2 = e1)
% 158.02/27.61 (65) ~ (all_52_6 = all_52_7)
% 158.02/27.61 (66) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.02/27.61 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.02/27.61 (67) ~ (all_52_4 = e3)
% 158.02/27.61 (68) all_54_6 = all_52_9
% 158.02/27.61 (69) all_58_15 = e2
% 158.02/27.61 (70) ~ (e2 = e1)
% 158.02/27.61 (71) ~ (all_52_8 = all_52_11)
% 158.02/27.61 (72) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.02/27.61 (73) ~ (e1 = e0)
% 158.02/27.61 (74) ~ (all_52_2 = e2)
% 158.02/27.61 (75) all_58_3 = e3
% 158.02/27.61 (76) op(e3, e1) = all_52_8
% 158.02/27.61 (77) ~ (all_6_2 = e2)
% 158.02/27.61 (78) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.02/27.61 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.02/27.61 e3)
% 158.02/27.61 (79) all_56_13 = e3
% 158.02/27.61 (80) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.02/27.61 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.02/27.61 (81) ~ (all_52_9 = e2)
% 158.02/27.61 (82) ~ (all_52_8 = e3)
% 158.02/27.61 (83) all_54_14 = all_52_11
% 158.02/27.61 (84) ~ (all_52_7 = all_4_2)
% 158.02/27.61 (85) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.02/27.61 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.02/27.61 (86) op(e0, e2) = all_52_7
% 158.02/27.61 (87) all_54_15 = all_4_2
% 158.02/27.61 (88) all_58_0 = e0
% 158.02/27.61 (89) ~ (all_52_8 = e1)
% 158.02/27.61 (90) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.02/27.61 (91) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/27.61 (92) ~ (all_52_6 = e3)
% 158.02/27.61 (93) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.02/27.61 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.02/27.61 (94) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.02/27.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.02/27.61 (95) all_54_11 = all_52_14
% 158.02/27.61 (96) ~ (all_52_13 = all_52_14)
% 158.02/27.61 (97) ~ (e3 = e2)
% 158.02/27.61 (98) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.02/27.61 (99) all_58_12 = e1
% 158.02/27.61 (100) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.02/27.61 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.02/27.61 (101) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 158.02/27.61 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.02/27.61 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 158.02/27.61 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.02/27.61 e0)))
% 158.02/27.61 (102) all_54_9 = all_52_6
% 158.02/27.61 (103) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.02/27.61 (104) ~ (all_52_14 = all_4_2)
% 158.02/27.61 (105) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.02/27.61
% 158.02/27.61 Begin of proof
% 158.02/27.61 |
% 158.02/27.61 | BETA: splitting (101) gives:
% 158.02/27.61 |
% 158.02/27.61 | Case 1:
% 158.02/27.61 | |
% 158.02/27.61 | | (106) all_58_15 = e0 & op(e0, e0) = e0
% 158.02/27.61 | |
% 158.02/27.61 | | REF_CLOSE: (40), (69), (106) are inconsistent by sub-proof #885.
% 158.02/27.61 | |
% 158.02/27.61 | Case 2:
% 158.02/27.61 | |
% 158.02/27.61 | | (107) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 158.02/27.61 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 158.02/27.61 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 158.02/27.61 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.02/27.61 | |
% 158.02/27.61 | | ALPHA: (107) implies:
% 158.02/27.61 | | (108) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 158.02/27.61 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.61 | |
% 158.02/27.61 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.02/27.61 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 158.02/27.61 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.02/27.61 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 158.02/27.61 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 158.02/27.61 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 158.02/27.61 | | (68), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 158.02/27.61 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 158.02/27.61 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 158.02/27.61 | | (101), (102), (103), (104), (105), (108) are inconsistent by
% 158.02/27.61 | | sub-proof #442.
% 158.02/27.61 | |
% 158.02/27.61 | End of split
% 158.02/27.61 |
% 158.02/27.61 End of proof
% 158.02/27.61
% 158.02/27.61 Sub-proof #440 shows that the following formulas are inconsistent:
% 158.02/27.61 ----------------------------------------------------------------
% 158.02/27.61 (1) op(e1, e3) = e3
% 158.02/27.61 (2) op(e1, e1) = e3
% 158.02/27.61 (3) op(e1, e1) = all_32_1
% 158.02/27.61 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.02/27.61 (5) op(e3, e1) = e3
% 158.02/27.61 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.02/27.61 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.02/27.61 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.61 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.61 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.02/27.61 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.02/27.61 (9) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.61 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.02/27.61 (10) all_58_14 = e3
% 158.02/27.61 (11) all_54_13 = all_52_7
% 158.02/27.61 (12) op(e1, e1) = all_6_2
% 158.02/27.61 (13) ~ (all_52_7 = e3)
% 158.02/27.61 (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.61 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.02/27.61 e1)
% 158.02/27.61 (15) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.02/27.61 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.02/27.61 (16) ~ (all_52_6 = all_52_14)
% 158.02/27.61 (17) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.02/27.61 (18) op(e1, e2) = all_14_0
% 158.02/27.61 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.02/27.61 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.02/27.61 (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.02/27.61 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.02/27.61 (21) all_58_6 = e3
% 158.02/27.61 (22) ~ (all_52_14 = e3)
% 158.02/27.61 (23) op(e3, e2) = all_52_4
% 158.02/27.61 (24) ~ (all_4_2 = e2)
% 158.02/27.61 (25) op(e2, e3) = all_52_1
% 158.02/27.61 (26) ~ (all_52_13 = e3)
% 158.02/27.61 (27) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.02/27.61 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.02/27.61 (28) all_58_13 = e1
% 158.02/27.61 (29) ~ (e3 = e0)
% 158.02/27.61 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.02/27.61 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.02/27.61 (31) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.02/27.61 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.02/27.61 (32) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.02/27.61 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.02/27.61 e2)
% 158.02/27.61 (33) ~ (e2 = e0)
% 158.02/27.61 (34) ~ (all_52_2 = all_52_6)
% 158.02/27.61 (35) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.02/27.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.02/27.61 (36) op(e1, e3) = all_52_2
% 158.02/27.61 (37) op(e2, e0) = all_52_13
% 158.02/27.61 (38) op(e2, e3) = e2
% 158.02/27.61 (39) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.61 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.02/27.61 (40) ~ (e3 = e1)
% 158.02/27.62 (41) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.02/27.62 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.62 (42) op(e1, e2) = all_52_6
% 158.02/27.62 (43) ~ (all_4_2 = e1)
% 158.02/27.62 (44) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.62 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.02/27.62 (45) op(e0, e0) = all_4_2
% 158.02/27.62 (46) all_54_8 = all_52_2
% 158.02/27.62 (47) all_54_7 = all_52_13
% 158.02/27.62 (48) ~ (all_52_2 = e3)
% 158.02/27.62 (49) ~ (all_52_13 = e2)
% 158.02/27.62 (50) all_56_15 = all_4_2
% 158.02/27.62 (51) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.02/27.62 (52) ~ (all_52_13 = all_4_2)
% 158.02/27.62 (53) ~ (all_52_2 = e1)
% 158.02/27.62 (54) ~ (all_52_6 = all_52_7)
% 158.02/27.62 (55) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.02/27.62 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.02/27.62 (56) ~ (all_52_4 = e3)
% 158.02/27.62 (57) ~ (e2 = e1)
% 158.02/27.62 (58) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.02/27.62 (59) ~ (e1 = e0)
% 158.02/27.62 (60) ~ (all_52_2 = e2)
% 158.02/27.62 (61) all_58_3 = e3
% 158.02/27.62 (62) ~ (all_6_2 = e2)
% 158.02/27.62 (63) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.02/27.62 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.02/27.62 e3)
% 158.02/27.62 (64) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.02/27.62 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.02/27.62 (65) ~ (all_52_7 = all_4_2)
% 158.02/27.62 (66) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.02/27.62 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.02/27.62 (67) op(e0, e2) = all_52_7
% 158.02/27.62 (68) all_54_15 = all_4_2
% 158.02/27.62 (69) all_58_0 = e0
% 158.02/27.62 (70) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.02/27.62 (71) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/27.62 (72) ~ (all_52_6 = e3)
% 158.02/27.62 (73) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.02/27.62 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.02/27.62 (74) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.02/27.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.02/27.62 (75) all_54_11 = all_52_14
% 158.02/27.62 (76) ~ (all_52_13 = all_52_14)
% 158.02/27.62 (77) ~ (e3 = e2)
% 158.02/27.62 (78) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.02/27.62 (79) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.02/27.62 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.02/27.62 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.02/27.62 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.02/27.62 (80) all_54_9 = all_52_6
% 158.02/27.62 (81) ~ (all_52_14 = all_4_2)
% 158.02/27.62
% 158.02/27.62 Begin of proof
% 158.02/27.62 |
% 158.02/27.62 | BETA: splitting (32) gives:
% 158.02/27.62 |
% 158.02/27.62 | Case 1:
% 158.02/27.62 | |
% 158.02/27.62 | | (82) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 158.02/27.62 | | e2)
% 158.02/27.62 | |
% 158.02/27.62 | | BETA: splitting (82) gives:
% 158.02/27.62 | |
% 158.02/27.62 | | Case 1:
% 158.02/27.62 | | |
% 158.02/27.62 | | | (83) all_58_12 = e2 & op(e0, e3) = e2
% 158.02/27.62 | | |
% 158.02/27.62 | | | ALPHA: (83) implies:
% 158.02/27.62 | | | (84) all_58_12 = e2
% 158.02/27.62 | | |
% 158.02/27.62 | | | REF_CLOSE: (19), (25), (29), (30), (38), (40), (57), (59), (69), (74),
% 158.02/27.62 | | | (77), (84) are inconsistent by sub-proof #1066.
% 158.02/27.62 | | |
% 158.02/27.62 | | Case 2:
% 158.02/27.62 | | |
% 158.02/27.62 | | | (85) all_58_13 = e2 & op(e0, e2) = e2
% 158.02/27.62 | | |
% 158.02/27.62 | | | REF_CLOSE: (28), (57), (85) are inconsistent by sub-proof #727.
% 158.02/27.62 | | |
% 158.02/27.62 | | End of split
% 158.02/27.62 | |
% 158.02/27.62 | Case 2:
% 158.02/27.62 | |
% 158.02/27.62 | | (86) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.02/27.62 | | e2)
% 158.02/27.62 | |
% 158.02/27.62 | | BETA: splitting (86) gives:
% 158.02/27.62 | |
% 158.02/27.62 | | Case 1:
% 158.02/27.62 | | |
% 158.02/27.62 | | | (87) all_58_14 = e2 & op(e0, e1) = e2
% 158.02/27.62 | | |
% 158.02/27.62 | | | REF_CLOSE: (10), (19), (21), (25), (29), (30), (38), (40), (57), (59),
% 158.02/27.62 | | | (69), (74), (77), (87) are inconsistent by sub-proof #441.
% 158.02/27.62 | | |
% 158.02/27.62 | | Case 2:
% 158.02/27.62 | | |
% 158.02/27.62 | | | (88) all_58_15 = e2 & op(e0, e0) = e2
% 158.02/27.62 | | |
% 158.02/27.62 | | | ALPHA: (88) implies:
% 158.02/27.62 | | | (89) all_58_15 = e2
% 158.02/27.62 | | |
% 158.02/27.62 | | | BETA: splitting (79) gives:
% 158.02/27.62 | | |
% 158.02/27.62 | | | Case 1:
% 158.02/27.62 | | | |
% 158.02/27.62 | | | | (90) all_58_15 = e0 & op(e0, e0) = e0
% 158.02/27.62 | | | |
% 158.02/27.62 | | | | REF_CLOSE: (33), (89), (90) are inconsistent by sub-proof #885.
% 158.02/27.62 | | | |
% 158.02/27.62 | | | Case 2:
% 158.02/27.62 | | | |
% 158.02/27.62 | | | | (91) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 158.02/27.62 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 158.02/27.62 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 158.02/27.62 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.02/27.62 | | | |
% 158.02/27.62 | | | | ALPHA: (91) implies:
% 158.02/27.62 | | | | (92) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 158.02/27.62 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.62 | | | |
% 158.02/27.62 | | | | BETA: splitting (92) gives:
% 158.02/27.62 | | | |
% 158.02/27.62 | | | | Case 1:
% 158.02/27.62 | | | | |
% 158.02/27.62 | | | | | (93) all_58_12 = e0 & op(e0, e3) = e0
% 158.02/27.62 | | | | |
% 158.02/27.62 | | | | | ALPHA: (93) implies:
% 158.02/27.62 | | | | | (94) all_58_12 = e0
% 158.02/27.62 | | | | |
% 158.02/27.62 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 158.02/27.62 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 158.02/27.62 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 158.02/27.62 | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 158.02/27.62 | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 158.02/27.62 | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 158.02/27.62 | | | | | (62), (63), (64), (65), (66), (67), (68), (70), (71), (72),
% 158.02/27.62 | | | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (94)
% 158.02/27.62 | | | | | are inconsistent by sub-proof #457.
% 158.02/27.62 | | | | |
% 158.02/27.62 | | | | Case 2:
% 158.02/27.62 | | | | |
% 158.02/27.62 | | | | | (95) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 158.02/27.62 | | | | | e1) = e0)
% 158.02/27.62 | | | | |
% 158.02/27.62 | | | | | BETA: splitting (95) gives:
% 158.02/27.62 | | | | |
% 158.02/27.62 | | | | | Case 1:
% 158.02/27.62 | | | | | |
% 158.02/27.62 | | | | | | (96) all_58_13 = e0 & op(e0, e2) = e0
% 158.02/27.62 | | | | | |
% 158.02/27.62 | | | | | | ALPHA: (96) implies:
% 158.02/27.62 | | | | | | (97) all_58_13 = e0
% 158.02/27.62 | | | | | |
% 158.02/27.62 | | | | | | REF_CLOSE: (28), (59), (97) are inconsistent by sub-proof #988.
% 158.02/27.62 | | | | | |
% 158.02/27.62 | | | | | Case 2:
% 158.02/27.62 | | | | | |
% 158.02/27.62 | | | | | | (98) all_58_14 = e0 & op(e0, e1) = e0
% 158.02/27.62 | | | | | |
% 158.02/27.62 | | | | | | ALPHA: (98) implies:
% 158.02/27.62 | | | | | | (99) all_58_14 = e0
% 158.02/27.62 | | | | | |
% 158.02/27.62 | | | | | | REF_CLOSE: (10), (29), (99) are inconsistent by sub-proof #1444.
% 158.02/27.62 | | | | | |
% 158.02/27.62 | | | | | End of split
% 158.02/27.62 | | | | |
% 158.02/27.62 | | | | End of split
% 158.02/27.62 | | | |
% 158.02/27.62 | | | End of split
% 158.02/27.62 | | |
% 158.02/27.62 | | End of split
% 158.02/27.62 | |
% 158.02/27.62 | End of split
% 158.02/27.62 |
% 158.02/27.62 End of proof
% 158.02/27.62
% 158.02/27.62 Sub-proof #441 shows that the following formulas are inconsistent:
% 158.02/27.62 ----------------------------------------------------------------
% 158.02/27.62 (1) all_58_14 = e3
% 158.02/27.62 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.02/27.62 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.02/27.62 (3) all_58_6 = e3
% 158.02/27.62 (4) op(e2, e3) = all_52_1
% 158.02/27.62 (5) ~ (e3 = e0)
% 158.02/27.62 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.02/27.62 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.02/27.62 (7) op(e2, e3) = e2
% 158.02/27.62 (8) ~ (e3 = e1)
% 158.02/27.62 (9) ~ (e2 = e1)
% 158.02/27.62 (10) ~ (e1 = e0)
% 158.02/27.62 (11) all_58_14 = e2 & op(e0, e1) = e2
% 158.02/27.62 (12) all_58_0 = e0
% 158.02/27.62 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.02/27.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.02/27.62 (14) ~ (e3 = e2)
% 158.02/27.62
% 158.02/27.62 Begin of proof
% 158.02/27.62 |
% 158.02/27.62 | ALPHA: (11) implies:
% 158.02/27.62 | (15) all_58_14 = e2
% 158.02/27.62 |
% 158.02/27.62 | COMBINE_EQS: (1), (15) imply:
% 158.02/27.62 | (16) e3 = e2
% 158.02/27.62 |
% 158.02/27.62 | SIMP: (16) implies:
% 158.02/27.62 | (17) e3 = e2
% 158.02/27.62 |
% 158.02/27.62 | COMBINE_EQS: (3), (17) imply:
% 158.02/27.62 | (18) all_58_6 = e2
% 158.02/27.62 |
% 158.02/27.62 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), (18) are
% 158.02/27.62 | inconsistent by sub-proof #1157.
% 158.02/27.62 |
% 158.02/27.62 End of proof
% 158.02/27.62
% 158.02/27.62 Sub-proof #442 shows that the following formulas are inconsistent:
% 158.02/27.62 ----------------------------------------------------------------
% 158.02/27.62 (1) op(e1, e3) = e3
% 158.02/27.62 (2) op(e1, e1) = e3
% 158.02/27.62 (3) op(e1, e1) = all_32_1
% 158.02/27.62 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.02/27.62 (5) all_56_14 = e3
% 158.02/27.62 (6) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.02/27.62 (7) op(e3, e1) = e3
% 158.02/27.62 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.02/27.62 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.02/27.62 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.62 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.62 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.02/27.62 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.02/27.62 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.62 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.02/27.62 (12) all_58_14 = e3
% 158.02/27.62 (13) all_54_13 = all_52_7
% 158.02/27.62 (14) op(e1, e1) = all_6_2
% 158.02/27.62 (15) ~ (all_52_7 = e3)
% 158.02/27.62 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.62 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.02/27.62 e1)
% 158.02/27.62 (17) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.02/27.62 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.02/27.62 (18) ~ (all_52_6 = all_52_14)
% 158.02/27.62 (19) ~ (all_52_11 = e3)
% 158.02/27.62 (20) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.02/27.62 (21) ~ (all_52_7 = all_52_11)
% 158.02/27.62 (22) op(e1, e2) = all_14_0
% 158.02/27.62 (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.02/27.62 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.02/27.62 (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.02/27.62 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.02/27.62 (25) all_58_6 = e3
% 158.02/27.62 (26) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.02/27.62 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.02/27.62 (27) ~ (all_52_14 = e3)
% 158.02/27.62 (28) op(e3, e2) = all_52_4
% 158.02/27.62 (29) ~ (all_4_2 = e2)
% 158.02/27.62 (30) op(e2, e3) = all_52_1
% 158.02/27.62 (31) ~ (all_52_13 = e3)
% 158.02/27.62 (32) all_54_2 = all_52_8
% 158.02/27.62 (33) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.02/27.62 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.02/27.62 (34) ~ (all_52_8 = all_52_9)
% 158.02/27.62 (35) ~ (e3 = e0)
% 158.02/27.62 (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.02/27.62 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.02/27.62 (37) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.02/27.62 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.02/27.62 (38) ~ (all_52_9 = all_52_13)
% 158.02/27.62 (39) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.02/27.62 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.02/27.62 e2)
% 158.02/27.62 (40) ~ (e2 = e0)
% 158.02/27.62 (41) ~ (all_52_9 = e3)
% 158.02/27.62 (42) ~ (all_52_2 = all_52_6)
% 158.02/27.62 (43) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.02/27.62 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.02/27.62 (44) op(e1, e3) = all_52_2
% 158.02/27.62 (45) op(e2, e0) = all_52_13
% 158.02/27.62 (46) op(e2, e3) = e2
% 158.02/27.62 (47) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.62 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.02/27.62 (48) ~ (e3 = e1)
% 158.02/27.62 (49) all_56_12 = e1
% 158.02/27.62 (50) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.02/27.62 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.62 (51) op(e1, e2) = all_52_6
% 158.02/27.62 (52) ~ (all_4_2 = e1)
% 158.02/27.62 (53) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.02/27.63 (54) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.63 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.02/27.63 (55) op(e0, e0) = all_4_2
% 158.02/27.63 (56) all_54_8 = all_52_2
% 158.02/27.63 (57) all_54_7 = all_52_13
% 158.02/27.63 (58) ~ (all_52_2 = e3)
% 158.02/27.63 (59) ~ (all_52_13 = e2)
% 158.02/27.63 (60) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.02/27.63 | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.63 (61) all_56_15 = all_4_2
% 158.02/27.63 (62) ~ (all_52_9 = all_52_11)
% 158.02/27.63 (63) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.02/27.63 (64) ~ (all_52_13 = all_4_2)
% 158.02/27.63 (65) ~ (all_52_2 = e1)
% 158.02/27.63 (66) ~ (all_52_6 = all_52_7)
% 158.02/27.63 (67) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.02/27.63 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.02/27.63 (68) ~ (all_52_4 = e3)
% 158.02/27.63 (69) all_54_6 = all_52_9
% 158.02/27.63 (70) ~ (e2 = e1)
% 158.02/27.63 (71) ~ (all_52_8 = all_52_11)
% 158.02/27.63 (72) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.02/27.63 (73) ~ (e1 = e0)
% 158.02/27.63 (74) ~ (all_52_2 = e2)
% 158.02/27.63 (75) all_58_3 = e3
% 158.02/27.63 (76) op(e3, e1) = all_52_8
% 158.02/27.63 (77) ~ (all_6_2 = e2)
% 158.02/27.63 (78) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.02/27.63 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.02/27.63 e3)
% 158.02/27.63 (79) all_56_13 = e3
% 158.02/27.63 (80) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.02/27.63 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.02/27.63 (81) ~ (all_52_9 = e2)
% 158.02/27.63 (82) ~ (all_52_8 = e3)
% 158.02/27.63 (83) all_54_14 = all_52_11
% 158.02/27.63 (84) ~ (all_52_7 = all_4_2)
% 158.02/27.63 (85) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.02/27.63 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.02/27.63 (86) op(e0, e2) = all_52_7
% 158.02/27.63 (87) all_54_15 = all_4_2
% 158.02/27.63 (88) all_58_0 = e0
% 158.02/27.63 (89) ~ (all_52_8 = e1)
% 158.02/27.63 (90) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.02/27.63 (91) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/27.63 (92) ~ (all_52_6 = e3)
% 158.02/27.63 (93) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.02/27.63 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.02/27.63 (94) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.02/27.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.02/27.63 (95) all_54_11 = all_52_14
% 158.02/27.63 (96) ~ (all_52_13 = all_52_14)
% 158.02/27.63 (97) ~ (e3 = e2)
% 158.02/27.63 (98) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.02/27.63 (99) all_58_12 = e1
% 158.02/27.63 (100) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.02/27.63 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.02/27.63 (101) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 158.02/27.63 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.02/27.63 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 158.02/27.63 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.02/27.63 e0)))
% 158.02/27.63 (102) all_54_9 = all_52_6
% 158.02/27.63 (103) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.02/27.63 (104) ~ (all_52_14 = all_4_2)
% 158.02/27.63 (105) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.02/27.63
% 158.02/27.63 Begin of proof
% 158.02/27.63 |
% 158.02/27.63 | BETA: splitting (60) gives:
% 158.02/27.63 |
% 158.02/27.63 | Case 1:
% 158.02/27.63 | |
% 158.02/27.63 | | (106) all_58_12 = e0 & op(e0, e3) = e0
% 158.02/27.63 | |
% 158.02/27.63 | | ALPHA: (106) implies:
% 158.02/27.63 | | (107) all_58_12 = e0
% 158.02/27.63 | |
% 158.02/27.63 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.02/27.63 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 158.02/27.63 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.02/27.63 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 158.02/27.63 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 158.02/27.63 | | (57), (58), (59), (61), (62), (63), (64), (65), (66), (67), (68),
% 158.02/27.63 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 158.02/27.63 | | (80), (81), (82), (83), (84), (85), (86), (87), (89), (90), (91),
% 158.02/27.63 | | (92), (93), (94), (95), (96), (97), (98), (100), (101), (102),
% 158.02/27.63 | | (103), (104), (105), (107) are inconsistent by sub-proof #444.
% 158.02/27.63 | |
% 158.02/27.63 | Case 2:
% 158.02/27.63 | |
% 158.02/27.63 | | (108) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.02/27.63 | | e0)
% 158.02/27.63 | |
% 158.02/27.63 | | BETA: splitting (108) gives:
% 158.02/27.63 | |
% 158.02/27.63 | | Case 1:
% 158.02/27.63 | | |
% 158.02/27.63 | | | (109) all_58_13 = e0 & op(e0, e2) = e0
% 158.02/27.63 | | |
% 158.02/27.63 | | | ALPHA: (109) implies:
% 158.02/27.63 | | | (110) op(e0, e2) = e0
% 158.02/27.63 | | |
% 158.02/27.63 | | | BETA: splitting (105) gives:
% 158.02/27.63 | | |
% 158.02/27.63 | | | Case 1:
% 158.02/27.63 | | | |
% 158.02/27.63 | | | | (111) all_56_12 = e3
% 158.02/27.63 | | | |
% 158.02/27.63 | | | | REF_CLOSE: (48), (49), (111) are inconsistent by sub-proof #1191.
% 158.02/27.63 | | | |
% 158.02/27.63 | | | Case 2:
% 158.02/27.63 | | | |
% 158.02/27.63 | | | | (112) ~ (all_56_12 = e3)
% 158.02/27.63 | | | | (113) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.02/27.63 | | | |
% 158.02/27.63 | | | | REDUCE: (49), (112) imply:
% 158.02/27.63 | | | | (114) ~ (e3 = e1)
% 158.02/27.63 | | | |
% 158.02/27.63 | | | | BETA: splitting (113) gives:
% 158.02/27.63 | | | |
% 158.02/27.63 | | | | Case 1:
% 158.02/27.63 | | | | |
% 158.02/27.63 | | | | | (115) all_56_13 = e2
% 158.02/27.63 | | | | |
% 158.02/27.63 | | | | | COMBINE_EQS: (79), (115) imply:
% 158.02/27.63 | | | | | (116) e3 = e2
% 158.02/27.63 | | | | |
% 158.02/27.63 | | | | | COMBINE_EQS: (25), (116) imply:
% 158.02/27.63 | | | | | (117) all_58_6 = e2
% 158.02/27.63 | | | | |
% 158.02/27.63 | | | | | REF_CLOSE: (23), (30), (35), (46), (48), (88), (94), (97), (99), (117)
% 158.02/27.63 | | | | | are inconsistent by sub-proof #1125.
% 158.02/27.63 | | | | |
% 158.02/27.63 | | | | Case 2:
% 158.02/27.63 | | | | |
% 158.02/27.63 | | | | | (118) all_56_14 = e1 | all_56_15 = e0
% 158.02/27.63 | | | | |
% 158.02/27.63 | | | | | REF_CLOSE: (5), (6), (13), (15), (19), (20), (21), (31), (32), (34),
% 158.02/27.63 | | | | | (38), (41), (48), (53), (57), (59), (61), (62), (64), (69),
% 158.02/27.63 | | | | | (71), (81), (82), (83), (84), (86), (89), (91), (94),
% 158.02/27.63 | | | | | (103), (110), (118) are inconsistent by sub-proof #472.
% 158.02/27.63 | | | | |
% 158.02/27.63 | | | | End of split
% 158.02/27.63 | | | |
% 158.02/27.63 | | | End of split
% 158.02/27.63 | | |
% 158.02/27.63 | | Case 2:
% 158.02/27.63 | | |
% 158.02/27.63 | | | (119) all_58_14 = e0 & op(e0, e1) = e0
% 158.02/27.63 | | |
% 158.02/27.63 | | | ALPHA: (119) implies:
% 158.02/27.63 | | | (120) all_58_14 = e0
% 158.02/27.63 | | |
% 158.02/27.63 | | | REF_CLOSE: (12), (35), (120) are inconsistent by sub-proof #1444.
% 158.02/27.63 | | |
% 158.02/27.63 | | End of split
% 158.02/27.63 | |
% 158.02/27.63 | End of split
% 158.02/27.63 |
% 158.02/27.63 End of proof
% 158.02/27.63
% 158.02/27.63 Sub-proof #443 shows that the following formulas are inconsistent:
% 158.02/27.63 ----------------------------------------------------------------
% 158.02/27.63 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.63 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.02/27.63 (2) all_58_14 = e3
% 158.02/27.63 (3) op(e1, e1) = all_6_2
% 158.02/27.63 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.02/27.63 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.02/27.63 (5) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.02/27.63 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.02/27.63 (6) op(e2, e3) = all_52_1
% 158.02/27.63 (7) ~ (e3 = e0)
% 158.02/27.63 (8) ~ (e2 = e0)
% 158.02/27.63 (9) op(e2, e3) = e2
% 158.02/27.63 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 158.02/27.63 (11) ~ (e3 = e1)
% 158.02/27.63 (12) all_58_7 = e1
% 158.02/27.63 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.63 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.02/27.63 (14) all_58_4 = e2
% 158.02/27.63 (15) ~ (e2 = e1)
% 158.02/27.63 (16) ~ (e1 = e0)
% 158.02/27.63 (17) all_58_3 = e3
% 158.02/27.63 (18) ~ (all_6_2 = e2)
% 158.02/27.63 (19) all_58_0 = e0
% 158.02/27.63 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.02/27.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.02/27.63 (21) ~ (e3 = e2)
% 158.02/27.63 (22) all_58_12 = e1
% 158.02/27.63
% 158.02/27.63 Begin of proof
% 158.02/27.63 |
% 158.02/27.63 | BETA: splitting (10) gives:
% 158.02/27.63 |
% 158.02/27.63 | Case 1:
% 158.02/27.63 | |
% 158.02/27.63 | | (23) all_58_6 = e2 & op(e1, e3) = e2
% 158.02/27.63 | |
% 158.02/27.63 | | ALPHA: (23) implies:
% 158.02/27.63 | | (24) all_58_6 = e2
% 158.02/27.63 | |
% 158.02/27.63 | | REF_CLOSE: (4), (6), (7), (9), (11), (19), (20), (21), (22), (24) are
% 158.02/27.63 | | inconsistent by sub-proof #1125.
% 158.02/27.63 | |
% 158.02/27.63 | Case 2:
% 158.02/27.63 | |
% 158.02/27.63 | | (25) all_58_7 = e2 & op(e1, e2) = e2
% 158.02/27.63 | |
% 158.02/27.63 | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (12), (13), (14), (15),
% 158.02/27.63 | | (16), (17), (18), (20), (21), (25) are inconsistent by sub-proof
% 158.02/27.63 | | #763.
% 158.02/27.63 | |
% 158.02/27.63 | End of split
% 158.02/27.63 |
% 158.02/27.63 End of proof
% 158.02/27.63
% 158.02/27.63 Sub-proof #444 shows that the following formulas are inconsistent:
% 158.02/27.63 ----------------------------------------------------------------
% 158.02/27.63 (1) op(e1, e3) = e3
% 158.02/27.63 (2) op(e1, e1) = e3
% 158.02/27.63 (3) op(e1, e1) = all_32_1
% 158.02/27.63 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.02/27.63 (5) all_56_14 = e3
% 158.02/27.63 (6) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.02/27.63 (7) op(e3, e1) = e3
% 158.02/27.63 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.02/27.63 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.02/27.63 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.63 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.63 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.02/27.63 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.02/27.63 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.63 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.02/27.63 (12) all_58_14 = e3
% 158.02/27.63 (13) all_54_13 = all_52_7
% 158.02/27.63 (14) op(e1, e1) = all_6_2
% 158.02/27.63 (15) ~ (all_52_7 = e3)
% 158.02/27.63 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.63 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.02/27.63 e1)
% 158.02/27.63 (17) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.02/27.63 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.02/27.63 (18) ~ (all_52_6 = all_52_14)
% 158.02/27.63 (19) ~ (all_52_11 = e3)
% 158.02/27.63 (20) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.02/27.63 (21) ~ (all_52_7 = all_52_11)
% 158.02/27.63 (22) op(e1, e2) = all_14_0
% 158.02/27.63 (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.02/27.63 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.02/27.63 (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.02/27.63 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.02/27.63 (25) all_58_6 = e3
% 158.02/27.63 (26) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.02/27.63 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.02/27.63 (27) ~ (all_52_14 = e3)
% 158.02/27.63 (28) all_58_12 = e0
% 158.02/27.63 (29) op(e3, e2) = all_52_4
% 158.02/27.63 (30) ~ (all_4_2 = e2)
% 158.02/27.63 (31) op(e2, e3) = all_52_1
% 158.02/27.63 (32) ~ (all_52_13 = e3)
% 158.02/27.63 (33) all_54_2 = all_52_8
% 158.02/27.63 (34) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.02/27.63 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.02/27.63 (35) ~ (all_52_8 = all_52_9)
% 158.02/27.63 (36) ~ (e3 = e0)
% 158.02/27.63 (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.02/27.63 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.02/27.63 (38) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.02/27.63 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.02/27.63 (39) ~ (all_52_9 = all_52_13)
% 158.02/27.63 (40) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.02/27.63 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.02/27.63 e2)
% 158.02/27.63 (41) ~ (e2 = e0)
% 158.02/27.63 (42) ~ (all_52_9 = e3)
% 158.02/27.63 (43) ~ (all_52_2 = all_52_6)
% 158.02/27.63 (44) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.02/27.63 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.02/27.63 (45) op(e1, e3) = all_52_2
% 158.02/27.63 (46) op(e2, e0) = all_52_13
% 158.02/27.63 (47) op(e2, e3) = e2
% 158.02/27.63 (48) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.63 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.02/27.63 (49) ~ (e3 = e1)
% 158.02/27.63 (50) all_56_12 = e1
% 158.02/27.63 (51) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.02/27.63 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.63 (52) op(e1, e2) = all_52_6
% 158.02/27.63 (53) ~ (all_4_2 = e1)
% 158.02/27.63 (54) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.02/27.63 (55) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.63 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.02/27.63 (56) op(e0, e0) = all_4_2
% 158.02/27.63 (57) all_54_8 = all_52_2
% 158.02/27.63 (58) all_54_7 = all_52_13
% 158.02/27.63 (59) ~ (all_52_2 = e3)
% 158.02/27.63 (60) ~ (all_52_13 = e2)
% 158.02/27.63 (61) all_56_15 = all_4_2
% 158.02/27.63 (62) ~ (all_52_9 = all_52_11)
% 158.02/27.63 (63) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.02/27.63 (64) ~ (all_52_13 = all_4_2)
% 158.02/27.63 (65) ~ (all_52_2 = e1)
% 158.02/27.63 (66) ~ (all_52_6 = all_52_7)
% 158.02/27.63 (67) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.02/27.63 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.02/27.63 (68) ~ (all_52_4 = e3)
% 158.02/27.63 (69) all_54_6 = all_52_9
% 158.02/27.63 (70) ~ (e2 = e1)
% 158.02/27.63 (71) ~ (all_52_8 = all_52_11)
% 158.02/27.63 (72) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.02/27.63 (73) ~ (e1 = e0)
% 158.02/27.63 (74) ~ (all_52_2 = e2)
% 158.02/27.63 (75) all_58_3 = e3
% 158.02/27.63 (76) op(e3, e1) = all_52_8
% 158.02/27.63 (77) ~ (all_6_2 = e2)
% 158.02/27.63 (78) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.02/27.63 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.02/27.63 e3)
% 158.02/27.63 (79) all_56_13 = e3
% 158.02/27.63 (80) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.02/27.63 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.02/27.63 (81) ~ (all_52_9 = e2)
% 158.02/27.63 (82) ~ (all_52_8 = e3)
% 158.02/27.63 (83) all_54_14 = all_52_11
% 158.02/27.63 (84) ~ (all_52_7 = all_4_2)
% 158.02/27.63 (85) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.02/27.63 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.02/27.63 (86) op(e0, e2) = all_52_7
% 158.02/27.63 (87) all_54_15 = all_4_2
% 158.02/27.63 (88) ~ (all_52_8 = e1)
% 158.02/27.63 (89) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.02/27.63 (90) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.02/27.63 (91) ~ (all_52_6 = e3)
% 158.02/27.63 (92) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.02/27.63 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.02/27.63 (93) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.02/27.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.02/27.63 (94) all_54_11 = all_52_14
% 158.02/27.63 (95) ~ (all_52_13 = all_52_14)
% 158.02/27.63 (96) ~ (e3 = e2)
% 158.02/27.63 (97) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.02/27.64 (98) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.02/27.64 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.02/27.64 (99) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.02/27.64 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.02/27.64 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.02/27.64 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.02/27.64 (100) all_54_9 = all_52_6
% 158.02/27.64 (101) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.02/27.64 (102) ~ (all_52_14 = all_4_2)
% 158.02/27.64 (103) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.02/27.64
% 158.02/27.64 Begin of proof
% 158.02/27.64 |
% 158.02/27.64 | BETA: splitting (16) gives:
% 158.02/27.64 |
% 158.02/27.64 | Case 1:
% 158.02/27.64 | |
% 158.02/27.64 | | (104) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 158.02/27.64 | | e1)
% 158.02/27.64 | |
% 158.02/27.64 | | BETA: splitting (104) gives:
% 158.02/27.64 | |
% 158.02/27.64 | | Case 1:
% 158.02/27.64 | | |
% 158.02/27.64 | | | (105) all_58_12 = e1 & op(e0, e3) = e1
% 158.02/27.64 | | |
% 158.02/27.64 | | | ALPHA: (105) implies:
% 158.02/27.64 | | | (106) all_58_12 = e1
% 158.02/27.64 | | |
% 158.02/27.64 | | | REF_CLOSE: (28), (73), (106) are inconsistent by sub-proof #1513.
% 158.02/27.64 | | |
% 158.02/27.64 | | Case 2:
% 158.02/27.64 | | |
% 158.02/27.64 | | | (107) all_58_13 = e1 & op(e0, e2) = e1
% 158.02/27.64 | | |
% 158.02/27.64 | | | ALPHA: (107) implies:
% 158.02/27.64 | | | (108) all_58_13 = e1
% 158.02/27.64 | | |
% 158.02/27.64 | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13),
% 158.02/27.64 | | | (14), (15), (16), (17), (18), (20), (22), (23), (24), (25),
% 158.02/27.64 | | | (27), (28), (29), (30), (31), (32), (34), (36), (37), (38),
% 158.02/27.64 | | | (40), (41), (43), (44), (45), (46), (47), (48), (49), (51),
% 158.02/27.64 | | | (52), (53), (55), (56), (57), (58), (59), (60), (61), (63),
% 158.02/27.64 | | | (64), (65), (66), (67), (68), (70), (72), (73), (74), (75),
% 158.02/27.64 | | | (77), (78), (80), (84), (85), (86), (87), (89), (90), (91),
% 158.02/27.64 | | | (92), (93), (94), (95), (96), (97), (99), (100), (102), (108)
% 158.02/27.64 | | | are inconsistent by sub-proof #457.
% 158.02/27.64 | | |
% 158.02/27.64 | | End of split
% 158.02/27.64 | |
% 158.02/27.64 | Case 2:
% 158.02/27.64 | |
% 158.02/27.64 | | (109) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.02/27.64 | | e1)
% 158.02/27.64 | |
% 158.02/27.64 | | BETA: splitting (109) gives:
% 158.02/27.64 | |
% 158.02/27.64 | | Case 1:
% 158.02/27.64 | | |
% 158.02/27.64 | | | (110) all_58_14 = e1 & op(e0, e1) = e1
% 158.02/27.64 | | |
% 158.02/27.64 | | | ALPHA: (110) implies:
% 158.02/27.64 | | | (111) all_58_14 = e1
% 158.02/27.64 | | |
% 158.02/27.64 | | | REF_CLOSE: (12), (49), (111) are inconsistent by sub-proof #1147.
% 158.02/27.64 | | |
% 158.02/27.64 | | Case 2:
% 158.02/27.64 | | |
% 158.02/27.64 | | | (112) all_58_15 = e1 & op(e0, e0) = e1
% 158.02/27.64 | | |
% 158.02/27.64 | | | ALPHA: (112) implies:
% 158.02/27.64 | | | (113) op(e0, e0) = e1
% 158.02/27.64 | | |
% 158.02/27.64 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.02/27.64 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 158.02/27.64 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 158.02/27.64 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 158.02/27.64 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 158.02/27.64 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 158.02/27.64 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 158.02/27.64 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 158.02/27.64 | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 158.02/27.64 | | | (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 158.02/27.64 | | | (103), (113) are inconsistent by sub-proof #445.
% 158.02/27.64 | | |
% 158.02/27.64 | | End of split
% 158.02/27.64 | |
% 158.02/27.64 | End of split
% 158.02/27.64 |
% 158.02/27.64 End of proof
% 158.02/27.64
% 158.02/27.64 Sub-proof #445 shows that the following formulas are inconsistent:
% 158.02/27.64 ----------------------------------------------------------------
% 158.02/27.64 (1) op(e1, e3) = e3
% 158.02/27.64 (2) op(e1, e1) = e3
% 158.02/27.64 (3) op(e1, e1) = all_32_1
% 158.02/27.64 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.02/27.64 (5) all_56_14 = e3
% 158.02/27.64 (6) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.02/27.64 (7) op(e3, e1) = e3
% 158.02/27.64 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.02/27.64 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.02/27.64 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.64 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.64 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.02/27.64 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.02/27.64 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.02/27.64 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.02/27.64 (12) all_58_14 = e3
% 158.02/27.64 (13) all_54_13 = all_52_7
% 158.02/27.64 (14) op(e1, e1) = all_6_2
% 158.02/27.64 (15) ~ (all_52_7 = e3)
% 158.02/27.64 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.02/27.64 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.02/27.64 e1)
% 158.02/27.64 (17) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.02/27.64 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.02/27.64 (18) ~ (all_52_6 = all_52_14)
% 158.02/27.64 (19) ~ (all_52_11 = e3)
% 158.02/27.64 (20) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.02/27.64 (21) ~ (all_52_7 = all_52_11)
% 158.02/27.64 (22) op(e1, e2) = all_14_0
% 158.02/27.64 (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.02/27.64 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.02/27.64 (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.02/27.64 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.02/27.64 (25) all_58_6 = e3
% 158.02/27.64 (26) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.02/27.64 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.02/27.64 (27) ~ (all_52_14 = e3)
% 158.02/27.64 (28) all_58_12 = e0
% 158.02/27.64 (29) op(e3, e2) = all_52_4
% 158.02/27.64 (30) ~ (all_4_2 = e2)
% 158.02/27.64 (31) op(e2, e3) = all_52_1
% 158.02/27.64 (32) ~ (all_52_13 = e3)
% 158.02/27.64 (33) all_54_2 = all_52_8
% 158.02/27.64 (34) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.02/27.64 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.02/27.64 (35) ~ (all_52_8 = all_52_9)
% 158.02/27.64 (36) ~ (e3 = e0)
% 158.02/27.64 (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.02/27.64 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.02/27.64 (38) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.02/27.64 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.02/27.64 (39) ~ (all_52_9 = all_52_13)
% 158.02/27.64 (40) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.02/27.64 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.02/27.64 e2)
% 158.02/27.64 (41) ~ (e2 = e0)
% 158.02/27.64 (42) ~ (all_52_9 = e3)
% 158.02/27.64 (43) ~ (all_52_2 = all_52_6)
% 158.02/27.64 (44) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.02/27.64 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.02/27.64 (45) op(e1, e3) = all_52_2
% 158.02/27.64 (46) op(e2, e0) = all_52_13
% 158.02/27.64 (47) op(e2, e3) = e2
% 158.02/27.64 (48) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.64 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.02/27.64 (49) ~ (e3 = e1)
% 158.02/27.64 (50) all_56_12 = e1
% 158.02/27.64 (51) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.02/27.64 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.02/27.64 (52) op(e1, e2) = all_52_6
% 158.02/27.64 (53) ~ (all_4_2 = e1)
% 158.02/27.64 (54) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.02/27.64 (55) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.02/27.64 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.02/27.64 (56) op(e0, e0) = all_4_2
% 158.02/27.64 (57) all_54_8 = all_52_2
% 158.02/27.64 (58) all_54_7 = all_52_13
% 158.02/27.64 (59) ~ (all_52_2 = e3)
% 158.02/27.64 (60) ~ (all_52_13 = e2)
% 158.02/27.64 (61) all_56_15 = all_4_2
% 158.02/27.64 (62) ~ (all_52_9 = all_52_11)
% 158.02/27.64 (63) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.02/27.64 (64) ~ (all_52_13 = all_4_2)
% 158.02/27.64 (65) ~ (all_52_2 = e1)
% 158.02/27.64 (66) ~ (all_52_6 = all_52_7)
% 158.02/27.64 (67) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.02/27.64 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.02/27.64 (68) ~ (all_52_4 = e3)
% 158.02/27.64 (69) all_54_6 = all_52_9
% 158.02/27.64 (70) ~ (e2 = e1)
% 158.28/27.64 (71) ~ (all_52_8 = all_52_11)
% 158.28/27.64 (72) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.28/27.64 (73) ~ (e1 = e0)
% 158.28/27.64 (74) ~ (all_52_2 = e2)
% 158.28/27.64 (75) all_58_3 = e3
% 158.28/27.64 (76) op(e3, e1) = all_52_8
% 158.28/27.64 (77) ~ (all_6_2 = e2)
% 158.28/27.64 (78) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.28/27.64 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.28/27.64 e3)
% 158.28/27.64 (79) all_56_13 = e3
% 158.28/27.64 (80) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.28/27.64 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.28/27.64 (81) ~ (all_52_9 = e2)
% 158.28/27.64 (82) ~ (all_52_8 = e3)
% 158.28/27.64 (83) all_54_14 = all_52_11
% 158.28/27.64 (84) ~ (all_52_7 = all_4_2)
% 158.28/27.64 (85) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.28/27.64 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.28/27.64 (86) op(e0, e2) = all_52_7
% 158.28/27.64 (87) all_54_15 = all_4_2
% 158.28/27.64 (88) ~ (all_52_8 = e1)
% 158.28/27.64 (89) op(e0, e0) = e1
% 158.28/27.64 (90) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.28/27.64 (91) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.28/27.64 (92) ~ (all_52_6 = e3)
% 158.28/27.64 (93) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.28/27.64 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.28/27.64 (94) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.28/27.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.28/27.64 (95) all_54_11 = all_52_14
% 158.28/27.64 (96) ~ (all_52_13 = all_52_14)
% 158.28/27.64 (97) ~ (e3 = e2)
% 158.28/27.64 (98) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.28/27.64 (99) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.28/27.64 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.28/27.64 (100) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 158.28/27.64 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.28/27.64 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 158.28/27.64 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.28/27.64 e0)))
% 158.28/27.64 (101) all_54_9 = all_52_6
% 158.28/27.64 (102) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.28/27.64 (103) ~ (all_52_14 = all_4_2)
% 158.28/27.64 (104) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.28/27.64
% 158.28/27.64 Begin of proof
% 158.28/27.64 |
% 158.28/27.64 | BETA: splitting (17) gives:
% 158.28/27.64 |
% 158.28/27.64 | Case 1:
% 158.28/27.64 | |
% 158.28/27.64 | | (105) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 158.28/27.64 | | e3)
% 158.28/27.64 | |
% 158.28/27.64 | | BETA: splitting (105) gives:
% 158.28/27.64 | |
% 158.28/27.64 | | Case 1:
% 158.28/27.64 | | |
% 158.28/27.64 | | | (106) all_58_9 = e3 & op(e3, e0) = e3
% 158.28/27.64 | | |
% 158.28/27.64 | | | ALPHA: (106) implies:
% 158.28/27.64 | | | (107) all_58_9 = e3
% 158.28/27.64 | | |
% 158.28/27.64 | | | BETA: splitting (37) gives:
% 158.28/27.64 | | |
% 158.28/27.64 | | | Case 1:
% 158.28/27.64 | | | |
% 158.28/27.64 | | | | (108) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 158.28/27.64 | | | | = e1)
% 158.28/27.64 | | | |
% 158.28/27.64 | | | | BETA: splitting (108) gives:
% 158.28/27.64 | | | |
% 158.28/27.64 | | | | Case 1:
% 158.28/27.64 | | | | |
% 158.28/27.64 | | | | | (109) all_58_0 = e1 & op(e3, e3) = e1
% 158.28/27.64 | | | | |
% 158.28/27.64 | | | | | ALPHA: (109) implies:
% 158.28/27.64 | | | | | (110) all_58_0 = e1
% 158.28/27.64 | | | | |
% 158.28/27.64 | | | | | BETA: splitting (67) gives:
% 158.28/27.64 | | | | |
% 158.28/27.64 | | | | | Case 1:
% 158.28/27.64 | | | | | |
% 158.28/27.64 | | | | | | (111) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 158.28/27.64 | | | | | | e1) = e1)
% 158.28/27.64 | | | | | |
% 158.28/27.64 | | | | | | BETA: splitting (111) gives:
% 158.28/27.64 | | | | | |
% 158.28/27.64 | | | | | | Case 1:
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | (112) all_58_4 = e1 & op(e3, e1) = e1
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | ALPHA: (112) implies:
% 158.28/27.64 | | | | | | | (113) all_58_4 = e1
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | REF_CLOSE: (11), (12), (14), (24), (36), (41), (47), (49), (55),
% 158.28/27.64 | | | | | | | (70), (73), (75), (77), (94), (97), (113) are
% 158.28/27.64 | | | | | | | inconsistent by sub-proof #850.
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | Case 2:
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | (114) all_58_5 = e1 & op(e2, e1) = e1
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | ALPHA: (114) implies:
% 158.28/27.64 | | | | | | | (115) all_58_5 = e1
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (11), (12), (14), (19),
% 158.28/27.64 | | | | | | | (20), (23), (24), (25), (26), (28), (30), (31), (32),
% 158.28/27.64 | | | | | | | (33), (35), (36), (39), (41), (42), (44), (47), (49),
% 158.28/27.64 | | | | | | | (50), (51), (54), (55), (58), (60), (61), (62), (64),
% 158.28/27.64 | | | | | | | (69), (70), (71), (73), (75), (76), (77), (79), (81),
% 158.28/27.64 | | | | | | | (82), (83), (88), (89), (94), (97), (102), (104),
% 158.28/27.64 | | | | | | | (107), (110), (115) are inconsistent by sub-proof #454.
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | End of split
% 158.28/27.64 | | | | | |
% 158.28/27.64 | | | | | Case 2:
% 158.28/27.64 | | | | | |
% 158.28/27.64 | | | | | | (116) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 158.28/27.64 | | | | | | op(e0, e1) = e1)
% 158.28/27.64 | | | | | |
% 158.28/27.64 | | | | | | BETA: splitting (116) gives:
% 158.28/27.64 | | | | | |
% 158.28/27.64 | | | | | | Case 1:
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | (117) all_58_8 = e1 & op(e1, e1) = e1
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | ALPHA: (117) implies:
% 158.28/27.64 | | | | | | | (118) all_58_8 = e1
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | BETA: splitting (55) gives:
% 158.28/27.64 | | | | | | |
% 158.28/27.64 | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | |
% 158.28/27.64 | | | | | | | | (119) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 158.28/27.64 | | | | | | | | op(e2, e2) = e0)
% 158.28/27.64 | | | | | | | |
% 158.28/27.64 | | | | | | | | REF_CLOSE: (36), (41), (47), (75), (94), (119) are inconsistent
% 158.28/27.64 | | | | | | | | by sub-proof #755.
% 158.28/27.64 | | | | | | | |
% 158.28/27.64 | | | | | | | Case 2:
% 158.28/27.64 | | | | | | | |
% 158.28/27.64 | | | | | | | | (120) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 158.28/27.64 | | | | | | | | op(e2, e0) = e0)
% 158.28/27.64 | | | | | | | |
% 158.28/27.64 | | | | | | | | BETA: splitting (120) gives:
% 158.28/27.64 | | | | | | | |
% 158.28/27.64 | | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | | |
% 158.28/27.64 | | | | | | | | | (121) all_58_5 = e0 & op(e2, e1) = e0
% 158.28/27.64 | | | | | | | | |
% 158.28/27.64 | | | | | | | | | ALPHA: (121) implies:
% 158.28/27.64 | | | | | | | | | (122) all_58_5 = e0
% 158.28/27.64 | | | | | | | | |
% 158.28/27.64 | | | | | | | | | BETA: splitting (26) gives:
% 158.28/27.64 | | | | | | | | |
% 158.28/27.64 | | | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | (123) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 158.28/27.64 | | | | | | | | | | & op(e2, e0) = e2)
% 158.28/27.64 | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | REF_CLOSE: (11), (23), (25), (28), (31), (36), (41), (47),
% 158.28/27.64 | | | | | | | | | | (49), (55), (70), (73), (75), (94), (97), (107),
% 158.28/27.64 | | | | | | | | | | (110), (123) are inconsistent by sub-proof #453.
% 158.28/27.64 | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | Case 2:
% 158.28/27.64 | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | (124) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 158.28/27.64 | | | | | | | | | | e2 & op(e0, e0) = e2)
% 158.28/27.64 | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | BETA: splitting (124) gives:
% 158.28/27.64 | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | (125) all_58_11 = e2 & op(e1, e0) = e2
% 158.28/27.64 | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | ALPHA: (125) implies:
% 158.28/27.64 | | | | | | | | | | | (126) all_58_11 = e2
% 158.28/27.64 | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | BETA: splitting (40) gives:
% 158.28/27.64 | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | (127) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 158.28/27.64 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 158.28/27.64 | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | BETA: splitting (127) gives:
% 158.28/27.64 | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | (128) all_58_12 = e2 & op(e0, e3) = e2
% 158.28/27.64 | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | ALPHA: (128) implies:
% 158.28/27.64 | | | | | | | | | | | | | (129) all_58_12 = e2
% 158.28/27.64 | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | REF_CLOSE: (23), (31), (36), (37), (41), (47), (49), (70),
% 158.28/27.64 | | | | | | | | | | | | | (73), (93), (94), (97), (129) are inconsistent by
% 158.28/27.64 | | | | | | | | | | | | | sub-proof #1062.
% 158.28/27.64 | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | Case 2:
% 158.28/27.64 | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | (130) all_58_13 = e2 & op(e0, e2) = e2
% 158.28/27.64 | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | ALPHA: (130) implies:
% 158.28/27.64 | | | | | | | | | | | | | (131) all_58_13 = e2
% 158.28/27.64 | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | BETA: splitting (9) gives:
% 158.28/27.64 | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | (132) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 158.28/27.64 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 158.28/27.64 | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 158.28/27.64 | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | (133) all_58_1 = e1 & op(e3, e2) = e1
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 158.28/27.64 | | | | | | | | | | | | | | | (134) all_58_1 = e1
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (14), (23), (24), (25), (28), (29),
% 158.28/27.64 | | | | | | | | | | | | | | | (31), (36), (37), (41), (47), (49), (55), (68),
% 158.28/27.64 | | | | | | | | | | | | | | | (70), (73), (75), (77), (85), (94), (97), (99),
% 158.28/27.64 | | | | | | | | | | | | | | | (107), (110), (122), (134) are inconsistent by
% 158.28/27.64 | | | | | | | | | | | | | | | sub-proof #820.
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | Case 2:
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | (135) all_58_3 = e1 & op(e2, e2) = e1
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (14), (23), (24), (25), (28), (29),
% 158.28/27.64 | | | | | | | | | | | | | | | (31), (36), (37), (41), (47), (49), (55), (68),
% 158.28/27.64 | | | | | | | | | | | | | | | (70), (73), (75), (77), (85), (94), (97), (107),
% 158.28/27.64 | | | | | | | | | | | | | | | (110), (122), (135) are inconsistent by sub-proof
% 158.28/27.64 | | | | | | | | | | | | | | | #452.
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | End of split
% 158.28/27.64 | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | Case 2:
% 158.28/27.64 | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | (136) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 158.28/27.64 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 158.28/27.64 | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 158.28/27.64 | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | Case 1:
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | (137) all_58_7 = e1 & op(e1, e2) = e1
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 158.28/27.64 | | | | | | | | | | | | | | | (138) all_58_7 = e1
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (12), (14), (23), (24), (25),
% 158.28/27.64 | | | | | | | | | | | | | | | (28), (29), (31), (36), (37), (41), (44), (47),
% 158.28/27.64 | | | | | | | | | | | | | | | (49), (55), (68), (70), (73), (75), (77), (85),
% 158.28/27.64 | | | | | | | | | | | | | | | (94), (97), (99), (107), (110), (118), (122),
% 158.28/27.64 | | | | | | | | | | | | | | | (126), (131), (138) are inconsistent by sub-proof
% 158.28/27.64 | | | | | | | | | | | | | | | #449.
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | Case 2:
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | (139) all_58_13 = e1 & op(e0, e2) = e1
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 158.28/27.64 | | | | | | | | | | | | | | | (140) all_58_13 = e1
% 158.28/27.64 | | | | | | | | | | | | | | |
% 158.28/27.64 | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (9), (10), (11), (12), (13), (14),
% 158.28/27.64 | | | | | | | | | | | | | | | (15), (16), (18), (20), (22), (23), (24), (25),
% 158.28/27.64 | | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (34), (37),
% 158.28/27.64 | | | | | | | | | | | | | | | (38), (40), (43), (44), (45), (47), (48), (49),
% 158.28/27.64 | | | | | | | | | | | | | | | (52), (53), (55), (56), (57), (58), (59), (60),
% 158.28/27.65 | | | | | | | | | | | | | | | (61), (63), (64), (65), (66), (68), (70), (72),
% 158.28/27.65 | | | | | | | | | | | | | | | (74), (75), (77), (78), (80), (84), (85), (86),
% 158.28/27.65 | | | | | | | | | | | | | | | (87), (90), (91), (92), (93), (94), (95), (96),
% 158.28/27.65 | | | | | | | | | | | | | | | (97), (98), (100), (101), (103), (110), (118),
% 158.28/27.65 | | | | | | | | | | | | | | | (140) are inconsistent by sub-proof #458.
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | (141) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 158.28/27.65 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | REF_CLOSE: (10), (12), (23), (25), (28), (31), (36), (41),
% 158.28/27.65 | | | | | | | | | | | | (47), (49), (70), (73), (94), (97), (100), (107),
% 158.28/27.65 | | | | | | | | | | | | (110), (126), (141) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | | | | #448.
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (142) all_58_15 = e2 & op(e0, e0) = e2
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (142) implies:
% 158.28/27.65 | | | | | | | | | | | (143) op(e0, e0) = e2
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (70), (89), (94), (143) are inconsistent by
% 158.28/27.65 | | | | | | | | | | | sub-proof #1386.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | (144) all_58_10 = e0 & op(e2, e0) = e0
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | ALPHA: (144) implies:
% 158.28/27.65 | | | | | | | | | (145) all_58_10 = e0
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | BETA: splitting (26) gives:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | (146) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 158.28/27.65 | | | | | | | | | | & op(e2, e0) = e2)
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | REF_CLOSE: (11), (23), (25), (28), (31), (36), (41), (47),
% 158.28/27.65 | | | | | | | | | | (49), (55), (70), (73), (75), (94), (97), (107),
% 158.28/27.65 | | | | | | | | | | (110), (146) are inconsistent by sub-proof #453.
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | (147) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 158.28/27.65 | | | | | | | | | | e2 & op(e0, e0) = e2)
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | BETA: splitting (147) gives:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (148) all_58_11 = e2 & op(e1, e0) = e2
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (148) implies:
% 158.28/27.65 | | | | | | | | | | | (149) all_58_11 = e2
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | BETA: splitting (40) gives:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | (150) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 158.28/27.65 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | BETA: splitting (150) gives:
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | (151) all_58_12 = e2 & op(e0, e3) = e2
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | ALPHA: (151) implies:
% 158.28/27.65 | | | | | | | | | | | | | (152) all_58_12 = e2
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | REF_CLOSE: (23), (31), (36), (37), (41), (47), (49), (70),
% 158.28/27.65 | | | | | | | | | | | | | (73), (93), (94), (97), (152) are inconsistent by
% 158.28/27.65 | | | | | | | | | | | | | sub-proof #1062.
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | (153) all_58_13 = e2 & op(e0, e2) = e2
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | ALPHA: (153) implies:
% 158.28/27.65 | | | | | | | | | | | | | (154) all_58_13 = e2
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | BETA: splitting (9) gives:
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | (155) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 158.28/27.65 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | (156) all_58_1 = e1 & op(e3, e2) = e1
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 158.28/27.65 | | | | | | | | | | | | | | | (157) all_58_1 = e1
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (14), (23), (24), (25), (28), (29),
% 158.28/27.65 | | | | | | | | | | | | | | | (31), (36), (37), (41), (47), (49), (55), (68),
% 158.28/27.65 | | | | | | | | | | | | | | | (70), (73), (75), (77), (85), (94), (97), (99),
% 158.28/27.65 | | | | | | | | | | | | | | | (107), (110), (145), (157) are inconsistent by
% 158.28/27.65 | | | | | | | | | | | | | | | sub-proof #818.
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | (158) all_58_3 = e1 & op(e2, e2) = e1
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 158.28/27.65 | | | | | | | | | | | | | | | (159) all_58_3 = e1
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | REF_CLOSE: (49), (75), (159) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | | | | | | | #841.
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | (160) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 158.28/27.65 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | (161) all_58_7 = e1 & op(e1, e2) = e1
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 158.28/27.65 | | | | | | | | | | | | | | | (162) all_58_7 = e1
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (12), (14), (23), (24), (25),
% 158.28/27.65 | | | | | | | | | | | | | | | (28), (29), (31), (36), (37), (41), (44), (47),
% 158.28/27.65 | | | | | | | | | | | | | | | (49), (51), (55), (68), (70), (73), (75), (77),
% 158.28/27.65 | | | | | | | | | | | | | | | (85), (94), (97), (99), (107), (110), (118),
% 158.28/27.65 | | | | | | | | | | | | | | | (145), (149), (154), (162) are inconsistent by
% 158.28/27.65 | | | | | | | | | | | | | | | sub-proof #447.
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | (163) all_58_13 = e1 & op(e0, e2) = e1
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 158.28/27.65 | | | | | | | | | | | | | | | (164) all_58_13 = e1
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (9), (10), (11), (12), (13), (14),
% 158.28/27.65 | | | | | | | | | | | | | | | (15), (16), (18), (20), (22), (23), (24), (25),
% 158.28/27.65 | | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (34), (37),
% 158.28/27.65 | | | | | | | | | | | | | | | (38), (40), (43), (44), (45), (47), (48), (49),
% 158.28/27.65 | | | | | | | | | | | | | | | (52), (53), (55), (56), (57), (58), (59), (60),
% 158.28/27.65 | | | | | | | | | | | | | | | (61), (63), (64), (65), (66), (68), (70), (72),
% 158.28/27.65 | | | | | | | | | | | | | | | (74), (75), (77), (78), (80), (84), (85), (86),
% 158.28/27.65 | | | | | | | | | | | | | | | (87), (90), (91), (92), (93), (94), (95), (96),
% 158.28/27.65 | | | | | | | | | | | | | | | (97), (98), (100), (101), (103), (110), (118),
% 158.28/27.65 | | | | | | | | | | | | | | | (164) are inconsistent by sub-proof #458.
% 158.28/27.65 | | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | (165) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 158.28/27.65 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | | REF_CLOSE: (10), (12), (23), (25), (28), (31), (36), (41),
% 158.28/27.65 | | | | | | | | | | | | (47), (49), (70), (73), (94), (97), (100), (107),
% 158.28/27.65 | | | | | | | | | | | | (110), (149), (165) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | | | | #448.
% 158.28/27.65 | | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (166) all_58_15 = e2 & op(e0, e0) = e2
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (166) implies:
% 158.28/27.65 | | | | | | | | | | | (167) op(e0, e0) = e2
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (70), (89), (94), (167) are inconsistent by
% 158.28/27.65 | | | | | | | | | | | sub-proof #1386.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | End of split
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | End of split
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | Case 2:
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | (168) all_58_14 = e1 & op(e0, e1) = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | ALPHA: (168) implies:
% 158.28/27.65 | | | | | | | (169) all_58_14 = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | REF_CLOSE: (12), (49), (169) are inconsistent by sub-proof #1147.
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | End of split
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | End of split
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | Case 2:
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | (170) all_58_2 = e1 & op(e2, e3) = e1
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | ALPHA: (170) implies:
% 158.28/27.65 | | | | | (171) op(e2, e3) = e1
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | REF_CLOSE: (47), (70), (94), (171) are inconsistent by sub-proof
% 158.28/27.65 | | | | | #1430.
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | End of split
% 158.28/27.65 | | | |
% 158.28/27.65 | | | Case 2:
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | (172) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 158.28/27.65 | | | | e3) = e1)
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | REF_CLOSE: (25), (28), (49), (73), (172) are inconsistent by sub-proof
% 158.28/27.65 | | | | #862.
% 158.28/27.65 | | | |
% 158.28/27.65 | | | End of split
% 158.28/27.65 | | |
% 158.28/27.65 | | Case 2:
% 158.28/27.65 | | |
% 158.28/27.65 | | | (173) all_58_10 = e3 & op(e2, e0) = e3
% 158.28/27.65 | | |
% 158.28/27.65 | | | ALPHA: (173) implies:
% 158.28/27.65 | | | (174) op(e2, e0) = e3
% 158.28/27.65 | | |
% 158.28/27.65 | | | REF_CLOSE: (32), (46), (94), (174) are inconsistent by sub-proof #1364.
% 158.28/27.65 | | |
% 158.28/27.65 | | End of split
% 158.28/27.65 | |
% 158.28/27.65 | Case 2:
% 158.28/27.65 | |
% 158.28/27.65 | | (175) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.28/27.65 | | e3)
% 158.28/27.65 | |
% 158.28/27.65 | | BETA: splitting (175) gives:
% 158.28/27.65 | |
% 158.28/27.65 | | Case 1:
% 158.28/27.65 | | |
% 158.28/27.65 | | | (176) all_58_11 = e3 & op(e1, e0) = e3
% 158.28/27.65 | | |
% 158.28/27.65 | | | ALPHA: (176) implies:
% 158.28/27.65 | | | (177) all_58_11 = e3
% 158.28/27.65 | | |
% 158.28/27.65 | | | BETA: splitting (34) gives:
% 158.28/27.65 | | |
% 158.28/27.65 | | | Case 1:
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | (178) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 158.28/27.65 | | | | = e2)
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | BETA: splitting (178) gives:
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | Case 1:
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | (179) all_58_6 = e2 & op(e1, e3) = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | ALPHA: (179) implies:
% 158.28/27.65 | | | | | (180) all_58_6 = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | REF_CLOSE: (23), (28), (31), (36), (37), (47), (49), (70), (73), (94),
% 158.28/27.65 | | | | | (97), (180) are inconsistent by sub-proof #1153.
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | Case 2:
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | (181) all_58_7 = e2 & op(e1, e2) = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | ALPHA: (181) implies:
% 158.28/27.65 | | | | | (182) all_58_7 = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | BETA: splitting (67) gives:
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | Case 1:
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | | (183) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 158.28/27.65 | | | | | | e1) = e1)
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | | BETA: splitting (183) gives:
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | | Case 1:
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | (184) all_58_4 = e1 & op(e3, e1) = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | ALPHA: (184) implies:
% 158.28/27.65 | | | | | | | (185) all_58_4 = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | REF_CLOSE: (11), (12), (14), (24), (36), (41), (47), (49), (55),
% 158.28/27.65 | | | | | | | (70), (73), (75), (77), (94), (97), (185) are
% 158.28/27.65 | | | | | | | inconsistent by sub-proof #850.
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | Case 2:
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | (186) all_58_5 = e1 & op(e2, e1) = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | ALPHA: (186) implies:
% 158.28/27.65 | | | | | | | (187) all_58_5 = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | BETA: splitting (37) gives:
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | (188) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 158.28/27.65 | | | | | | | | op(e2, e3) = e1)
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | BETA: splitting (188) gives:
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | (189) all_58_0 = e1 & op(e3, e3) = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | ALPHA: (189) implies:
% 158.28/27.65 | | | | | | | | | (190) all_58_0 = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | BETA: splitting (9) gives:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | (191) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 158.28/27.65 | | | | | | | | | | & op(e2, e2) = e1)
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | BETA: splitting (191) gives:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (192) all_58_1 = e1 & op(e3, e2) = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (192) implies:
% 158.28/27.65 | | | | | | | | | | | (193) all_58_1 = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (5), (6), (13), (15), (19), (20), (21), (23),
% 158.28/27.65 | | | | | | | | | | | (25), (28), (31), (32), (33), (35), (36), (39),
% 158.28/27.65 | | | | | | | | | | | (41), (42), (47), (48), (49), (50), (54), (58),
% 158.28/27.65 | | | | | | | | | | | (60), (61), (62), (64), (69), (71), (73), (75),
% 158.28/27.65 | | | | | | | | | | | (79), (81), (82), (83), (84), (86), (88), (91),
% 158.28/27.65 | | | | | | | | | | | (94), (97), (102), (104), (182), (190), (193) are
% 158.28/27.65 | | | | | | | | | | | inconsistent by sub-proof #446.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (194) all_58_3 = e1 & op(e2, e2) = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (194) implies:
% 158.28/27.65 | | | | | | | | | | | (195) all_58_3 = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (49), (75), (195) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | | | #841.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | (196) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1
% 158.28/27.65 | | | | | | | | | | & op(e0, e2) = e1)
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | BETA: splitting (196) gives:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (197) all_58_7 = e1 & op(e1, e2) = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (197) implies:
% 158.28/27.65 | | | | | | | | | | | (198) all_58_7 = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (70), (182), (198) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | | | #721.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (199) all_58_13 = e1 & op(e0, e2) = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (199) implies:
% 158.28/27.65 | | | | | | | | | | | (200) all_58_13 = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12),
% 158.28/27.65 | | | | | | | | | | | (13), (14), (15), (16), (17), (18), (20), (22),
% 158.28/27.65 | | | | | | | | | | | (23), (24), (25), (27), (28), (30), (31), (32),
% 158.28/27.65 | | | | | | | | | | | (34), (36), (37), (40), (41), (43), (46), (47),
% 158.28/27.65 | | | | | | | | | | | (48), (49), (51), (52), (53), (55), (56), (57),
% 158.28/27.65 | | | | | | | | | | | (58), (59), (60), (61), (63), (64), (65), (66),
% 158.28/27.65 | | | | | | | | | | | (70), (72), (73), (74), (75), (77), (78), (80),
% 158.28/27.65 | | | | | | | | | | | (84), (86), (87), (90), (91), (92), (93), (94),
% 158.28/27.65 | | | | | | | | | | | (95), (96), (97), (98), (100), (101), (103),
% 158.28/27.65 | | | | | | | | | | | (187), (190), (200) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | | | #461.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | (201) all_58_2 = e1 & op(e2, e3) = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | ALPHA: (201) implies:
% 158.28/27.65 | | | | | | | | | (202) op(e2, e3) = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | REF_CLOSE: (47), (70), (94), (202) are inconsistent by
% 158.28/27.65 | | | | | | | | | sub-proof #1430.
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | End of split
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | (203) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 158.28/27.65 | | | | | | | | op(e0, e3) = e1)
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | BETA: splitting (203) gives:
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | (204) all_58_6 = e1 & op(e1, e3) = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | REF_CLOSE: (25), (49), (204) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | #1347.
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | (205) all_58_12 = e1 & op(e0, e3) = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | ALPHA: (205) implies:
% 158.28/27.65 | | | | | | | | | (206) all_58_12 = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | REF_CLOSE: (28), (73), (206) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | #1513.
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | End of split
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | End of split
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | End of split
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | Case 2:
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | | (207) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 158.28/27.65 | | | | | | op(e0, e1) = e1)
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | | BETA: splitting (207) gives:
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | | Case 1:
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | (208) all_58_8 = e1 & op(e1, e1) = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | ALPHA: (208) implies:
% 158.28/27.65 | | | | | | | (209) all_58_8 = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | BETA: splitting (37) gives:
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | (210) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 158.28/27.65 | | | | | | | | op(e2, e3) = e1)
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | BETA: splitting (210) gives:
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | (211) all_58_0 = e1 & op(e3, e3) = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | ALPHA: (211) implies:
% 158.28/27.65 | | | | | | | | | (212) all_58_0 = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | BETA: splitting (9) gives:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | (213) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 158.28/27.65 | | | | | | | | | | & op(e2, e2) = e1)
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | BETA: splitting (213) gives:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (214) all_58_1 = e1 & op(e3, e2) = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (214) implies:
% 158.28/27.65 | | | | | | | | | | | (215) all_58_1 = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (5), (6), (13), (15), (19), (20), (21), (23),
% 158.28/27.65 | | | | | | | | | | | (25), (28), (31), (32), (33), (35), (36), (39),
% 158.28/27.65 | | | | | | | | | | | (41), (42), (47), (48), (49), (50), (54), (58),
% 158.28/27.65 | | | | | | | | | | | (60), (61), (62), (64), (69), (71), (73), (75),
% 158.28/27.65 | | | | | | | | | | | (79), (81), (82), (83), (84), (86), (88), (91),
% 158.28/27.65 | | | | | | | | | | | (94), (97), (102), (104), (182), (212), (215) are
% 158.28/27.65 | | | | | | | | | | | inconsistent by sub-proof #446.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (216) all_58_3 = e1 & op(e2, e2) = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (216) implies:
% 158.28/27.65 | | | | | | | | | | | (217) all_58_3 = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (49), (75), (217) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | | | #841.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | (218) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1
% 158.28/27.65 | | | | | | | | | | & op(e0, e2) = e1)
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | BETA: splitting (218) gives:
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 1:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (219) all_58_7 = e1 & op(e1, e2) = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (70), (182), (219) are inconsistent by sub-proof
% 158.28/27.65 | | | | | | | | | | | #1045.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | (220) all_58_13 = e1 & op(e0, e2) = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | ALPHA: (220) implies:
% 158.28/27.65 | | | | | | | | | | | (221) all_58_13 = e1
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (9), (10), (11), (12), (13), (14),
% 158.28/27.65 | | | | | | | | | | | (15), (16), (18), (20), (22), (23), (24), (25),
% 158.28/27.65 | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (34), (37),
% 158.28/27.65 | | | | | | | | | | | (38), (40), (43), (44), (45), (47), (48), (49),
% 158.28/27.65 | | | | | | | | | | | (52), (53), (55), (56), (57), (58), (59), (60),
% 158.28/27.65 | | | | | | | | | | | (61), (63), (64), (65), (66), (68), (70), (72),
% 158.28/27.65 | | | | | | | | | | | (74), (75), (77), (78), (80), (84), (85), (86),
% 158.28/27.65 | | | | | | | | | | | (87), (90), (91), (92), (93), (94), (95), (96),
% 158.28/27.65 | | | | | | | | | | | (97), (98), (100), (101), (103), (209), (212),
% 158.28/27.65 | | | | | | | | | | | (221) are inconsistent by sub-proof #458.
% 158.28/27.65 | | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | | |
% 158.28/27.65 | | | | | | | | | End of split
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | (222) all_58_2 = e1 & op(e2, e3) = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | ALPHA: (222) implies:
% 158.28/27.65 | | | | | | | | | (223) op(e2, e3) = e1
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | | REF_CLOSE: (47), (70), (94), (223) are inconsistent by
% 158.28/27.65 | | | | | | | | | sub-proof #1430.
% 158.28/27.65 | | | | | | | | |
% 158.28/27.65 | | | | | | | | End of split
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | Case 2:
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | (224) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 158.28/27.65 | | | | | | | | op(e0, e3) = e1)
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | | REF_CLOSE: (25), (28), (49), (73), (224) are inconsistent by
% 158.28/27.65 | | | | | | | | sub-proof #862.
% 158.28/27.65 | | | | | | | |
% 158.28/27.65 | | | | | | | End of split
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | Case 2:
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | (225) all_58_14 = e1 & op(e0, e1) = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | ALPHA: (225) implies:
% 158.28/27.65 | | | | | | | (226) all_58_14 = e1
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | | REF_CLOSE: (12), (49), (226) are inconsistent by sub-proof #1147.
% 158.28/27.65 | | | | | | |
% 158.28/27.65 | | | | | | End of split
% 158.28/27.65 | | | | | |
% 158.28/27.65 | | | | | End of split
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | End of split
% 158.28/27.65 | | | |
% 158.28/27.65 | | | Case 2:
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | (227) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 158.28/27.65 | | | | e0) = e2)
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | BETA: splitting (227) gives:
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | Case 1:
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | (228) all_58_8 = e2 & op(e1, e1) = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | REF_CLOSE: (14), (77), (94), (228) are inconsistent by sub-proof
% 158.28/27.65 | | | | | #1440.
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | Case 2:
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | (229) all_58_11 = e2 & op(e1, e0) = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | ALPHA: (229) implies:
% 158.28/27.65 | | | | | (230) all_58_11 = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | COMBINE_EQS: (177), (230) imply:
% 158.28/27.65 | | | | | (231) e3 = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | COMBINE_EQS: (25), (231) imply:
% 158.28/27.65 | | | | | (232) all_58_6 = e2
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | | REF_CLOSE: (23), (28), (31), (36), (37), (47), (49), (70), (73), (94),
% 158.28/27.65 | | | | | (97), (232) are inconsistent by sub-proof #1153.
% 158.28/27.65 | | | | |
% 158.28/27.65 | | | | End of split
% 158.28/27.65 | | | |
% 158.28/27.65 | | | End of split
% 158.28/27.65 | | |
% 158.28/27.65 | | Case 2:
% 158.28/27.65 | | |
% 158.28/27.65 | | | (233) all_58_15 = e3 & op(e0, e0) = e3
% 158.28/27.65 | | |
% 158.28/27.65 | | | ALPHA: (233) implies:
% 158.28/27.65 | | | (234) all_58_15 = e3
% 158.28/27.65 | | | (235) op(e0, e0) = e3
% 158.28/27.65 | | |
% 158.28/27.65 | | | REF_CLOSE: (12), (16), (23), (25), (28), (31), (36), (37), (40), (41),
% 158.28/27.65 | | | (47), (49), (70), (73), (93), (94), (97), (234), (235) are
% 158.28/27.65 | | | inconsistent by sub-proof #786.
% 158.28/27.65 | | |
% 158.28/27.65 | | End of split
% 158.28/27.65 | |
% 158.28/27.65 | End of split
% 158.28/27.65 |
% 158.28/27.65 End of proof
% 158.28/27.65
% 158.28/27.65 Sub-proof #446 shows that the following formulas are inconsistent:
% 158.28/27.65 ----------------------------------------------------------------
% 158.28/27.65 (1) all_56_14 = e3
% 158.28/27.65 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.28/27.65 (3) all_54_13 = all_52_7
% 158.28/27.65 (4) ~ (all_52_7 = e3)
% 158.28/27.65 (5) ~ (all_52_11 = e3)
% 158.28/27.65 (6) all_58_7 = e2
% 158.28/27.65 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.28/27.65 (8) ~ (all_52_7 = all_52_11)
% 158.28/27.65 (9) all_58_0 = e1
% 158.28/27.65 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.28/27.65 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.28/27.65 (11) all_58_6 = e3
% 158.28/27.65 (12) all_58_12 = e0
% 158.28/27.65 (13) op(e2, e3) = all_52_1
% 158.28/27.65 (14) ~ (all_52_13 = e3)
% 158.28/27.65 (15) all_54_2 = all_52_8
% 158.28/27.65 (16) ~ (all_52_8 = all_52_9)
% 158.28/27.65 (17) ~ (e3 = e0)
% 158.28/27.65 (18) ~ (all_52_9 = all_52_13)
% 158.28/27.65 (19) ~ (e2 = e0)
% 158.28/27.65 (20) ~ (all_52_9 = e3)
% 158.28/27.65 (21) op(e2, e3) = e2
% 158.28/27.65 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.28/27.65 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.28/27.65 (23) ~ (e3 = e1)
% 158.28/27.65 (24) all_56_12 = e1
% 158.28/27.65 (25) all_58_1 = e1
% 158.28/27.65 (26) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.28/27.65 (27) all_54_7 = all_52_13
% 158.28/27.65 (28) ~ (all_52_13 = e2)
% 158.28/27.65 (29) all_56_15 = all_4_2
% 158.28/27.65 (30) ~ (all_52_9 = all_52_11)
% 158.28/27.65 (31) ~ (all_52_13 = all_4_2)
% 158.28/27.65 (32) all_54_6 = all_52_9
% 158.28/27.65 (33) ~ (all_52_8 = all_52_11)
% 158.28/27.65 (34) ~ (e1 = e0)
% 158.28/27.65 (35) all_58_3 = e3
% 158.28/27.65 (36) all_56_13 = e3
% 158.28/27.65 (37) ~ (all_52_9 = e2)
% 158.28/27.65 (38) ~ (all_52_8 = e3)
% 158.28/27.65 (39) all_54_14 = all_52_11
% 158.28/27.65 (40) ~ (all_52_7 = all_4_2)
% 158.28/27.65 (41) op(e0, e2) = all_52_7
% 158.28/27.65 (42) ~ (all_52_8 = e1)
% 158.28/27.65 (43) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.28/27.65 (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.28/27.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.28/27.65 (45) ~ (e3 = e2)
% 158.28/27.65 (46) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.28/27.65 (47) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.28/27.65
% 158.28/27.65 Begin of proof
% 158.28/27.65 |
% 158.28/27.65 | BETA: splitting (22) gives:
% 158.28/27.65 |
% 158.28/27.65 | Case 1:
% 158.28/27.65 | |
% 158.28/27.65 | | (48) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 158.28/27.65 | | e0)
% 158.28/27.65 | |
% 158.28/27.65 | | BETA: splitting (48) gives:
% 158.28/27.65 | |
% 158.28/27.65 | | Case 1:
% 158.28/27.65 | | |
% 158.28/27.65 | | | (49) all_58_1 = e0 & op(e3, e2) = e0
% 158.28/27.65 | | |
% 158.28/27.65 | | | REF_CLOSE: (25), (34), (49) are inconsistent by sub-proof #1327.
% 158.28/27.65 | | |
% 158.28/27.65 | | Case 2:
% 158.28/27.65 | | |
% 158.28/27.65 | | | (50) all_58_3 = e0 & op(e2, e2) = e0
% 158.28/27.65 | | |
% 158.28/27.65 | | | REF_CLOSE: (17), (35), (50) are inconsistent by sub-proof #910.
% 158.28/27.65 | | |
% 158.28/27.65 | | End of split
% 158.28/27.65 | |
% 158.28/27.65 | Case 2:
% 158.28/27.65 | |
% 158.28/27.65 | | (51) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 158.28/27.65 | | e0)
% 158.28/27.65 | |
% 158.28/27.65 | | BETA: splitting (51) gives:
% 158.28/27.65 | |
% 158.28/27.65 | | Case 1:
% 158.28/27.65 | | |
% 158.28/27.65 | | | (52) all_58_7 = e0 & op(e1, e2) = e0
% 158.28/27.65 | | |
% 158.28/27.65 | | | ALPHA: (52) implies:
% 158.28/27.65 | | | (53) all_58_7 = e0
% 158.28/27.65 | | |
% 158.28/27.65 | | | REF_CLOSE: (6), (19), (53) are inconsistent by sub-proof #1086.
% 158.28/27.65 | | |
% 158.28/27.65 | | Case 2:
% 158.28/27.65 | | |
% 158.28/27.65 | | | (54) all_58_13 = e0 & op(e0, e2) = e0
% 158.28/27.65 | | |
% 158.28/27.65 | | | ALPHA: (54) implies:
% 158.28/27.65 | | | (55) op(e0, e2) = e0
% 158.28/27.65 | | |
% 158.28/27.65 | | | BETA: splitting (47) gives:
% 158.28/27.65 | | |
% 158.28/27.65 | | | Case 1:
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | (56) all_56_12 = e3
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | REF_CLOSE: (23), (24), (56) are inconsistent by sub-proof #1191.
% 158.28/27.65 | | | |
% 158.28/27.65 | | | Case 2:
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | (57) ~ (all_56_12 = e3)
% 158.28/27.65 | | | | (58) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.28/27.65 | | | |
% 158.28/27.65 | | | | REDUCE: (24), (57) imply:
% 158.28/27.65 | | | | (59) ~ (e3 = e1)
% 158.28/27.66 | | | |
% 158.28/27.66 | | | | BETA: splitting (58) gives:
% 158.28/27.66 | | | |
% 158.28/27.66 | | | | Case 1:
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | (60) all_56_13 = e2
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | COMBINE_EQS: (36), (60) imply:
% 158.28/27.66 | | | | | (61) e3 = e2
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | COMBINE_EQS: (11), (61) imply:
% 158.28/27.66 | | | | | (62) all_58_6 = e2
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | REF_CLOSE: (9), (10), (12), (13), (17), (21), (23), (44), (45), (62)
% 158.28/27.66 | | | | | are inconsistent by sub-proof #1154.
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | Case 2:
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | (63) all_56_14 = e1 | all_56_15 = e0
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (14), (15), (16), (18),
% 158.28/27.66 | | | | | (20), (23), (26), (27), (28), (29), (30), (31), (32), (33),
% 158.28/27.66 | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (46), (55),
% 158.28/27.66 | | | | | (63) are inconsistent by sub-proof #472.
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | End of split
% 158.28/27.66 | | | |
% 158.28/27.66 | | | End of split
% 158.28/27.66 | | |
% 158.28/27.66 | | End of split
% 158.28/27.66 | |
% 158.28/27.66 | End of split
% 158.28/27.66 |
% 158.28/27.66 End of proof
% 158.28/27.66
% 158.28/27.66 Sub-proof #447 shows that the following formulas are inconsistent:
% 158.28/27.66 ----------------------------------------------------------------
% 158.28/27.66 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.28/27.66 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.28/27.66 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.28/27.66 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.28/27.66 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.28/27.66 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.28/27.66 (4) all_58_14 = e3
% 158.28/27.66 (5) op(e1, e1) = all_6_2
% 158.28/27.66 (6) all_58_0 = e1
% 158.28/27.66 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.28/27.66 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.28/27.66 (8) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.28/27.66 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.28/27.66 (9) all_58_6 = e3
% 158.28/27.66 (10) all_58_12 = e0
% 158.28/27.66 (11) op(e3, e2) = all_52_4
% 158.28/27.66 (12) op(e2, e3) = all_52_1
% 158.28/27.66 (13) ~ (e3 = e0)
% 158.28/27.66 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.28/27.66 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.28/27.66 (15) ~ (e2 = e0)
% 158.28/27.66 (16) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.28/27.66 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.28/27.66 (17) all_58_9 = e3
% 158.28/27.66 (18) op(e2, e3) = e2
% 158.28/27.66 (19) ~ (e3 = e1)
% 158.28/27.66 (20) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.28/27.66 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.28/27.66 (21) all_58_7 = e1
% 158.28/27.66 (22) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.28/27.66 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.28/27.66 (23) all_58_11 = e2
% 158.28/27.66 (24) ~ (all_52_4 = e3)
% 158.28/27.66 (25) ~ (e2 = e1)
% 158.28/27.66 (26) ~ (e1 = e0)
% 158.28/27.66 (27) all_58_3 = e3
% 158.28/27.66 (28) ~ (all_6_2 = e2)
% 158.28/27.66 (29) all_58_13 = e2
% 158.28/27.66 (30) all_58_10 = e0
% 158.28/27.66 (31) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.28/27.66 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.28/27.66 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.28/27.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.28/27.66 (33) ~ (e3 = e2)
% 158.28/27.66 (34) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.28/27.66 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.28/27.66 (35) all_58_8 = e1
% 158.28/27.66
% 158.28/27.66 Begin of proof
% 158.28/27.66 |
% 158.28/27.66 | BETA: splitting (3) gives:
% 158.28/27.66 |
% 158.28/27.66 | Case 1:
% 158.28/27.66 | |
% 158.28/27.66 | | (36) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 158.28/27.66 | | e1)
% 158.28/27.66 | |
% 158.28/27.66 | | REF_CLOSE: (18), (19), (25), (27), (32), (36) are inconsistent by sub-proof
% 158.28/27.66 | | #840.
% 158.28/27.66 | |
% 158.28/27.66 | Case 2:
% 158.28/27.66 | |
% 158.28/27.66 | | (37) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 158.28/27.66 | | e1)
% 158.28/27.66 | |
% 158.28/27.66 | | BETA: splitting (37) gives:
% 158.28/27.66 | |
% 158.28/27.66 | | Case 1:
% 158.28/27.66 | | |
% 158.28/27.66 | | | (38) all_58_5 = e1 & op(e2, e1) = e1
% 158.28/27.66 | | |
% 158.28/27.66 | | | ALPHA: (38) implies:
% 158.28/27.66 | | | (39) all_58_5 = e1
% 158.28/27.66 | | |
% 158.28/27.66 | | | BETA: splitting (8) gives:
% 158.28/27.66 | | |
% 158.28/27.66 | | | Case 1:
% 158.28/27.66 | | | |
% 158.28/27.66 | | | | (40) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 158.28/27.66 | | | | = e2)
% 158.28/27.66 | | | |
% 158.28/27.66 | | | | BETA: splitting (40) gives:
% 158.28/27.66 | | | |
% 158.28/27.66 | | | | Case 1:
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | (41) all_58_4 = e2 & op(e3, e1) = e2
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | ALPHA: (41) implies:
% 158.28/27.66 | | | | | (42) all_58_4 = e2
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | BETA: splitting (34) gives:
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | Case 1:
% 158.28/27.66 | | | | | |
% 158.28/27.66 | | | | | | (43) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 158.28/27.66 | | | | | | e2) = e0)
% 158.28/27.66 | | | | | |
% 158.28/27.66 | | | | | | BETA: splitting (43) gives:
% 158.28/27.66 | | | | | |
% 158.28/27.66 | | | | | | Case 1:
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | (44) all_58_0 = e0 & op(e3, e3) = e0
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | ALPHA: (44) implies:
% 158.28/27.66 | | | | | | | (45) all_58_0 = e0
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | COMBINE_EQS: (6), (45) imply:
% 158.28/27.66 | | | | | | | (46) e1 = e0
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | COMBINE_EQS: (39), (46) imply:
% 158.28/27.66 | | | | | | | (47) all_58_5 = e0
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.28/27.66 | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 158.28/27.66 | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 158.28/27.66 | | | | | | | (31), (32), (33), (34), (35), (47) are inconsistent by
% 158.28/27.66 | | | | | | | sub-proof #449.
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | Case 2:
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | (48) all_58_1 = e0 & op(e3, e2) = e0
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | ALPHA: (48) implies:
% 158.28/27.66 | | | | | | | (49) all_58_1 = e0
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | BETA: splitting (20) gives:
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | | Case 1:
% 158.28/27.66 | | | | | | | |
% 158.28/27.66 | | | | | | | | (50) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 158.28/27.66 | | | | | | | | op(e2, e1) = e0)
% 158.28/27.66 | | | | | | | |
% 158.28/27.66 | | | | | | | | BETA: splitting (50) gives:
% 158.28/27.66 | | | | | | | |
% 158.28/27.66 | | | | | | | | Case 1:
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | (51) all_58_4 = e0 & op(e3, e1) = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | ALPHA: (51) implies:
% 158.28/27.66 | | | | | | | | | (52) all_58_4 = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | REF_CLOSE: (3), (4), (5), (8), (13), (15), (18), (19), (22),
% 158.28/27.66 | | | | | | | | | (25), (26), (27), (28), (32), (33), (52) are
% 158.28/27.66 | | | | | | | | | inconsistent by sub-proof #854.
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | Case 2:
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | (53) all_58_5 = e0 & op(e2, e1) = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | ALPHA: (53) implies:
% 158.28/27.66 | | | | | | | | | (54) all_58_5 = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 158.28/27.66 | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19),
% 158.28/27.66 | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 158.28/27.66 | | | | | | | | | (29), (31), (32), (33), (35), (42), (49), (54) are
% 158.28/27.66 | | | | | | | | | inconsistent by sub-proof #451.
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | End of split
% 158.28/27.66 | | | | | | | |
% 158.28/27.66 | | | | | | | Case 2:
% 158.28/27.66 | | | | | | | |
% 158.28/27.66 | | | | | | | | (55) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 158.28/27.66 | | | | | | | | op(e0, e1) = e0)
% 158.28/27.66 | | | | | | | |
% 158.28/27.66 | | | | | | | | BETA: splitting (55) gives:
% 158.28/27.66 | | | | | | | |
% 158.28/27.66 | | | | | | | | Case 1:
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | (56) all_58_8 = e0 & op(e1, e1) = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | ALPHA: (56) implies:
% 158.28/27.66 | | | | | | | | | (57) all_58_8 = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | COMBINE_EQS: (35), (57) imply:
% 158.28/27.66 | | | | | | | | | (58) e1 = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | COMBINE_EQS: (39), (58) imply:
% 158.28/27.66 | | | | | | | | | (59) all_58_5 = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 158.28/27.66 | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19),
% 158.28/27.66 | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 158.28/27.66 | | | | | | | | | (29), (31), (32), (33), (35), (42), (49), (59) are
% 158.28/27.66 | | | | | | | | | inconsistent by sub-proof #451.
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | Case 2:
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | (60) all_58_14 = e0 & op(e0, e1) = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | ALPHA: (60) implies:
% 158.28/27.66 | | | | | | | | | (61) all_58_14 = e0
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | | REF_CLOSE: (4), (13), (61) are inconsistent by sub-proof
% 158.28/27.66 | | | | | | | | | #1444.
% 158.28/27.66 | | | | | | | | |
% 158.28/27.66 | | | | | | | | End of split
% 158.28/27.66 | | | | | | | |
% 158.28/27.66 | | | | | | | End of split
% 158.28/27.66 | | | | | | |
% 158.28/27.66 | | | | | | End of split
% 158.28/27.66 | | | | | |
% 158.28/27.66 | | | | | Case 2:
% 158.28/27.66 | | | | | |
% 158.28/27.66 | | | | | | (62) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 158.28/27.66 | | | | | | e0) = e0)
% 158.28/27.66 | | | | | |
% 158.28/27.66 | | | | | | REF_CLOSE: (3), (4), (5), (8), (13), (15), (17), (18), (19), (22),
% 158.28/27.66 | | | | | | (25), (26), (27), (28), (32), (33), (62) are inconsistent
% 158.28/27.66 | | | | | | by sub-proof #819.
% 158.28/27.66 | | | | | |
% 158.28/27.66 | | | | | End of split
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | Case 2:
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | (63) all_58_5 = e2 & op(e2, e1) = e2
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | ALPHA: (63) implies:
% 158.28/27.66 | | | | | (64) all_58_5 = e2
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | | REF_CLOSE: (3), (13), (15), (18), (19), (22), (25), (26), (27), (32),
% 158.28/27.66 | | | | | (64) are inconsistent by sub-proof #898.
% 158.28/27.66 | | | | |
% 158.28/27.66 | | | | End of split
% 158.28/27.66 | | | |
% 158.28/27.66 | | | Case 2:
% 158.28/27.66 | | | |
% 158.28/27.66 | | | | (65) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 158.28/27.66 | | | | = e2)
% 158.28/27.66 | | | |
% 158.28/27.66 | | | | REF_CLOSE: (1), (4), (6), (7), (9), (10), (12), (13), (15), (16), (18),
% 158.28/27.66 | | | | (19), (23), (25), (26), (32), (33), (65) are inconsistent by
% 158.28/27.66 | | | | sub-proof #450.
% 158.28/27.66 | | | |
% 158.28/27.66 | | | End of split
% 158.28/27.66 | | |
% 158.28/27.66 | | Case 2:
% 158.28/27.66 | | |
% 158.28/27.66 | | | (66) all_58_10 = e1 & op(e2, e0) = e1
% 158.28/27.66 | | |
% 158.28/27.66 | | | ALPHA: (66) implies:
% 158.28/27.66 | | | (67) all_58_10 = e1
% 158.28/27.66 | | |
% 158.28/27.66 | | | REF_CLOSE: (26), (30), (67) are inconsistent by sub-proof #1279.
% 158.28/27.66 | | |
% 158.28/27.66 | | End of split
% 158.28/27.66 | |
% 158.28/27.66 | End of split
% 158.28/27.66 |
% 158.28/27.66 End of proof
% 158.28/27.66
% 158.28/27.66 Sub-proof #448 shows that the following formulas are inconsistent:
% 158.28/27.66 ----------------------------------------------------------------
% 158.28/27.66 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.28/27.66 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.28/27.66 (2) all_58_14 = e3
% 158.28/27.66 (3) all_58_0 = e1
% 158.28/27.66 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.28/27.66 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.28/27.66 (5) all_58_6 = e3
% 158.28/27.66 (6) all_58_12 = e0
% 158.28/27.66 (7) op(e2, e3) = all_52_1
% 158.28/27.66 (8) ~ (e3 = e0)
% 158.28/27.66 (9) ~ (e2 = e0)
% 158.28/27.66 (10) all_58_9 = e3
% 158.28/27.66 (11) op(e2, e3) = e2
% 158.28/27.66 (12) ~ (e3 = e1)
% 158.28/27.66 (13) all_58_11 = e2
% 158.28/27.66 (14) ~ (e2 = e1)
% 158.28/27.66 (15) ~ (e1 = e0)
% 158.28/27.66 (16) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.28/27.66 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.28/27.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.28/27.66 (18) ~ (e3 = e2)
% 158.28/27.66 (19) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.28/27.66 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.28/27.66 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.28/27.66 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.28/27.66
% 158.28/27.66 Begin of proof
% 158.28/27.66 |
% 158.28/27.66 | BETA: splitting (16) gives:
% 158.28/27.66 |
% 158.28/27.66 | Case 1:
% 158.28/27.66 | |
% 158.28/27.66 | | (20) all_58_14 = e2 & op(e0, e1) = e2
% 158.28/27.66 | |
% 158.28/27.66 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (12), (17), (18), (20)
% 158.28/27.66 | | are inconsistent by sub-proof #829.
% 158.28/27.66 | |
% 158.28/27.66 | Case 2:
% 158.28/27.66 | |
% 158.28/27.66 | | (21) all_58_15 = e2 & op(e0, e0) = e2
% 158.28/27.66 | |
% 158.28/27.66 | | ALPHA: (21) implies:
% 158.28/27.66 | | (22) all_58_15 = e2
% 158.28/27.66 | |
% 158.28/27.66 | | REF_CLOSE: (1), (8), (9), (10), (12), (13), (14), (15), (19), (22) are
% 158.28/27.66 | | inconsistent by sub-proof #1453.
% 158.28/27.66 | |
% 158.28/27.66 | End of split
% 158.28/27.66 |
% 158.28/27.66 End of proof
% 158.28/27.66
% 158.28/27.66 Sub-proof #449 shows that the following formulas are inconsistent:
% 158.28/27.66 ----------------------------------------------------------------
% 158.28/27.66 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.28/27.66 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.28/27.66 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.28/27.66 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.28/27.66 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.28/27.66 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.28/27.66 (4) all_58_14 = e3
% 158.28/27.66 (5) op(e1, e1) = all_6_2
% 158.28/27.66 (6) all_58_0 = e1
% 158.28/27.66 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.28/27.66 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.28/27.66 (8) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.28/27.66 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.28/27.66 (9) all_58_6 = e3
% 158.28/27.66 (10) all_58_12 = e0
% 158.28/27.66 (11) op(e3, e2) = all_52_4
% 158.28/27.66 (12) op(e2, e3) = all_52_1
% 158.28/27.66 (13) ~ (e3 = e0)
% 158.28/27.66 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.28/27.66 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.28/27.66 (15) ~ (e2 = e0)
% 158.28/27.66 (16) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.28/27.66 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.28/27.66 (17) all_58_9 = e3
% 158.28/27.66 (18) op(e2, e3) = e2
% 158.28/27.66 (19) ~ (e3 = e1)
% 158.28/27.66 (20) all_58_7 = e1
% 158.28/27.66 (21) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.28/27.66 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.28/27.66 (22) all_58_5 = e0
% 158.28/27.66 (23) all_58_11 = e2
% 158.28/27.66 (24) ~ (all_52_4 = e3)
% 158.28/27.66 (25) ~ (e2 = e1)
% 158.28/27.66 (26) ~ (e1 = e0)
% 158.28/27.66 (27) all_58_3 = e3
% 158.28/27.66 (28) ~ (all_6_2 = e2)
% 158.28/27.66 (29) all_58_13 = e2
% 158.28/27.66 (30) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.37/27.66 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.37/27.66 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.66 (32) ~ (e3 = e2)
% 158.37/27.66 (33) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.37/27.66 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.37/27.66 (34) all_58_8 = e1
% 158.37/27.66
% 158.37/27.66 Begin of proof
% 158.37/27.66 |
% 158.37/27.66 | BETA: splitting (3) gives:
% 158.37/27.66 |
% 158.37/27.66 | Case 1:
% 158.37/27.66 | |
% 158.37/27.66 | | (35) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 158.37/27.66 | | e1)
% 158.37/27.66 | |
% 158.37/27.66 | | BETA: splitting (35) gives:
% 158.37/27.66 | |
% 158.37/27.66 | | Case 1:
% 158.37/27.66 | | |
% 158.37/27.66 | | | (36) all_58_2 = e1 & op(e2, e3) = e1
% 158.37/27.66 | | |
% 158.37/27.66 | | | ALPHA: (36) implies:
% 158.37/27.66 | | | (37) op(e2, e3) = e1
% 158.37/27.66 | | |
% 158.37/27.66 | | | REF_CLOSE: (18), (25), (31), (37) are inconsistent by sub-proof #1430.
% 158.37/27.66 | | |
% 158.37/27.66 | | Case 2:
% 158.37/27.66 | | |
% 158.37/27.66 | | | (38) all_58_3 = e1 & op(e2, e2) = e1
% 158.37/27.66 | | |
% 158.37/27.66 | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 158.37/27.66 | | | (14), (15), (17), (18), (19), (21), (22), (24), (25), (26),
% 158.37/27.66 | | | (27), (28), (30), (31), (32), (38) are inconsistent by
% 158.37/27.66 | | | sub-proof #452.
% 158.37/27.66 | | |
% 158.37/27.66 | | End of split
% 158.37/27.66 | |
% 158.37/27.66 | Case 2:
% 158.37/27.66 | |
% 158.37/27.66 | | (39) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 158.37/27.66 | | e1)
% 158.37/27.66 | |
% 158.37/27.66 | | BETA: splitting (39) gives:
% 158.37/27.66 | |
% 158.37/27.66 | | Case 1:
% 158.37/27.66 | | |
% 158.37/27.66 | | | (40) all_58_5 = e1 & op(e2, e1) = e1
% 158.37/27.66 | | |
% 158.37/27.66 | | | ALPHA: (40) implies:
% 158.37/27.66 | | | (41) all_58_5 = e1
% 158.37/27.66 | | |
% 158.37/27.66 | | | REF_CLOSE: (22), (26), (41) are inconsistent by sub-proof #935.
% 158.37/27.66 | | |
% 158.37/27.66 | | Case 2:
% 158.37/27.66 | | |
% 158.37/27.66 | | | (42) all_58_10 = e1 & op(e2, e0) = e1
% 158.37/27.66 | | |
% 158.37/27.66 | | | ALPHA: (42) implies:
% 158.37/27.66 | | | (43) all_58_10 = e1
% 158.37/27.66 | | |
% 158.37/27.66 | | | BETA: splitting (8) gives:
% 158.37/27.66 | | |
% 158.37/27.66 | | | Case 1:
% 158.37/27.66 | | | |
% 158.37/27.66 | | | | (44) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 158.37/27.66 | | | | = e2)
% 158.37/27.66 | | | |
% 158.37/27.66 | | | | BETA: splitting (44) gives:
% 158.37/27.66 | | | |
% 158.37/27.66 | | | | Case 1:
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | | (45) all_58_4 = e2 & op(e3, e1) = e2
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | | ALPHA: (45) implies:
% 158.37/27.66 | | | | | (46) all_58_4 = e2
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | | BETA: splitting (33) gives:
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | | Case 1:
% 158.37/27.66 | | | | | |
% 158.37/27.66 | | | | | | (47) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 158.37/27.66 | | | | | | e2) = e0)
% 158.37/27.66 | | | | | |
% 158.37/27.66 | | | | | | BETA: splitting (47) gives:
% 158.37/27.66 | | | | | |
% 158.37/27.66 | | | | | | Case 1:
% 158.37/27.66 | | | | | | |
% 158.37/27.66 | | | | | | | (48) all_58_0 = e0 & op(e3, e3) = e0
% 158.37/27.66 | | | | | | |
% 158.37/27.66 | | | | | | | REF_CLOSE: (3), (6), (18), (19), (22), (25), (26), (27), (31),
% 158.37/27.66 | | | | | | | (43), (48) are inconsistent by sub-proof #824.
% 158.37/27.66 | | | | | | |
% 158.37/27.66 | | | | | | Case 2:
% 158.37/27.66 | | | | | | |
% 158.37/27.66 | | | | | | | (49) all_58_1 = e0 & op(e3, e2) = e0
% 158.37/27.66 | | | | | | |
% 158.37/27.66 | | | | | | | ALPHA: (49) implies:
% 158.37/27.66 | | | | | | | (50) all_58_1 = e0
% 158.37/27.66 | | | | | | |
% 158.37/27.66 | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 158.37/27.66 | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 158.37/27.66 | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 158.37/27.66 | | | | | | | (30), (31), (32), (34), (46), (50) are inconsistent by
% 158.37/27.66 | | | | | | | sub-proof #451.
% 158.37/27.66 | | | | | | |
% 158.37/27.66 | | | | | | End of split
% 158.37/27.66 | | | | | |
% 158.37/27.66 | | | | | Case 2:
% 158.37/27.66 | | | | | |
% 158.37/27.66 | | | | | | (51) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 158.37/27.66 | | | | | | e0) = e0)
% 158.37/27.66 | | | | | |
% 158.37/27.66 | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.37/27.66 | | | | | | (13), (14), (15), (18), (19), (21), (22), (24), (25),
% 158.37/27.66 | | | | | | (26), (27), (28), (30), (31), (32), (51) are inconsistent
% 158.37/27.66 | | | | | | by sub-proof #821.
% 158.37/27.66 | | | | | |
% 158.37/27.66 | | | | | End of split
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | Case 2:
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | | (52) all_58_5 = e2 & op(e2, e1) = e2
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | | ALPHA: (52) implies:
% 158.37/27.66 | | | | | (53) all_58_5 = e2
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | | REF_CLOSE: (13), (15), (18), (21), (26), (27), (31), (43), (53) are
% 158.37/27.66 | | | | | inconsistent by sub-proof #899.
% 158.37/27.66 | | | | |
% 158.37/27.66 | | | | End of split
% 158.37/27.66 | | | |
% 158.37/27.66 | | | Case 2:
% 158.37/27.66 | | | |
% 158.37/27.66 | | | | (54) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 158.37/27.66 | | | | = e2)
% 158.37/27.66 | | | |
% 158.37/27.66 | | | | REF_CLOSE: (1), (4), (6), (7), (9), (10), (12), (13), (15), (16), (18),
% 158.37/27.66 | | | | (19), (23), (25), (26), (31), (32), (54) are inconsistent by
% 158.37/27.66 | | | | sub-proof #450.
% 158.37/27.66 | | | |
% 158.37/27.66 | | | End of split
% 158.37/27.66 | | |
% 158.37/27.66 | | End of split
% 158.37/27.66 | |
% 158.37/27.66 | End of split
% 158.37/27.66 |
% 158.37/27.66 End of proof
% 158.37/27.66
% 158.37/27.66 Sub-proof #450 shows that the following formulas are inconsistent:
% 158.37/27.66 ----------------------------------------------------------------
% 158.37/27.66 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.37/27.66 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.37/27.66 (2) all_58_14 = e3
% 158.37/27.66 (3) all_58_0 = e1
% 158.37/27.66 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.66 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.66 (5) all_58_6 = e3
% 158.37/27.66 (6) all_58_12 = e0
% 158.37/27.66 (7) op(e2, e3) = all_52_1
% 158.37/27.66 (8) ~ (e3 = e0)
% 158.37/27.66 (9) ~ (e2 = e0)
% 158.37/27.66 (10) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.37/27.66 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.37/27.66 (11) op(e2, e3) = e2
% 158.37/27.66 (12) ~ (e3 = e1)
% 158.37/27.66 (13) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.66 (14) all_58_11 = e2
% 158.37/27.66 (15) ~ (e2 = e1)
% 158.37/27.66 (16) ~ (e1 = e0)
% 158.37/27.66 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.66 (18) ~ (e3 = e2)
% 158.37/27.66
% 158.37/27.66 Begin of proof
% 158.37/27.66 |
% 158.37/27.66 | BETA: splitting (13) gives:
% 158.37/27.66 |
% 158.37/27.66 | Case 1:
% 158.37/27.66 | |
% 158.37/27.66 | | (19) all_58_8 = e2 & op(e1, e1) = e2
% 158.37/27.66 | |
% 158.37/27.66 | | ALPHA: (19) implies:
% 158.37/27.66 | | (20) all_58_8 = e2
% 158.37/27.66 | |
% 158.37/27.66 | | REF_CLOSE: (1), (5), (8), (9), (10), (12), (14), (15), (16), (20) are
% 158.37/27.66 | | inconsistent by sub-proof #1070.
% 158.37/27.66 | |
% 158.37/27.66 | Case 2:
% 158.37/27.66 | |
% 158.37/27.66 | | (21) all_58_14 = e2 & op(e0, e1) = e2
% 158.37/27.66 | |
% 158.37/27.66 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (12), (17), (18), (21)
% 158.37/27.66 | | are inconsistent by sub-proof #805.
% 158.37/27.66 | |
% 158.37/27.66 | End of split
% 158.37/27.66 |
% 158.37/27.66 End of proof
% 158.37/27.66
% 158.37/27.66 Sub-proof #451 shows that the following formulas are inconsistent:
% 158.37/27.66 ----------------------------------------------------------------
% 158.37/27.66 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.66 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.66 (2) all_58_1 = e0
% 158.37/27.66 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.66 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.66 (4) all_58_14 = e3
% 158.37/27.66 (5) op(e1, e1) = all_6_2
% 158.37/27.66 (6) all_58_0 = e1
% 158.37/27.66 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.66 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.66 (8) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.37/27.66 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.66 (9) all_58_6 = e3
% 158.37/27.66 (10) all_58_12 = e0
% 158.37/27.66 (11) op(e3, e2) = all_52_4
% 158.37/27.66 (12) op(e2, e3) = all_52_1
% 158.37/27.66 (13) ~ (e3 = e0)
% 158.37/27.66 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.37/27.66 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.37/27.66 (15) ~ (e2 = e0)
% 158.37/27.66 (16) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.37/27.66 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.37/27.66 (17) all_58_9 = e3
% 158.37/27.66 (18) op(e2, e3) = e2
% 158.37/27.66 (19) ~ (e3 = e1)
% 158.37/27.66 (20) all_58_7 = e1
% 158.37/27.67 (21) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.67 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.67 (22) all_58_5 = e0
% 158.37/27.67 (23) all_58_11 = e2
% 158.37/27.67 (24) all_58_4 = e2
% 158.37/27.67 (25) ~ (all_52_4 = e3)
% 158.37/27.67 (26) ~ (e2 = e1)
% 158.37/27.67 (27) ~ (e1 = e0)
% 158.37/27.67 (28) all_58_3 = e3
% 158.37/27.67 (29) ~ (all_6_2 = e2)
% 158.37/27.67 (30) all_58_13 = e2
% 158.37/27.67 (31) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.37/27.67 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.37/27.67 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.67 (33) ~ (e3 = e2)
% 158.37/27.67 (34) all_58_8 = e1
% 158.37/27.67
% 158.37/27.67 Begin of proof
% 158.37/27.67 |
% 158.37/27.67 | BETA: splitting (16) gives:
% 158.37/27.67 |
% 158.37/27.67 | Case 1:
% 158.37/27.67 | |
% 158.37/27.67 | | (35) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 158.37/27.67 | | e0)
% 158.37/27.67 | |
% 158.37/27.67 | | BETA: splitting (35) gives:
% 158.37/27.67 | |
% 158.37/27.67 | | Case 1:
% 158.37/27.67 | | |
% 158.37/27.67 | | | (36) all_58_6 = e0 & op(e1, e3) = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | ALPHA: (36) implies:
% 158.37/27.67 | | | (37) all_58_6 = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | COMBINE_EQS: (9), (37) imply:
% 158.37/27.67 | | | (38) e3 = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | SIMP: (38) implies:
% 158.37/27.67 | | | (39) e3 = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | COMBINE_EQS: (17), (39) imply:
% 158.37/27.67 | | | (40) all_58_9 = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 158.37/27.67 | | | (14), (15), (18), (19), (21), (22), (25), (26), (27), (28),
% 158.37/27.67 | | | (29), (31), (32), (33), (40) are inconsistent by sub-proof
% 158.37/27.67 | | | #822.
% 158.37/27.67 | | |
% 158.37/27.67 | | Case 2:
% 158.37/27.67 | | |
% 158.37/27.67 | | | (41) all_58_7 = e0 & op(e1, e2) = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | ALPHA: (41) implies:
% 158.37/27.67 | | | (42) all_58_7 = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | REF_CLOSE: (1), (2), (19), (26), (27), (28), (30), (42) are inconsistent
% 158.37/27.67 | | | by sub-proof #752.
% 158.37/27.67 | | |
% 158.37/27.67 | | End of split
% 158.37/27.67 | |
% 158.37/27.67 | Case 2:
% 158.37/27.67 | |
% 158.37/27.67 | | (43) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 158.37/27.67 | | e0)
% 158.37/27.67 | |
% 158.37/27.67 | | BETA: splitting (43) gives:
% 158.37/27.67 | |
% 158.37/27.67 | | Case 1:
% 158.37/27.67 | | |
% 158.37/27.67 | | | (44) all_58_8 = e0 & op(e1, e1) = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | ALPHA: (44) implies:
% 158.37/27.67 | | | (45) all_58_8 = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | COMBINE_EQS: (34), (45) imply:
% 158.37/27.67 | | | (46) e1 = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | COMBINE_EQS: (20), (46) imply:
% 158.37/27.67 | | | (47) all_58_7 = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | REF_CLOSE: (1), (2), (19), (26), (27), (28), (30), (47) are inconsistent
% 158.37/27.67 | | | by sub-proof #752.
% 158.37/27.67 | | |
% 158.37/27.67 | | Case 2:
% 158.37/27.67 | | |
% 158.37/27.67 | | | (48) all_58_11 = e0 & op(e1, e0) = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | REF_CLOSE: (3), (4), (5), (8), (13), (15), (18), (19), (21), (23), (24),
% 158.37/27.67 | | | (26), (27), (28), (29), (32), (33), (48) are inconsistent by
% 158.37/27.67 | | | sub-proof #816.
% 158.37/27.67 | | |
% 158.37/27.67 | | End of split
% 158.37/27.67 | |
% 158.37/27.67 | End of split
% 158.37/27.67 |
% 158.37/27.67 End of proof
% 158.37/27.67
% 158.37/27.67 Sub-proof #452 shows that the following formulas are inconsistent:
% 158.37/27.67 ----------------------------------------------------------------
% 158.37/27.67 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.67 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.67 (2) all_58_14 = e3
% 158.37/27.67 (3) op(e1, e1) = all_6_2
% 158.37/27.67 (4) all_58_0 = e1
% 158.37/27.67 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.67 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.67 (6) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.37/27.67 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.67 (7) all_58_6 = e3
% 158.37/27.67 (8) all_58_12 = e0
% 158.37/27.67 (9) op(e3, e2) = all_52_4
% 158.37/27.67 (10) op(e2, e3) = all_52_1
% 158.37/27.67 (11) ~ (e3 = e0)
% 158.37/27.67 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.37/27.67 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.37/27.67 (13) ~ (e2 = e0)
% 158.37/27.67 (14) all_58_9 = e3
% 158.37/27.67 (15) op(e2, e3) = e2
% 158.37/27.67 (16) ~ (e3 = e1)
% 158.37/27.67 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.67 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.67 (18) all_58_3 = e1 & op(e2, e2) = e1
% 158.37/27.67 (19) all_58_5 = e0
% 158.37/27.67 (20) ~ (all_52_4 = e3)
% 158.37/27.67 (21) ~ (e2 = e1)
% 158.37/27.67 (22) ~ (e1 = e0)
% 158.37/27.67 (23) all_58_3 = e3
% 158.37/27.67 (24) ~ (all_6_2 = e2)
% 158.37/27.67 (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.37/27.67 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.37/27.67 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.67 (27) ~ (e3 = e2)
% 158.37/27.67
% 158.37/27.67 Begin of proof
% 158.37/27.67 |
% 158.37/27.67 | ALPHA: (18) implies:
% 158.37/27.67 | (28) all_58_3 = e1
% 158.37/27.67 |
% 158.37/27.67 | COMBINE_EQS: (23), (28) imply:
% 158.37/27.67 | (29) e3 = e1
% 158.37/27.67 |
% 158.37/27.67 | SIMP: (29) implies:
% 158.37/27.67 | (30) e3 = e1
% 158.37/27.67 |
% 158.37/27.67 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.37/27.67 | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 158.37/27.67 | (25), (26), (27), (30) are inconsistent by sub-proof #825.
% 158.37/27.67 |
% 158.37/27.67 End of proof
% 158.37/27.67
% 158.37/27.67 Sub-proof #453 shows that the following formulas are inconsistent:
% 158.37/27.67 ----------------------------------------------------------------
% 158.37/27.67 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.67 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.67 (2) all_58_0 = e1
% 158.37/27.67 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.67 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.67 (4) all_58_6 = e3
% 158.37/27.67 (5) all_58_12 = e0
% 158.37/27.67 (6) op(e2, e3) = all_52_1
% 158.37/27.67 (7) ~ (e3 = e0)
% 158.37/27.67 (8) ~ (e2 = e0)
% 158.37/27.67 (9) all_58_9 = e3
% 158.37/27.67 (10) op(e2, e3) = e2
% 158.37/27.67 (11) ~ (e3 = e1)
% 158.37/27.67 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.67 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.67 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 158.37/27.67 (14) ~ (e2 = e1)
% 158.37/27.67 (15) ~ (e1 = e0)
% 158.37/27.67 (16) all_58_3 = e3
% 158.37/27.67 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.67 (18) ~ (e3 = e2)
% 158.37/27.67
% 158.37/27.67 Begin of proof
% 158.37/27.67 |
% 158.37/27.67 | BETA: splitting (13) gives:
% 158.37/27.67 |
% 158.37/27.67 | Case 1:
% 158.37/27.67 | |
% 158.37/27.67 | | (19) all_58_9 = e2 & op(e3, e0) = e2
% 158.37/27.67 | |
% 158.37/27.67 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (17), (18), (19)
% 158.37/27.67 | | are inconsistent by sub-proof #456.
% 158.37/27.67 | |
% 158.37/27.67 | Case 2:
% 158.37/27.67 | |
% 158.37/27.67 | | (20) all_58_10 = e2 & op(e2, e0) = e2
% 158.37/27.67 | |
% 158.37/27.67 | | ALPHA: (20) implies:
% 158.37/27.67 | | (21) all_58_10 = e2
% 158.37/27.67 | |
% 158.37/27.67 | | REF_CLOSE: (1), (7), (8), (10), (11), (12), (14), (15), (16), (17), (21) are
% 158.37/27.67 | | inconsistent by sub-proof #906.
% 158.37/27.67 | |
% 158.37/27.67 | End of split
% 158.37/27.67 |
% 158.37/27.67 End of proof
% 158.37/27.67
% 158.37/27.67 Sub-proof #454 shows that the following formulas are inconsistent:
% 158.37/27.67 ----------------------------------------------------------------
% 158.37/27.67 (1) op(e1, e1) = e3
% 158.37/27.67 (2) op(e1, e1) = all_32_1
% 158.37/27.67 (3) all_56_14 = e3
% 158.37/27.67 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.37/27.67 (5) op(e3, e1) = e3
% 158.37/27.67 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.37/27.67 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.37/27.67 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.67 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.67 (8) all_58_14 = e3
% 158.37/27.67 (9) op(e1, e1) = all_6_2
% 158.37/27.67 (10) ~ (all_52_11 = e3)
% 158.37/27.67 (11) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.37/27.67 (12) all_58_0 = e1
% 158.37/27.67 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.67 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.67 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.37/27.67 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.67 (15) all_58_6 = e3
% 158.37/27.67 (16) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.37/27.67 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.37/27.67 (17) all_58_12 = e0
% 158.37/27.67 (18) ~ (all_4_2 = e2)
% 158.37/27.67 (19) op(e2, e3) = all_52_1
% 158.37/27.67 (20) ~ (all_52_13 = e3)
% 158.37/27.67 (21) all_54_2 = all_52_8
% 158.37/27.67 (22) ~ (all_52_8 = all_52_9)
% 158.37/27.67 (23) ~ (e3 = e0)
% 158.37/27.67 (24) ~ (all_52_9 = all_52_13)
% 158.37/27.67 (25) ~ (e2 = e0)
% 158.37/27.67 (26) ~ (all_52_9 = e3)
% 158.37/27.67 (27) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.37/27.67 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.37/27.67 (28) all_58_9 = e3
% 158.37/27.67 (29) op(e2, e3) = e2
% 158.37/27.67 (30) ~ (e3 = e1)
% 158.37/27.67 (31) all_58_5 = e1
% 158.37/27.67 (32) all_56_12 = e1
% 158.37/27.67 (33) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.37/27.67 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.37/27.67 (34) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.37/27.67 (35) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.67 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.67 (36) all_54_7 = all_52_13
% 158.37/27.67 (37) ~ (all_52_13 = e2)
% 158.37/27.67 (38) all_56_15 = all_4_2
% 158.37/27.67 (39) ~ (all_52_9 = all_52_11)
% 158.37/27.67 (40) ~ (all_52_13 = all_4_2)
% 158.37/27.67 (41) all_54_6 = all_52_9
% 158.37/27.67 (42) ~ (e2 = e1)
% 158.37/27.67 (43) ~ (all_52_8 = all_52_11)
% 158.37/27.67 (44) ~ (e1 = e0)
% 158.37/27.67 (45) all_58_3 = e3
% 158.37/27.67 (46) op(e3, e1) = all_52_8
% 158.37/27.67 (47) ~ (all_6_2 = e2)
% 158.37/27.67 (48) all_56_13 = e3
% 158.37/27.67 (49) ~ (all_52_9 = e2)
% 158.37/27.67 (50) ~ (all_52_8 = e3)
% 158.37/27.67 (51) all_54_14 = all_52_11
% 158.37/27.67 (52) ~ (all_52_8 = e1)
% 158.37/27.67 (53) op(e0, e0) = e1
% 158.37/27.67 (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.67 (55) ~ (e3 = e2)
% 158.37/27.67 (56) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.37/27.67 (57) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.37/27.67
% 158.37/27.67 Begin of proof
% 158.37/27.67 |
% 158.37/27.67 | BETA: splitting (33) gives:
% 158.37/27.67 |
% 158.37/27.67 | Case 1:
% 158.37/27.67 | |
% 158.37/27.67 | | (58) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 158.37/27.67 | | e0)
% 158.37/27.67 | |
% 158.37/27.67 | | REF_CLOSE: (7), (8), (9), (14), (23), (25), (29), (30), (31), (35), (42),
% 158.37/27.67 | | (44), (45), (47), (54), (55), (58) are inconsistent by sub-proof
% 158.37/27.67 | | #652.
% 158.37/27.67 | |
% 158.37/27.67 | Case 2:
% 158.37/27.67 | |
% 158.37/27.67 | | (59) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.37/27.67 | | e0)
% 158.37/27.67 | |
% 158.37/27.67 | | BETA: splitting (59) gives:
% 158.37/27.67 | |
% 158.37/27.67 | | Case 1:
% 158.37/27.67 | | |
% 158.37/27.67 | | | (60) all_58_8 = e0 & op(e1, e1) = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | ALPHA: (60) implies:
% 158.37/27.67 | | | (61) op(e1, e1) = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | BETA: splitting (16) gives:
% 158.37/27.67 | | |
% 158.37/27.67 | | | Case 1:
% 158.37/27.67 | | | |
% 158.37/27.67 | | | | (62) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 158.37/27.67 | | | | = e2)
% 158.37/27.67 | | | |
% 158.37/27.67 | | | | BETA: splitting (62) gives:
% 158.37/27.67 | | | |
% 158.37/27.67 | | | | Case 1:
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | (63) all_58_9 = e2 & op(e3, e0) = e2
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (23), (28), (29), (30), (54),
% 158.37/27.67 | | | | | (55), (63) are inconsistent by sub-proof #456.
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | Case 2:
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | (64) all_58_10 = e2 & op(e2, e0) = e2
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | ALPHA: (64) implies:
% 158.37/27.67 | | | | | (65) all_58_10 = e2
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | REF_CLOSE: (23), (25), (29), (31), (35), (44), (45), (54), (65) are
% 158.37/27.67 | | | | | inconsistent by sub-proof #907.
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | End of split
% 158.37/27.67 | | | |
% 158.37/27.67 | | | Case 2:
% 158.37/27.67 | | | |
% 158.37/27.67 | | | | (66) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 158.37/27.67 | | | | e0) = e2)
% 158.37/27.67 | | | |
% 158.37/27.67 | | | | BETA: splitting (66) gives:
% 158.37/27.67 | | | |
% 158.37/27.67 | | | | Case 1:
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | (67) all_58_11 = e2 & op(e1, e0) = e2
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | ALPHA: (67) implies:
% 158.37/27.67 | | | | | (68) all_58_11 = e2
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | BETA: splitting (57) gives:
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | Case 1:
% 158.37/27.67 | | | | | |
% 158.37/27.67 | | | | | | (69) all_56_12 = e3
% 158.37/27.67 | | | | | |
% 158.37/27.67 | | | | | | REF_CLOSE: (30), (32), (69) are inconsistent by sub-proof #1191.
% 158.37/27.67 | | | | | |
% 158.37/27.67 | | | | | Case 2:
% 158.37/27.67 | | | | | |
% 158.37/27.67 | | | | | | (70) ~ (all_56_12 = e3)
% 158.37/27.67 | | | | | | (71) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.37/27.67 | | | | | |
% 158.37/27.67 | | | | | | REDUCE: (32), (70) imply:
% 158.37/27.67 | | | | | | (72) ~ (e3 = e1)
% 158.37/27.67 | | | | | |
% 158.37/27.67 | | | | | | BETA: splitting (71) gives:
% 158.37/27.67 | | | | | |
% 158.37/27.67 | | | | | | Case 1:
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | | (73) all_56_13 = e2
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | | COMBINE_EQS: (48), (73) imply:
% 158.37/27.67 | | | | | | | (74) e3 = e2
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | | COMBINE_EQS: (15), (74) imply:
% 158.37/27.67 | | | | | | | (75) all_58_6 = e2
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | | REF_CLOSE: (12), (13), (17), (19), (23), (29), (30), (54), (55),
% 158.37/27.67 | | | | | | | (75) are inconsistent by sub-proof #1154.
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | Case 2:
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | | (76) ~ (all_56_13 = e2)
% 158.37/27.67 | | | | | | | (77) all_56_14 = e1 | all_56_15 = e0
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | | BETA: splitting (77) gives:
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | (78) all_56_14 = e1
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | COMBINE_EQS: (3), (78) imply:
% 158.37/27.67 | | | | | | | | (79) e3 = e1
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | REDUCE: (30), (79) imply:
% 158.37/27.67 | | | | | | | | (80) $false
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | CLOSE: (80) is inconsistent.
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | (81) all_56_15 = e0
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | COMBINE_EQS: (38), (81) imply:
% 158.37/27.67 | | | | | | | | (82) all_4_2 = e0
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | REDUCE: (40), (82) imply:
% 158.37/27.67 | | | | | | | | (83) ~ (all_52_13 = e0)
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | REDUCE: (18), (82) imply:
% 158.37/27.67 | | | | | | | | (84) ~ (e2 = e0)
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | BETA: splitting (11) gives:
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | | |
% 158.37/27.67 | | | | | | | | | (85) all_54_7 = e3
% 158.37/27.67 | | | | | | | | |
% 158.37/27.67 | | | | | | | | | REF_CLOSE: (20), (36), (85) are inconsistent by sub-proof
% 158.37/27.67 | | | | | | | | | #1428.
% 158.37/27.67 | | | | | | | | |
% 158.37/27.67 | | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | | |
% 158.37/27.67 | | | | | | | | | (86) ~ (all_54_7 = e3)
% 158.37/27.67 | | | | | | | | | (87) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.37/27.67 | | | | | | | | |
% 158.37/27.67 | | | | | | | | | BETA: splitting (87) gives:
% 158.37/27.67 | | | | | | | | |
% 158.37/27.67 | | | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | (88) all_54_7 = e2
% 158.37/27.67 | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | REF_CLOSE: (36), (37), (88) are inconsistent by sub-proof
% 158.37/27.67 | | | | | | | | | | #1427.
% 158.37/27.67 | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | (89) ~ (all_54_7 = e2)
% 158.37/27.67 | | | | | | | | | | (90) all_54_7 = e1 | all_54_7 = e0
% 158.37/27.67 | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | BETA: splitting (90) gives:
% 158.37/27.67 | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | (91) all_54_7 = e1
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | COMBINE_EQS: (36), (91) imply:
% 158.37/27.67 | | | | | | | | | | | (92) all_52_13 = e1
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | SIMP: (92) implies:
% 158.37/27.67 | | | | | | | | | | | (93) all_52_13 = e1
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | REDUCE: (24), (93) imply:
% 158.37/27.67 | | | | | | | | | | | (94) ~ (all_52_9 = e1)
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | REDUCE: (37), (93) imply:
% 158.37/27.67 | | | | | | | | | | | (95) ~ (e2 = e1)
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | BETA: splitting (4) gives:
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | (96) all_54_6 = e3
% 158.37/27.67 | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | REF_CLOSE: (26), (41), (96) are inconsistent by sub-proof
% 158.37/27.67 | | | | | | | | | | | | #1193.
% 158.37/27.67 | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | (97) ~ (all_54_6 = e3)
% 158.37/27.67 | | | | | | | | | | | | (98) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.37/27.67 | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | BETA: splitting (98) gives:
% 158.37/27.67 | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | (99) all_54_6 = e2
% 158.37/27.67 | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | REF_CLOSE: (41), (49), (99) are inconsistent by sub-proof
% 158.37/27.67 | | | | | | | | | | | | | #1192.
% 158.37/27.67 | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | (100) all_54_6 = e1 | all_54_6 = e0
% 158.37/27.67 | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | BETA: splitting (14) gives:
% 158.37/27.67 | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | (101) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 158.37/27.67 | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 158.37/27.67 | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 158.37/27.67 | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | (102) all_58_4 = e2 & op(e3, e1) = e2
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 158.37/27.67 | | | | | | | | | | | | | | | (103) all_58_4 = e2
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (14), (21),
% 158.37/27.67 | | | | | | | | | | | | | | | (22), (26), (29), (34), (35), (39), (41), (43),
% 158.37/27.67 | | | | | | | | | | | | | | | (45), (46), (47), (50), (51), (52), (54), (56),
% 158.37/27.67 | | | | | | | | | | | | | | | (61), (94), (100), (103) are inconsistent by
% 158.37/27.67 | | | | | | | | | | | | | | | sub-proof #455.
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | (104) all_58_5 = e2 & op(e2, e1) = e2
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 158.37/27.67 | | | | | | | | | | | | | | | (105) all_58_5 = e2
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | REF_CLOSE: (7), (23), (25), (29), (30), (35), (42), (44),
% 158.37/27.67 | | | | | | | | | | | | | | | (45), (54), (105) are inconsistent by sub-proof
% 158.37/27.67 | | | | | | | | | | | | | | | #898.
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | End of split
% 158.37/27.67 | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | (106) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 158.37/27.67 | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 158.37/27.67 | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 158.37/27.67 | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | Case 1:
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | (107) all_58_8 = e2 & op(e1, e1) = e2
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 158.37/27.67 | | | | | | | | | | | | | | | (108) all_58_8 = e2
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (23), (25), (27), (30), (42), (44),
% 158.37/27.67 | | | | | | | | | | | | | | | (68), (108) are inconsistent by sub-proof #1070.
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | (109) all_58_14 = e2 & op(e0, e1) = e2
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (13), (15), (17), (19), (23), (29),
% 158.37/27.67 | | | | | | | | | | | | | | | (30), (54), (55), (109) are inconsistent by
% 158.37/27.67 | | | | | | | | | | | | | | | sub-proof #829.
% 158.37/27.67 | | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | | End of split
% 158.37/27.67 | | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | | End of split
% 158.37/27.67 | | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | | End of split
% 158.37/27.67 | | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | End of split
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | Case 2:
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | (110) all_54_7 = e0
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | | REF_CLOSE: (36), (83), (110) are inconsistent by sub-proof
% 158.37/27.67 | | | | | | | | | | | #1112.
% 158.37/27.67 | | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | | End of split
% 158.37/27.67 | | | | | | | | | |
% 158.37/27.67 | | | | | | | | | End of split
% 158.37/27.67 | | | | | | | | |
% 158.37/27.67 | | | | | | | | End of split
% 158.37/27.67 | | | | | | | |
% 158.37/27.67 | | | | | | | End of split
% 158.37/27.67 | | | | | | |
% 158.37/27.67 | | | | | | End of split
% 158.37/27.67 | | | | | |
% 158.37/27.67 | | | | | End of split
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | Case 2:
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | (111) all_58_15 = e2 & op(e0, e0) = e2
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | ALPHA: (111) implies:
% 158.37/27.67 | | | | | (112) op(e0, e0) = e2
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | | REF_CLOSE: (42), (53), (54), (112) are inconsistent by sub-proof
% 158.37/27.67 | | | | | #1386.
% 158.37/27.67 | | | | |
% 158.37/27.67 | | | | End of split
% 158.37/27.67 | | | |
% 158.37/27.67 | | | End of split
% 158.37/27.67 | | |
% 158.37/27.67 | | Case 2:
% 158.37/27.67 | | |
% 158.37/27.67 | | | (113) all_58_14 = e0 & op(e0, e1) = e0
% 158.37/27.67 | | |
% 158.37/27.67 | | | REF_CLOSE: (8), (23), (113) are inconsistent by sub-proof #882.
% 158.37/27.67 | | |
% 158.37/27.67 | | End of split
% 158.37/27.67 | |
% 158.37/27.67 | End of split
% 158.37/27.67 |
% 158.37/27.67 End of proof
% 158.37/27.67
% 158.37/27.67 Sub-proof #455 shows that the following formulas are inconsistent:
% 158.37/27.67 ----------------------------------------------------------------
% 158.37/27.67 (1) op(e1, e1) = e3
% 158.37/27.67 (2) op(e1, e1) = all_32_1
% 158.37/27.67 (3) op(e3, e1) = e3
% 158.37/27.67 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.67 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.67 (5) all_58_14 = e3
% 158.37/27.67 (6) op(e1, e1) = all_6_2
% 158.37/27.67 (7) ~ (all_52_11 = e3)
% 158.37/27.67 (8) op(e1, e1) = e0
% 158.37/27.67 (9) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.37/27.67 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.67 (10) all_54_2 = all_52_8
% 158.37/27.67 (11) ~ (all_52_8 = all_52_9)
% 158.37/27.67 (12) ~ (all_52_9 = e3)
% 158.37/27.67 (13) op(e2, e3) = e2
% 158.37/27.67 (14) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.37/27.67 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.67 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.67 (16) ~ (all_52_9 = all_52_11)
% 158.37/27.67 (17) all_58_4 = e2
% 158.37/27.67 (18) all_54_6 = all_52_9
% 158.37/27.67 (19) ~ (all_52_8 = all_52_11)
% 158.37/27.67 (20) all_58_3 = e3
% 158.37/27.67 (21) op(e3, e1) = all_52_8
% 158.37/27.67 (22) ~ (all_6_2 = e2)
% 158.37/27.67 (23) ~ (all_52_8 = e3)
% 158.37/27.67 (24) all_54_14 = all_52_11
% 158.37/27.67 (25) ~ (all_52_8 = e1)
% 158.37/27.67 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.67 (27) ~ (all_52_9 = e1)
% 158.37/27.67 (28) all_54_6 = e1 | all_54_6 = e0
% 158.37/27.67 (29) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.37/27.67
% 158.37/27.67 Begin of proof
% 158.37/27.67 |
% 158.37/27.67 | BETA: splitting (28) gives:
% 158.37/27.67 |
% 158.37/27.67 | Case 1:
% 158.37/27.67 | |
% 158.37/27.67 | | (30) all_54_6 = e1
% 158.37/27.67 | |
% 158.37/27.67 | | REF_CLOSE: (18), (27), (30) are inconsistent by sub-proof #562.
% 158.37/27.67 | |
% 158.37/27.67 | Case 2:
% 158.37/27.67 | |
% 158.37/27.67 | | (31) all_54_6 = e0
% 158.37/27.67 | |
% 158.37/27.67 | | COMBINE_EQS: (18), (31) imply:
% 158.37/27.68 | | (32) all_52_9 = e0
% 158.37/27.68 | |
% 158.37/27.68 | | SIMP: (32) implies:
% 158.37/27.68 | | (33) all_52_9 = e0
% 158.37/27.68 | |
% 158.37/27.68 | | REDUCE: (11), (33) imply:
% 158.37/27.68 | | (34) ~ (all_52_8 = e0)
% 158.37/27.68 | |
% 158.37/27.68 | | REDUCE: (16), (33) imply:
% 158.37/27.68 | | (35) ~ (all_52_11 = e0)
% 158.37/27.68 | |
% 158.37/27.68 | | SIMP: (35) implies:
% 158.37/27.68 | | (36) ~ (all_52_11 = e0)
% 158.37/27.68 | |
% 158.37/27.68 | | REDUCE: (12), (33) imply:
% 158.37/27.68 | | (37) ~ (e3 = e0)
% 158.37/27.68 | |
% 158.37/27.68 | | SIMP: (37) implies:
% 158.37/27.68 | | (38) ~ (e3 = e0)
% 158.37/27.68 | |
% 158.37/27.68 | | BETA: splitting (14) gives:
% 158.37/27.68 | |
% 158.37/27.68 | | Case 1:
% 158.37/27.68 | | |
% 158.37/27.68 | | | (39) all_54_2 = e3
% 158.37/27.68 | | |
% 158.37/27.68 | | | COMBINE_EQS: (10), (39) imply:
% 158.37/27.68 | | | (40) all_52_8 = e3
% 158.37/27.68 | | |
% 158.37/27.68 | | | REDUCE: (23), (40) imply:
% 158.37/27.68 | | | (41) $false
% 158.37/27.68 | | |
% 158.37/27.68 | | | CLOSE: (41) is inconsistent.
% 158.37/27.68 | | |
% 158.37/27.68 | | Case 2:
% 158.37/27.68 | | |
% 158.37/27.68 | | | (42) ~ (all_54_2 = e3)
% 158.37/27.68 | | | (43) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.37/27.68 | | |
% 158.37/27.68 | | | BETA: splitting (43) gives:
% 158.37/27.68 | | |
% 158.37/27.68 | | | Case 1:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | (44) all_54_2 = e2
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | COMBINE_EQS: (10), (44) imply:
% 158.37/27.68 | | | | (45) all_52_8 = e2
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | REDUCE: (19), (45) imply:
% 158.37/27.68 | | | | (46) ~ (all_52_11 = e2)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | SIMP: (46) implies:
% 158.37/27.68 | | | | (47) ~ (all_52_11 = e2)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | REDUCE: (23), (45) imply:
% 158.37/27.68 | | | | (48) ~ (e3 = e2)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | SIMP: (48) implies:
% 158.37/27.68 | | | | (49) ~ (e3 = e2)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | REDUCE: (34), (45) imply:
% 158.37/27.68 | | | | (50) ~ (e2 = e0)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | REDUCE: (21), (45) imply:
% 158.37/27.68 | | | | (51) op(e3, e1) = e2
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | BETA: splitting (29) gives:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | Case 1:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | (52) all_54_14 = e3
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | REF_CLOSE: (7), (24), (52) are inconsistent by sub-proof #1413.
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | Case 2:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | (53) ~ (all_54_14 = e3)
% 158.37/27.68 | | | | | (54) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | BETA: splitting (54) gives:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | Case 1:
% 158.37/27.68 | | | | | |
% 158.37/27.68 | | | | | | (55) all_54_14 = e2
% 158.37/27.68 | | | | | |
% 158.37/27.68 | | | | | | REF_CLOSE: (24), (47), (55) are inconsistent by sub-proof #1232.
% 158.37/27.68 | | | | | |
% 158.37/27.68 | | | | | Case 2:
% 158.37/27.68 | | | | | |
% 158.37/27.68 | | | | | | (56) ~ (all_54_14 = e2)
% 158.37/27.68 | | | | | | (57) all_54_14 = e1 | all_54_14 = e0
% 158.37/27.68 | | | | | |
% 158.37/27.68 | | | | | | BETA: splitting (57) gives:
% 158.37/27.68 | | | | | |
% 158.37/27.68 | | | | | | Case 1:
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | (58) all_54_14 = e1
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | COMBINE_EQS: (24), (58) imply:
% 158.37/27.68 | | | | | | | (59) all_52_11 = e1
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | SIMP: (59) implies:
% 158.37/27.68 | | | | | | | (60) all_52_11 = e1
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | REDUCE: (7), (60) imply:
% 158.37/27.68 | | | | | | | (61) ~ (e3 = e1)
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | SIMP: (61) implies:
% 158.37/27.68 | | | | | | | (62) ~ (e3 = e1)
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | REDUCE: (47), (60) imply:
% 158.37/27.68 | | | | | | | (63) ~ (e2 = e1)
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | SIMP: (63) implies:
% 158.37/27.68 | | | | | | | (64) ~ (e2 = e1)
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | REDUCE: (36), (60) imply:
% 158.37/27.68 | | | | | | | (65) ~ (e1 = e0)
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | GROUND_INST: instantiating (26) with e3, all_32_1, e1, e1,
% 158.37/27.68 | | | | | | | simplifying with (1), (2) gives:
% 158.37/27.68 | | | | | | | (66) all_32_1 = e3
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | GROUND_INST: instantiating (26) with e0, all_32_1, e1, e1,
% 158.37/27.68 | | | | | | | simplifying with (2), (8) gives:
% 158.37/27.68 | | | | | | | (67) all_32_1 = e0
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | GROUND_INST: instantiating (26) with e2, e3, e1, e3, simplifying
% 158.37/27.68 | | | | | | | with (3), (51) gives:
% 158.37/27.68 | | | | | | | (68) e3 = e2
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | COMBINE_EQS: (66), (67) imply:
% 158.37/27.68 | | | | | | | (69) e3 = e0
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | SIMP: (69) implies:
% 158.37/27.68 | | | | | | | (70) e3 = e0
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | COMBINE_EQS: (68), (70) imply:
% 158.37/27.68 | | | | | | | (71) e2 = e0
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | SIMP: (71) implies:
% 158.37/27.68 | | | | | | | (72) e2 = e0
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | COMBINE_EQS: (17), (72) imply:
% 158.37/27.68 | | | | | | | (73) all_58_4 = e0
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | REF_CLOSE: (4), (5), (6), (9), (13), (15), (20), (22), (26), (38),
% 158.37/27.68 | | | | | | | (49), (50), (62), (64), (65), (73) are inconsistent by
% 158.37/27.68 | | | | | | | sub-proof #854.
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | Case 2:
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | (74) all_54_14 = e0
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | | REF_CLOSE: (24), (36), (74) are inconsistent by sub-proof #1400.
% 158.37/27.68 | | | | | | |
% 158.37/27.68 | | | | | | End of split
% 158.37/27.68 | | | | | |
% 158.37/27.68 | | | | | End of split
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | End of split
% 158.37/27.68 | | | |
% 158.37/27.68 | | | Case 2:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | (75) all_54_2 = e1 | all_54_2 = e0
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | REF_CLOSE: (10), (25), (34), (75) are inconsistent by sub-proof #561.
% 158.37/27.68 | | | |
% 158.37/27.68 | | | End of split
% 158.37/27.68 | | |
% 158.37/27.68 | | End of split
% 158.37/27.68 | |
% 158.37/27.68 | End of split
% 158.37/27.68 |
% 158.37/27.68 End of proof
% 158.37/27.68
% 158.37/27.68 Sub-proof #456 shows that the following formulas are inconsistent:
% 158.37/27.68 ----------------------------------------------------------------
% 158.37/27.68 (1) all_58_0 = e1
% 158.37/27.68 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.68 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.68 (3) all_58_6 = e3
% 158.37/27.68 (4) all_58_12 = e0
% 158.37/27.68 (5) all_58_9 = e2 & op(e3, e0) = e2
% 158.37/27.68 (6) op(e2, e3) = all_52_1
% 158.37/27.68 (7) ~ (e3 = e0)
% 158.37/27.68 (8) all_58_9 = e3
% 158.37/27.68 (9) op(e2, e3) = e2
% 158.37/27.68 (10) ~ (e3 = e1)
% 158.37/27.68 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.68 (12) ~ (e3 = e2)
% 158.37/27.68
% 158.37/27.68 Begin of proof
% 158.37/27.68 |
% 158.37/27.68 | ALPHA: (5) implies:
% 158.37/27.68 | (13) all_58_9 = e2
% 158.37/27.68 |
% 158.37/27.68 | COMBINE_EQS: (8), (13) imply:
% 158.37/27.68 | (14) e3 = e2
% 158.37/27.68 |
% 158.37/27.68 | SIMP: (14) implies:
% 158.37/27.68 | (15) e3 = e2
% 158.37/27.68 |
% 158.37/27.68 | COMBINE_EQS: (3), (15) imply:
% 158.37/27.68 | (16) all_58_6 = e2
% 158.37/27.68 |
% 158.37/27.68 | REF_CLOSE: (1), (2), (4), (6), (7), (9), (10), (11), (12), (16) are
% 158.37/27.68 | inconsistent by sub-proof #1154.
% 158.37/27.68 |
% 158.37/27.68 End of proof
% 158.37/27.68
% 158.37/27.68 Sub-proof #457 shows that the following formulas are inconsistent:
% 158.37/27.68 ----------------------------------------------------------------
% 158.37/27.68 (1) op(e1, e3) = e3
% 158.37/27.68 (2) op(e1, e1) = e3
% 158.37/27.68 (3) op(e1, e1) = all_32_1
% 158.37/27.68 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.37/27.68 (5) op(e3, e1) = e3
% 158.37/27.68 (6) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.37/27.68 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.37/27.68 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.68 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.68 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.37/27.68 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.37/27.68 (9) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.68 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.68 (10) all_58_14 = e3
% 158.37/27.68 (11) all_54_13 = all_52_7
% 158.37/27.68 (12) op(e1, e1) = all_6_2
% 158.37/27.68 (13) ~ (all_52_7 = e3)
% 158.37/27.68 (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.68 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.37/27.68 e1)
% 158.37/27.68 (15) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.37/27.68 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.37/27.68 (16) ~ (all_52_6 = all_52_14)
% 158.37/27.68 (17) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.37/27.68 (18) op(e1, e2) = all_14_0
% 158.37/27.68 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.68 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.68 (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.37/27.68 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.68 (21) all_58_6 = e3
% 158.37/27.68 (22) ~ (all_52_14 = e3)
% 158.37/27.68 (23) all_58_12 = e0
% 158.37/27.68 (24) op(e3, e2) = all_52_4
% 158.37/27.68 (25) ~ (all_4_2 = e2)
% 158.37/27.68 (26) op(e2, e3) = all_52_1
% 158.37/27.68 (27) ~ (all_52_13 = e3)
% 158.37/27.68 (28) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.37/27.68 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.37/27.68 (29) all_58_13 = e1
% 158.37/27.68 (30) ~ (e3 = e0)
% 158.37/27.68 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.37/27.68 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.37/27.68 (32) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.37/27.68 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.37/27.68 (33) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.37/27.68 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.37/27.68 e2)
% 158.37/27.68 (34) ~ (e2 = e0)
% 158.37/27.68 (35) ~ (all_52_2 = all_52_6)
% 158.37/27.68 (36) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.37/27.68 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.37/27.68 (37) op(e1, e3) = all_52_2
% 158.37/27.68 (38) op(e2, e0) = all_52_13
% 158.37/27.68 (39) op(e2, e3) = e2
% 158.37/27.68 (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.68 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.37/27.68 (41) ~ (e3 = e1)
% 158.37/27.68 (42) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.37/27.68 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.37/27.68 (43) op(e1, e2) = all_52_6
% 158.37/27.68 (44) ~ (all_4_2 = e1)
% 158.37/27.68 (45) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.68 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.68 (46) op(e0, e0) = all_4_2
% 158.37/27.68 (47) all_54_8 = all_52_2
% 158.37/27.68 (48) all_54_7 = all_52_13
% 158.37/27.68 (49) ~ (all_52_2 = e3)
% 158.37/27.68 (50) ~ (all_52_13 = e2)
% 158.37/27.68 (51) all_56_15 = all_4_2
% 158.37/27.68 (52) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.37/27.68 (53) ~ (all_52_13 = all_4_2)
% 158.37/27.68 (54) ~ (all_52_2 = e1)
% 158.37/27.68 (55) ~ (all_52_6 = all_52_7)
% 158.37/27.68 (56) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.37/27.68 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.37/27.68 (57) ~ (all_52_4 = e3)
% 158.37/27.68 (58) ~ (e2 = e1)
% 158.37/27.68 (59) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.37/27.68 (60) ~ (e1 = e0)
% 158.37/27.68 (61) ~ (all_52_2 = e2)
% 158.37/27.68 (62) all_58_3 = e3
% 158.37/27.68 (63) ~ (all_6_2 = e2)
% 158.37/27.68 (64) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.37/27.68 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.37/27.68 e3)
% 158.37/27.68 (65) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.37/27.68 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.37/27.68 (66) ~ (all_52_7 = all_4_2)
% 158.37/27.68 (67) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.37/27.68 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.37/27.68 (68) op(e0, e2) = all_52_7
% 158.37/27.68 (69) all_54_15 = all_4_2
% 158.37/27.68 (70) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.37/27.68 (71) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.37/27.68 (72) ~ (all_52_6 = e3)
% 158.37/27.68 (73) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.37/27.68 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.37/27.68 (74) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.68 (75) all_54_11 = all_52_14
% 158.37/27.68 (76) ~ (all_52_13 = all_52_14)
% 158.37/27.68 (77) ~ (e3 = e2)
% 158.37/27.68 (78) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.37/27.68 (79) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.37/27.68 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.37/27.68 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.37/27.68 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.37/27.68 (80) all_54_9 = all_52_6
% 158.37/27.68 (81) ~ (all_52_14 = all_4_2)
% 158.37/27.68
% 158.37/27.68 Begin of proof
% 158.37/27.68 |
% 158.37/27.68 | BETA: splitting (56) gives:
% 158.37/27.68 |
% 158.37/27.68 | Case 1:
% 158.37/27.68 | |
% 158.37/27.68 | | (82) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 158.37/27.68 | | e1)
% 158.37/27.68 | |
% 158.37/27.68 | | BETA: splitting (82) gives:
% 158.37/27.68 | |
% 158.37/27.68 | | Case 1:
% 158.37/27.68 | | |
% 158.37/27.68 | | | (83) all_58_4 = e1 & op(e3, e1) = e1
% 158.37/27.68 | | |
% 158.37/27.68 | | | ALPHA: (83) implies:
% 158.37/27.68 | | | (84) all_58_4 = e1
% 158.37/27.68 | | |
% 158.37/27.68 | | | REF_CLOSE: (9), (10), (12), (20), (30), (34), (39), (41), (45), (58),
% 158.37/27.68 | | | (60), (62), (63), (74), (77), (84) are inconsistent by
% 158.37/27.68 | | | sub-proof #850.
% 158.37/27.68 | | |
% 158.37/27.68 | | Case 2:
% 158.37/27.68 | | |
% 158.37/27.68 | | | (85) all_58_5 = e1 & op(e2, e1) = e1
% 158.37/27.68 | | |
% 158.37/27.68 | | | ALPHA: (85) implies:
% 158.37/27.68 | | | (86) all_58_5 = e1
% 158.37/27.68 | | |
% 158.37/27.68 | | | BETA: splitting (31) gives:
% 158.37/27.68 | | |
% 158.37/27.68 | | | Case 1:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | (87) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 158.37/27.68 | | | | = e1)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | BETA: splitting (87) gives:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | Case 1:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | (88) all_58_0 = e1 & op(e3, e3) = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | ALPHA: (88) implies:
% 158.37/27.68 | | | | | (89) all_58_0 = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.37/27.68 | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 158.37/27.68 | | | | | (23), (25), (26), (27), (28), (29), (30), (31), (33), (34),
% 158.37/27.68 | | | | | (35), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 158.37/27.68 | | | | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (58),
% 158.37/27.68 | | | | | (59), (60), (61), (62), (63), (64), (65), (66), (68), (69),
% 158.37/27.68 | | | | | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 158.37/27.68 | | | | | (80), (81), (86), (89) are inconsistent by sub-proof #461.
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | Case 2:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | (90) all_58_2 = e1 & op(e2, e3) = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | ALPHA: (90) implies:
% 158.37/27.68 | | | | | (91) op(e2, e3) = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | REF_CLOSE: (39), (58), (74), (91) are inconsistent by sub-proof #1430.
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | End of split
% 158.37/27.68 | | | |
% 158.37/27.68 | | | Case 2:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | (92) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 158.37/27.68 | | | | = e1)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | BETA: splitting (92) gives:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | Case 1:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | (93) all_58_6 = e1 & op(e1, e3) = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | REF_CLOSE: (21), (41), (93) are inconsistent by sub-proof #1347.
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | Case 2:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | (94) all_58_12 = e1 & op(e0, e3) = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | REF_CLOSE: (23), (60), (94) are inconsistent by sub-proof #1422.
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | End of split
% 158.37/27.68 | | | |
% 158.37/27.68 | | | End of split
% 158.37/27.68 | | |
% 158.37/27.68 | | End of split
% 158.37/27.68 | |
% 158.37/27.68 | Case 2:
% 158.37/27.68 | |
% 158.37/27.68 | | (95) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 158.37/27.68 | | e1)
% 158.37/27.68 | |
% 158.37/27.68 | | BETA: splitting (95) gives:
% 158.37/27.68 | |
% 158.37/27.68 | | Case 1:
% 158.37/27.68 | | |
% 158.37/27.68 | | | (96) all_58_8 = e1 & op(e1, e1) = e1
% 158.37/27.68 | | |
% 158.37/27.68 | | | ALPHA: (96) implies:
% 158.37/27.68 | | | (97) all_58_8 = e1
% 158.37/27.68 | | |
% 158.37/27.68 | | | BETA: splitting (31) gives:
% 158.37/27.68 | | |
% 158.37/27.68 | | | Case 1:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | (98) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 158.37/27.68 | | | | = e1)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | BETA: splitting (98) gives:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | Case 1:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | (99) all_58_0 = e1 & op(e3, e3) = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | ALPHA: (99) implies:
% 158.37/27.68 | | | | | (100) all_58_0 = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.37/27.68 | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 158.37/27.68 | | | | | (26), (27), (28), (29), (31), (32), (33), (35), (36), (37),
% 158.37/27.68 | | | | | (39), (40), (41), (43), (44), (45), (46), (47), (48), (49),
% 158.37/27.68 | | | | | (50), (51), (52), (53), (54), (55), (57), (58), (59), (61),
% 158.37/27.68 | | | | | (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 158.37/27.68 | | | | | (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 158.37/27.68 | | | | | (97), (100) are inconsistent by sub-proof #458.
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | Case 2:
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | (101) all_58_2 = e1 & op(e2, e3) = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | ALPHA: (101) implies:
% 158.37/27.68 | | | | | (102) op(e2, e3) = e1
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | | REF_CLOSE: (39), (58), (74), (102) are inconsistent by sub-proof
% 158.37/27.68 | | | | | #1430.
% 158.37/27.68 | | | | |
% 158.37/27.68 | | | | End of split
% 158.37/27.68 | | | |
% 158.37/27.68 | | | Case 2:
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | (103) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 158.37/27.68 | | | | e3) = e1)
% 158.37/27.68 | | | |
% 158.37/27.68 | | | | REF_CLOSE: (21), (23), (41), (60), (103) are inconsistent by sub-proof
% 158.37/27.68 | | | | #862.
% 158.37/27.68 | | | |
% 158.37/27.68 | | | End of split
% 158.37/27.68 | | |
% 158.37/27.68 | | Case 2:
% 158.37/27.68 | | |
% 158.37/27.68 | | | (104) all_58_14 = e1 & op(e0, e1) = e1
% 158.37/27.68 | | |
% 158.37/27.68 | | | ALPHA: (104) implies:
% 158.37/27.68 | | | (105) all_58_14 = e1
% 158.37/27.68 | | |
% 158.37/27.68 | | | REF_CLOSE: (10), (41), (105) are inconsistent by sub-proof #1147.
% 158.37/27.68 | | |
% 158.37/27.68 | | End of split
% 158.37/27.68 | |
% 158.37/27.68 | End of split
% 158.37/27.68 |
% 158.37/27.68 End of proof
% 158.37/27.68
% 158.37/27.68 Sub-proof #458 shows that the following formulas are inconsistent:
% 158.37/27.68 ----------------------------------------------------------------
% 158.37/27.68 (1) op(e1, e3) = e3
% 158.37/27.68 (2) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.37/27.68 (3) op(e3, e1) = e3
% 158.37/27.68 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.68 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.68 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.37/27.68 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.37/27.68 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.68 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.68 (7) all_58_14 = e3
% 158.37/27.68 (8) all_54_13 = all_52_7
% 158.37/27.68 (9) op(e1, e1) = all_6_2
% 158.37/27.68 (10) ~ (all_52_7 = e3)
% 158.37/27.68 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.68 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.37/27.68 e1)
% 158.37/27.68 (12) ~ (all_52_6 = all_52_14)
% 158.37/27.68 (13) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.37/27.68 (14) all_58_0 = e1
% 158.37/27.68 (15) op(e1, e2) = all_14_0
% 158.37/27.68 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.68 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.68 (17) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.37/27.68 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.68 (18) all_58_6 = e3
% 158.37/27.68 (19) ~ (all_52_14 = e3)
% 158.37/27.68 (20) all_58_12 = e0
% 158.37/27.68 (21) op(e3, e2) = all_52_4
% 158.37/27.68 (22) ~ (all_4_2 = e2)
% 158.37/27.68 (23) op(e2, e3) = all_52_1
% 158.37/27.68 (24) ~ (all_52_13 = e3)
% 158.37/27.68 (25) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.37/27.68 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.37/27.68 (26) all_58_13 = e1
% 158.37/27.68 (27) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.37/27.68 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.37/27.68 (28) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.37/27.68 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.37/27.68 (29) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.37/27.68 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.37/27.68 e2)
% 158.37/27.68 (30) ~ (all_52_2 = all_52_6)
% 158.37/27.68 (31) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.37/27.68 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.37/27.68 (32) op(e1, e3) = all_52_2
% 158.37/27.68 (33) op(e2, e3) = e2
% 158.37/27.68 (34) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.68 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.37/27.68 (35) ~ (e3 = e1)
% 158.37/27.68 (36) op(e1, e2) = all_52_6
% 158.37/27.68 (37) ~ (all_4_2 = e1)
% 158.37/27.68 (38) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.68 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.68 (39) op(e0, e0) = all_4_2
% 158.37/27.68 (40) all_54_8 = all_52_2
% 158.37/27.68 (41) all_54_7 = all_52_13
% 158.37/27.68 (42) ~ (all_52_2 = e3)
% 158.37/27.68 (43) ~ (all_52_13 = e2)
% 158.37/27.68 (44) all_56_15 = all_4_2
% 158.37/27.68 (45) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.37/27.68 (46) ~ (all_52_13 = all_4_2)
% 158.37/27.68 (47) ~ (all_52_2 = e1)
% 158.37/27.68 (48) ~ (all_52_6 = all_52_7)
% 158.37/27.68 (49) ~ (all_52_4 = e3)
% 158.37/27.68 (50) ~ (e2 = e1)
% 158.37/27.68 (51) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.37/27.68 (52) ~ (all_52_2 = e2)
% 158.37/27.68 (53) all_58_3 = e3
% 158.37/27.68 (54) ~ (all_6_2 = e2)
% 158.37/27.68 (55) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.37/27.68 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.37/27.68 e3)
% 158.37/27.69 (56) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.37/27.69 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.37/27.69 (57) ~ (all_52_7 = all_4_2)
% 158.37/27.69 (58) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.37/27.69 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.37/27.69 (59) op(e0, e2) = all_52_7
% 158.37/27.69 (60) all_54_15 = all_4_2
% 158.37/27.69 (61) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.37/27.69 (62) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.37/27.69 (63) ~ (all_52_6 = e3)
% 158.37/27.69 (64) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.37/27.69 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.37/27.69 (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.69 (66) all_54_11 = all_52_14
% 158.37/27.69 (67) ~ (all_52_13 = all_52_14)
% 158.37/27.69 (68) ~ (e3 = e2)
% 158.37/27.69 (69) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.37/27.69 (70) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.37/27.69 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.37/27.69 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.37/27.69 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.37/27.69 (71) all_54_9 = all_52_6
% 158.37/27.69 (72) ~ (all_52_14 = all_4_2)
% 158.37/27.69 (73) all_58_8 = e1
% 158.37/27.69
% 158.37/27.69 Begin of proof
% 158.37/27.69 |
% 158.37/27.69 | BETA: splitting (61) gives:
% 158.37/27.69 |
% 158.37/27.69 | Case 1:
% 158.37/27.69 | |
% 158.37/27.69 | | (74) all_54_8 = e2
% 158.37/27.69 | |
% 158.37/27.69 | | REF_CLOSE: (40), (52), (74) are inconsistent by sub-proof #1231.
% 158.37/27.69 | |
% 158.37/27.69 | Case 2:
% 158.37/27.69 | |
% 158.37/27.69 | | (75) ~ (all_54_8 = e2)
% 158.37/27.69 | | (76) all_54_8 = e1 | all_54_8 = e0
% 158.37/27.69 | |
% 158.37/27.69 | | BETA: splitting (76) gives:
% 158.37/27.69 | |
% 158.37/27.69 | | Case 1:
% 158.37/27.69 | | |
% 158.37/27.69 | | | (77) all_54_8 = e1
% 158.37/27.69 | | |
% 158.37/27.69 | | | REF_CLOSE: (40), (47), (77) are inconsistent by sub-proof #1379.
% 158.37/27.69 | | |
% 158.37/27.69 | | Case 2:
% 158.37/27.69 | | |
% 158.37/27.69 | | | (78) all_54_8 = e0
% 158.37/27.69 | | |
% 158.37/27.69 | | | COMBINE_EQS: (40), (78) imply:
% 158.37/27.69 | | | (79) all_52_2 = e0
% 158.37/27.69 | | |
% 158.37/27.69 | | | SIMP: (79) implies:
% 158.37/27.69 | | | (80) all_52_2 = e0
% 158.37/27.69 | | |
% 158.37/27.69 | | | REDUCE: (30), (80) imply:
% 158.37/27.69 | | | (81) ~ (all_52_6 = e0)
% 158.37/27.69 | | |
% 158.37/27.69 | | | SIMP: (81) implies:
% 158.37/27.69 | | | (82) ~ (all_52_6 = e0)
% 158.37/27.69 | | |
% 158.37/27.69 | | | REDUCE: (42), (80) imply:
% 158.37/27.69 | | | (83) ~ (e3 = e0)
% 158.37/27.69 | | |
% 158.37/27.69 | | | SIMP: (83) implies:
% 158.37/27.69 | | | (84) ~ (e3 = e0)
% 158.37/27.69 | | |
% 158.37/27.69 | | | REDUCE: (52), (80) imply:
% 158.37/27.69 | | | (85) ~ (e2 = e0)
% 158.37/27.69 | | |
% 158.37/27.69 | | | SIMP: (85) implies:
% 158.37/27.69 | | | (86) ~ (e2 = e0)
% 158.37/27.69 | | |
% 158.37/27.69 | | | REDUCE: (47), (80) imply:
% 158.37/27.69 | | | (87) ~ (e1 = e0)
% 158.37/27.69 | | |
% 158.37/27.69 | | | SIMP: (87) implies:
% 158.37/27.69 | | | (88) ~ (e1 = e0)
% 158.37/27.69 | | |
% 158.37/27.69 | | | REDUCE: (32), (80) imply:
% 158.37/27.69 | | | (89) op(e1, e3) = e0
% 158.37/27.69 | | |
% 158.37/27.69 | | | BETA: splitting (45) gives:
% 158.37/27.69 | | |
% 158.37/27.69 | | | Case 1:
% 158.37/27.69 | | | |
% 158.37/27.69 | | | | (90) ~ (all_56_15 = e3)
% 158.37/27.69 | | | |
% 158.37/27.69 | | | | REDUCE: (44), (90) imply:
% 158.37/27.69 | | | | (91) ~ (all_4_2 = e3)
% 158.37/27.69 | | | |
% 158.37/27.69 | | | | BETA: splitting (70) gives:
% 158.37/27.69 | | | |
% 158.37/27.69 | | | | Case 1:
% 158.37/27.69 | | | | |
% 158.37/27.69 | | | | | (92) all_58_15 = e0 & op(e0, e0) = e0
% 158.37/27.69 | | | | |
% 158.37/27.69 | | | | | ALPHA: (92) implies:
% 158.37/27.69 | | | | | (93) all_58_15 = e0
% 158.37/27.69 | | | | |
% 158.37/27.69 | | | | | REF_CLOSE: (7), (14), (16), (18), (20), (23), (26), (27), (29), (33),
% 158.37/27.69 | | | | | (35), (50), (64), (65), (68), (84), (86), (88), (93) are
% 158.37/27.69 | | | | | inconsistent by sub-proof #460.
% 158.37/27.69 | | | | |
% 158.37/27.69 | | | | Case 2:
% 158.37/27.69 | | | | |
% 158.37/27.69 | | | | | (94) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 158.37/27.69 | | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 158.37/27.69 | | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 158.37/27.69 | | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.37/27.69 | | | | |
% 158.37/27.69 | | | | | ALPHA: (94) implies:
% 158.37/27.69 | | | | | (95) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 158.37/27.69 | | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.37/27.69 | | | | |
% 158.37/27.69 | | | | | BETA: splitting (29) gives:
% 158.37/27.69 | | | | |
% 158.37/27.69 | | | | | Case 1:
% 158.37/27.69 | | | | | |
% 158.37/27.69 | | | | | | (96) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 158.37/27.69 | | | | | | op(e0, e2) = e2)
% 158.37/27.69 | | | | | |
% 158.37/27.69 | | | | | | BETA: splitting (96) gives:
% 158.37/27.69 | | | | | |
% 158.37/27.69 | | | | | | Case 1:
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | (97) all_58_12 = e2 & op(e0, e3) = e2
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | ALPHA: (97) implies:
% 158.37/27.69 | | | | | | | (98) all_58_12 = e2
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | REF_CLOSE: (16), (23), (27), (33), (35), (50), (64), (65), (68),
% 158.37/27.69 | | | | | | | (84), (86), (88), (98) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | #1062.
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | Case 2:
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | (99) all_58_13 = e2 & op(e0, e2) = e2
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | REF_CLOSE: (26), (50), (99) are inconsistent by sub-proof #727.
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | End of split
% 158.37/27.69 | | | | | |
% 158.37/27.69 | | | | | Case 2:
% 158.37/27.69 | | | | | |
% 158.37/27.69 | | | | | | (100) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 158.37/27.69 | | | | | | op(e0, e0) = e2)
% 158.37/27.69 | | | | | |
% 158.37/27.69 | | | | | | BETA: splitting (100) gives:
% 158.37/27.69 | | | | | |
% 158.37/27.69 | | | | | | Case 1:
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | (101) all_58_14 = e2 & op(e0, e1) = e2
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | REF_CLOSE: (7), (14), (16), (18), (20), (23), (33), (35), (65),
% 158.37/27.69 | | | | | | | (68), (84), (101) are inconsistent by sub-proof #829.
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | Case 2:
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | (102) all_58_15 = e2 & op(e0, e0) = e2
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | ALPHA: (102) implies:
% 158.37/27.69 | | | | | | | (103) all_58_15 = e2
% 158.37/27.69 | | | | | | | (104) op(e0, e0) = e2
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | BETA: splitting (31) gives:
% 158.37/27.69 | | | | | | |
% 158.37/27.69 | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | |
% 158.37/27.69 | | | | | | | | (105) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 158.37/27.69 | | | | | | | | op(e1, e2) = e0)
% 158.37/27.69 | | | | | | | |
% 158.37/27.69 | | | | | | | | BETA: splitting (105) gives:
% 158.37/27.69 | | | | | | | |
% 158.37/27.69 | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | (106) all_58_6 = e0 & op(e1, e3) = e0
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | REF_CLOSE: (18), (84), (106) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | #1350.
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | (107) all_58_7 = e0 & op(e1, e2) = e0
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | ALPHA: (107) implies:
% 158.37/27.69 | | | | | | | | | (108) all_58_7 = e0
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | BETA: splitting (17) gives:
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | (109) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 158.37/27.69 | | | | | | | | | | & op(e2, e1) = e2)
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | BETA: splitting (109) gives:
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | (110) all_58_4 = e2 & op(e3, e1) = e2
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | ALPHA: (110) implies:
% 158.37/27.69 | | | | | | | | | | | (111) all_58_4 = e2
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | BETA: splitting (25) gives:
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | (112) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 158.37/27.69 | | | | | | | | | | | | & op(e1, e2) = e2)
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | BETA: splitting (112) gives:
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | (113) all_58_6 = e2 & op(e1, e3) = e2
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | ALPHA: (113) implies:
% 158.37/27.69 | | | | | | | | | | | | | (114) all_58_6 = e2
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | REF_CLOSE: (14), (16), (20), (23), (33), (35), (65), (68),
% 158.37/27.69 | | | | | | | | | | | | | (84), (114) are inconsistent by sub-proof #1154.
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | (115) all_58_7 = e2 & op(e1, e2) = e2
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (17), (33), (35), (38), (50), (53),
% 158.37/27.69 | | | | | | | | | | | | | (54), (65), (68), (84), (86), (88), (108), (111),
% 158.37/27.69 | | | | | | | | | | | | | (115) are inconsistent by sub-proof #636.
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | (116) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 158.37/27.69 | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | BETA: splitting (116) gives:
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | (117) all_58_8 = e2 & op(e1, e1) = e2
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | REF_CLOSE: (9), (54), (65), (117) are inconsistent by
% 158.37/27.69 | | | | | | | | | | | | | sub-proof #1440.
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | (118) all_58_11 = e2 & op(e1, e0) = e2
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | ALPHA: (118) implies:
% 158.37/27.69 | | | | | | | | | | | | | (119) all_58_11 = e2
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | BETA: splitting (58) gives:
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | (120) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 158.37/27.69 | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | REF_CLOSE: (14), (21), (35), (49), (65), (120) are
% 158.37/27.69 | | | | | | | | | | | | | | inconsistent by sub-proof #1306.
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | (121) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 158.37/27.69 | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | (122) all_58_4 = e3 & op(e3, e1) = e3
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | (123) all_58_4 = e3
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (10), (11), (14), (16), (17), (18),
% 158.37/27.69 | | | | | | | | | | | | | | | (20), (23), (33), (35), (38), (50), (53), (54),
% 158.37/27.69 | | | | | | | | | | | | | | | (55), (59), (65), (68), (70), (84), (86), (88),
% 158.37/27.69 | | | | | | | | | | | | | | | (103), (104), (123) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | #812.
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | (124) all_58_9 = e3 & op(e3, e0) = e3
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | REF_CLOSE: (5), (35), (50), (65), (84), (86), (88), (95),
% 158.37/27.69 | | | | | | | | | | | | | | | (104), (119), (124) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | #491.
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | (125) all_58_5 = e2 & op(e2, e1) = e2
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | ALPHA: (125) implies:
% 158.37/27.69 | | | | | | | | | | | (126) all_58_5 = e2
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | REF_CLOSE: (6), (33), (35), (38), (50), (53), (65), (84),
% 158.37/27.69 | | | | | | | | | | | (86), (88), (126) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | #898.
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | (127) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2
% 158.37/27.69 | | | | | | | | | | & op(e0, e1) = e2)
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | REF_CLOSE: (9), (10), (11), (35), (50), (54), (55), (59),
% 158.37/27.69 | | | | | | | | | | (65), (68), (70), (84), (86), (88), (103), (104),
% 158.37/27.69 | | | | | | | | | | (127) are inconsistent by sub-proof #891.
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | End of split
% 158.37/27.69 | | | | | | | |
% 158.37/27.69 | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | |
% 158.37/27.69 | | | | | | | | (128) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 158.37/27.69 | | | | | | | | op(e1, e0) = e0)
% 158.37/27.69 | | | | | | | |
% 158.37/27.69 | | | | | | | | BETA: splitting (128) gives:
% 158.37/27.69 | | | | | | | |
% 158.37/27.69 | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | (129) all_58_8 = e0 & op(e1, e1) = e0
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | REF_CLOSE: (73), (88), (129) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | #1271.
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | (130) all_58_11 = e0 & op(e1, e0) = e0
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | ALPHA: (130) implies:
% 158.37/27.69 | | | | | | | | | (131) all_58_11 = e0
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | BETA: splitting (69) gives:
% 158.37/27.69 | | | | | | | | |
% 158.37/27.69 | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | (132) all_54_15 = e3
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | REF_CLOSE: (60), (91), (132) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | #1543.
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | (133) ~ (all_54_15 = e3)
% 158.37/27.69 | | | | | | | | | | (134) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | BETA: splitting (5) gives:
% 158.37/27.69 | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | (135) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 158.37/27.69 | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | BETA: splitting (135) gives:
% 158.37/27.69 | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | (136) all_58_9 = e1 & op(e3, e0) = e1
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | ALPHA: (136) implies:
% 158.37/27.69 | | | | | | | | | | | | (137) all_58_9 = e1
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | REF_CLOSE: (6), (9), (10), (11), (14), (16), (17), (18),
% 158.37/27.69 | | | | | | | | | | | | (20), (21), (23), (33), (35), (38), (49), (50),
% 158.37/27.69 | | | | | | | | | | | | (53), (54), (55), (58), (59), (65), (68), (70),
% 158.37/27.69 | | | | | | | | | | | | (84), (86), (88), (103), (104), (137) are
% 158.37/27.69 | | | | | | | | | | | | inconsistent by sub-proof #811.
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | (138) all_58_10 = e1 & op(e2, e0) = e1
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | ALPHA: (138) implies:
% 158.37/27.69 | | | | | | | | | | | | (139) all_58_10 = e1
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | BETA: splitting (25) gives:
% 158.37/27.69 | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | (140) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 158.37/27.69 | | | | | | | | | | | | | & op(e1, e2) = e2)
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | BETA: splitting (140) gives:
% 158.37/27.69 | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | (141) all_58_6 = e2 & op(e1, e3) = e2
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | ALPHA: (141) implies:
% 158.37/27.69 | | | | | | | | | | | | | | (142) all_58_6 = e2
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (20), (23), (33), (35), (65), (68),
% 158.37/27.69 | | | | | | | | | | | | | | (84), (142) are inconsistent by sub-proof #1154.
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | (143) all_58_7 = e2 & op(e1, e2) = e2
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | ALPHA: (143) implies:
% 158.37/27.69 | | | | | | | | | | | | | | (144) all_58_7 = e2
% 158.37/27.69 | | | | | | | | | | | | | | (145) op(e1, e2) = e2
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 158.37/27.69 | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | (146) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | REF_CLOSE: (33), (53), (65), (84), (86), (146) are
% 158.37/27.69 | | | | | | | | | | | | | | | inconsistent by sub-proof #755.
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | (147) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 158.37/27.69 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 158.37/27.69 | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | (148) all_58_5 = e0 & op(e2, e1) = e0
% 158.37/27.69 | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | (149) all_58_5 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | (150) all_54_15 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (150) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | (151) all_4_2 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | REDUCE: (22), (151) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | (152) $false
% 158.37/27.69 | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 158.37/27.69 | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | (153) all_54_15 = e1 | all_54_15 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | (154) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 158.37/27.69 | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (21), (35), (49), (65), (154) are
% 158.37/27.69 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1306.
% 158.37/27.69 | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | (155) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 158.37/27.69 | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | (156) all_58_4 = e3 & op(e3, e1) = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | (157) all_58_4 = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (16), (17), (18), (20), (23), (27),
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | (33), (35), (38), (50), (53), (54), (65), (68),
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | (84), (86), (88), (149), (157) are inconsistent by
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | sub-proof #826.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | (158) all_58_9 = e3 & op(e3, e0) = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | (159) all_58_9 = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | (160) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | (161) all_58_1 = e0 & op(e3, e2) = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | (162) all_58_1 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | (163) all_54_15 = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (60), (163) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | #1541.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | (164) all_54_15 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (164) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | (165) all_4_2 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | SIMP: (165) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | (166) all_4_2 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (166) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | (167) ~ (all_52_7 = e0)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (166) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | (168) ~ (all_52_13 = e0)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (166) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | (169) ~ (all_52_14 = e0)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | (170) all_54_7 = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (41), (170) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | #1428.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | (171) ~ (all_54_7 = e3)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | (172) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | (173) all_54_7 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (43), (173) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | #1427.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | (174) all_54_7 = e1 | all_54_7 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_54_7 = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (175) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_52_13 = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (176) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_52_13 = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (177) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | (178) ~ (all_52_14 = e1)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (178) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | (179) ~ (all_52_14 = e1)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (177) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | (180) ~ (e3 = e1)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_54_11 = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (66), (181) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | #1415.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (182) ~ (all_54_11 = e3)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_54_11 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (184) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_52_14 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (185) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_52_14 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (186) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) ~ (all_52_6 = e2)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (186) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) ~ (e3 = e2)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_54_9 = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (71), (189) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1181.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) ~ (all_54_9 = e3)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_58_0 = e2 & op(e3, e3) = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (50), (193) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #802.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_58_1 = e2 & op(e3, e2) = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_58_1 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (195) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) e2 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) e2 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (197) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_15 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14), (16), (18), (20), (23), (26), (27),
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (29), (33), (35), (50), (64), (65), (68), (84),
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (86), (88), (198) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #460.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_58_4 = e2 & op(e3, e1) = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_58_4 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) op(e3, e1) = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_54_9 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (187), (203) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1180.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_54_9 = e1 | all_54_9 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_54_9 = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (205) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_52_6 = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (206) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_52_6 = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (207) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) ~ (all_52_7 = e1)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (208) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) ~ (all_52_7 = e1)
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (207) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) op(e1, e2) = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_54_13 = e3
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (211) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1435.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_54_13 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (213) imply:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_52_7 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_52_7 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with e2, all_14_0, e2, e1,
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (145) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_14_0 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with e1, all_14_0, e2, e1,
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (210) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_14_0 = e1
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with e0, e3, e3, e1,
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1), (89) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) e3 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with e2, e3, e1, e3,
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (3), (202) gives:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) e3 = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (26), (35), (50), (53), (56), (88),
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (159), (162), (201), (216), (217), (218),
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) are inconsistent by sub-proof #463.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_54_13 = e1 | all_54_13 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (209), (220) are inconsistent by
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #875.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_54_9 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (82), (221) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1170.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_9 = e2 & op(e3, e0) = e2
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (20), (23), (33), (35), (65),
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (84), (159), (222) are inconsistent by
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #800.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_54_11 = e1 | all_54_11 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (169), (179), (223) are inconsistent by
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1227.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_54_7 = e0
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (168), (224) are inconsistent by sub-proof
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | | #1112.
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.69 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (225) all_58_3 = e0 & op(e2, e2) = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (226) all_58_3 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (226) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (227) e3 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (227) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (228) all_58_9 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (14), (16), (17), (18), (20), (21),
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (23), (27), (33), (35), (38), (49), (50), (53),
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (54), (58), (65), (68), (84), (86), (88), (149),
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (228) are inconsistent by sub-proof #822.
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | (229) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (230) all_58_7 = e0 & op(e1, e2) = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (231) all_58_7 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (231) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (232) e2 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (232) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (233) all_58_15 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14), (16), (18), (20), (23), (26), (27),
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (29), (33), (35), (50), (64), (65), (68), (84),
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (86), (88), (233) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | #460.
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (234) all_58_13 = e0 & op(e0, e2) = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (235) all_58_13 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (235) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (236) e1 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (236) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (237) all_58_10 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (35), (50), (53), (65), (88), (149),
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (237) are inconsistent by sub-proof #839.
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | (238) all_58_10 = e0 & op(e2, e0) = e0
% 158.37/27.70 | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | (239) all_58_10 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | REF_CLOSE: (88), (139), (239) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | | | | #1279.
% 158.37/27.70 | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | (240) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 158.37/27.70 | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | BETA: splitting (240) gives:
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | (241) all_58_8 = e2 & op(e1, e1) = e2
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | REF_CLOSE: (9), (54), (65), (241) are inconsistent by
% 158.37/27.70 | | | | | | | | | | | | | | sub-proof #1440.
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | (242) all_58_11 = e2 & op(e1, e0) = e2
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | ALPHA: (242) implies:
% 158.37/27.70 | | | | | | | | | | | | | | (243) all_58_11 = e2
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | COMBINE_EQS: (131), (243) imply:
% 158.37/27.70 | | | | | | | | | | | | | | (244) e2 = e0
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | COMBINE_EQS: (103), (244) imply:
% 158.37/27.70 | | | | | | | | | | | | | | (245) all_58_15 = e0
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | REF_CLOSE: (7), (14), (16), (18), (20), (23), (26), (27),
% 158.37/27.70 | | | | | | | | | | | | | | (29), (33), (35), (50), (64), (65), (68), (84),
% 158.37/27.70 | | | | | | | | | | | | | | (86), (88), (245) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | | #460.
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | (246) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 158.37/27.70 | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 158.37/27.70 | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | BETA: splitting (246) gives:
% 158.37/27.70 | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | (247) all_58_11 = e1 & op(e1, e0) = e1
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | REF_CLOSE: (88), (131), (247) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | #459.
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | (248) all_58_15 = e1 & op(e0, e0) = e1
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | ALPHA: (248) implies:
% 158.37/27.70 | | | | | | | | | | | | (249) op(e0, e0) = e1
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | REF_CLOSE: (50), (65), (104), (249) are inconsistent by
% 158.37/27.70 | | | | | | | | | | | | sub-proof #1386.
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | End of split
% 158.37/27.70 | | | | | | | | |
% 158.37/27.70 | | | | | | | | End of split
% 158.37/27.70 | | | | | | | |
% 158.37/27.70 | | | | | | | End of split
% 158.37/27.70 | | | | | | |
% 158.37/27.70 | | | | | | End of split
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | End of split
% 158.37/27.70 | | | | |
% 158.37/27.70 | | | | End of split
% 158.37/27.70 | | | |
% 158.37/27.70 | | | Case 2:
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | (250) all_56_15 = e3
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | COMBINE_EQS: (44), (250) imply:
% 158.37/27.70 | | | | (251) all_4_2 = e3
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | SIMP: (251) implies:
% 158.37/27.70 | | | | (252) all_4_2 = e3
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | REDUCE: (39), (252) imply:
% 158.37/27.70 | | | | (253) op(e0, e0) = e3
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | REF_CLOSE: (7), (16), (18), (20), (23), (26), (27), (29), (33), (35),
% 158.37/27.70 | | | | (50), (64), (65), (68), (84), (86), (88), (253) are
% 158.37/27.70 | | | | inconsistent by sub-proof #787.
% 158.37/27.70 | | | |
% 158.37/27.70 | | | End of split
% 158.37/27.70 | | |
% 158.37/27.70 | | End of split
% 158.37/27.70 | |
% 158.37/27.70 | End of split
% 158.37/27.70 |
% 158.37/27.70 End of proof
% 158.37/27.70
% 158.37/27.70 Sub-proof #459 shows that the following formulas are inconsistent:
% 158.37/27.70 ----------------------------------------------------------------
% 158.37/27.70 (1) all_58_11 = e1 & op(e1, e0) = e1
% 158.37/27.70 (2) all_58_11 = e0
% 158.37/27.70 (3) ~ (e1 = e0)
% 158.37/27.70
% 158.37/27.70 Begin of proof
% 158.37/27.70 |
% 158.37/27.70 | ALPHA: (1) implies:
% 158.37/27.70 | (4) all_58_11 = e1
% 158.37/27.70 |
% 158.37/27.70 | COMBINE_EQS: (2), (4) imply:
% 158.37/27.70 | (5) e1 = e0
% 158.37/27.70 |
% 158.37/27.70 | REDUCE: (3), (5) imply:
% 158.37/27.70 | (6) $false
% 158.37/27.70 |
% 158.37/27.70 | CLOSE: (6) is inconsistent.
% 158.37/27.70 |
% 158.37/27.70 End of proof
% 158.37/27.70
% 158.37/27.70 Sub-proof #460 shows that the following formulas are inconsistent:
% 158.37/27.70 ----------------------------------------------------------------
% 158.37/27.70 (1) all_58_15 = e0
% 158.37/27.70 (2) all_58_14 = e3
% 158.37/27.70 (3) all_58_0 = e1
% 158.37/27.70 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.70 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.70 (5) all_58_6 = e3
% 158.37/27.70 (6) all_58_12 = e0
% 158.37/27.70 (7) op(e2, e3) = all_52_1
% 158.37/27.70 (8) all_58_13 = e1
% 158.37/27.70 (9) ~ (e3 = e0)
% 158.37/27.70 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.37/27.70 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.37/27.70 (11) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.37/27.70 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.37/27.70 e2)
% 158.37/27.70 (12) ~ (e2 = e0)
% 158.37/27.70 (13) op(e2, e3) = e2
% 158.37/27.70 (14) ~ (e3 = e1)
% 158.37/27.70 (15) ~ (e2 = e1)
% 158.37/27.70 (16) ~ (e1 = e0)
% 158.37/27.70 (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.37/27.70 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.37/27.70 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.70 (19) ~ (e3 = e2)
% 158.37/27.70
% 158.37/27.70 Begin of proof
% 158.37/27.70 |
% 158.37/27.70 | BETA: splitting (11) gives:
% 158.37/27.70 |
% 158.37/27.70 | Case 1:
% 158.37/27.70 | |
% 158.37/27.70 | | (20) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 158.37/27.70 | | e2)
% 158.37/27.70 | |
% 158.37/27.70 | | REF_CLOSE: (4), (7), (8), (9), (10), (12), (13), (14), (15), (16), (17),
% 158.37/27.70 | | (18), (19), (20) are inconsistent by sub-proof #806.
% 158.37/27.70 | |
% 158.37/27.70 | Case 2:
% 158.37/27.70 | |
% 158.37/27.70 | | (21) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.37/27.70 | | e2)
% 158.37/27.70 | |
% 158.37/27.70 | | BETA: splitting (21) gives:
% 158.37/27.70 | |
% 158.37/27.70 | | Case 1:
% 158.37/27.70 | | |
% 158.37/27.70 | | | (22) all_58_14 = e2 & op(e0, e1) = e2
% 158.37/27.70 | | |
% 158.37/27.70 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (13), (14), (18), (19), (22)
% 158.37/27.70 | | | are inconsistent by sub-proof #829.
% 158.37/27.70 | | |
% 158.37/27.70 | | Case 2:
% 158.37/27.70 | | |
% 158.37/27.70 | | | (23) all_58_15 = e2 & op(e0, e0) = e2
% 158.37/27.70 | | |
% 158.37/27.70 | | | REF_CLOSE: (1), (12), (23) are inconsistent by sub-proof #900.
% 158.37/27.70 | | |
% 158.37/27.70 | | End of split
% 158.37/27.70 | |
% 158.37/27.70 | End of split
% 158.37/27.70 |
% 158.37/27.70 End of proof
% 158.37/27.70
% 158.37/27.70 Sub-proof #461 shows that the following formulas are inconsistent:
% 158.37/27.70 ----------------------------------------------------------------
% 158.37/27.70 (1) op(e1, e1) = e3
% 158.37/27.70 (2) op(e1, e1) = all_32_1
% 158.37/27.70 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.37/27.70 (4) op(e3, e1) = e3
% 158.37/27.70 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.37/27.70 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.37/27.70 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.70 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.70 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.37/27.70 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.37/27.70 (8) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.70 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.70 (9) all_58_14 = e3
% 158.37/27.70 (10) all_54_13 = all_52_7
% 158.37/27.70 (11) op(e1, e1) = all_6_2
% 158.37/27.70 (12) ~ (all_52_7 = e3)
% 158.37/27.70 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.70 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.37/27.70 e1)
% 158.37/27.70 (14) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.37/27.70 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.37/27.70 (15) ~ (all_52_6 = all_52_14)
% 158.37/27.70 (16) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.37/27.70 (17) all_58_0 = e1
% 158.37/27.70 (18) op(e1, e2) = all_14_0
% 158.37/27.70 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.70 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.70 (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.37/27.70 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.70 (21) all_58_6 = e3
% 158.37/27.70 (22) ~ (all_52_14 = e3)
% 158.37/27.70 (23) all_58_12 = e0
% 158.37/27.70 (24) ~ (all_4_2 = e2)
% 158.37/27.70 (25) op(e2, e3) = all_52_1
% 158.37/27.70 (26) ~ (all_52_13 = e3)
% 158.37/27.70 (27) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.37/27.70 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.37/27.70 (28) all_58_13 = e1
% 158.37/27.70 (29) ~ (e3 = e0)
% 158.37/27.70 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.37/27.70 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.37/27.70 (31) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.37/27.70 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.37/27.70 e2)
% 158.37/27.70 (32) ~ (e2 = e0)
% 158.37/27.70 (33) ~ (all_52_2 = all_52_6)
% 158.37/27.70 (34) op(e2, e0) = all_52_13
% 158.37/27.70 (35) op(e2, e3) = e2
% 158.37/27.70 (36) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.70 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.37/27.70 (37) ~ (e3 = e1)
% 158.37/27.70 (38) all_58_5 = e1
% 158.37/27.70 (39) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.37/27.70 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.37/27.70 (40) op(e1, e2) = all_52_6
% 158.37/27.70 (41) ~ (all_4_2 = e1)
% 158.37/27.70 (42) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.70 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.70 (43) op(e0, e0) = all_4_2
% 158.37/27.70 (44) all_54_8 = all_52_2
% 158.37/27.70 (45) all_54_7 = all_52_13
% 158.37/27.70 (46) ~ (all_52_2 = e3)
% 158.37/27.70 (47) ~ (all_52_13 = e2)
% 158.37/27.70 (48) all_56_15 = all_4_2
% 158.37/27.70 (49) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 158.37/27.70 (50) ~ (all_52_13 = all_4_2)
% 158.37/27.70 (51) ~ (all_52_2 = e1)
% 158.37/27.70 (52) ~ (all_52_6 = all_52_7)
% 158.37/27.70 (53) ~ (e2 = e1)
% 158.37/27.70 (54) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.37/27.70 (55) ~ (e1 = e0)
% 158.37/27.70 (56) ~ (all_52_2 = e2)
% 158.37/27.70 (57) all_58_3 = e3
% 158.37/27.70 (58) ~ (all_6_2 = e2)
% 158.37/27.70 (59) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.37/27.70 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.37/27.70 e3)
% 158.37/27.70 (60) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.37/27.70 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.37/27.70 (61) ~ (all_52_7 = all_4_2)
% 158.37/27.70 (62) op(e0, e2) = all_52_7
% 158.37/27.70 (63) all_54_15 = all_4_2
% 158.37/27.70 (64) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.37/27.70 (65) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.37/27.70 (66) ~ (all_52_6 = e3)
% 158.37/27.70 (67) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.37/27.70 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.37/27.70 (68) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.70 (69) all_54_11 = all_52_14
% 158.37/27.70 (70) ~ (all_52_13 = all_52_14)
% 158.37/27.70 (71) ~ (e3 = e2)
% 158.37/27.70 (72) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.37/27.70 (73) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.37/27.70 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.37/27.70 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.37/27.70 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.37/27.70 (74) all_54_9 = all_52_6
% 158.37/27.70 (75) ~ (all_52_14 = all_4_2)
% 158.37/27.70
% 158.37/27.70 Begin of proof
% 158.37/27.70 |
% 158.37/27.70 | BETA: splitting (64) gives:
% 158.37/27.70 |
% 158.37/27.70 | Case 1:
% 158.37/27.70 | |
% 158.37/27.70 | | (76) all_54_8 = e2
% 158.37/27.70 | |
% 158.37/27.70 | | REF_CLOSE: (44), (56), (76) are inconsistent by sub-proof #1231.
% 158.37/27.70 | |
% 158.37/27.70 | Case 2:
% 158.37/27.70 | |
% 158.37/27.70 | | (77) ~ (all_54_8 = e2)
% 158.37/27.70 | | (78) all_54_8 = e1 | all_54_8 = e0
% 158.37/27.70 | |
% 158.37/27.70 | | BETA: splitting (42) gives:
% 158.37/27.70 | |
% 158.37/27.70 | | Case 1:
% 158.37/27.70 | | |
% 158.37/27.70 | | | (79) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 158.37/27.70 | | | e0)
% 158.37/27.70 | | |
% 158.37/27.70 | | | REF_CLOSE: (29), (32), (35), (57), (68), (79) are inconsistent by
% 158.37/27.70 | | | sub-proof #755.
% 158.37/27.70 | | |
% 158.37/27.70 | | Case 2:
% 158.37/27.70 | | |
% 158.37/27.70 | | | (80) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 158.37/27.70 | | | e0)
% 158.37/27.70 | | |
% 158.37/27.70 | | | BETA: splitting (80) gives:
% 158.37/27.70 | | |
% 158.37/27.70 | | | Case 1:
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | (81) all_58_5 = e0 & op(e2, e1) = e0
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | REF_CLOSE: (38), (55), (81) are inconsistent by sub-proof #1343.
% 158.37/27.70 | | | |
% 158.37/27.70 | | | Case 2:
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | (82) all_58_10 = e0 & op(e2, e0) = e0
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | ALPHA: (82) implies:
% 158.37/27.70 | | | | (83) all_58_10 = e0
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | BETA: splitting (39) gives:
% 158.37/27.70 | | | |
% 158.37/27.70 | | | | Case 1:
% 158.37/27.70 | | | | |
% 158.37/27.70 | | | | | (84) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 158.37/27.70 | | | | | e1) = e0)
% 158.37/27.70 | | | | |
% 158.37/27.70 | | | | | BETA: splitting (84) gives:
% 158.37/27.70 | | | | |
% 158.37/27.70 | | | | | Case 1:
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | (85) all_58_4 = e0 & op(e3, e1) = e0
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | ALPHA: (85) implies:
% 158.37/27.70 | | | | | | (86) all_58_4 = e0
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | REF_CLOSE: (8), (9), (11), (20), (29), (32), (35), (37), (42), (53),
% 158.37/27.70 | | | | | | (55), (57), (58), (68), (71), (86) are inconsistent by
% 158.37/27.70 | | | | | | sub-proof #854.
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | Case 2:
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | (87) all_58_5 = e0 & op(e2, e1) = e0
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | ALPHA: (87) implies:
% 158.37/27.70 | | | | | | (88) all_58_5 = e0
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | REF_CLOSE: (8), (35), (37), (53), (55), (57), (68), (83), (88) are
% 158.37/27.70 | | | | | | inconsistent by sub-proof #839.
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | End of split
% 158.37/27.70 | | | | |
% 158.37/27.70 | | | | Case 2:
% 158.37/27.70 | | | | |
% 158.37/27.70 | | | | | (89) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 158.37/27.70 | | | | | e1) = e0)
% 158.37/27.70 | | | | |
% 158.37/27.70 | | | | | BETA: splitting (89) gives:
% 158.37/27.70 | | | | |
% 158.37/27.70 | | | | | Case 1:
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | (90) all_58_8 = e0 & op(e1, e1) = e0
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | ALPHA: (90) implies:
% 158.37/27.70 | | | | | | (91) all_58_8 = e0
% 158.37/27.70 | | | | | | (92) op(e1, e1) = e0
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | BETA: splitting (31) gives:
% 158.37/27.70 | | | | | |
% 158.37/27.70 | | | | | | Case 1:
% 158.37/27.70 | | | | | | |
% 158.37/27.70 | | | | | | | (93) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 158.37/27.70 | | | | | | | op(e0, e2) = e2)
% 158.37/27.70 | | | | | | |
% 158.37/27.70 | | | | | | | REF_CLOSE: (19), (25), (28), (29), (30), (32), (35), (37), (53),
% 158.37/27.70 | | | | | | | (55), (67), (68), (71), (93) are inconsistent by
% 158.37/27.70 | | | | | | | sub-proof #806.
% 158.37/27.70 | | | | | | |
% 158.37/27.70 | | | | | | Case 2:
% 158.37/27.70 | | | | | | |
% 158.37/27.70 | | | | | | | (94) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 158.37/27.70 | | | | | | | op(e0, e0) = e2)
% 158.37/27.70 | | | | | | |
% 158.37/27.70 | | | | | | | BETA: splitting (94) gives:
% 158.37/27.70 | | | | | | |
% 158.37/27.70 | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | |
% 158.37/27.70 | | | | | | | | (95) all_58_14 = e2 & op(e0, e1) = e2
% 158.37/27.70 | | | | | | | |
% 158.37/27.70 | | | | | | | | REF_CLOSE: (9), (17), (19), (21), (23), (25), (29), (35), (37),
% 158.37/27.70 | | | | | | | | (68), (71), (95) are inconsistent by sub-proof #829.
% 158.37/27.70 | | | | | | | |
% 158.37/27.70 | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | |
% 158.37/27.70 | | | | | | | | (96) all_58_15 = e2 & op(e0, e0) = e2
% 158.37/27.70 | | | | | | | |
% 158.37/27.70 | | | | | | | | ALPHA: (96) implies:
% 158.37/27.70 | | | | | | | | (97) all_58_15 = e2
% 158.37/27.70 | | | | | | | | (98) op(e0, e0) = e2
% 158.37/27.70 | | | | | | | |
% 158.37/27.70 | | | | | | | | BETA: splitting (20) gives:
% 158.37/27.70 | | | | | | | |
% 158.37/27.70 | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | |
% 158.37/27.70 | | | | | | | | | (99) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 158.37/27.70 | | | | | | | | | op(e2, e1) = e2)
% 158.37/27.70 | | | | | | | | |
% 158.37/27.70 | | | | | | | | | BETA: splitting (99) gives:
% 158.37/27.70 | | | | | | | | |
% 158.37/27.70 | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | (100) all_58_4 = e2 & op(e3, e1) = e2
% 158.37/27.70 | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | ALPHA: (100) implies:
% 158.37/27.70 | | | | | | | | | | (101) all_58_4 = e2
% 158.37/27.70 | | | | | | | | | | (102) op(e3, e1) = e2
% 158.37/27.70 | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | BETA: splitting (14) gives:
% 158.37/27.70 | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | (103) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 158.37/27.70 | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 158.37/27.70 | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | BETA: splitting (103) gives:
% 158.37/27.70 | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | (104) all_58_9 = e3 & op(e3, e0) = e3
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | ALPHA: (104) implies:
% 158.37/27.70 | | | | | | | | | | | | (105) all_58_9 = e3
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | BETA: splitting (78) gives:
% 158.37/27.70 | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | (106) all_54_8 = e1
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | REF_CLOSE: (44), (51), (106) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | #1379.
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | (107) all_54_8 = e0
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | COMBINE_EQS: (44), (107) imply:
% 158.37/27.70 | | | | | | | | | | | | | (108) all_52_2 = e0
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | SIMP: (108) implies:
% 158.37/27.70 | | | | | | | | | | | | | (109) all_52_2 = e0
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | REDUCE: (33), (109) imply:
% 158.37/27.70 | | | | | | | | | | | | | (110) ~ (all_52_6 = e0)
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | SIMP: (110) implies:
% 158.37/27.70 | | | | | | | | | | | | | (111) ~ (all_52_6 = e0)
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | REDUCE: (46), (109) imply:
% 158.37/27.70 | | | | | | | | | | | | | (112) ~ (e3 = e0)
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | REDUCE: (56), (109) imply:
% 158.37/27.70 | | | | | | | | | | | | | (113) ~ (e2 = e0)
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | REDUCE: (51), (109) imply:
% 158.37/27.70 | | | | | | | | | | | | | (114) ~ (e1 = e0)
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | BETA: splitting (49) gives:
% 158.37/27.70 | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | (115) ~ (all_56_15 = e3)
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | REDUCE: (48), (115) imply:
% 158.37/27.70 | | | | | | | | | | | | | | (116) ~ (all_4_2 = e3)
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 158.37/27.70 | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | (117) all_54_15 = e3
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | COMBINE_EQS: (63), (117) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | (118) all_4_2 = e3
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | REDUCE: (116), (118) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | (119) $false
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | CLOSE: (119) is inconsistent.
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | (120) ~ (all_54_15 = e3)
% 158.37/27.70 | | | | | | | | | | | | | | | (121) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 158.37/27.70 | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | (122) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.37/27.70 | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | (123) all_58_1 = e0 & op(e3, e2) = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | | (124) all_58_1 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | (125) all_54_15 = e2
% 158.37/27.70 | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (63), (125) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | | | | | | #1542.
% 158.37/27.70 | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | (126) all_54_15 = e1 | all_54_15 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | (127) all_54_15 = e1
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (63), (127) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | #1541.
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | (128) all_54_15 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (128) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | (129) all_4_2 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | SIMP: (129) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | (130) all_4_2 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | REDUCE: (61), (130) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | (131) ~ (all_52_7 = e0)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | REDUCE: (50), (130) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | (132) ~ (all_52_13 = e0)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | REDUCE: (75), (130) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | (133) ~ (all_52_14 = e0)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | (134) all_54_7 = e3
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (45), (134) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | #1428.
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | (135) ~ (all_54_7 = e3)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | (136) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (137) all_54_7 = e2
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (47), (137) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | #1427.
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | (138) all_54_7 = e1 | all_54_7 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | (139) all_54_7 = e1
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (139) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | (140) all_52_13 = e1
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | SIMP: (140) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | (141) all_52_13 = e1
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (141) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | (142) ~ (all_52_14 = e1)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | SIMP: (142) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | (143) ~ (all_52_14 = e1)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (141) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | (144) ~ (e3 = e1)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | (145) all_54_11 = e3
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (69), (145) are inconsistent by sub-proof
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | #1415.
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | (146) ~ (all_54_11 = e3)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | (147) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | (148) all_54_11 = e2
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (148) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | (149) all_52_14 = e2
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | (150) all_52_14 = e2
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (150) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | (151) ~ (all_52_6 = e2)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (150) imply:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | (152) ~ (e3 = e2)
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | (153) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (154) all_58_6 = e2 & op(e1, e3) = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (155) all_58_6 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (23), (25), (29), (35), (37), (68),
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (155) are inconsistent by sub-proof #1154.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (156) all_58_7 = e2 & op(e1, e2) = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (157) all_58_7 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (158) op(e1, e2) = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) all_54_9 = e3
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (74), (159) are inconsistent by sub-proof
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1181.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) ~ (all_54_9 = e3)
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) all_54_13 = e3
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (162) are inconsistent by sub-proof
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1435.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_54_9 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (151), (164) are inconsistent by sub-proof
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1180.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_54_9 = e1 | all_54_9 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_54_9 = e1
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (166) imply:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_52_6 = e1
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_52_6 = e1
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (168) imply:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) ~ (all_52_7 = e1)
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (169) implies:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) ~ (all_52_7 = e1)
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (168) imply:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) op(e1, e2) = e1
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_54_13 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (172) imply:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_52_7 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_52_7 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (68) with e3, all_32_1, e1, e1,
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1), (2) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_32_1 = e3
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (68) with e0, all_32_1, e1, e1,
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (2), (92) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_32_1 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (68) with e2, all_14_0, e2, e1,
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (18), (158) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_14_0 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (68) with e1, all_14_0, e2, e1,
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (18), (171) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_14_0 = e1
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (68) with e2, e3, e1, e3,
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (4), (102) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) e3 = e2
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (176) imply:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) e3 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (28), (37), (53), (55), (57), (60),
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (101), (105), (124), (157), (177), (178), (179),
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) are inconsistent by sub-proof #463.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_54_13 = e1 | all_54_13 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (131), (170), (181) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #875.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_54_9 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (111), (182) are inconsistent by sub-proof
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1170.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | (183) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (29), (32), (37), (53), (55), (58),
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | (68), (73), (97), (105), (183) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #656.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | (184) all_54_11 = e1 | all_54_11 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (133), (143), (184) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1227.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | (185) all_54_7 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (132), (185) are inconsistent by sub-proof
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | | #1112.
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | (186) all_58_3 = e0 & op(e2, e2) = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (57), (186) are inconsistent by sub-proof
% 158.37/27.71 | | | | | | | | | | | | | | | | | #756.
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | (187) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 158.37/27.71 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | (188) all_58_7 = e0 & op(e1, e2) = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 158.37/27.71 | | | | | | | | | | | | | | | | | (189) all_58_7 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (11), (19), (21), (25), (27), (29),
% 158.37/27.71 | | | | | | | | | | | | | | | | | (30), (32), (35), (37), (38), (53), (55), (57),
% 158.37/27.71 | | | | | | | | | | | | | | | | | (58), (67), (68), (71), (83), (91), (189) are
% 158.37/27.71 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #462.
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | (190) all_58_13 = e0 & op(e0, e2) = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 158.37/27.71 | | | | | | | | | | | | | | | | | (191) all_58_13 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (191) imply:
% 158.37/27.71 | | | | | | | | | | | | | | | | | (192) e1 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (192) imply:
% 158.37/27.71 | | | | | | | | | | | | | | | | | (193) all_58_5 = e0
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (35), (37), (53), (55), (57), (68), (83),
% 158.37/27.71 | | | | | | | | | | | | | | | | | (193) are inconsistent by sub-proof #839.
% 158.37/27.71 | | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | (194) all_56_15 = e3
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | COMBINE_EQS: (48), (194) imply:
% 158.37/27.71 | | | | | | | | | | | | | | (195) all_4_2 = e3
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | SIMP: (195) implies:
% 158.37/27.71 | | | | | | | | | | | | | | (196) all_4_2 = e3
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | REDUCE: (43), (196) imply:
% 158.37/27.71 | | | | | | | | | | | | | | (197) op(e0, e0) = e3
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | REF_CLOSE: (68), (71), (98), (197) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | | | sub-proof #1382.
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | (198) all_58_10 = e3 & op(e2, e0) = e3
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | ALPHA: (198) implies:
% 158.37/27.71 | | | | | | | | | | | | (199) op(e2, e0) = e3
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | REF_CLOSE: (26), (34), (68), (199) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | sub-proof #1364.
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | (200) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 158.37/27.71 | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.37/27.71 | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | BETA: splitting (200) gives:
% 158.37/27.71 | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | (201) all_58_11 = e3 & op(e1, e0) = e3
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | ALPHA: (201) implies:
% 158.37/27.71 | | | | | | | | | | | | (202) all_58_11 = e3
% 158.37/27.71 | | | | | | | | | | | | (203) op(e1, e0) = e3
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | BETA: splitting (27) gives:
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | (204) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 158.37/27.71 | | | | | | | | | | | | | & op(e1, e2) = e2)
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | (205) all_58_6 = e2 & op(e1, e3) = e2
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | ALPHA: (205) implies:
% 158.37/27.71 | | | | | | | | | | | | | | (206) all_58_6 = e2
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (23), (25), (29), (35), (37), (68),
% 158.37/27.71 | | | | | | | | | | | | | | (71), (206) are inconsistent by sub-proof #1154.
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | (207) all_58_7 = e2 & op(e1, e2) = e2
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | ALPHA: (207) implies:
% 158.37/27.71 | | | | | | | | | | | | | | (208) all_58_7 = e2
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | (209) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 158.37/27.71 | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 158.37/27.71 | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 158.37/27.71 | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | (210) all_58_6 = e1 & op(e1, e3) = e1
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | REF_CLOSE: (21), (37), (210) are inconsistent by sub-proof
% 158.37/27.71 | | | | | | | | | | | | | | | | #1347.
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | (211) all_58_7 = e1 & op(e1, e2) = e1
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (20), (29), (32), (35), (37),
% 158.37/27.71 | | | | | | | | | | | | | | | | (42), (53), (55), (57), (58), (68), (71), (101),
% 158.37/27.71 | | | | | | | | | | | | | | | | (208), (211) are inconsistent by sub-proof #650.
% 158.37/27.71 | | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | (212) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 158.37/27.71 | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 158.37/27.71 | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | | REF_CLOSE: (8), (35), (37), (38), (53), (55), (57), (68),
% 158.37/27.71 | | | | | | | | | | | | | | | (83), (91), (203), (212) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | | | | sub-proof #793.
% 158.37/27.71 | | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | (213) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 158.37/27.71 | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | BETA: splitting (213) gives:
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | Case 1:
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | (214) all_58_8 = e2 & op(e1, e1) = e2
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | REF_CLOSE: (11), (58), (68), (214) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | | | sub-proof #1440.
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | (215) all_58_11 = e2 & op(e1, e0) = e2
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (21), (23), (25), (29), (35), (37),
% 158.37/27.71 | | | | | | | | | | | | | | (68), (71), (202), (215) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | | | sub-proof #792.
% 158.37/27.71 | | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | (216) all_58_15 = e3 & op(e0, e0) = e3
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | ALPHA: (216) implies:
% 158.37/27.71 | | | | | | | | | | | | (217) op(e0, e0) = e3
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | | REF_CLOSE: (68), (71), (98), (217) are inconsistent by
% 158.37/27.71 | | | | | | | | | | | | sub-proof #1382.
% 158.37/27.71 | | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | (218) all_58_5 = e2 & op(e2, e1) = e2
% 158.37/27.71 | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | ALPHA: (218) implies:
% 158.37/27.71 | | | | | | | | | | (219) all_58_5 = e2
% 158.37/27.71 | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | | REF_CLOSE: (8), (29), (32), (35), (37), (42), (53), (55),
% 158.37/27.71 | | | | | | | | | | (57), (68), (219) are inconsistent by sub-proof
% 158.37/27.71 | | | | | | | | | | #898.
% 158.37/27.71 | | | | | | | | | |
% 158.37/27.71 | | | | | | | | | End of split
% 158.37/27.71 | | | | | | | | |
% 158.37/27.71 | | | | | | | | Case 2:
% 158.37/27.71 | | | | | | | | |
% 158.37/27.71 | | | | | | | | | (220) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 158.37/27.71 | | | | | | | | | op(e0, e1) = e2)
% 158.37/27.71 | | | | | | | | |
% 158.37/27.71 | | | | | | | | | REF_CLOSE: (11), (12), (13), (29), (32), (37), (53), (55),
% 158.37/27.71 | | | | | | | | | (58), (59), (62), (68), (71), (73), (97), (98),
% 158.37/27.71 | | | | | | | | | (220) are inconsistent by sub-proof #891.
% 158.37/27.71 | | | | | | | | |
% 158.37/27.71 | | | | | | | | End of split
% 158.37/27.71 | | | | | | | |
% 158.37/27.71 | | | | | | | End of split
% 158.37/27.71 | | | | | | |
% 158.37/27.71 | | | | | | End of split
% 158.37/27.71 | | | | | |
% 158.37/27.71 | | | | | Case 2:
% 158.37/27.71 | | | | | |
% 158.37/27.71 | | | | | | (221) all_58_14 = e0 & op(e0, e1) = e0
% 158.37/27.71 | | | | | |
% 158.37/27.71 | | | | | | REF_CLOSE: (9), (29), (221) are inconsistent by sub-proof #882.
% 158.37/27.71 | | | | | |
% 158.37/27.71 | | | | | End of split
% 158.37/27.71 | | | | |
% 158.37/27.71 | | | | End of split
% 158.37/27.71 | | | |
% 158.37/27.71 | | | End of split
% 158.37/27.71 | | |
% 158.37/27.71 | | End of split
% 158.37/27.71 | |
% 158.37/27.71 | End of split
% 158.37/27.71 |
% 158.37/27.71 End of proof
% 158.37/27.71
% 158.37/27.71 Sub-proof #462 shows that the following formulas are inconsistent:
% 158.37/27.71 ----------------------------------------------------------------
% 158.37/27.71 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.37/27.71 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.37/27.71 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.71 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.71 (3) op(e1, e1) = all_6_2
% 158.37/27.71 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.71 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.71 (5) all_58_6 = e3
% 158.37/27.71 (6) all_58_7 = e0
% 158.37/27.71 (7) op(e2, e3) = all_52_1
% 158.37/27.71 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.37/27.71 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.37/27.71 (9) ~ (e3 = e0)
% 158.37/27.71 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.37/27.71 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.37/27.71 (11) ~ (e2 = e0)
% 158.37/27.71 (12) op(e2, e3) = e2
% 158.37/27.71 (13) ~ (e3 = e1)
% 158.37/27.71 (14) all_58_5 = e1
% 158.37/27.71 (15) ~ (e2 = e1)
% 158.37/27.71 (16) ~ (e1 = e0)
% 158.37/27.71 (17) all_58_3 = e3
% 158.37/27.71 (18) ~ (all_6_2 = e2)
% 158.37/27.71 (19) all_58_10 = e0
% 158.37/27.71 (20) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.37/27.71 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.37/27.71 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.71 (22) all_58_8 = e0
% 158.37/27.71 (23) ~ (e3 = e2)
% 158.37/27.71
% 158.37/27.71 Begin of proof
% 158.37/27.71 |
% 158.37/27.71 | BETA: splitting (1) gives:
% 158.37/27.71 |
% 158.37/27.71 | Case 1:
% 158.37/27.71 | |
% 158.37/27.71 | | (24) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 158.37/27.71 | | e1)
% 158.37/27.71 | |
% 158.37/27.71 | | BETA: splitting (24) gives:
% 158.37/27.71 | |
% 158.37/27.71 | | Case 1:
% 158.37/27.71 | | |
% 158.37/27.71 | | | (25) all_58_6 = e1 & op(e1, e3) = e1
% 158.37/27.71 | | |
% 158.37/27.71 | | | REF_CLOSE: (5), (13), (25) are inconsistent by sub-proof #1347.
% 158.37/27.71 | | |
% 158.37/27.71 | | Case 2:
% 158.37/27.71 | | |
% 158.37/27.71 | | | (26) all_58_7 = e1 & op(e1, e2) = e1
% 158.37/27.71 | | |
% 158.37/27.71 | | | ALPHA: (26) implies:
% 158.37/27.71 | | | (27) all_58_7 = e1
% 158.37/27.71 | | |
% 158.37/27.71 | | | COMBINE_EQS: (6), (27) imply:
% 158.37/27.71 | | | (28) e1 = e0
% 158.37/27.71 | | |
% 158.37/27.71 | | | COMBINE_EQS: (14), (28) imply:
% 158.37/27.71 | | | (29) all_58_5 = e0
% 158.37/27.71 | | |
% 158.37/27.71 | | | REF_CLOSE: (2), (12), (13), (15), (16), (17), (19), (21), (29) are
% 158.37/27.71 | | | inconsistent by sub-proof #839.
% 158.37/27.71 | | |
% 158.37/27.71 | | End of split
% 158.37/27.71 | |
% 158.37/27.71 | Case 2:
% 158.37/27.71 | |
% 158.37/27.71 | | (30) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 158.37/27.71 | | e1)
% 158.37/27.71 | |
% 158.37/27.71 | | BETA: splitting (30) gives:
% 158.37/27.71 | |
% 158.37/27.71 | | Case 1:
% 158.37/27.71 | | |
% 158.37/27.71 | | | (31) all_58_8 = e1 & op(e1, e1) = e1
% 158.37/27.71 | | |
% 158.37/27.71 | | | REF_CLOSE: (2), (12), (13), (14), (15), (16), (17), (19), (21), (22), (31)
% 158.37/27.71 | | | are inconsistent by sub-proof #794.
% 158.37/27.71 | | |
% 158.37/27.71 | | Case 2:
% 158.37/27.71 | | |
% 158.37/27.71 | | | (32) all_58_11 = e1 & op(e1, e0) = e1
% 158.37/27.71 | | |
% 158.37/27.71 | | | ALPHA: (32) implies:
% 158.37/27.71 | | | (33) all_58_11 = e1
% 158.37/27.71 | | |
% 158.37/27.71 | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (15),
% 158.37/27.71 | | | (16), (18), (20), (21), (23), (33) are inconsistent by
% 158.37/27.71 | | | sub-proof #743.
% 158.37/27.71 | | |
% 158.37/27.71 | | End of split
% 158.37/27.71 | |
% 158.37/27.71 | End of split
% 158.37/27.71 |
% 158.37/27.71 End of proof
% 158.37/27.71
% 158.37/27.71 Sub-proof #463 shows that the following formulas are inconsistent:
% 158.37/27.71 ----------------------------------------------------------------
% 158.37/27.71 (1) all_14_0 = e2
% 158.37/27.71 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.71 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.71 (3) all_58_1 = e0
% 158.37/27.71 (4) all_58_7 = e2
% 158.37/27.71 (5) all_58_0 = e1
% 158.37/27.71 (6) all_14_0 = e1
% 158.37/27.71 (7) all_58_13 = e1
% 158.37/27.71 (8) e3 = e0
% 158.37/27.71 (9) all_58_9 = e3
% 158.37/27.71 (10) ~ (e3 = e1)
% 158.37/27.71 (11) all_58_4 = e2
% 158.37/27.71 (12) ~ (e2 = e1)
% 158.37/27.71 (13) ~ (e1 = e0)
% 158.37/27.71 (14) all_58_3 = e3
% 158.37/27.71 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.37/27.71 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.37/27.71 (16) e3 = e2
% 158.37/27.71
% 158.37/27.71 Begin of proof
% 158.37/27.71 |
% 158.37/27.71 | COMBINE_EQS: (1), (6) imply:
% 158.37/27.71 | (17) e2 = e1
% 158.37/27.71 |
% 158.37/27.71 | COMBINE_EQS: (8), (16) imply:
% 158.37/27.71 | (18) e2 = e0
% 158.37/27.71 |
% 158.37/27.71 | SIMP: (18) implies:
% 158.37/27.71 | (19) e2 = e0
% 158.37/27.71 |
% 158.37/27.71 | COMBINE_EQS: (17), (19) imply:
% 158.37/27.71 | (20) e1 = e0
% 158.37/27.71 |
% 158.37/27.71 | COMBINE_EQS: (5), (20) imply:
% 158.37/27.71 | (21) all_58_0 = e0
% 158.37/27.71 |
% 158.37/27.71 | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (12), (13), (14), (15), (21)
% 158.37/27.71 | are inconsistent by sub-proof #641.
% 158.37/27.71 |
% 158.37/27.71 End of proof
% 158.37/27.71
% 158.37/27.71 Sub-proof #464 shows that the following formulas are inconsistent:
% 158.37/27.71 ----------------------------------------------------------------
% 158.37/27.71 (1) op(e1, e1) = e3
% 158.37/27.71 (2) op(e1, e1) = all_32_1
% 158.37/27.71 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.37/27.71 (4) all_56_14 = e3
% 158.37/27.71 (5) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.37/27.71 (6) ~ (all_52_3 = e1)
% 158.37/27.71 (7) op(e3, e1) = e3
% 158.37/27.71 (8) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.37/27.71 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.37/27.71 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.71 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.71 (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.37/27.71 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.37/27.71 (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.37/27.71 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.37/27.71 (12) all_54_13 = all_52_7
% 158.37/27.71 (13) op(e1, e1) = all_6_2
% 158.37/27.71 (14) ~ (all_52_7 = e3)
% 158.37/27.71 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.37/27.71 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.37/27.71 e1)
% 158.37/27.71 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.37/27.71 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.37/27.71 (17) ~ (all_52_6 = all_52_14)
% 158.37/27.71 (18) ~ (all_52_11 = e3)
% 158.37/27.71 (19) ~ (all_52_2 = all_52_3)
% 158.37/27.71 (20) ~ (all_52_4 = all_52_6)
% 158.37/27.71 (21) op(e3, e3) = all_28_1
% 158.37/27.71 (22) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.37/27.71 (23) ~ (all_52_7 = all_52_11)
% 158.37/27.71 (24) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.37/27.71 (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.37/27.71 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.37/27.71 (26) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.37/27.71 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.37/27.71 (27) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.37/27.71 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.37/27.71 (28) ~ (all_52_14 = e3)
% 158.37/27.71 (29) all_54_1 = all_52_4
% 158.37/27.71 (30) op(e3, e2) = all_52_4
% 158.37/27.71 (31) ~ (all_4_2 = e2)
% 158.37/27.71 (32) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.37/27.71 (33) op(e2, e3) = all_52_1
% 158.37/27.71 (34) ~ (all_52_13 = e3)
% 158.37/27.71 (35) all_54_2 = all_52_8
% 158.37/27.71 (36) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.37/27.71 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.37/27.71 (37) ~ (all_52_8 = all_52_9)
% 158.37/27.71 (38) ~ (e3 = e0)
% 158.37/27.71 (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.37/27.71 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.37/27.71 (40) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.37/27.71 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.37/27.71 (41) ~ (all_52_9 = all_52_13)
% 158.37/27.71 (42) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.37/27.71 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.37/27.71 e2)
% 158.37/27.71 (43) ~ (e2 = e0)
% 158.37/27.71 (44) ~ (all_52_9 = e3)
% 158.37/27.71 (45) ~ (all_52_2 = all_52_6)
% 158.37/27.71 (46) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.37/27.71 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.37/27.71 (47) ~ (all_52_3 = e2)
% 158.37/27.71 (48) op(e2, e0) = all_52_13
% 158.37/27.71 (49) op(e2, e3) = e2
% 158.37/27.71 (50) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.71 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.37/27.71 (51) ~ (e3 = e1)
% 158.37/27.71 (52) all_56_12 = e1
% 158.37/27.71 (53) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.37/27.71 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.37/27.71 (54) ~ (all_4_2 = e1)
% 158.37/27.71 (55) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.37/27.71 (56) ~ (all_52_3 = all_4_2)
% 158.37/27.71 (57) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.37/27.71 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.37/27.71 (58) op(e0, e0) = all_4_2
% 158.37/27.71 (59) all_54_8 = all_52_2
% 158.37/27.71 (60) all_54_7 = all_52_13
% 158.37/27.71 (61) ~ (all_52_2 = e3)
% 158.37/27.71 (62) op(e3, e3) = e1
% 158.37/27.71 (63) ~ (all_52_13 = e2)
% 158.37/27.71 (64) all_56_15 = all_4_2
% 158.37/27.71 (65) ~ (all_52_9 = all_52_11)
% 158.37/27.71 (66) ~ (all_52_13 = all_4_2)
% 158.37/27.71 (67) ~ (all_52_2 = e1)
% 158.37/27.71 (68) ~ (all_52_6 = all_52_7)
% 158.37/27.71 (69) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.37/27.71 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.37/27.71 (70) ~ (all_52_4 = e3)
% 158.37/27.71 (71) all_54_6 = all_52_9
% 158.37/27.71 (72) ~ (e2 = e1)
% 158.37/27.71 (73) ~ (all_52_4 = all_52_7)
% 158.37/27.71 (74) ~ (all_52_8 = all_52_11)
% 158.37/27.71 (75) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.37/27.71 (76) ~ (e1 = e0)
% 158.37/27.71 (77) ~ (all_52_2 = e2)
% 158.37/27.71 (78) all_58_4 = e3
% 158.37/27.71 (79) all_58_3 = e3
% 158.37/27.71 (80) op(e3, e1) = all_52_8
% 158.37/27.71 (81) ~ (all_6_2 = e2)
% 158.37/27.71 (82) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.37/27.71 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.37/27.71 e3)
% 158.37/27.71 (83) all_56_13 = e3
% 158.37/27.72 (84) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.37/27.72 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.37/27.72 (85) ~ (all_52_9 = e2)
% 158.37/27.72 (86) ~ (all_52_8 = e3)
% 158.37/27.72 (87) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 158.37/27.72 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.37/27.72 (88) all_54_14 = all_52_11
% 158.37/27.72 (89) ~ (all_52_7 = all_4_2)
% 158.37/27.72 (90) op(e1, e3) = e1
% 158.37/27.72 (91) op(e1, e0) = e3
% 158.37/27.72 (92) op(e0, e2) = all_52_7
% 158.37/27.72 (93) op(e1, e0) = all_52_14
% 158.37/27.72 (94) op(e3, e3) = all_22_1
% 158.37/27.72 (95) all_54_15 = all_4_2
% 158.37/27.72 (96) ~ (all_52_8 = e1)
% 158.37/27.72 (97) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.37/27.72 (98) ~ (all_52_6 = e3)
% 158.37/27.72 (99) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.37/27.72 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.37/27.72 (100) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.37/27.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.37/27.72 (101) ~ (all_52_3 = all_52_11)
% 158.37/27.72 (102) ~ (all_52_11 = all_4_2)
% 158.37/27.72 (103) all_54_11 = all_52_14
% 158.37/27.72 (104) ~ (all_52_13 = all_52_14)
% 158.37/27.72 (105) ~ (e3 = e2)
% 158.37/27.72 (106) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 158.37/27.72 (107) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.37/27.72 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.37/27.72 (108) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 158.37/27.72 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.37/27.72 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 158.37/27.72 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.37/27.72 e0)))
% 158.37/27.72 (109) all_54_9 = all_52_6
% 158.37/27.72 (110) all_58_11 = e3
% 158.37/27.72 (111) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 158.37/27.72 (112) all_54_12 = all_52_3
% 158.37/27.72 (113) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.37/27.72 (114) ~ (all_52_14 = all_4_2)
% 158.37/27.72 (115) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.37/27.72 (116) ~ (all_52_3 = all_52_7)
% 158.37/27.72
% 158.37/27.72 Begin of proof
% 158.37/27.72 |
% 158.37/27.72 | BETA: splitting (25) gives:
% 158.37/27.72 |
% 158.37/27.72 | Case 1:
% 158.37/27.72 | |
% 158.37/27.72 | | (117) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 158.37/27.72 | | e3)
% 158.37/27.72 | |
% 158.37/27.72 | | BETA: splitting (117) gives:
% 158.37/27.72 | |
% 158.37/27.72 | | Case 1:
% 158.37/27.72 | | |
% 158.37/27.72 | | | (118) all_58_0 = e3 & op(e3, e3) = e3
% 158.37/27.72 | | |
% 158.37/27.72 | | | ALPHA: (118) implies:
% 158.37/27.72 | | | (119) all_58_0 = e3
% 158.37/27.72 | | | (120) op(e3, e3) = e3
% 158.37/27.72 | | |
% 158.37/27.72 | | | BETA: splitting (27) gives:
% 158.37/27.72 | | |
% 158.37/27.72 | | | Case 1:
% 158.37/27.72 | | | |
% 158.37/27.72 | | | | (121) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 158.37/27.72 | | | | e0) = e2)
% 158.37/27.72 | | | |
% 158.37/27.72 | | | | BETA: splitting (121) gives:
% 158.37/27.72 | | | |
% 158.37/27.72 | | | | Case 1:
% 158.37/27.72 | | | | |
% 158.37/27.72 | | | | | (122) all_58_9 = e2 & op(e3, e0) = e2
% 158.37/27.72 | | | | |
% 158.37/27.72 | | | | | ALPHA: (122) implies:
% 158.37/27.72 | | | | | (123) all_58_9 = e2
% 158.37/27.72 | | | | |
% 158.37/27.72 | | | | | BETA: splitting (99) gives:
% 158.37/27.72 | | | | |
% 158.37/27.72 | | | | | Case 1:
% 158.37/27.72 | | | | | |
% 158.37/27.72 | | | | | | (124) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 158.37/27.72 | | | | | | e3) = e0)
% 158.37/27.72 | | | | | |
% 158.37/27.72 | | | | | | REF_CLOSE: (38), (43), (49), (100), (119), (124) are inconsistent by
% 158.37/27.72 | | | | | | sub-proof #615.
% 158.37/27.72 | | | | | |
% 158.37/27.72 | | | | | Case 2:
% 158.37/27.72 | | | | | |
% 158.37/27.72 | | | | | | (125) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 158.37/27.72 | | | | | | op(e0, e3) = e0)
% 158.37/27.72 | | | | | |
% 158.37/27.72 | | | | | | BETA: splitting (125) gives:
% 158.37/27.72 | | | | | |
% 158.37/27.72 | | | | | | Case 1:
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | | (126) all_58_6 = e0 & op(e1, e3) = e0
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | | ALPHA: (126) implies:
% 158.37/27.72 | | | | | | | (127) all_58_6 = e0
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | | BETA: splitting (26) gives:
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | | Case 1:
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | (128) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 158.37/27.72 | | | | | | | | op(e2, e1) = e2)
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | REF_CLOSE: (11), (38), (43), (49), (51), (57), (72), (76), (78),
% 158.37/27.72 | | | | | | | | (79), (100), (105), (128) are inconsistent by
% 158.37/27.72 | | | | | | | | sub-proof #835.
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | Case 2:
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | (129) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 158.37/27.72 | | | | | | | | op(e0, e1) = e2)
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | BETA: splitting (129) gives:
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | Case 1:
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | (130) all_58_8 = e2 & op(e1, e1) = e2
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | REF_CLOSE: (13), (81), (100), (130) are inconsistent by
% 158.37/27.72 | | | | | | | | | sub-proof #1440.
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | Case 2:
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | (131) all_58_14 = e2 & op(e0, e1) = e2
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | ALPHA: (131) implies:
% 158.37/27.72 | | | | | | | | | (132) all_58_14 = e2
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (11), (14), (18), (21), (22),
% 158.37/27.72 | | | | | | | | | (25), (31), (33), (34), (35), (36), (37), (38),
% 158.37/27.72 | | | | | | | | | (39), (41), (43), (44), (49), (51), (52), (53),
% 158.37/27.72 | | | | | | | | | (54), (55), (60), (62), (63), (64), (65), (66),
% 158.37/27.72 | | | | | | | | | (69), (71), (72), (74), (76), (78), (79), (82),
% 158.37/27.72 | | | | | | | | | (83), (85), (86), (88), (90), (91), (92), (94),
% 158.37/27.72 | | | | | | | | | (96), (99), (100), (105), (107), (108), (110),
% 158.37/27.72 | | | | | | | | | (113), (115), (119), (120), (123), (127), (132) are
% 158.37/27.72 | | | | | | | | | inconsistent by sub-proof #474.
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | End of split
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | End of split
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | Case 2:
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | | (133) all_58_12 = e0 & op(e0, e3) = e0
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | | ALPHA: (133) implies:
% 158.37/27.72 | | | | | | | (134) all_58_12 = e0
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | | BETA: splitting (26) gives:
% 158.37/27.72 | | | | | | |
% 158.37/27.72 | | | | | | | Case 1:
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | (135) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 158.37/27.72 | | | | | | | | op(e2, e1) = e2)
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | REF_CLOSE: (11), (38), (43), (49), (51), (57), (72), (76), (78),
% 158.37/27.72 | | | | | | | | (79), (100), (105), (135) are inconsistent by
% 158.37/27.72 | | | | | | | | sub-proof #835.
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | Case 2:
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | (136) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 158.37/27.72 | | | | | | | | op(e0, e1) = e2)
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | BETA: splitting (136) gives:
% 158.37/27.72 | | | | | | | |
% 158.37/27.72 | | | | | | | | Case 1:
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | (137) all_58_8 = e2 & op(e1, e1) = e2
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | REF_CLOSE: (13), (81), (100), (137) are inconsistent by
% 158.37/27.72 | | | | | | | | | sub-proof #1440.
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | Case 2:
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | (138) all_58_14 = e2 & op(e0, e1) = e2
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | ALPHA: (138) implies:
% 158.37/27.72 | | | | | | | | | (139) all_58_14 = e2
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | BETA: splitting (8) gives:
% 158.37/27.72 | | | | | | | | |
% 158.37/27.72 | | | | | | | | | Case 1:
% 158.37/27.72 | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | (140) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 158.37/27.72 | | | | | | | | | | & op(e1, e2) = e1)
% 158.37/27.72 | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | BETA: splitting (140) gives:
% 158.37/27.72 | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | Case 1:
% 158.37/27.72 | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | (141) all_58_6 = e1 & op(e1, e3) = e1
% 158.37/27.72 | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | ALPHA: (141) implies:
% 158.37/27.72 | | | | | | | | | | | (142) all_58_6 = e1
% 158.37/27.72 | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | BETA: splitting (46) gives:
% 158.37/27.72 | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | Case 1:
% 158.37/27.72 | | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | | (143) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 158.37/27.72 | | | | | | | | | | | | & op(e1, e2) = e0)
% 158.37/27.72 | | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | | BETA: splitting (143) gives:
% 158.37/27.72 | | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | | Case 1:
% 158.37/27.72 | | | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | | | (144) all_58_6 = e0 & op(e1, e3) = e0
% 158.37/27.72 | | | | | | | | | | | | |
% 158.37/27.72 | | | | | | | | | | | | | ALPHA: (144) implies:
% 158.37/27.72 | | | | | | | | | | | | | (145) all_58_6 = e0
% 158.37/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (11), (14), (18), (21), (22),
% 158.60/27.72 | | | | | | | | | | | | | (25), (31), (33), (34), (35), (36), (37), (38),
% 158.60/27.72 | | | | | | | | | | | | | (39), (41), (43), (44), (49), (51), (52), (53),
% 158.60/27.72 | | | | | | | | | | | | | (54), (55), (60), (62), (63), (64), (65), (66),
% 158.60/27.72 | | | | | | | | | | | | | (69), (71), (72), (74), (76), (78), (79), (82),
% 158.60/27.72 | | | | | | | | | | | | | (83), (85), (86), (88), (90), (91), (92), (94),
% 158.60/27.72 | | | | | | | | | | | | | (96), (99), (100), (105), (107), (108), (110),
% 158.60/27.72 | | | | | | | | | | | | | (113), (115), (119), (120), (123), (139), (145)
% 158.60/27.72 | | | | | | | | | | | | | are inconsistent by sub-proof #474.
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | (146) all_58_7 = e0 & op(e1, e2) = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | ALPHA: (146) implies:
% 158.60/27.72 | | | | | | | | | | | | | (147) all_58_7 = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (11), (12), (13), (14), (15), (18),
% 158.60/27.72 | | | | | | | | | | | | | (22), (23), (25), (27), (31), (33), (34), (35),
% 158.60/27.72 | | | | | | | | | | | | | (36), (37), (38), (39), (40), (41), (43), (44),
% 158.60/27.72 | | | | | | | | | | | | | (49), (50), (51), (52), (54), (55), (57), (60),
% 158.60/27.72 | | | | | | | | | | | | | (63), (64), (65), (66), (71), (72), (74), (76),
% 158.60/27.72 | | | | | | | | | | | | | (78), (79), (81), (82), (83), (84), (85), (86),
% 158.60/27.72 | | | | | | | | | | | | | (87), (88), (89), (90), (92), (96), (97), (99),
% 158.60/27.72 | | | | | | | | | | | | | (100), (105), (107), (108), (110), (113), (115),
% 158.60/27.72 | | | | | | | | | | | | | (119), (123), (139), (147) are inconsistent by
% 158.60/27.72 | | | | | | | | | | | | | sub-proof #465.
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | (148) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 158.60/27.72 | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | BETA: splitting (148) gives:
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | (149) all_58_8 = e0 & op(e1, e1) = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | ALPHA: (149) implies:
% 158.60/27.72 | | | | | | | | | | | | | (150) all_58_8 = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | BETA: splitting (82) gives:
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | (151) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 158.60/27.72 | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 158.60/27.72 | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 158.60/27.72 | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | (152) all_58_12 = e3 & op(e0, e3) = e3
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (11), (12), (13), (14), (18), (22),
% 158.60/27.72 | | | | | | | | | | | | | | | (23), (25), (27), (31), (33), (34), (35), (36),
% 158.60/27.72 | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (43), (44), (49),
% 158.60/27.72 | | | | | | | | | | | | | | | (50), (51), (52), (54), (55), (57), (60), (63),
% 158.60/27.72 | | | | | | | | | | | | | | | (64), (65), (66), (71), (72), (74), (76), (78),
% 158.60/27.72 | | | | | | | | | | | | | | | (79), (81), (83), (84), (85), (86), (88), (89),
% 158.60/27.72 | | | | | | | | | | | | | | | (90), (92), (96), (97), (99), (100), (105), (110),
% 158.60/27.72 | | | | | | | | | | | | | | | (113), (115), (152) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | | | | | #466.
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | (153) all_58_13 = e3 & op(e0, e2) = e3
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | REF_CLOSE: (14), (92), (100), (153) are inconsistent by
% 158.60/27.72 | | | | | | | | | | | | | | | sub-proof #1449.
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | (154) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 158.60/27.72 | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.60/27.72 | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 158.60/27.72 | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | (155) all_58_14 = e3 & op(e0, e1) = e3
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 158.60/27.72 | | | | | | | | | | | | | | | (156) all_58_14 = e3
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | REF_CLOSE: (105), (139), (156) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | | | | | #1405.
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | (157) all_58_15 = e3 & op(e0, e0) = e3
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 158.60/27.72 | | | | | | | | | | | | | | | (158) all_58_15 = e3
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | (159) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 158.60/27.72 | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 158.60/27.72 | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | (160) all_58_4 = e1 & op(e3, e1) = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (78), (160) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | | | | | | | #1345.
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | (161) all_58_5 = e1 & op(e2, e1) = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 158.60/27.72 | | | | | | | | | | | | | | | | | (162) all_58_5 = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | (163) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 158.60/27.72 | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 158.60/27.72 | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 158.60/27.72 | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | (164) all_58_9 = e1 & op(e3, e0) = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (123), (164) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | #1325.
% 158.60/27.72 | | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | (165) all_58_10 = e1 & op(e2, e0) = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | (166) all_58_10 = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (38), (43), (49), (51), (57), (72), (76),
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | (79), (100), (162), (166) are inconsistent by
% 158.60/27.72 | | | | | | | | | | | | | | | | | | | sub-proof #754.
% 158.60/27.72 | | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | (167) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 158.60/27.72 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 158.60/27.72 | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (91), (100), (158), (167) are inconsistent
% 158.60/27.72 | | | | | | | | | | | | | | | | | | by sub-proof #836.
% 158.60/27.72 | | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | (168) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 158.60/27.72 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 158.60/27.72 | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 158.60/27.72 | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | (169) all_58_8 = e1 & op(e1, e1) = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 158.60/27.72 | | | | | | | | | | | | | | | | | (170) all_58_8 = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (170) imply:
% 158.60/27.72 | | | | | | | | | | | | | | | | | (171) e1 = e0
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (171) imply:
% 158.60/27.72 | | | | | | | | | | | | | | | | | (172) all_58_6 = e0
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (11), (14), (18), (21), (22), (25),
% 158.60/27.72 | | | | | | | | | | | | | | | | | (31), (33), (34), (35), (37), (38), (39), (41),
% 158.60/27.72 | | | | | | | | | | | | | | | | | (43), (44), (49), (51), (52), (53), (54), (55),
% 158.60/27.72 | | | | | | | | | | | | | | | | | (60), (62), (63), (64), (65), (66), (71), (72),
% 158.60/27.72 | | | | | | | | | | | | | | | | | (74), (76), (78), (79), (82), (83), (85), (86),
% 158.60/27.72 | | | | | | | | | | | | | | | | | (88), (90), (92), (94), (96), (99), (100), (105),
% 158.60/27.72 | | | | | | | | | | | | | | | | | (108), (110), (113), (115), (120), (123), (139),
% 158.60/27.72 | | | | | | | | | | | | | | | | | (170), (172) are inconsistent by sub-proof #475.
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | (173) all_58_14 = e1 & op(e0, e1) = e1
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (139), (173) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | | | | | | | #1339.
% 158.60/27.72 | | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | (174) all_58_11 = e0 & op(e1, e0) = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | ALPHA: (174) implies:
% 158.60/27.72 | | | | | | | | | | | | | (175) all_58_11 = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | REF_CLOSE: (38), (110), (175) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | | | #1216.
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | (176) all_58_7 = e1 & op(e1, e2) = e1
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | ALPHA: (176) implies:
% 158.60/27.72 | | | | | | | | | | | (177) all_58_7 = e1
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | REF_CLOSE: (25), (33), (36), (38), (39), (43), (49), (51),
% 158.60/27.72 | | | | | | | | | | | (53), (69), (72), (76), (78), (100), (105), (110),
% 158.60/27.72 | | | | | | | | | | | (134), (139), (177) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | #725.
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | (178) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1
% 158.60/27.72 | | | | | | | | | | & op(e1, e0) = e1)
% 158.60/27.72 | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | BETA: splitting (178) gives:
% 158.60/27.72 | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | (179) all_58_8 = e1 & op(e1, e1) = e1
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | ALPHA: (179) implies:
% 158.60/27.72 | | | | | | | | | | | (180) all_58_8 = e1
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | BETA: splitting (46) gives:
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | (181) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 158.60/27.72 | | | | | | | | | | | | & op(e1, e2) = e0)
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | BETA: splitting (181) gives:
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | (182) all_58_6 = e0 & op(e1, e3) = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | ALPHA: (182) implies:
% 158.60/27.72 | | | | | | | | | | | | | (183) all_58_6 = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (11), (14), (18), (21), (22), (25),
% 158.60/27.72 | | | | | | | | | | | | | (31), (33), (34), (35), (37), (38), (39), (41),
% 158.60/27.72 | | | | | | | | | | | | | (43), (44), (49), (51), (52), (53), (54), (55),
% 158.60/27.72 | | | | | | | | | | | | | (60), (62), (63), (64), (65), (66), (71), (72),
% 158.60/27.72 | | | | | | | | | | | | | (74), (76), (78), (79), (82), (83), (85), (86),
% 158.60/27.72 | | | | | | | | | | | | | (88), (90), (92), (94), (96), (99), (100), (105),
% 158.60/27.72 | | | | | | | | | | | | | (108), (110), (113), (115), (120), (123), (139),
% 158.60/27.72 | | | | | | | | | | | | | (180), (183) are inconsistent by sub-proof #475.
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | (184) all_58_7 = e0 & op(e1, e2) = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | ALPHA: (184) implies:
% 158.60/27.72 | | | | | | | | | | | | | (185) all_58_7 = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (11), (12), (13), (14), (15), (18),
% 158.60/27.72 | | | | | | | | | | | | | (22), (23), (25), (27), (31), (33), (34), (35),
% 158.60/27.72 | | | | | | | | | | | | | (36), (37), (38), (39), (40), (41), (43), (44),
% 158.60/27.72 | | | | | | | | | | | | | (49), (50), (51), (52), (54), (55), (57), (60),
% 158.60/27.72 | | | | | | | | | | | | | (63), (64), (65), (66), (71), (72), (74), (76),
% 158.60/27.72 | | | | | | | | | | | | | (78), (79), (81), (82), (83), (84), (85), (86),
% 158.60/27.72 | | | | | | | | | | | | | (87), (88), (89), (90), (92), (96), (97), (99),
% 158.60/27.72 | | | | | | | | | | | | | (100), (105), (107), (108), (110), (113), (115),
% 158.60/27.72 | | | | | | | | | | | | | (119), (123), (139), (185) are inconsistent by
% 158.60/27.72 | | | | | | | | | | | | | sub-proof #465.
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | (186) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 158.60/27.72 | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | BETA: splitting (186) gives:
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | Case 1:
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | (187) all_58_8 = e0 & op(e1, e1) = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | REF_CLOSE: (76), (180), (187) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | | | #1271.
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | (188) all_58_11 = e0 & op(e1, e0) = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | ALPHA: (188) implies:
% 158.60/27.72 | | | | | | | | | | | | | (189) all_58_11 = e0
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | | REF_CLOSE: (38), (110), (189) are inconsistent by sub-proof
% 158.60/27.72 | | | | | | | | | | | | | #1216.
% 158.60/27.72 | | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | Case 2:
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | (190) all_58_11 = e1 & op(e1, e0) = e1
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | ALPHA: (190) implies:
% 158.60/27.72 | | | | | | | | | | | (191) op(e1, e0) = e1
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | | REF_CLOSE: (51), (91), (100), (191) are inconsistent by
% 158.60/27.72 | | | | | | | | | | | sub-proof #1275.
% 158.60/27.72 | | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | | |
% 158.60/27.72 | | | | | | | | | End of split
% 158.60/27.72 | | | | | | | | |
% 158.60/27.72 | | | | | | | | End of split
% 158.60/27.72 | | | | | | | |
% 158.60/27.72 | | | | | | | End of split
% 158.60/27.72 | | | | | | |
% 158.60/27.72 | | | | | | End of split
% 158.60/27.72 | | | | | |
% 158.60/27.72 | | | | | End of split
% 158.60/27.72 | | | | |
% 158.60/27.72 | | | | Case 2:
% 158.60/27.72 | | | | |
% 158.60/27.72 | | | | | (192) all_58_10 = e2 & op(e2, e0) = e2
% 158.60/27.72 | | | | |
% 158.60/27.72 | | | | | ALPHA: (192) implies:
% 158.60/27.72 | | | | | (193) all_58_10 = e2
% 158.60/27.72 | | | | |
% 158.60/27.72 | | | | | REF_CLOSE: (11), (38), (43), (49), (51), (57), (72), (76), (79),
% 158.60/27.72 | | | | | (100), (193) are inconsistent by sub-proof #906.
% 158.60/27.72 | | | | |
% 158.60/27.72 | | | | End of split
% 158.60/27.72 | | | |
% 158.60/27.72 | | | Case 2:
% 158.60/27.72 | | | |
% 158.60/27.72 | | | | (194) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 158.60/27.72 | | | | e0) = e2)
% 158.60/27.72 | | | |
% 158.60/27.72 | | | | REF_CLOSE: (11), (13), (14), (15), (26), (38), (43), (49), (51), (57),
% 158.60/27.72 | | | | (72), (76), (78), (79), (81), (82), (92), (100), (105),
% 158.60/27.72 | | | | (108), (110), (194) are inconsistent by sub-proof #834.
% 158.60/27.72 | | | |
% 158.60/27.72 | | | End of split
% 158.60/27.72 | | |
% 158.60/27.72 | | Case 2:
% 158.60/27.72 | | |
% 158.60/27.72 | | | (195) all_58_2 = e3 & op(e2, e3) = e3
% 158.60/27.72 | | |
% 158.60/27.72 | | | ALPHA: (195) implies:
% 158.60/27.72 | | | (196) op(e2, e3) = e3
% 158.60/27.72 | | |
% 158.60/27.72 | | | REF_CLOSE: (33), (49), (100), (105), (196) are inconsistent by sub-proof
% 158.60/27.72 | | | #1159.
% 158.60/27.72 | | |
% 158.60/27.72 | | End of split
% 158.60/27.72 | |
% 158.60/27.72 | Case 2:
% 158.60/27.72 | |
% 158.60/27.72 | | (197) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 158.60/27.72 | | e3)
% 158.60/27.72 | |
% 158.60/27.72 | | BETA: splitting (197) gives:
% 158.60/27.72 | |
% 158.60/27.72 | | Case 1:
% 158.60/27.72 | | |
% 158.60/27.72 | | | (198) all_58_6 = e3 & op(e1, e3) = e3
% 158.60/27.72 | | |
% 158.60/27.72 | | | ALPHA: (198) implies:
% 158.60/27.72 | | | (199) all_58_6 = e3
% 158.60/27.72 | | | (200) op(e1, e3) = e3
% 158.60/27.72 | | |
% 158.60/27.72 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.60/27.72 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 158.60/27.72 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 158.60/27.72 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 158.60/27.72 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 158.60/27.72 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 158.60/27.72 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 158.60/27.72 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 158.60/27.72 | | | (83), (84), (85), (86), (88), (89), (90), (92), (93), (94),
% 158.60/27.72 | | | (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 158.60/27.72 | | | (104), (105), (106), (107), (108), (109), (111), (112), (113),
% 158.60/27.72 | | | (114), (115), (116), (199), (200) are inconsistent by sub-proof
% 158.60/27.72 | | | #535.
% 158.60/27.72 | | |
% 158.60/27.72 | | Case 2:
% 158.60/27.72 | | |
% 158.60/27.72 | | | (201) all_58_12 = e3 & op(e0, e3) = e3
% 158.60/27.72 | | |
% 158.60/27.72 | | | REF_CLOSE: (4), (5), (11), (12), (13), (14), (18), (22), (23), (25), (27),
% 158.60/27.72 | | | (31), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 158.60/27.72 | | | (43), (44), (49), (50), (51), (52), (54), (55), (57), (60),
% 158.60/27.72 | | | (63), (64), (65), (66), (71), (72), (74), (76), (78), (79),
% 158.60/27.72 | | | (81), (83), (84), (85), (86), (88), (89), (90), (92), (96),
% 158.60/27.72 | | | (97), (99), (100), (105), (110), (113), (115), (201) are
% 158.60/27.72 | | | inconsistent by sub-proof #466.
% 158.60/27.72 | | |
% 158.60/27.72 | | End of split
% 158.60/27.72 | |
% 158.60/27.72 | End of split
% 158.60/27.72 |
% 158.60/27.72 End of proof
% 158.60/27.72
% 158.60/27.72 Sub-proof #465 shows that the following formulas are inconsistent:
% 158.60/27.72 ----------------------------------------------------------------
% 158.60/27.72 (1) all_56_14 = e3
% 158.60/27.72 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.72 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.60/27.72 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.60/27.72 (4) all_54_13 = all_52_7
% 158.60/27.72 (5) op(e1, e1) = all_6_2
% 158.60/27.72 (6) ~ (all_52_7 = e3)
% 158.60/27.72 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 158.60/27.72 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.60/27.72 (8) ~ (all_52_11 = e3)
% 158.60/27.72 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.72 (10) ~ (all_52_7 = all_52_11)
% 158.60/27.72 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.72 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.72 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.60/27.72 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.60/27.72 (13) ~ (all_4_2 = e2)
% 158.60/27.72 (14) all_58_7 = e0
% 158.60/27.72 (15) all_58_14 = e2
% 158.60/27.72 (16) op(e2, e3) = all_52_1
% 158.60/27.72 (17) ~ (all_52_13 = e3)
% 158.60/27.72 (18) all_54_2 = all_52_8
% 158.60/27.72 (19) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.60/27.72 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.60/27.72 (20) ~ (all_52_8 = all_52_9)
% 158.60/27.73 (21) ~ (e3 = e0)
% 158.60/27.73 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.73 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.73 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.60/27.73 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.60/27.73 (24) ~ (all_52_9 = all_52_13)
% 158.60/27.73 (25) ~ (e2 = e0)
% 158.60/27.73 (26) ~ (all_52_9 = e3)
% 158.60/27.73 (27) op(e2, e3) = e2
% 158.60/27.73 (28) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.60/27.73 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.60/27.73 (29) ~ (e3 = e1)
% 158.60/27.73 (30) all_56_12 = e1
% 158.60/27.73 (31) ~ (all_4_2 = e1)
% 158.60/27.73 (32) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.73 (33) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.60/27.73 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.60/27.73 (34) all_54_7 = all_52_13
% 158.60/27.73 (35) ~ (all_52_13 = e2)
% 158.60/27.73 (36) all_56_15 = all_4_2
% 158.60/27.73 (37) ~ (all_52_9 = all_52_11)
% 158.60/27.73 (38) ~ (all_52_13 = all_4_2)
% 158.60/27.73 (39) all_58_0 = e3
% 158.60/27.73 (40) all_54_6 = all_52_9
% 158.60/27.73 (41) ~ (e2 = e1)
% 158.60/27.73 (42) ~ (all_52_8 = all_52_11)
% 158.60/27.73 (43) ~ (e1 = e0)
% 158.60/27.73 (44) all_58_4 = e3
% 158.60/27.73 (45) all_58_3 = e3
% 158.60/27.73 (46) ~ (all_6_2 = e2)
% 158.60/27.73 (47) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.60/27.73 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.60/27.73 e3)
% 158.60/27.73 (48) all_56_13 = e3
% 158.60/27.73 (49) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.60/27.73 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.60/27.73 (50) ~ (all_52_9 = e2)
% 158.60/27.73 (51) ~ (all_52_8 = e3)
% 158.60/27.73 (52) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 158.60/27.73 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.60/27.73 (53) all_54_14 = all_52_11
% 158.60/27.73 (54) ~ (all_52_7 = all_4_2)
% 158.60/27.73 (55) op(e1, e3) = e1
% 158.60/27.73 (56) all_58_9 = e2
% 158.60/27.73 (57) op(e0, e2) = all_52_7
% 158.60/27.73 (58) ~ (all_52_8 = e1)
% 158.60/27.73 (59) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.60/27.73 (60) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.60/27.73 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.73 (61) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.73 (62) ~ (e3 = e2)
% 158.60/27.73 (63) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.60/27.73 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.60/27.73 (64) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.60/27.73 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.60/27.73 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.60/27.73 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.60/27.73 (65) all_58_11 = e3
% 158.60/27.73 (66) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.73 (67) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.73
% 158.60/27.73 Begin of proof
% 158.60/27.73 |
% 158.60/27.73 | BETA: splitting (63) gives:
% 158.60/27.73 |
% 158.60/27.73 | Case 1:
% 158.60/27.73 | |
% 158.60/27.73 | | (68) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 158.60/27.73 | | e0)
% 158.60/27.73 | |
% 158.60/27.73 | | BETA: splitting (68) gives:
% 158.60/27.73 | |
% 158.60/27.73 | | Case 1:
% 158.60/27.73 | | |
% 158.60/27.73 | | | (69) all_58_0 = e0 & op(e3, e3) = e0
% 158.60/27.73 | | |
% 158.60/27.73 | | | REF_CLOSE: (21), (39), (69) are inconsistent by sub-proof #859.
% 158.60/27.73 | | |
% 158.60/27.73 | | Case 2:
% 158.60/27.73 | | |
% 158.60/27.73 | | | (70) all_58_1 = e0 & op(e3, e2) = e0
% 158.60/27.73 | | |
% 158.60/27.73 | | | ALPHA: (70) implies:
% 158.60/27.73 | | | (71) all_58_1 = e0
% 158.60/27.73 | | |
% 158.60/27.73 | | | BETA: splitting (47) gives:
% 158.60/27.73 | | |
% 158.60/27.73 | | | Case 1:
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | (72) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 158.60/27.73 | | | | e2) = e3)
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | BETA: splitting (72) gives:
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | Case 1:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | (73) all_58_12 = e3 & op(e0, e3) = e3
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 158.60/27.73 | | | | | (13), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 158.60/27.73 | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.60/27.73 | | | | | (35), (36), (37), (38), (40), (41), (42), (43), (44), (45),
% 158.60/27.73 | | | | | (46), (48), (49), (50), (51), (53), (54), (55), (57), (58),
% 158.60/27.73 | | | | | (59), (60), (61), (62), (65), (66), (67), (73) are
% 158.60/27.73 | | | | | inconsistent by sub-proof #466.
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | Case 2:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | (74) all_58_13 = e3 & op(e0, e2) = e3
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | REF_CLOSE: (6), (57), (61), (74) are inconsistent by sub-proof #1449.
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | End of split
% 158.60/27.73 | | | |
% 158.60/27.73 | | | Case 2:
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | (75) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 158.60/27.73 | | | | e0) = e3)
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | BETA: splitting (75) gives:
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | Case 1:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | (76) all_58_14 = e3 & op(e0, e1) = e3
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | ALPHA: (76) implies:
% 158.60/27.73 | | | | | (77) all_58_14 = e3
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | REF_CLOSE: (15), (62), (77) are inconsistent by sub-proof #1405.
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | Case 2:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | (78) all_58_15 = e3 & op(e0, e0) = e3
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | ALPHA: (78) implies:
% 158.60/27.73 | | | | | (79) all_58_15 = e3
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | REF_CLOSE: (7), (14), (15), (21), (25), (29), (41), (43), (45), (52),
% 158.60/27.73 | | | | | (62), (64), (71), (79) are inconsistent by sub-proof #683.
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | End of split
% 158.60/27.73 | | | |
% 158.60/27.73 | | | End of split
% 158.60/27.73 | | |
% 158.60/27.73 | | End of split
% 158.60/27.73 | |
% 158.60/27.73 | Case 2:
% 158.60/27.73 | |
% 158.60/27.73 | | (80) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 158.60/27.73 | | e0)
% 158.60/27.73 | |
% 158.60/27.73 | | REF_CLOSE: (21), (25), (44), (56), (80) are inconsistent by sub-proof #606.
% 158.60/27.73 | |
% 158.60/27.73 | End of split
% 158.60/27.73 |
% 158.60/27.73 End of proof
% 158.60/27.73
% 158.60/27.73 Sub-proof #466 shows that the following formulas are inconsistent:
% 158.60/27.73 ----------------------------------------------------------------
% 158.60/27.73 (1) all_56_14 = e3
% 158.60/27.73 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.73 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.60/27.73 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.60/27.73 (4) all_54_13 = all_52_7
% 158.60/27.73 (5) op(e1, e1) = all_6_2
% 158.60/27.73 (6) ~ (all_52_7 = e3)
% 158.60/27.73 (7) ~ (all_52_11 = e3)
% 158.60/27.73 (8) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.73 (9) ~ (all_52_7 = all_52_11)
% 158.60/27.73 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.73 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.73 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.60/27.73 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.60/27.73 (12) ~ (all_4_2 = e2)
% 158.60/27.73 (13) op(e2, e3) = all_52_1
% 158.60/27.73 (14) ~ (all_52_13 = e3)
% 158.60/27.73 (15) all_54_2 = all_52_8
% 158.60/27.73 (16) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.60/27.73 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.60/27.73 (17) ~ (all_52_8 = all_52_9)
% 158.60/27.73 (18) ~ (e3 = e0)
% 158.60/27.73 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.73 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.73 (20) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.60/27.73 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.60/27.73 (21) ~ (all_52_9 = all_52_13)
% 158.60/27.73 (22) ~ (e2 = e0)
% 158.60/27.73 (23) ~ (all_52_9 = e3)
% 158.60/27.73 (24) op(e2, e3) = e2
% 158.60/27.73 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.60/27.73 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.60/27.73 (26) ~ (e3 = e1)
% 158.60/27.73 (27) all_56_12 = e1
% 158.60/27.73 (28) ~ (all_4_2 = e1)
% 158.60/27.73 (29) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.73 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.60/27.73 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.60/27.73 (31) all_54_7 = all_52_13
% 158.60/27.73 (32) ~ (all_52_13 = e2)
% 158.60/27.73 (33) all_56_15 = all_4_2
% 158.60/27.73 (34) ~ (all_52_9 = all_52_11)
% 158.60/27.73 (35) ~ (all_52_13 = all_4_2)
% 158.60/27.73 (36) all_54_6 = all_52_9
% 158.60/27.73 (37) ~ (e2 = e1)
% 158.60/27.73 (38) ~ (all_52_8 = all_52_11)
% 158.60/27.73 (39) ~ (e1 = e0)
% 158.60/27.73 (40) all_58_4 = e3
% 158.60/27.73 (41) all_58_3 = e3
% 158.60/27.73 (42) ~ (all_6_2 = e2)
% 158.60/27.73 (43) all_56_13 = e3
% 158.60/27.73 (44) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.60/27.73 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.60/27.73 (45) ~ (all_52_9 = e2)
% 158.60/27.73 (46) ~ (all_52_8 = e3)
% 158.60/27.73 (47) all_54_14 = all_52_11
% 158.60/27.73 (48) ~ (all_52_7 = all_4_2)
% 158.60/27.73 (49) op(e1, e3) = e1
% 158.60/27.73 (50) op(e0, e2) = all_52_7
% 158.60/27.73 (51) all_58_12 = e3 & op(e0, e3) = e3
% 158.60/27.73 (52) ~ (all_52_8 = e1)
% 158.60/27.73 (53) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.60/27.73 (54) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.60/27.73 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.73 (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.73 (56) ~ (e3 = e2)
% 158.60/27.73 (57) all_58_11 = e3
% 158.60/27.73 (58) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.73 (59) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.73
% 158.60/27.73 Begin of proof
% 158.60/27.73 |
% 158.60/27.73 | ALPHA: (51) implies:
% 158.60/27.73 | (60) all_58_12 = e3
% 158.60/27.73 |
% 158.60/27.73 | BETA: splitting (54) gives:
% 158.60/27.73 |
% 158.60/27.73 | Case 1:
% 158.60/27.73 | |
% 158.60/27.73 | | (61) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 158.60/27.73 | | e0)
% 158.60/27.73 | |
% 158.60/27.73 | | BETA: splitting (61) gives:
% 158.60/27.73 | |
% 158.60/27.73 | | Case 1:
% 158.60/27.73 | | |
% 158.60/27.73 | | | (62) all_58_0 = e0 & op(e3, e3) = e0
% 158.60/27.73 | | |
% 158.60/27.73 | | | ALPHA: (62) implies:
% 158.60/27.73 | | | (63) all_58_0 = e0
% 158.60/27.73 | | |
% 158.60/27.73 | | | BETA: splitting (44) gives:
% 158.60/27.73 | | |
% 158.60/27.73 | | | Case 1:
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | (64) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 158.60/27.73 | | | | = e1)
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | BETA: splitting (64) gives:
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | Case 1:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | (65) all_58_0 = e1 & op(e3, e3) = e1
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | REF_CLOSE: (39), (63), (65) are inconsistent by sub-proof #1495.
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | Case 2:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | (66) all_58_1 = e1 & op(e3, e2) = e1
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | ALPHA: (66) implies:
% 158.60/27.73 | | | | | (67) all_58_1 = e1
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | BETA: splitting (16) gives:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | Case 1:
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | (68) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 158.60/27.73 | | | | | | e2) = e2)
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | BETA: splitting (68) gives:
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | Case 1:
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | (69) all_58_6 = e2 & op(e1, e3) = e2
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | ALPHA: (69) implies:
% 158.60/27.73 | | | | | | | (70) all_58_6 = e2
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | REF_CLOSE: (10), (13), (18), (19), (24), (26), (37), (39), (55),
% 158.60/27.73 | | | | | | | (56), (63), (70) are inconsistent by sub-proof #1157.
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | Case 2:
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | (71) all_58_7 = e2 & op(e1, e2) = e2
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | ALPHA: (71) implies:
% 158.60/27.73 | | | | | | | (72) all_58_7 = e2
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (13), (14),
% 158.60/27.73 | | | | | | | (15), (17), (18), (19), (21), (22), (23), (24), (25),
% 158.60/27.73 | | | | | | | (26), (27), (29), (31), (32), (33), (34), (35), (36),
% 158.60/27.73 | | | | | | | (37), (38), (39), (41), (43), (45), (46), (47), (48),
% 158.60/27.73 | | | | | | | (50), (52), (53), (55), (56), (58), (59), (60), (63),
% 158.60/27.73 | | | | | | | (67), (72) are inconsistent by sub-proof #469.
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | End of split
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | Case 2:
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | (73) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 158.60/27.73 | | | | | | e0) = e2)
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | REF_CLOSE: (5), (10), (13), (18), (19), (24), (26), (37), (39),
% 158.60/27.73 | | | | | | (42), (55), (56), (57), (60), (63), (73) are inconsistent
% 158.60/27.73 | | | | | | by sub-proof #468.
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | End of split
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | End of split
% 158.60/27.73 | | | |
% 158.60/27.73 | | | Case 2:
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | (74) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 158.60/27.73 | | | | = e1)
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | BETA: splitting (74) gives:
% 158.60/27.73 | | | |
% 158.60/27.73 | | | | Case 1:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | (75) all_58_4 = e1 & op(e3, e1) = e1
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | REF_CLOSE: (26), (40), (75) are inconsistent by sub-proof #1345.
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | Case 2:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | (76) all_58_9 = e1 & op(e3, e0) = e1
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | ALPHA: (76) implies:
% 158.60/27.73 | | | | | (77) all_58_9 = e1
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | BETA: splitting (16) gives:
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | | Case 1:
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | (78) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 158.60/27.73 | | | | | | e2) = e2)
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | BETA: splitting (78) gives:
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | Case 1:
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | (79) all_58_6 = e2 & op(e1, e3) = e2
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | ALPHA: (79) implies:
% 158.60/27.73 | | | | | | | (80) all_58_6 = e2
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | REF_CLOSE: (10), (13), (18), (19), (24), (26), (37), (39), (55),
% 158.60/27.73 | | | | | | | (56), (63), (80) are inconsistent by sub-proof #1157.
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | Case 2:
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | (81) all_58_7 = e2 & op(e1, e2) = e2
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | ALPHA: (81) implies:
% 158.60/27.73 | | | | | | | (82) all_58_7 = e2
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | BETA: splitting (25) gives:
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | | Case 1:
% 158.60/27.73 | | | | | | | |
% 158.60/27.73 | | | | | | | | (83) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 158.60/27.73 | | | | | | | | op(e2, e2) = e0)
% 158.60/27.73 | | | | | | | |
% 158.60/27.73 | | | | | | | | BETA: splitting (83) gives:
% 158.60/27.73 | | | | | | | |
% 158.60/27.73 | | | | | | | | Case 1:
% 158.60/27.73 | | | | | | | | |
% 158.60/27.73 | | | | | | | | | (84) all_58_1 = e0 & op(e3, e2) = e0
% 158.60/27.73 | | | | | | | | |
% 158.60/27.73 | | | | | | | | | ALPHA: (84) implies:
% 158.60/27.73 | | | | | | | | | (85) all_58_1 = e0
% 158.60/27.73 | | | | | | | | |
% 158.60/27.73 | | | | | | | | | BETA: splitting (11) gives:
% 158.60/27.73 | | | | | | | | |
% 158.60/27.73 | | | | | | | | | Case 1:
% 158.60/27.73 | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | (86) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 158.60/27.73 | | | | | | | | | | & op(e2, e0) = e2)
% 158.60/27.73 | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | REF_CLOSE: (3), (18), (22), (24), (26), (30), (37), (39),
% 158.60/27.73 | | | | | | | | | | (41), (55), (77), (86) are inconsistent by
% 158.60/27.73 | | | | | | | | | | sub-proof #686.
% 158.60/27.73 | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | Case 2:
% 158.60/27.73 | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | (87) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2
% 158.60/27.73 | | | | | | | | | | & op(e0, e0) = e2)
% 158.60/27.73 | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | BETA: splitting (87) gives:
% 158.60/27.73 | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | Case 1:
% 158.60/27.73 | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | (88) all_58_11 = e2 & op(e1, e0) = e2
% 158.60/27.73 | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | REF_CLOSE: (10), (13), (18), (19), (24), (26), (37), (39),
% 158.60/27.73 | | | | | | | | | | | (55), (56), (57), (60), (63), (88) are
% 158.60/27.73 | | | | | | | | | | | inconsistent by sub-proof #692.
% 158.60/27.73 | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | Case 2:
% 158.60/27.73 | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | (89) all_58_15 = e2 & op(e0, e0) = e2
% 158.60/27.73 | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | ALPHA: (89) implies:
% 158.60/27.73 | | | | | | | | | | | (90) all_58_15 = e2
% 158.60/27.73 | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | BETA: splitting (20) gives:
% 158.60/27.73 | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | Case 1:
% 158.60/27.73 | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | (91) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 158.60/27.73 | | | | | | | | | | | | & op(e3, e2) = e2)
% 158.60/27.73 | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | BETA: splitting (91) gives:
% 158.60/27.73 | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | Case 1:
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | (92) all_58_0 = e2 & op(e3, e3) = e2
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | ALPHA: (92) implies:
% 158.60/27.73 | | | | | | | | | | | | | (93) all_58_0 = e2
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | COMBINE_EQS: (63), (93) imply:
% 158.60/27.73 | | | | | | | | | | | | | (94) e2 = e0
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | SIMP: (94) implies:
% 158.60/27.73 | | | | | | | | | | | | | (95) e2 = e0
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | COMBINE_EQS: (90), (95) imply:
% 158.60/27.73 | | | | | | | | | | | | | (96) all_58_15 = e0
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | REF_CLOSE: (3), (10), (11), (13), (18), (19), (22), (24),
% 158.60/27.73 | | | | | | | | | | | | | (26), (30), (37), (39), (41), (55), (56), (57),
% 158.60/27.73 | | | | | | | | | | | | | (60), (63), (77), (96) are inconsistent by
% 158.60/27.73 | | | | | | | | | | | | | sub-proof #691.
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | Case 2:
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | (97) all_58_1 = e2 & op(e3, e2) = e2
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | ALPHA: (97) implies:
% 158.60/27.73 | | | | | | | | | | | | | (98) all_58_1 = e2
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | COMBINE_EQS: (85), (98) imply:
% 158.60/27.73 | | | | | | | | | | | | | (99) e2 = e0
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | SIMP: (99) implies:
% 158.60/27.73 | | | | | | | | | | | | | (100) e2 = e0
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | COMBINE_EQS: (90), (100) imply:
% 158.60/27.73 | | | | | | | | | | | | | (101) all_58_15 = e0
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | REF_CLOSE: (3), (10), (11), (13), (18), (19), (22), (24),
% 158.60/27.73 | | | | | | | | | | | | | (26), (30), (37), (39), (41), (55), (56), (57),
% 158.60/27.73 | | | | | | | | | | | | | (60), (63), (77), (101) are inconsistent by
% 158.60/27.73 | | | | | | | | | | | | | sub-proof #691.
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | End of split
% 158.60/27.73 | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | Case 2:
% 158.60/27.73 | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | (102) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 158.60/27.73 | | | | | | | | | | | | & op(e3, e0) = e2)
% 158.60/27.73 | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | BETA: splitting (102) gives:
% 158.60/27.73 | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | Case 1:
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | (103) all_58_4 = e2 & op(e3, e1) = e2
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | REF_CLOSE: (10), (13), (18), (19), (24), (26), (37), (39),
% 158.60/27.73 | | | | | | | | | | | | | (40), (55), (56), (60), (63), (103) are
% 158.60/27.73 | | | | | | | | | | | | | inconsistent by sub-proof #587.
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | Case 2:
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | (104) all_58_9 = e2 & op(e3, e0) = e2
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | ALPHA: (104) implies:
% 158.60/27.73 | | | | | | | | | | | | | (105) all_58_9 = e2
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | | REF_CLOSE: (37), (77), (105) are inconsistent by sub-proof
% 158.60/27.73 | | | | | | | | | | | | | #1324.
% 158.60/27.73 | | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | | End of split
% 158.60/27.73 | | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | | End of split
% 158.60/27.73 | | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | | End of split
% 158.60/27.73 | | | | | | | | | |
% 158.60/27.73 | | | | | | | | | End of split
% 158.60/27.73 | | | | | | | | |
% 158.60/27.73 | | | | | | | | Case 2:
% 158.60/27.73 | | | | | | | | |
% 158.60/27.73 | | | | | | | | | (106) all_58_3 = e0 & op(e2, e2) = e0
% 158.60/27.73 | | | | | | | | |
% 158.60/27.73 | | | | | | | | | REF_CLOSE: (18), (41), (106) are inconsistent by sub-proof
% 158.60/27.73 | | | | | | | | | #756.
% 158.60/27.73 | | | | | | | | |
% 158.60/27.73 | | | | | | | | End of split
% 158.60/27.73 | | | | | | | |
% 158.60/27.73 | | | | | | | Case 2:
% 158.60/27.73 | | | | | | | |
% 158.60/27.73 | | | | | | | | (107) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 158.60/27.73 | | | | | | | | op(e0, e2) = e0)
% 158.60/27.73 | | | | | | | |
% 158.60/27.73 | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (13), (14),
% 158.60/27.73 | | | | | | | | (15), (17), (18), (19), (21), (22), (23), (24), (26),
% 158.60/27.73 | | | | | | | | (27), (29), (31), (32), (33), (34), (35), (36), (37),
% 158.60/27.73 | | | | | | | | (38), (39), (43), (45), (46), (47), (48), (50), (52),
% 158.60/27.73 | | | | | | | | (53), (55), (56), (58), (59), (60), (63), (82), (107)
% 158.60/27.73 | | | | | | | | are inconsistent by sub-proof #470.
% 158.60/27.73 | | | | | | | |
% 158.60/27.73 | | | | | | | End of split
% 158.60/27.73 | | | | | | |
% 158.60/27.73 | | | | | | End of split
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | Case 2:
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | (108) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 158.60/27.73 | | | | | | op(e1, e0) = e2)
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | | REF_CLOSE: (5), (10), (13), (18), (19), (24), (26), (37), (39),
% 158.60/27.73 | | | | | | (42), (55), (56), (57), (60), (63), (108) are
% 158.60/27.73 | | | | | | inconsistent by sub-proof #468.
% 158.60/27.73 | | | | | |
% 158.60/27.73 | | | | | End of split
% 158.60/27.73 | | | | |
% 158.60/27.73 | | | | End of split
% 158.60/27.73 | | | |
% 158.60/27.73 | | | End of split
% 158.60/27.73 | | |
% 158.60/27.73 | | Case 2:
% 158.60/27.73 | | |
% 158.60/27.73 | | | (109) all_58_2 = e0 & op(e2, e3) = e0
% 158.60/27.73 | | |
% 158.60/27.73 | | | ALPHA: (109) implies:
% 158.60/27.73 | | | (110) op(e2, e3) = e0
% 158.60/27.73 | | |
% 158.60/27.73 | | | REF_CLOSE: (22), (24), (55), (110) are inconsistent by sub-proof #1156.
% 158.60/27.73 | | |
% 158.60/27.73 | | End of split
% 158.60/27.73 | |
% 158.60/27.73 | Case 2:
% 158.60/27.73 | |
% 158.60/27.73 | | (111) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 158.60/27.73 | | e0)
% 158.60/27.73 | |
% 158.60/27.73 | | REF_CLOSE: (1), (2), (7), (8), (10), (12), (13), (14), (15), (17), (18),
% 158.60/27.73 | | (19), (21), (23), (24), (26), (27), (28), (29), (31), (32), (33),
% 158.60/27.73 | | (34), (35), (36), (37), (38), (39), (43), (45), (46), (47), (49),
% 158.60/27.73 | | (52), (54), (55), (56), (58), (59), (60), (111) are inconsistent
% 158.60/27.73 | | by sub-proof #467.
% 158.60/27.73 | |
% 158.60/27.73 | End of split
% 158.60/27.73 |
% 158.60/27.73 End of proof
% 158.60/27.73
% 158.60/27.73 Sub-proof #467 shows that the following formulas are inconsistent:
% 158.60/27.73 ----------------------------------------------------------------
% 158.60/27.73 (1) all_56_14 = e3
% 158.60/27.73 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.73 (3) ~ (all_52_11 = e3)
% 158.60/27.73 (4) all_58_12 = e3
% 158.60/27.73 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.73 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.73 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.73 (7) ~ (all_4_2 = e2)
% 158.60/27.73 (8) op(e2, e3) = all_52_1
% 158.60/27.73 (9) ~ (all_52_13 = e3)
% 158.60/27.73 (10) all_54_2 = all_52_8
% 158.60/27.73 (11) ~ (all_52_8 = all_52_9)
% 158.60/27.73 (12) ~ (e3 = e0)
% 158.60/27.73 (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.73 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.73 (14) ~ (all_52_9 = all_52_13)
% 158.60/27.73 (15) ~ (all_52_9 = e3)
% 158.60/27.73 (16) op(e2, e3) = e2
% 158.60/27.73 (17) ~ (e3 = e1)
% 158.60/27.73 (18) all_56_12 = e1
% 158.60/27.73 (19) ~ (all_4_2 = e1)
% 158.60/27.73 (20) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.73 (21) all_54_7 = all_52_13
% 158.60/27.73 (22) ~ (all_52_13 = e2)
% 158.60/27.73 (23) all_56_15 = all_4_2
% 158.60/27.73 (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.73 (25) ~ (all_52_9 = all_52_11)
% 158.60/27.73 (26) ~ (all_52_13 = all_4_2)
% 158.60/27.73 (27) all_54_6 = all_52_9
% 158.60/27.73 (28) ~ (e2 = e1)
% 158.60/27.73 (29) ~ (all_52_8 = all_52_11)
% 158.60/27.73 (30) ~ (e1 = e0)
% 158.60/27.73 (31) all_56_13 = e3
% 158.60/27.73 (32) ~ (all_52_9 = e2)
% 158.60/27.73 (33) ~ (all_52_8 = e3)
% 158.60/27.73 (34) all_54_14 = all_52_11
% 158.60/27.73 (35) op(e1, e3) = e1
% 158.60/27.73 (36) ~ (all_52_8 = e1)
% 158.60/27.73 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.60/27.73 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.73 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.73 (39) ~ (e3 = e2)
% 158.60/27.73 (40) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.73 (41) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.73
% 158.60/27.73 Begin of proof
% 158.60/27.73 |
% 158.60/27.73 | BETA: splitting (24) gives:
% 158.60/27.73 |
% 158.60/27.73 | Case 1:
% 158.60/27.73 | |
% 158.60/27.73 | | (42) all_58_6 = e0 & op(e1, e3) = e0
% 158.60/27.73 | |
% 158.60/27.73 | | ALPHA: (42) implies:
% 158.60/27.73 | | (43) all_58_6 = e0
% 158.60/27.73 | |
% 158.60/27.74 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.60/27.74 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 158.60/27.74 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 158.60/27.74 | | (36), (37), (38), (39), (40), (41), (43) are inconsistent by
% 158.60/27.74 | | sub-proof #477.
% 158.60/27.74 | |
% 158.60/27.74 | Case 2:
% 158.60/27.74 | |
% 158.60/27.74 | | (44) all_58_12 = e0 & op(e0, e3) = e0
% 158.60/27.74 | |
% 158.60/27.74 | | ALPHA: (44) implies:
% 158.60/27.74 | | (45) all_58_12 = e0
% 158.60/27.74 | |
% 158.60/27.74 | | REF_CLOSE: (4), (12), (45) are inconsistent by sub-proof #1463.
% 158.60/27.74 | |
% 158.60/27.74 | End of split
% 158.60/27.74 |
% 158.60/27.74 End of proof
% 158.60/27.74
% 158.60/27.74 Sub-proof #468 shows that the following formulas are inconsistent:
% 158.60/27.74 ----------------------------------------------------------------
% 158.60/27.74 (1) op(e1, e1) = all_6_2
% 158.60/27.74 (2) all_58_12 = e3
% 158.60/27.74 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.74 (4) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.60/27.74 (5) op(e2, e3) = all_52_1
% 158.60/27.74 (6) ~ (e3 = e0)
% 158.60/27.74 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.74 (8) op(e2, e3) = e2
% 158.60/27.74 (9) ~ (e3 = e1)
% 158.60/27.74 (10) ~ (e2 = e1)
% 158.60/27.74 (11) ~ (e1 = e0)
% 158.60/27.74 (12) ~ (all_6_2 = e2)
% 158.60/27.74 (13) all_58_0 = e0
% 158.60/27.74 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.74 (15) ~ (e3 = e2)
% 158.60/27.74 (16) all_58_11 = e3
% 158.60/27.74
% 158.60/27.74 Begin of proof
% 158.60/27.74 |
% 158.60/27.74 | BETA: splitting (4) gives:
% 158.60/27.74 |
% 158.60/27.74 | Case 1:
% 158.60/27.74 | |
% 158.60/27.74 | | (17) all_58_8 = e2 & op(e1, e1) = e2
% 158.60/27.74 | |
% 158.60/27.74 | | REF_CLOSE: (1), (12), (14), (17) are inconsistent by sub-proof #1440.
% 158.60/27.74 | |
% 158.60/27.74 | Case 2:
% 158.60/27.74 | |
% 158.60/27.74 | | (18) all_58_11 = e2 & op(e1, e0) = e2
% 158.60/27.74 | |
% 158.60/27.74 | | ALPHA: (18) implies:
% 158.60/27.74 | | (19) all_58_11 = e2
% 158.60/27.74 | |
% 158.60/27.74 | | COMBINE_EQS: (16), (19) imply:
% 158.60/27.74 | | (20) e3 = e2
% 158.60/27.74 | |
% 158.60/27.74 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 158.60/27.74 | | (20) are inconsistent by sub-proof #777.
% 158.60/27.74 | |
% 158.60/27.74 | End of split
% 158.60/27.74 |
% 158.60/27.74 End of proof
% 158.60/27.74
% 158.60/27.74 Sub-proof #469 shows that the following formulas are inconsistent:
% 158.60/27.74 ----------------------------------------------------------------
% 158.60/27.74 (1) all_56_14 = e3
% 158.60/27.74 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.74 (3) all_54_13 = all_52_7
% 158.60/27.74 (4) ~ (all_52_7 = e3)
% 158.60/27.74 (5) ~ (all_52_11 = e3)
% 158.60/27.74 (6) all_58_12 = e3
% 158.60/27.74 (7) all_58_7 = e2
% 158.60/27.74 (8) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.74 (9) ~ (all_52_7 = all_52_11)
% 158.60/27.74 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.74 (11) op(e2, e3) = all_52_1
% 158.60/27.74 (12) ~ (all_52_13 = e3)
% 158.60/27.74 (13) all_54_2 = all_52_8
% 158.60/27.74 (14) ~ (all_52_8 = all_52_9)
% 158.60/27.74 (15) ~ (e3 = e0)
% 158.60/27.74 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.74 (17) ~ (all_52_9 = all_52_13)
% 158.60/27.74 (18) ~ (e2 = e0)
% 158.60/27.74 (19) ~ (all_52_9 = e3)
% 158.60/27.74 (20) op(e2, e3) = e2
% 158.60/27.74 (21) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.60/27.74 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.60/27.74 (22) ~ (e3 = e1)
% 158.60/27.74 (23) all_56_12 = e1
% 158.60/27.74 (24) all_58_1 = e1
% 158.60/27.74 (25) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.74 (26) all_54_7 = all_52_13
% 158.60/27.74 (27) ~ (all_52_13 = e2)
% 158.60/27.74 (28) all_56_15 = all_4_2
% 158.60/27.74 (29) ~ (all_52_9 = all_52_11)
% 158.60/27.74 (30) ~ (all_52_13 = all_4_2)
% 158.60/27.74 (31) all_54_6 = all_52_9
% 158.60/27.74 (32) ~ (e2 = e1)
% 158.60/27.74 (33) ~ (all_52_8 = all_52_11)
% 158.60/27.74 (34) ~ (e1 = e0)
% 158.60/27.74 (35) all_58_3 = e3
% 158.60/27.74 (36) all_56_13 = e3
% 158.60/27.74 (37) ~ (all_52_9 = e2)
% 158.60/27.74 (38) ~ (all_52_8 = e3)
% 158.60/27.74 (39) all_54_14 = all_52_11
% 158.60/27.74 (40) ~ (all_52_7 = all_4_2)
% 158.60/27.74 (41) op(e0, e2) = all_52_7
% 158.60/27.74 (42) all_58_0 = e0
% 158.60/27.74 (43) ~ (all_52_8 = e1)
% 158.60/27.74 (44) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.60/27.74 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.74 (46) ~ (e3 = e2)
% 158.60/27.74 (47) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.74 (48) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.74
% 158.60/27.74 Begin of proof
% 158.60/27.74 |
% 158.60/27.74 | BETA: splitting (21) gives:
% 158.60/27.74 |
% 158.60/27.74 | Case 1:
% 158.60/27.74 | |
% 158.60/27.74 | | (49) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 158.60/27.74 | | e0)
% 158.60/27.74 | |
% 158.60/27.74 | | BETA: splitting (49) gives:
% 158.60/27.74 | |
% 158.60/27.74 | | Case 1:
% 158.60/27.74 | | |
% 158.60/27.74 | | | (50) all_58_1 = e0 & op(e3, e2) = e0
% 158.60/27.74 | | |
% 158.60/27.74 | | | REF_CLOSE: (24), (34), (50) are inconsistent by sub-proof #1327.
% 158.60/27.74 | | |
% 158.60/27.74 | | Case 2:
% 158.60/27.74 | | |
% 158.60/27.74 | | | (51) all_58_3 = e0 & op(e2, e2) = e0
% 158.60/27.74 | | |
% 158.60/27.74 | | | REF_CLOSE: (15), (35), (51) are inconsistent by sub-proof #910.
% 158.60/27.74 | | |
% 158.60/27.74 | | End of split
% 158.60/27.74 | |
% 158.60/27.74 | Case 2:
% 158.60/27.74 | |
% 158.60/27.74 | | (52) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 158.60/27.74 | | e0)
% 158.60/27.74 | |
% 158.60/27.74 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.60/27.74 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (25),
% 158.60/27.74 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37),
% 158.60/27.74 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 158.60/27.74 | | (52) are inconsistent by sub-proof #470.
% 158.60/27.74 | |
% 158.60/27.74 | End of split
% 158.60/27.74 |
% 158.60/27.74 End of proof
% 158.60/27.74
% 158.60/27.74 Sub-proof #470 shows that the following formulas are inconsistent:
% 158.60/27.74 ----------------------------------------------------------------
% 158.60/27.74 (1) all_56_14 = e3
% 158.60/27.74 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.74 (3) all_54_13 = all_52_7
% 158.60/27.74 (4) ~ (all_52_7 = e3)
% 158.60/27.74 (5) ~ (all_52_11 = e3)
% 158.60/27.74 (6) all_58_12 = e3
% 158.60/27.74 (7) all_58_7 = e2
% 158.60/27.74 (8) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.74 (9) ~ (all_52_7 = all_52_11)
% 158.60/27.74 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.74 (11) op(e2, e3) = all_52_1
% 158.60/27.74 (12) ~ (all_52_13 = e3)
% 158.60/27.74 (13) all_54_2 = all_52_8
% 158.60/27.74 (14) ~ (all_52_8 = all_52_9)
% 158.60/27.74 (15) ~ (e3 = e0)
% 158.60/27.74 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.74 (17) ~ (all_52_9 = all_52_13)
% 158.60/27.74 (18) ~ (e2 = e0)
% 158.60/27.74 (19) ~ (all_52_9 = e3)
% 158.60/27.74 (20) op(e2, e3) = e2
% 158.60/27.74 (21) ~ (e3 = e1)
% 158.60/27.74 (22) all_56_12 = e1
% 158.60/27.74 (23) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.74 (24) all_54_7 = all_52_13
% 158.60/27.74 (25) ~ (all_52_13 = e2)
% 158.60/27.74 (26) all_56_15 = all_4_2
% 158.60/27.74 (27) ~ (all_52_9 = all_52_11)
% 158.60/27.74 (28) ~ (all_52_13 = all_4_2)
% 158.60/27.74 (29) all_54_6 = all_52_9
% 158.60/27.74 (30) ~ (e2 = e1)
% 158.60/27.74 (31) ~ (all_52_8 = all_52_11)
% 158.60/27.74 (32) ~ (e1 = e0)
% 158.60/27.74 (33) all_56_13 = e3
% 158.60/27.74 (34) ~ (all_52_9 = e2)
% 158.60/27.74 (35) ~ (all_52_8 = e3)
% 158.60/27.74 (36) all_54_14 = all_52_11
% 158.60/27.74 (37) ~ (all_52_7 = all_4_2)
% 158.60/27.74 (38) op(e0, e2) = all_52_7
% 158.60/27.74 (39) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.60/27.74 (40) all_58_0 = e0
% 158.60/27.74 (41) ~ (all_52_8 = e1)
% 158.60/27.74 (42) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.60/27.74 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.74 (44) ~ (e3 = e2)
% 158.60/27.74 (45) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.74 (46) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.74
% 158.60/27.74 Begin of proof
% 158.60/27.74 |
% 158.60/27.74 | BETA: splitting (39) gives:
% 158.60/27.74 |
% 158.60/27.74 | Case 1:
% 158.60/27.74 | |
% 158.60/27.74 | | (47) all_58_7 = e0 & op(e1, e2) = e0
% 158.60/27.74 | |
% 158.60/27.74 | | ALPHA: (47) implies:
% 158.60/27.74 | | (48) all_58_7 = e0
% 158.60/27.74 | |
% 158.60/27.74 | | REF_CLOSE: (7), (18), (48) are inconsistent by sub-proof #1086.
% 158.60/27.74 | |
% 158.60/27.74 | Case 2:
% 158.60/27.74 | |
% 158.60/27.74 | | (49) all_58_13 = e0 & op(e0, e2) = e0
% 158.60/27.74 | |
% 158.60/27.74 | | ALPHA: (49) implies:
% 158.60/27.74 | | (50) op(e0, e2) = e0
% 158.60/27.74 | |
% 158.60/27.74 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 158.60/27.74 | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 158.60/27.74 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 158.60/27.74 | | (37), (38), (40), (41), (42), (43), (44), (45), (46), (50) are
% 158.60/27.74 | | inconsistent by sub-proof #471.
% 158.60/27.74 | |
% 158.60/27.74 | End of split
% 158.60/27.74 |
% 158.60/27.74 End of proof
% 158.60/27.74
% 158.60/27.74 Sub-proof #471 shows that the following formulas are inconsistent:
% 158.60/27.74 ----------------------------------------------------------------
% 158.60/27.74 (1) all_56_14 = e3
% 158.60/27.74 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.74 (3) all_54_13 = all_52_7
% 158.60/27.74 (4) ~ (all_52_7 = e3)
% 158.60/27.74 (5) ~ (all_52_11 = e3)
% 158.60/27.74 (6) all_58_12 = e3
% 158.60/27.74 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.74 (8) ~ (all_52_7 = all_52_11)
% 158.60/27.74 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.74 (10) op(e2, e3) = all_52_1
% 158.60/27.74 (11) ~ (all_52_13 = e3)
% 158.60/27.74 (12) all_54_2 = all_52_8
% 158.60/27.74 (13) ~ (all_52_8 = all_52_9)
% 158.60/27.74 (14) ~ (e3 = e0)
% 158.60/27.74 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.74 (16) ~ (all_52_9 = all_52_13)
% 158.60/27.74 (17) ~ (all_52_9 = e3)
% 158.60/27.74 (18) op(e2, e3) = e2
% 158.60/27.74 (19) ~ (e3 = e1)
% 158.60/27.74 (20) all_56_12 = e1
% 158.60/27.74 (21) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.74 (22) all_54_7 = all_52_13
% 158.60/27.74 (23) ~ (all_52_13 = e2)
% 158.60/27.74 (24) all_56_15 = all_4_2
% 158.60/27.74 (25) ~ (all_52_9 = all_52_11)
% 158.60/27.74 (26) ~ (all_52_13 = all_4_2)
% 158.60/27.74 (27) all_54_6 = all_52_9
% 158.60/27.74 (28) op(e0, e2) = e0
% 158.60/27.74 (29) ~ (e2 = e1)
% 158.60/27.74 (30) ~ (all_52_8 = all_52_11)
% 158.60/27.74 (31) ~ (e1 = e0)
% 158.60/27.74 (32) all_56_13 = e3
% 158.60/27.74 (33) ~ (all_52_9 = e2)
% 158.60/27.74 (34) ~ (all_52_8 = e3)
% 158.60/27.74 (35) all_54_14 = all_52_11
% 158.60/27.74 (36) ~ (all_52_7 = all_4_2)
% 158.60/27.74 (37) op(e0, e2) = all_52_7
% 158.60/27.74 (38) all_58_0 = e0
% 158.60/27.74 (39) ~ (all_52_8 = e1)
% 158.60/27.74 (40) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.60/27.74 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.74 (42) ~ (e3 = e2)
% 158.60/27.74 (43) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.74 (44) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.74
% 158.60/27.74 Begin of proof
% 158.60/27.74 |
% 158.60/27.74 | BETA: splitting (44) gives:
% 158.60/27.74 |
% 158.60/27.74 | Case 1:
% 158.60/27.74 | |
% 158.60/27.74 | | (45) all_56_12 = e3
% 158.60/27.74 | |
% 158.60/27.74 | | COMBINE_EQS: (20), (45) imply:
% 158.60/27.74 | | (46) e3 = e1
% 158.60/27.74 | |
% 158.60/27.74 | | REDUCE: (19), (46) imply:
% 158.60/27.74 | | (47) $false
% 158.60/27.74 | |
% 158.60/27.74 | | CLOSE: (47) is inconsistent.
% 158.60/27.74 | |
% 158.60/27.74 | Case 2:
% 158.60/27.74 | |
% 158.60/27.74 | | (48) ~ (all_56_12 = e3)
% 158.60/27.74 | | (49) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.74 | |
% 158.60/27.74 | | REDUCE: (20), (48) imply:
% 158.60/27.74 | | (50) ~ (e3 = e1)
% 158.60/27.74 | |
% 158.60/27.74 | | BETA: splitting (49) gives:
% 158.60/27.74 | |
% 158.60/27.74 | | Case 1:
% 158.60/27.74 | | |
% 158.60/27.74 | | | (51) all_56_13 = e2
% 158.60/27.74 | | |
% 158.60/27.74 | | | REF_CLOSE: (6), (9), (10), (14), (15), (18), (19), (29), (31), (32), (38),
% 158.60/27.74 | | | (41), (42), (51) are inconsistent by sub-proof #473.
% 158.60/27.74 | | |
% 158.60/27.74 | | Case 2:
% 158.60/27.74 | | |
% 158.60/27.74 | | | (52) all_56_14 = e1 | all_56_15 = e0
% 158.60/27.74 | | |
% 158.60/27.74 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12), (13), (16),
% 158.60/27.74 | | | (17), (19), (21), (22), (23), (24), (25), (26), (27), (28),
% 158.60/27.74 | | | (30), (33), (34), (35), (36), (37), (39), (40), (41), (43),
% 158.60/27.74 | | | (52) are inconsistent by sub-proof #472.
% 158.60/27.74 | | |
% 158.60/27.74 | | End of split
% 158.60/27.74 | |
% 158.60/27.74 | End of split
% 158.60/27.74 |
% 158.60/27.74 End of proof
% 158.60/27.74
% 158.60/27.74 Sub-proof #472 shows that the following formulas are inconsistent:
% 158.60/27.74 ----------------------------------------------------------------
% 158.60/27.74 (1) all_56_14 = e3
% 158.60/27.74 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.74 (3) all_54_13 = all_52_7
% 158.60/27.74 (4) ~ (all_52_7 = e3)
% 158.60/27.74 (5) ~ (all_52_11 = e3)
% 158.60/27.74 (6) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.74 (7) ~ (all_52_7 = all_52_11)
% 158.60/27.74 (8) ~ (all_52_13 = e3)
% 158.60/27.74 (9) all_54_2 = all_52_8
% 158.60/27.74 (10) ~ (all_52_8 = all_52_9)
% 158.60/27.74 (11) ~ (all_52_9 = all_52_13)
% 158.60/27.74 (12) all_56_14 = e1 | all_56_15 = e0
% 158.60/27.74 (13) ~ (all_52_9 = e3)
% 158.60/27.74 (14) ~ (e3 = e1)
% 158.60/27.74 (15) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.74 (16) all_54_7 = all_52_13
% 158.60/27.74 (17) ~ (all_52_13 = e2)
% 158.60/27.74 (18) all_56_15 = all_4_2
% 158.60/27.74 (19) ~ (all_52_9 = all_52_11)
% 158.60/27.74 (20) ~ (all_52_13 = all_4_2)
% 158.60/27.74 (21) all_54_6 = all_52_9
% 158.60/27.74 (22) op(e0, e2) = e0
% 158.60/27.74 (23) ~ (all_52_8 = all_52_11)
% 158.60/27.74 (24) ~ (all_52_9 = e2)
% 158.60/27.74 (25) ~ (all_52_8 = e3)
% 158.60/27.74 (26) all_54_14 = all_52_11
% 158.60/27.74 (27) ~ (all_52_7 = all_4_2)
% 158.60/27.74 (28) op(e0, e2) = all_52_7
% 158.60/27.74 (29) ~ (all_52_8 = e1)
% 158.60/27.74 (30) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.60/27.74 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.74 (32) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.74
% 158.60/27.74 Begin of proof
% 158.60/27.74 |
% 158.60/27.74 | BETA: splitting (12) gives:
% 158.60/27.74 |
% 158.60/27.74 | Case 1:
% 158.60/27.74 | |
% 158.60/27.74 | | (33) all_56_14 = e1
% 158.60/27.74 | |
% 158.60/27.74 | | COMBINE_EQS: (1), (33) imply:
% 158.60/27.74 | | (34) e3 = e1
% 158.60/27.74 | |
% 158.60/27.74 | | REDUCE: (14), (34) imply:
% 158.60/27.74 | | (35) $false
% 158.60/27.74 | |
% 158.60/27.74 | | CLOSE: (35) is inconsistent.
% 158.60/27.74 | |
% 158.60/27.74 | Case 2:
% 158.60/27.74 | |
% 158.60/27.74 | | (36) all_56_15 = e0
% 158.60/27.74 | |
% 158.60/27.74 | | COMBINE_EQS: (18), (36) imply:
% 158.60/27.74 | | (37) all_4_2 = e0
% 158.60/27.74 | |
% 158.60/27.74 | | REDUCE: (27), (37) imply:
% 158.60/27.74 | | (38) ~ (all_52_7 = e0)
% 158.60/27.74 | |
% 158.60/27.74 | | REDUCE: (20), (37) imply:
% 158.60/27.74 | | (39) ~ (all_52_13 = e0)
% 158.60/27.74 | |
% 158.60/27.74 | | BETA: splitting (6) gives:
% 158.60/27.74 | |
% 158.60/27.74 | | Case 1:
% 158.60/27.74 | | |
% 158.60/27.74 | | | (40) all_54_7 = e3
% 158.60/27.74 | | |
% 158.60/27.74 | | | REF_CLOSE: (8), (16), (40) are inconsistent by sub-proof #1428.
% 158.60/27.74 | | |
% 158.60/27.74 | | Case 2:
% 158.60/27.74 | | |
% 158.60/27.74 | | | (41) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.74 | | |
% 158.60/27.74 | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (13), (15), (16),
% 158.60/27.74 | | | (17), (19), (21), (22), (23), (24), (25), (26), (28), (29),
% 158.60/27.74 | | | (30), (31), (32), (38), (39), (41) are inconsistent by
% 158.60/27.74 | | | sub-proof #559.
% 158.60/27.74 | | |
% 158.60/27.74 | | End of split
% 158.60/27.74 | |
% 158.60/27.74 | End of split
% 158.60/27.74 |
% 158.60/27.74 End of proof
% 158.60/27.74
% 158.60/27.74 Sub-proof #473 shows that the following formulas are inconsistent:
% 158.60/27.74 ----------------------------------------------------------------
% 158.60/27.74 (1) all_58_12 = e3
% 158.60/27.74 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.74 (3) op(e2, e3) = all_52_1
% 158.60/27.74 (4) ~ (e3 = e0)
% 158.60/27.74 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.74 (6) op(e2, e3) = e2
% 158.60/27.74 (7) ~ (e3 = e1)
% 158.60/27.74 (8) all_56_13 = e2
% 158.60/27.74 (9) ~ (e2 = e1)
% 158.60/27.74 (10) ~ (e1 = e0)
% 158.60/27.74 (11) all_56_13 = e3
% 158.60/27.74 (12) all_58_0 = e0
% 158.60/27.74 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.74 (14) ~ (e3 = e2)
% 158.60/27.74
% 158.60/27.74 Begin of proof
% 158.60/27.74 |
% 158.60/27.74 | COMBINE_EQS: (8), (11) imply:
% 158.60/27.74 | (15) e3 = e2
% 158.60/27.74 |
% 158.60/27.74 | COMBINE_EQS: (1), (15) imply:
% 158.60/27.74 | (16) all_58_12 = e2
% 158.60/27.74 |
% 158.60/27.74 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), (16) are
% 158.60/27.74 | inconsistent by sub-proof #1066.
% 158.60/27.74 |
% 158.60/27.74 End of proof
% 158.60/27.74
% 158.60/27.74 Sub-proof #474 shows that the following formulas are inconsistent:
% 158.60/27.74 ----------------------------------------------------------------
% 158.60/27.74 (1) all_56_14 = e3
% 158.60/27.74 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.74 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.60/27.74 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.60/27.74 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.60/27.74 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.60/27.74 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.60/27.74 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.60/27.74 (6) ~ (all_52_7 = e3)
% 158.60/27.74 (7) ~ (all_52_11 = e3)
% 158.60/27.74 (8) op(e3, e3) = all_28_1
% 158.60/27.74 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.74 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.74 (11) ~ (all_4_2 = e2)
% 158.60/27.74 (12) all_58_14 = e2
% 158.60/27.74 (13) op(e2, e3) = all_52_1
% 158.60/27.74 (14) ~ (all_52_13 = e3)
% 158.60/27.74 (15) all_54_2 = all_52_8
% 158.60/27.74 (16) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.60/27.74 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.60/27.74 (17) ~ (all_52_8 = all_52_9)
% 158.60/27.74 (18) ~ (e3 = e0)
% 158.60/27.74 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.74 (20) ~ (all_52_9 = all_52_13)
% 158.60/27.74 (21) ~ (e2 = e0)
% 158.60/27.74 (22) ~ (all_52_9 = e3)
% 158.60/27.74 (23) all_58_6 = e0
% 158.60/27.74 (24) op(e2, e3) = e2
% 158.60/27.74 (25) ~ (e3 = e1)
% 158.60/27.74 (26) all_56_12 = e1
% 158.60/27.74 (27) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.60/27.74 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.60/27.74 (28) ~ (all_4_2 = e1)
% 158.60/27.74 (29) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.74 (30) all_54_7 = all_52_13
% 158.60/27.74 (31) op(e3, e3) = e1
% 158.60/27.74 (32) ~ (all_52_13 = e2)
% 158.60/27.74 (33) all_56_15 = all_4_2
% 158.60/27.74 (34) ~ (all_52_9 = all_52_11)
% 158.60/27.74 (35) ~ (all_52_13 = all_4_2)
% 158.60/27.74 (36) all_58_0 = e3
% 158.60/27.74 (37) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.60/27.74 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.60/27.74 (38) all_54_6 = all_52_9
% 158.60/27.74 (39) ~ (e2 = e1)
% 158.60/27.74 (40) op(e3, e3) = e3
% 158.60/27.74 (41) ~ (all_52_8 = all_52_11)
% 158.60/27.74 (42) ~ (e1 = e0)
% 158.60/27.74 (43) all_58_4 = e3
% 158.60/27.74 (44) all_58_3 = e3
% 158.60/27.74 (45) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.60/27.74 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.60/27.74 e3)
% 158.60/27.74 (46) all_56_13 = e3
% 158.60/27.74 (47) ~ (all_52_9 = e2)
% 158.60/27.74 (48) ~ (all_52_8 = e3)
% 158.60/27.74 (49) all_54_14 = all_52_11
% 158.60/27.74 (50) op(e1, e3) = e1
% 158.60/27.74 (51) op(e1, e0) = e3
% 158.60/27.74 (52) all_58_9 = e2
% 158.60/27.74 (53) op(e0, e2) = all_52_7
% 158.60/27.74 (54) op(e3, e3) = all_22_1
% 158.60/27.74 (55) ~ (all_52_8 = e1)
% 158.60/27.74 (56) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.60/27.74 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.74 (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.74 (58) ~ (e3 = e2)
% 158.60/27.74 (59) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.60/27.74 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.60/27.74 (60) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.60/27.74 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.60/27.74 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.60/27.74 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.60/27.74 (61) all_58_11 = e3
% 158.60/27.75 (62) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.75 (63) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.75
% 158.60/27.75 Begin of proof
% 158.60/27.75 |
% 158.60/27.75 | BETA: splitting (3) gives:
% 158.60/27.75 |
% 158.60/27.75 | Case 1:
% 158.60/27.75 | |
% 158.60/27.75 | | (64) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 158.60/27.75 | | e1)
% 158.60/27.75 | |
% 158.60/27.75 | | BETA: splitting (64) gives:
% 158.60/27.75 | |
% 158.60/27.75 | | Case 1:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (65) all_58_6 = e1 & op(e1, e3) = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (65) implies:
% 158.60/27.75 | | | (66) all_58_6 = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (23), (42), (66) are inconsistent by sub-proof #735.
% 158.60/27.75 | | |
% 158.60/27.75 | | Case 2:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (67) all_58_7 = e1 & op(e1, e2) = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (67) implies:
% 158.60/27.75 | | | (68) all_58_7 = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | BETA: splitting (60) gives:
% 158.60/27.75 | | |
% 158.60/27.75 | | | Case 1:
% 158.60/27.75 | | | |
% 158.60/27.75 | | | | (69) all_58_15 = e0 & op(e0, e0) = e0
% 158.60/27.75 | | | |
% 158.60/27.75 | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.60/27.75 | | | | (15), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 158.60/27.75 | | | | (28), (29), (30), (31), (32), (33), (34), (35), (38), (39),
% 158.60/27.75 | | | | (40), (41), (42), (45), (46), (47), (48), (49), (50), (53),
% 158.60/27.75 | | | | (54), (55), (56), (57), (58), (62), (63), (69) are
% 158.60/27.75 | | | | inconsistent by sub-proof #476.
% 158.60/27.75 | | | |
% 158.60/27.75 | | | Case 2:
% 158.60/27.75 | | | |
% 158.60/27.75 | | | | (70) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 158.60/27.75 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 158.60/27.75 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 158.60/27.75 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.60/27.75 | | | |
% 158.60/27.75 | | | | ALPHA: (70) implies:
% 158.60/27.75 | | | | (71) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 158.60/27.75 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.60/27.75 | | | |
% 158.60/27.75 | | | | BETA: splitting (71) gives:
% 158.60/27.75 | | | |
% 158.60/27.75 | | | | Case 1:
% 158.60/27.75 | | | | |
% 158.60/27.75 | | | | | (72) all_58_12 = e0 & op(e0, e3) = e0
% 158.60/27.75 | | | | |
% 158.60/27.75 | | | | | ALPHA: (72) implies:
% 158.60/27.75 | | | | | (73) all_58_12 = e0
% 158.60/27.75 | | | | |
% 158.60/27.75 | | | | | REF_CLOSE: (10), (12), (13), (16), (18), (19), (21), (24), (25), (27),
% 158.60/27.75 | | | | | (37), (39), (42), (43), (57), (58), (61), (68), (73) are
% 158.60/27.75 | | | | | inconsistent by sub-proof #725.
% 158.60/27.75 | | | | |
% 158.60/27.75 | | | | Case 2:
% 158.60/27.75 | | | | |
% 158.60/27.75 | | | | | (74) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 158.60/27.75 | | | | | e1) = e0)
% 158.60/27.75 | | | | |
% 158.60/27.75 | | | | | BETA: splitting (74) gives:
% 158.60/27.75 | | | | |
% 158.60/27.75 | | | | | Case 1:
% 158.60/27.75 | | | | | |
% 158.60/27.75 | | | | | | (75) all_58_13 = e0 & op(e0, e2) = e0
% 158.60/27.75 | | | | | |
% 158.60/27.75 | | | | | | REF_CLOSE: (4), (10), (12), (13), (16), (18), (19), (21), (24),
% 158.60/27.75 | | | | | | (25), (27), (36), (37), (39), (42), (43), (44), (52),
% 158.60/27.75 | | | | | | (56), (57), (58), (59), (61), (75) are inconsistent by
% 158.60/27.75 | | | | | | sub-proof #618.
% 158.60/27.75 | | | | | |
% 158.60/27.75 | | | | | Case 2:
% 158.60/27.75 | | | | | |
% 158.60/27.75 | | | | | | (76) all_58_14 = e0 & op(e0, e1) = e0
% 158.60/27.75 | | | | | |
% 158.60/27.75 | | | | | | REF_CLOSE: (12), (21), (76) are inconsistent by sub-proof #1341.
% 158.60/27.75 | | | | | |
% 158.60/27.75 | | | | | End of split
% 158.60/27.75 | | | | |
% 158.60/27.75 | | | | End of split
% 158.60/27.75 | | | |
% 158.60/27.75 | | | End of split
% 158.60/27.75 | | |
% 158.60/27.75 | | End of split
% 158.60/27.75 | |
% 158.60/27.75 | Case 2:
% 158.60/27.75 | |
% 158.60/27.75 | | (77) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 158.60/27.75 | | e1)
% 158.60/27.75 | |
% 158.60/27.75 | | BETA: splitting (77) gives:
% 158.60/27.75 | |
% 158.60/27.75 | | Case 1:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (78) all_58_8 = e1 & op(e1, e1) = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (78) implies:
% 158.60/27.75 | | | (79) all_58_8 = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 158.60/27.75 | | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 158.60/27.75 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.60/27.75 | | | (35), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 158.60/27.75 | | | (47), (48), (49), (50), (52), (53), (54), (55), (56), (57),
% 158.60/27.75 | | | (58), (60), (61), (62), (63), (79) are inconsistent by
% 158.60/27.75 | | | sub-proof #475.
% 158.60/27.75 | | |
% 158.60/27.75 | | Case 2:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (80) all_58_11 = e1 & op(e1, e0) = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (80) implies:
% 158.60/27.75 | | | (81) op(e1, e0) = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (25), (51), (57), (81) are inconsistent by sub-proof #1275.
% 158.60/27.75 | | |
% 158.60/27.75 | | End of split
% 158.60/27.75 | |
% 158.60/27.75 | End of split
% 158.60/27.75 |
% 158.60/27.75 End of proof
% 158.60/27.75
% 158.60/27.75 Sub-proof #475 shows that the following formulas are inconsistent:
% 158.60/27.75 ----------------------------------------------------------------
% 158.60/27.75 (1) all_56_14 = e3
% 158.60/27.75 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.75 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.60/27.75 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.60/27.75 (4) ~ (all_52_7 = e3)
% 158.60/27.75 (5) ~ (all_52_11 = e3)
% 158.60/27.75 (6) op(e3, e3) = all_28_1
% 158.60/27.75 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.75 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.75 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.75 (9) ~ (all_4_2 = e2)
% 158.60/27.75 (10) all_58_14 = e2
% 158.60/27.75 (11) op(e2, e3) = all_52_1
% 158.60/27.75 (12) ~ (all_52_13 = e3)
% 158.60/27.75 (13) all_54_2 = all_52_8
% 158.60/27.75 (14) ~ (all_52_8 = all_52_9)
% 158.60/27.75 (15) ~ (e3 = e0)
% 158.60/27.75 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.75 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.75 (17) ~ (all_52_9 = all_52_13)
% 158.60/27.75 (18) ~ (e2 = e0)
% 158.60/27.75 (19) ~ (all_52_9 = e3)
% 158.60/27.75 (20) all_58_6 = e0
% 158.60/27.75 (21) op(e2, e3) = e2
% 158.60/27.75 (22) ~ (e3 = e1)
% 158.60/27.75 (23) all_56_12 = e1
% 158.60/27.75 (24) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.60/27.75 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.60/27.75 (25) ~ (all_4_2 = e1)
% 158.60/27.75 (26) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.75 (27) all_54_7 = all_52_13
% 158.60/27.75 (28) op(e3, e3) = e1
% 158.60/27.75 (29) ~ (all_52_13 = e2)
% 158.60/27.75 (30) all_56_15 = all_4_2
% 158.60/27.75 (31) ~ (all_52_9 = all_52_11)
% 158.60/27.75 (32) ~ (all_52_13 = all_4_2)
% 158.60/27.75 (33) all_54_6 = all_52_9
% 158.60/27.75 (34) ~ (e2 = e1)
% 158.60/27.75 (35) op(e3, e3) = e3
% 158.60/27.75 (36) ~ (all_52_8 = all_52_11)
% 158.60/27.75 (37) ~ (e1 = e0)
% 158.60/27.75 (38) all_58_4 = e3
% 158.60/27.75 (39) all_58_3 = e3
% 158.60/27.75 (40) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.60/27.75 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.60/27.75 e3)
% 158.60/27.75 (41) all_56_13 = e3
% 158.60/27.75 (42) ~ (all_52_9 = e2)
% 158.60/27.75 (43) ~ (all_52_8 = e3)
% 158.60/27.75 (44) all_54_14 = all_52_11
% 158.60/27.75 (45) op(e1, e3) = e1
% 158.60/27.75 (46) all_58_9 = e2
% 158.60/27.75 (47) op(e0, e2) = all_52_7
% 158.60/27.75 (48) op(e3, e3) = all_22_1
% 158.60/27.75 (49) ~ (all_52_8 = e1)
% 158.60/27.75 (50) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.60/27.75 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.75 (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.75 (52) ~ (e3 = e2)
% 158.60/27.75 (53) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.60/27.75 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.60/27.75 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.60/27.75 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.60/27.75 (54) all_58_11 = e3
% 158.60/27.75 (55) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.75 (56) all_58_8 = e1
% 158.60/27.75 (57) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.75
% 158.60/27.75 Begin of proof
% 158.60/27.75 |
% 158.60/27.75 | BETA: splitting (53) gives:
% 158.60/27.75 |
% 158.60/27.75 | Case 1:
% 158.60/27.75 | |
% 158.60/27.75 | | (58) all_58_15 = e0 & op(e0, e0) = e0
% 158.60/27.75 | |
% 158.60/27.75 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 158.60/27.75 | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (25), (26),
% 158.60/27.75 | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 158.60/27.75 | | (40), (41), (42), (43), (44), (45), (47), (48), (49), (50), (51),
% 158.60/27.75 | | (52), (55), (57), (58) are inconsistent by sub-proof #476.
% 158.60/27.75 | |
% 158.60/27.75 | Case 2:
% 158.60/27.75 | |
% 158.60/27.75 | | (59) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 158.60/27.75 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 158.60/27.75 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 158.60/27.75 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.60/27.75 | |
% 158.60/27.75 | | REF_CLOSE: (3), (10), (15), (18), (21), (22), (24), (34), (37), (38), (39),
% 158.60/27.75 | | (46), (51), (54), (56), (59) are inconsistent by sub-proof #704.
% 158.60/27.75 | |
% 158.60/27.75 | End of split
% 158.60/27.75 |
% 158.60/27.75 End of proof
% 158.60/27.75
% 158.60/27.75 Sub-proof #476 shows that the following formulas are inconsistent:
% 158.60/27.75 ----------------------------------------------------------------
% 158.60/27.75 (1) all_56_14 = e3
% 158.60/27.75 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.75 (3) ~ (all_52_7 = e3)
% 158.60/27.75 (4) ~ (all_52_11 = e3)
% 158.60/27.75 (5) op(e3, e3) = all_28_1
% 158.60/27.75 (6) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.75 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.75 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.75 (8) ~ (all_4_2 = e2)
% 158.60/27.75 (9) all_58_14 = e2
% 158.60/27.75 (10) op(e2, e3) = all_52_1
% 158.60/27.75 (11) ~ (all_52_13 = e3)
% 158.60/27.75 (12) all_54_2 = all_52_8
% 158.60/27.75 (13) ~ (all_52_8 = all_52_9)
% 158.60/27.75 (14) ~ (e3 = e0)
% 158.60/27.75 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.75 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.75 (16) ~ (all_52_9 = all_52_13)
% 158.60/27.75 (17) ~ (all_52_9 = e3)
% 158.60/27.75 (18) all_58_6 = e0
% 158.60/27.75 (19) op(e2, e3) = e2
% 158.60/27.75 (20) ~ (e3 = e1)
% 158.60/27.75 (21) all_56_12 = e1
% 158.60/27.75 (22) ~ (all_4_2 = e1)
% 158.60/27.75 (23) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.75 (24) all_54_7 = all_52_13
% 158.60/27.75 (25) op(e3, e3) = e1
% 158.60/27.75 (26) ~ (all_52_13 = e2)
% 158.60/27.75 (27) all_58_15 = e0 & op(e0, e0) = e0
% 158.60/27.75 (28) all_56_15 = all_4_2
% 158.60/27.75 (29) ~ (all_52_9 = all_52_11)
% 158.60/27.75 (30) ~ (all_52_13 = all_4_2)
% 158.60/27.75 (31) all_54_6 = all_52_9
% 158.60/27.75 (32) ~ (e2 = e1)
% 158.60/27.75 (33) op(e3, e3) = e3
% 158.60/27.75 (34) ~ (all_52_8 = all_52_11)
% 158.60/27.75 (35) ~ (e1 = e0)
% 158.60/27.75 (36) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.60/27.75 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.60/27.75 e3)
% 158.60/27.75 (37) all_56_13 = e3
% 158.60/27.75 (38) ~ (all_52_9 = e2)
% 158.60/27.75 (39) ~ (all_52_8 = e3)
% 158.60/27.75 (40) all_54_14 = all_52_11
% 158.60/27.75 (41) op(e1, e3) = e1
% 158.60/27.75 (42) op(e0, e2) = all_52_7
% 158.60/27.75 (43) op(e3, e3) = all_22_1
% 158.60/27.75 (44) ~ (all_52_8 = e1)
% 158.60/27.75 (45) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.60/27.75 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.75 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.75 (47) ~ (e3 = e2)
% 158.60/27.75 (48) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.75 (49) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.75
% 158.60/27.75 Begin of proof
% 158.60/27.75 |
% 158.60/27.75 | ALPHA: (27) implies:
% 158.60/27.75 | (50) op(e0, e0) = e0
% 158.60/27.75 |
% 158.60/27.75 | BETA: splitting (36) gives:
% 158.60/27.75 |
% 158.60/27.75 | Case 1:
% 158.60/27.75 | |
% 158.60/27.75 | | (51) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 158.60/27.75 | | e3)
% 158.60/27.75 | |
% 158.60/27.75 | | BETA: splitting (51) gives:
% 158.60/27.75 | |
% 158.60/27.75 | | Case 1:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (52) all_58_12 = e3 & op(e0, e3) = e3
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (52) implies:
% 158.60/27.75 | | | (53) all_58_12 = e3
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (12), (13), (14),
% 158.60/27.75 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 158.60/27.75 | | | (26), (28), (29), (30), (31), (32), (34), (35), (37), (38),
% 158.60/27.75 | | | (39), (40), (41), (44), (45), (46), (47), (48), (49), (53) are
% 158.60/27.75 | | | inconsistent by sub-proof #477.
% 158.60/27.75 | | |
% 158.60/27.75 | | Case 2:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (54) all_58_13 = e3 & op(e0, e2) = e3
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (3), (42), (46), (54) are inconsistent by sub-proof #1449.
% 158.60/27.75 | | |
% 158.60/27.75 | | End of split
% 158.60/27.75 | |
% 158.60/27.75 | Case 2:
% 158.60/27.75 | |
% 158.60/27.75 | | (55) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.60/27.75 | | e3)
% 158.60/27.75 | |
% 158.60/27.75 | | BETA: splitting (55) gives:
% 158.60/27.75 | |
% 158.60/27.75 | | Case 1:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (56) all_58_14 = e3 & op(e0, e1) = e3
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (56) implies:
% 158.60/27.75 | | | (57) all_58_14 = e3
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (9), (47), (57) are inconsistent by sub-proof #1405.
% 158.60/27.75 | | |
% 158.60/27.75 | | Case 2:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (58) all_58_15 = e3 & op(e0, e0) = e3
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (58) implies:
% 158.60/27.75 | | | (59) op(e0, e0) = e3
% 158.60/27.75 | | |
% 158.60/27.75 | | | GROUND_INST: instantiating (46) with e0, e3, e0, e0, simplifying with
% 158.60/27.75 | | | (50), (59) gives:
% 158.60/27.75 | | | (60) e3 = e0
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (5), (25), (33), (35), (43), (46), (60) are inconsistent by
% 158.60/27.75 | | | sub-proof #659.
% 158.60/27.75 | | |
% 158.60/27.75 | | End of split
% 158.60/27.75 | |
% 158.60/27.75 | End of split
% 158.60/27.75 |
% 158.60/27.75 End of proof
% 158.60/27.75
% 158.60/27.75 Sub-proof #477 shows that the following formulas are inconsistent:
% 158.60/27.75 ----------------------------------------------------------------
% 158.60/27.75 (1) all_56_14 = e3
% 158.60/27.75 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.75 (3) ~ (all_52_11 = e3)
% 158.60/27.75 (4) all_58_12 = e3
% 158.60/27.75 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.75 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.75 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.75 (7) ~ (all_4_2 = e2)
% 158.60/27.75 (8) op(e2, e3) = all_52_1
% 158.60/27.75 (9) ~ (all_52_13 = e3)
% 158.60/27.75 (10) all_54_2 = all_52_8
% 158.60/27.75 (11) ~ (all_52_8 = all_52_9)
% 158.60/27.75 (12) ~ (e3 = e0)
% 158.60/27.75 (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.75 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.75 (14) ~ (all_52_9 = all_52_13)
% 158.60/27.75 (15) ~ (all_52_9 = e3)
% 158.60/27.75 (16) all_58_6 = e0
% 158.60/27.75 (17) op(e2, e3) = e2
% 158.60/27.75 (18) ~ (e3 = e1)
% 158.60/27.75 (19) all_56_12 = e1
% 158.60/27.75 (20) ~ (all_4_2 = e1)
% 158.60/27.75 (21) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.75 (22) all_54_7 = all_52_13
% 158.60/27.75 (23) ~ (all_52_13 = e2)
% 158.60/27.75 (24) all_56_15 = all_4_2
% 158.60/27.75 (25) ~ (all_52_9 = all_52_11)
% 158.60/27.75 (26) ~ (all_52_13 = all_4_2)
% 158.60/27.75 (27) all_54_6 = all_52_9
% 158.60/27.75 (28) ~ (e2 = e1)
% 158.60/27.75 (29) ~ (all_52_8 = all_52_11)
% 158.60/27.75 (30) ~ (e1 = e0)
% 158.60/27.75 (31) all_56_13 = e3
% 158.60/27.75 (32) ~ (all_52_9 = e2)
% 158.60/27.75 (33) ~ (all_52_8 = e3)
% 158.60/27.75 (34) all_54_14 = all_52_11
% 158.60/27.75 (35) op(e1, e3) = e1
% 158.60/27.75 (36) ~ (all_52_8 = e1)
% 158.60/27.75 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.60/27.75 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.75 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.75 (39) ~ (e3 = e2)
% 158.60/27.75 (40) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.75 (41) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.75
% 158.60/27.75 Begin of proof
% 158.60/27.75 |
% 158.60/27.75 | BETA: splitting (13) gives:
% 158.60/27.75 |
% 158.60/27.75 | Case 1:
% 158.60/27.75 | |
% 158.60/27.75 | | (42) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 158.60/27.75 | | e1)
% 158.60/27.75 | |
% 158.60/27.75 | | BETA: splitting (42) gives:
% 158.60/27.75 | |
% 158.60/27.75 | | Case 1:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (43) all_58_0 = e1 & op(e3, e3) = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (43) implies:
% 158.60/27.75 | | | (44) all_58_0 = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.60/27.75 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 158.60/27.75 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 158.60/27.75 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (44) are
% 158.60/27.75 | | | inconsistent by sub-proof #478.
% 158.60/27.75 | | |
% 158.60/27.75 | | Case 2:
% 158.60/27.75 | | |
% 158.60/27.75 | | | (45) all_58_2 = e1 & op(e2, e3) = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | ALPHA: (45) implies:
% 158.60/27.75 | | | (46) op(e2, e3) = e1
% 158.60/27.75 | | |
% 158.60/27.75 | | | REF_CLOSE: (17), (28), (38), (46) are inconsistent by sub-proof #1430.
% 158.60/27.75 | | |
% 158.60/27.75 | | End of split
% 158.60/27.75 | |
% 158.60/27.75 | Case 2:
% 158.60/27.75 | |
% 158.60/27.75 | | (47) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 158.60/27.75 | | e1)
% 158.60/27.75 | |
% 158.60/27.75 | | REF_CLOSE: (4), (16), (18), (30), (47) are inconsistent by sub-proof #734.
% 158.60/27.75 | |
% 158.60/27.75 | End of split
% 158.60/27.75 |
% 158.60/27.75 End of proof
% 158.60/27.75
% 158.60/27.75 Sub-proof #478 shows that the following formulas are inconsistent:
% 158.60/27.75 ----------------------------------------------------------------
% 158.60/27.75 (1) all_56_14 = e3
% 158.60/27.75 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.60/27.75 (3) ~ (all_52_11 = e3)
% 158.60/27.75 (4) all_58_12 = e3
% 158.60/27.75 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.60/27.75 (6) all_58_0 = e1
% 158.60/27.75 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.60/27.75 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.60/27.75 (8) ~ (all_4_2 = e2)
% 158.60/27.75 (9) op(e2, e3) = all_52_1
% 158.60/27.75 (10) ~ (all_52_13 = e3)
% 158.60/27.75 (11) all_54_2 = all_52_8
% 158.60/27.75 (12) ~ (all_52_8 = all_52_9)
% 158.60/27.75 (13) ~ (e3 = e0)
% 158.60/27.75 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.60/27.75 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.60/27.75 (15) ~ (all_52_9 = all_52_13)
% 158.60/27.75 (16) ~ (all_52_9 = e3)
% 158.60/27.75 (17) all_58_6 = e0
% 158.60/27.75 (18) op(e2, e3) = e2
% 158.60/27.75 (19) ~ (e3 = e1)
% 158.60/27.75 (20) all_56_12 = e1
% 158.60/27.75 (21) ~ (all_4_2 = e1)
% 158.60/27.75 (22) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.60/27.75 (23) all_54_7 = all_52_13
% 158.60/27.75 (24) ~ (all_52_13 = e2)
% 158.60/27.75 (25) all_56_15 = all_4_2
% 158.60/27.75 (26) ~ (all_52_9 = all_52_11)
% 158.60/27.75 (27) ~ (all_52_13 = all_4_2)
% 158.60/27.75 (28) all_54_6 = all_52_9
% 158.60/27.75 (29) ~ (e2 = e1)
% 158.60/27.75 (30) ~ (all_52_8 = all_52_11)
% 158.60/27.75 (31) ~ (e1 = e0)
% 158.60/27.75 (32) all_56_13 = e3
% 158.60/27.75 (33) ~ (all_52_9 = e2)
% 158.60/27.75 (34) ~ (all_52_8 = e3)
% 158.60/27.75 (35) all_54_14 = all_52_11
% 158.60/27.75 (36) op(e1, e3) = e1
% 158.60/27.75 (37) ~ (all_52_8 = e1)
% 158.60/27.75 (38) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.60/27.75 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.60/27.75 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.60/27.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.60/27.75 (40) ~ (e3 = e2)
% 158.60/27.75 (41) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.60/27.75 (42) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.60/27.75
% 158.60/27.75 Begin of proof
% 158.60/27.75 |
% 158.60/27.75 | BETA: splitting (42) gives:
% 158.60/27.75 |
% 158.60/27.75 | Case 1:
% 158.60/27.75 | |
% 158.60/27.75 | | (43) all_56_12 = e3
% 158.74/27.75 | |
% 158.74/27.75 | | COMBINE_EQS: (20), (43) imply:
% 158.74/27.75 | | (44) e3 = e1
% 158.74/27.75 | |
% 158.74/27.75 | | REDUCE: (19), (44) imply:
% 158.74/27.75 | | (45) $false
% 158.74/27.75 | |
% 158.74/27.75 | | CLOSE: (45) is inconsistent.
% 158.74/27.75 | |
% 158.74/27.75 | Case 2:
% 158.74/27.75 | |
% 158.74/27.75 | | (46) ~ (all_56_12 = e3)
% 158.74/27.75 | | (47) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.74/27.75 | |
% 158.74/27.75 | | REDUCE: (20), (46) imply:
% 158.74/27.75 | | (48) ~ (e3 = e1)
% 158.74/27.75 | |
% 158.74/27.75 | | BETA: splitting (47) gives:
% 158.74/27.75 | |
% 158.74/27.75 | | Case 1:
% 158.74/27.75 | | |
% 158.74/27.75 | | | (49) all_56_13 = e2
% 158.74/27.75 | | |
% 158.74/27.75 | | | COMBINE_EQS: (32), (49) imply:
% 158.74/27.75 | | | (50) e3 = e2
% 158.74/27.75 | | |
% 158.74/27.75 | | | COMBINE_EQS: (4), (50) imply:
% 158.74/27.75 | | | (51) all_58_12 = e2
% 158.74/27.75 | | |
% 158.74/27.75 | | | REF_CLOSE: (7), (9), (13), (14), (17), (18), (19), (29), (31), (39), (40),
% 158.74/27.75 | | | (51) are inconsistent by sub-proof #1063.
% 158.74/27.75 | | |
% 158.74/27.75 | | Case 2:
% 158.74/27.75 | | |
% 158.74/27.75 | | | (52) all_56_14 = e1 | all_56_15 = e0
% 158.74/27.75 | | |
% 158.74/27.75 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13),
% 158.74/27.75 | | | (14), (15), (16), (18), (19), (21), (22), (23), (24), (25),
% 158.74/27.75 | | | (26), (27), (28), (30), (33), (34), (35), (36), (37), (38),
% 158.74/27.75 | | | (39), (41), (52) are inconsistent by sub-proof #479.
% 158.74/27.75 | | |
% 158.74/27.75 | | End of split
% 158.74/27.75 | |
% 158.74/27.75 | End of split
% 158.74/27.75 |
% 158.74/27.75 End of proof
% 158.74/27.75
% 158.74/27.75 Sub-proof #479 shows that the following formulas are inconsistent:
% 158.74/27.75 ----------------------------------------------------------------
% 158.74/27.75 (1) all_56_14 = e3
% 158.74/27.75 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.74/27.75 (3) ~ (all_52_11 = e3)
% 158.74/27.75 (4) all_58_12 = e3
% 158.74/27.75 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.74/27.75 (6) all_58_0 = e1
% 158.74/27.75 (7) ~ (all_4_2 = e2)
% 158.74/27.75 (8) ~ (all_52_13 = e3)
% 158.74/27.75 (9) all_54_2 = all_52_8
% 158.74/27.75 (10) ~ (all_52_8 = all_52_9)
% 158.74/27.75 (11) ~ (e3 = e0)
% 158.74/27.75 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.75 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.75 (13) ~ (all_52_9 = all_52_13)
% 158.74/27.75 (14) all_56_14 = e1 | all_56_15 = e0
% 158.74/27.75 (15) ~ (all_52_9 = e3)
% 158.74/27.76 (16) op(e2, e3) = e2
% 158.74/27.76 (17) ~ (e3 = e1)
% 158.74/27.76 (18) ~ (all_4_2 = e1)
% 158.74/27.76 (19) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.74/27.76 (20) all_54_7 = all_52_13
% 158.74/27.76 (21) ~ (all_52_13 = e2)
% 158.74/27.76 (22) all_56_15 = all_4_2
% 158.74/27.76 (23) ~ (all_52_9 = all_52_11)
% 158.74/27.76 (24) ~ (all_52_13 = all_4_2)
% 158.74/27.76 (25) all_54_6 = all_52_9
% 158.74/27.76 (26) ~ (all_52_8 = all_52_11)
% 158.74/27.76 (27) ~ (all_52_9 = e2)
% 158.74/27.76 (28) ~ (all_52_8 = e3)
% 158.74/27.76 (29) all_54_14 = all_52_11
% 158.74/27.76 (30) op(e1, e3) = e1
% 158.74/27.76 (31) ~ (all_52_8 = e1)
% 158.74/27.76 (32) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.76 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.76 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.76 (34) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.74/27.76
% 158.74/27.76 Begin of proof
% 158.74/27.76 |
% 158.74/27.76 | BETA: splitting (14) gives:
% 158.74/27.76 |
% 158.74/27.76 | Case 1:
% 158.74/27.76 | |
% 158.74/27.76 | | (35) all_56_14 = e1
% 158.74/27.76 | |
% 158.74/27.76 | | COMBINE_EQS: (1), (35) imply:
% 158.74/27.76 | | (36) e3 = e1
% 158.74/27.76 | |
% 158.74/27.76 | | REDUCE: (17), (36) imply:
% 158.74/27.76 | | (37) $false
% 158.74/27.76 | |
% 158.74/27.76 | | CLOSE: (37) is inconsistent.
% 158.74/27.76 | |
% 158.74/27.76 | Case 2:
% 158.74/27.76 | |
% 158.74/27.76 | | (38) all_56_15 = e0
% 158.74/27.76 | |
% 158.74/27.76 | | COMBINE_EQS: (22), (38) imply:
% 158.74/27.76 | | (39) all_4_2 = e0
% 158.74/27.76 | |
% 158.74/27.76 | | REDUCE: (24), (39) imply:
% 158.74/27.76 | | (40) ~ (all_52_13 = e0)
% 158.74/27.76 | |
% 158.74/27.76 | | REDUCE: (7), (39) imply:
% 158.74/27.76 | | (41) ~ (e2 = e0)
% 158.74/27.76 | |
% 158.74/27.76 | | SIMP: (41) implies:
% 158.74/27.76 | | (42) ~ (e2 = e0)
% 158.74/27.76 | |
% 158.74/27.76 | | REDUCE: (18), (39) imply:
% 158.74/27.76 | | (43) ~ (e1 = e0)
% 158.74/27.76 | |
% 158.74/27.76 | | SIMP: (43) implies:
% 158.74/27.76 | | (44) ~ (e1 = e0)
% 158.74/27.76 | |
% 158.74/27.76 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 158.74/27.76 | | (16), (19), (20), (21), (23), (25), (26), (27), (28), (29), (30),
% 158.74/27.76 | | (31), (32), (33), (34), (40), (42), (44) are inconsistent by
% 158.74/27.76 | | sub-proof #532.
% 158.74/27.76 | |
% 158.74/27.76 | End of split
% 158.74/27.76 |
% 158.74/27.76 End of proof
% 158.74/27.76
% 158.74/27.76 Sub-proof #480 shows that the following formulas are inconsistent:
% 158.74/27.76 ----------------------------------------------------------------
% 158.74/27.76 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.74/27.76 (2) all_56_14 = e3
% 158.74/27.76 (3) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.74/27.76 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.76 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.76 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.76 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.76 (6) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.76 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.76 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.76 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.76 (8) all_54_13 = all_52_7
% 158.74/27.76 (9) op(e1, e1) = all_6_2
% 158.74/27.76 (10) ~ (all_52_7 = e3)
% 158.74/27.76 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.76 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.74/27.76 e1)
% 158.74/27.76 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.74/27.76 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.74/27.76 (13) ~ (all_52_6 = all_52_14)
% 158.74/27.76 (14) ~ (all_52_11 = e3)
% 158.74/27.76 (15) ~ (all_52_4 = all_52_6)
% 158.74/27.76 (16) op(e3, e3) = all_28_1
% 158.74/27.76 (17) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.74/27.76 (18) all_58_8 = e3
% 158.74/27.76 (19) ~ (all_52_7 = all_52_11)
% 158.74/27.76 (20) op(e1, e2) = all_14_0
% 158.74/27.76 (21) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.74/27.76 (22) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.76 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.76 (23) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.76 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.76 (24) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.74/27.76 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.76 (25) ~ (all_52_14 = e3)
% 158.74/27.76 (26) all_54_1 = all_52_4
% 158.74/27.76 (27) op(e3, e2) = all_52_4
% 158.74/27.76 (28) ~ (all_4_2 = e2)
% 158.74/27.76 (29) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.74/27.76 (30) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.76 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.76 (31) op(e2, e3) = all_52_1
% 158.74/27.76 (32) ~ (all_52_13 = e3)
% 158.74/27.76 (33) all_54_2 = all_52_8
% 158.74/27.76 (34) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.76 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.76 (35) ~ (all_52_8 = all_52_9)
% 158.74/27.76 (36) ~ (e3 = e0)
% 158.74/27.76 (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.76 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.76 (38) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.74/27.76 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.74/27.76 (39) ~ (all_52_9 = all_52_13)
% 158.74/27.76 (40) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.76 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.76 e2)
% 158.74/27.76 (41) ~ (e2 = e0)
% 158.74/27.76 (42) ~ (all_52_9 = e3)
% 158.74/27.76 (43) ~ (all_52_2 = all_52_6)
% 158.74/27.76 (44) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.76 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.76 (45) op(e2, e0) = all_52_13
% 158.74/27.76 (46) op(e2, e3) = e2
% 158.74/27.76 (47) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.76 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.76 (48) ~ (e3 = e1)
% 158.74/27.76 (49) all_56_12 = e1
% 158.74/27.76 (50) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.74/27.76 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.76 (51) op(e1, e2) = all_52_6
% 158.74/27.76 (52) ~ (all_4_2 = e1)
% 158.74/27.76 (53) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.74/27.76 (54) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.76 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.76 (55) op(e0, e0) = all_4_2
% 158.74/27.76 (56) all_54_8 = all_52_2
% 158.74/27.76 (57) all_54_7 = all_52_13
% 158.74/27.76 (58) ~ (all_52_2 = e3)
% 158.74/27.76 (59) op(e3, e3) = e1
% 158.74/27.76 (60) ~ (all_52_13 = e2)
% 158.74/27.76 (61) all_56_15 = all_4_2
% 158.74/27.76 (62) ~ (all_52_4 = e1)
% 158.74/27.76 (63) ~ (all_52_9 = all_52_11)
% 158.74/27.76 (64) ~ (all_52_13 = all_4_2)
% 158.74/27.76 (65) ~ (all_52_2 = e1)
% 158.74/27.76 (66) ~ (all_52_2 = all_52_14)
% 158.74/27.76 (67) ~ (all_52_6 = all_52_7)
% 158.74/27.76 (68) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.74/27.76 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.74/27.76 (69) ~ (all_52_4 = e3)
% 158.74/27.76 (70) all_54_6 = all_52_9
% 158.74/27.76 (71) ~ (e2 = e1)
% 158.74/27.76 (72) ~ (all_52_8 = all_52_11)
% 158.74/27.76 (73) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.74/27.76 (74) ~ (e1 = e0)
% 158.74/27.76 (75) ~ (all_52_2 = e2)
% 158.74/27.76 (76) all_58_3 = e3
% 158.74/27.76 (77) ~ (all_6_2 = e2)
% 158.74/27.76 (78) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.74/27.76 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.74/27.76 e3)
% 158.74/27.76 (79) all_56_13 = e3
% 158.74/27.76 (80) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.74/27.76 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.74/27.76 (81) ~ (all_52_9 = e2)
% 158.74/27.76 (82) ~ (all_52_8 = e3)
% 158.74/27.76 (83) all_54_14 = all_52_11
% 158.74/27.76 (84) ~ (all_52_7 = all_4_2)
% 158.74/27.76 (85) op(e1, e3) = e1
% 158.74/27.76 (86) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.76 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.76 (87) op(e0, e2) = all_52_7
% 158.74/27.76 (88) op(e3, e3) = all_22_1
% 158.74/27.76 (89) ~ (all_52_8 = e1)
% 158.74/27.76 (90) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.74/27.76 (91) ~ (all_52_6 = e3)
% 158.74/27.76 (92) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.76 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.76 (93) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.76 (94) all_54_11 = all_52_14
% 158.74/27.76 (95) ~ (all_52_13 = all_52_14)
% 158.74/27.76 (96) ~ (e3 = e2)
% 158.74/27.76 (97) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.74/27.76 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.76 (98) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.76 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.76 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.74/27.76 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.74/27.76 (99) all_54_9 = all_52_6
% 158.74/27.76 (100) ~ (all_52_4 = all_52_8)
% 158.74/27.76 (101) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.74/27.76 (102) ~ (all_52_14 = all_4_2)
% 158.74/27.76 (103) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.74/27.76
% 158.74/27.76 Begin of proof
% 158.74/27.76 |
% 158.74/27.76 | BETA: splitting (37) gives:
% 158.74/27.76 |
% 158.74/27.76 | Case 1:
% 158.74/27.76 | |
% 158.74/27.76 | | (104) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 158.74/27.76 | | e1)
% 158.74/27.76 | |
% 158.74/27.76 | | BETA: splitting (104) gives:
% 158.74/27.76 | |
% 158.74/27.76 | | Case 1:
% 158.74/27.76 | | |
% 158.74/27.76 | | | (105) all_58_0 = e1 & op(e3, e3) = e1
% 158.74/27.76 | | |
% 158.74/27.76 | | | ALPHA: (105) implies:
% 158.74/27.76 | | | (106) all_58_0 = e1
% 158.74/27.76 | | |
% 158.74/27.76 | | | BETA: splitting (103) gives:
% 158.74/27.76 | | |
% 158.74/27.76 | | | Case 1:
% 158.74/27.76 | | | |
% 158.74/27.76 | | | | (107) all_56_12 = e3
% 158.74/27.76 | | | |
% 158.74/27.76 | | | | REF_CLOSE: (48), (49), (107) are inconsistent by sub-proof #1191.
% 158.74/27.76 | | | |
% 158.74/27.76 | | | Case 2:
% 158.74/27.76 | | | |
% 158.74/27.76 | | | | (108) ~ (all_56_12 = e3)
% 158.74/27.76 | | | | (109) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.74/27.76 | | | |
% 158.74/27.76 | | | | REDUCE: (49), (108) imply:
% 158.74/27.76 | | | | (110) ~ (e3 = e1)
% 158.74/27.76 | | | |
% 158.74/27.76 | | | | BETA: splitting (109) gives:
% 158.74/27.76 | | | |
% 158.74/27.76 | | | | Case 1:
% 158.74/27.76 | | | | |
% 158.74/27.76 | | | | | (111) all_56_13 = e2
% 158.74/27.76 | | | | |
% 158.74/27.76 | | | | | COMBINE_EQS: (79), (111) imply:
% 158.74/27.76 | | | | | (112) e3 = e2
% 158.74/27.76 | | | | |
% 158.74/27.76 | | | | | REDUCE: (96), (112) imply:
% 158.74/27.76 | | | | | (113) $false
% 158.74/27.76 | | | | |
% 158.74/27.76 | | | | | CLOSE: (113) is inconsistent.
% 158.74/27.76 | | | | |
% 158.74/27.76 | | | | Case 2:
% 158.74/27.76 | | | | |
% 158.74/27.76 | | | | | (114) ~ (all_56_13 = e2)
% 158.74/27.76 | | | | | (115) all_56_14 = e1 | all_56_15 = e0
% 158.74/27.76 | | | | |
% 158.74/27.76 | | | | | BETA: splitting (115) gives:
% 158.74/27.76 | | | | |
% 158.74/27.76 | | | | | Case 1:
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | (116) all_56_14 = e1
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | REF_CLOSE: (2), (48), (116) are inconsistent by sub-proof #585.
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | Case 2:
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | (117) all_56_15 = e0
% 158.74/27.76 | | | | | | (118) ~ (all_56_14 = e1)
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | COMBINE_EQS: (61), (117) imply:
% 158.74/27.76 | | | | | | (119) all_4_2 = e0
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | SIMP: (119) implies:
% 158.74/27.76 | | | | | | (120) all_4_2 = e0
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | REDUCE: (84), (120) imply:
% 158.74/27.76 | | | | | | (121) ~ (all_52_7 = e0)
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | REDUCE: (64), (120) imply:
% 158.74/27.76 | | | | | | (122) ~ (all_52_13 = e0)
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | REDUCE: (102), (120) imply:
% 158.74/27.76 | | | | | | (123) ~ (all_52_14 = e0)
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | REDUCE: (28), (120) imply:
% 158.74/27.76 | | | | | | (124) ~ (e2 = e0)
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | REDUCE: (52), (120) imply:
% 158.74/27.76 | | | | | | (125) ~ (e1 = e0)
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | REDUCE: (55), (120) imply:
% 158.74/27.76 | | | | | | (126) op(e0, e0) = e0
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | BETA: splitting (78) gives:
% 158.74/27.76 | | | | | |
% 158.74/27.76 | | | | | | Case 1:
% 158.74/27.76 | | | | | | |
% 158.74/27.76 | | | | | | | (127) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 158.74/27.76 | | | | | | | op(e0, e2) = e3)
% 158.74/27.76 | | | | | | |
% 158.74/27.76 | | | | | | | BETA: splitting (127) gives:
% 158.74/27.76 | | | | | | |
% 158.74/27.76 | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | (128) all_58_12 = e3 & op(e0, e3) = e3
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | ALPHA: (128) implies:
% 158.74/27.76 | | | | | | | | (129) all_58_12 = e3
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | REF_CLOSE: (3), (14), (17), (32), (33), (35), (36), (37), (39),
% 158.74/27.76 | | | | | | | | (41), (42), (46), (53), (57), (60), (63), (70), (72),
% 158.74/27.76 | | | | | | | | (74), (81), (82), (83), (85), (89), (92), (93),
% 158.74/27.76 | | | | | | | | (101), (106), (122), (129) are inconsistent by
% 158.74/27.76 | | | | | | | | sub-proof #532.
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | (130) all_58_13 = e3 & op(e0, e2) = e3
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | REF_CLOSE: (10), (87), (93), (130) are inconsistent by sub-proof
% 158.74/27.76 | | | | | | | | #1449.
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | End of split
% 158.74/27.76 | | | | | | |
% 158.74/27.76 | | | | | | Case 2:
% 158.74/27.76 | | | | | | |
% 158.74/27.76 | | | | | | | (131) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 158.74/27.76 | | | | | | | op(e0, e0) = e3)
% 158.74/27.76 | | | | | | |
% 158.74/27.76 | | | | | | | BETA: splitting (131) gives:
% 158.74/27.76 | | | | | | |
% 158.74/27.76 | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | (132) all_58_14 = e3 & op(e0, e1) = e3
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | ALPHA: (132) implies:
% 158.74/27.76 | | | | | | | | (133) all_58_14 = e3
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | REF_CLOSE: (7), (9), (18), (23), (36), (41), (46), (48), (50),
% 158.74/27.76 | | | | | | | | (54), (68), (71), (74), (76), (77), (93), (96), (133)
% 158.74/27.76 | | | | | | | | are inconsistent by sub-proof #780.
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | (134) all_58_15 = e3 & op(e0, e0) = e3
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | ALPHA: (134) implies:
% 158.74/27.76 | | | | | | | | (135) all_58_15 = e3
% 158.74/27.76 | | | | | | | | (136) op(e0, e0) = e3
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | BETA: splitting (17) gives:
% 158.74/27.76 | | | | | | | |
% 158.74/27.76 | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | |
% 158.74/27.76 | | | | | | | | | (137) all_54_7 = e3
% 158.74/27.76 | | | | | | | | |
% 158.74/27.76 | | | | | | | | | COMBINE_EQS: (57), (137) imply:
% 158.74/27.76 | | | | | | | | | (138) all_52_13 = e3
% 158.74/27.76 | | | | | | | | |
% 158.74/27.76 | | | | | | | | | REDUCE: (32), (138) imply:
% 158.74/27.76 | | | | | | | | | (139) $false
% 158.74/27.76 | | | | | | | | |
% 158.74/27.76 | | | | | | | | | CLOSE: (139) is inconsistent.
% 158.74/27.76 | | | | | | | | |
% 158.74/27.76 | | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | | |
% 158.74/27.76 | | | | | | | | | (140) ~ (all_54_7 = e3)
% 158.74/27.76 | | | | | | | | | (141) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.74/27.76 | | | | | | | | |
% 158.74/27.76 | | | | | | | | | BETA: splitting (141) gives:
% 158.74/27.76 | | | | | | | | |
% 158.74/27.76 | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | (142) all_54_7 = e2
% 158.74/27.76 | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | COMBINE_EQS: (57), (142) imply:
% 158.74/27.76 | | | | | | | | | | (143) all_52_13 = e2
% 158.74/27.76 | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | REDUCE: (60), (143) imply:
% 158.74/27.76 | | | | | | | | | | (144) $false
% 158.74/27.76 | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | CLOSE: (144) is inconsistent.
% 158.74/27.76 | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | (145) ~ (all_54_7 = e2)
% 158.74/27.76 | | | | | | | | | | (146) all_54_7 = e1 | all_54_7 = e0
% 158.74/27.76 | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | BETA: splitting (92) gives:
% 158.74/27.76 | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | (147) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 158.74/27.76 | | | | | | | | | | | & op(e2, e3) = e0)
% 158.74/27.76 | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | REF_CLOSE: (41), (46), (74), (93), (106), (147) are
% 158.74/27.76 | | | | | | | | | | | inconsistent by sub-proof #534.
% 158.74/27.76 | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | (148) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 158.74/27.76 | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 158.74/27.76 | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | BETA: splitting (148) gives:
% 158.74/27.76 | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | (149) all_58_6 = e0 & op(e1, e3) = e0
% 158.74/27.76 | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | ALPHA: (149) implies:
% 158.74/27.76 | | | | | | | | | | | | (150) all_58_6 = e0
% 158.74/27.76 | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | BETA: splitting (98) gives:
% 158.74/27.76 | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | (151) all_58_15 = e0 & op(e0, e0) = e0
% 158.74/27.76 | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | ALPHA: (151) implies:
% 158.74/27.76 | | | | | | | | | | | | | (152) all_58_15 = e0
% 158.74/27.76 | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | REF_CLOSE: (36), (135), (152) are inconsistent by sub-proof
% 158.74/27.76 | | | | | | | | | | | | | #1318.
% 158.74/27.76 | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | (153) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 158.74/27.76 | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.74/27.76 | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 158.74/27.76 | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 158.74/27.76 | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.74/27.76 | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | ALPHA: (153) implies:
% 158.74/27.76 | | | | | | | | | | | | | (154) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 158.74/27.76 | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 158.74/27.76 | | | | | | | | | | | | | e1) = e0)
% 158.74/27.76 | | | | | | | | | | | | | (155) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 158.74/27.76 | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 158.74/27.76 | | | | | | | | | | | | | e0) = e0)
% 158.74/27.76 | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | BETA: splitting (154) gives:
% 158.74/27.76 | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | (156) all_58_12 = e0 & op(e0, e3) = e0
% 158.74/27.76 | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | ALPHA: (156) implies:
% 158.74/27.76 | | | | | | | | | | | | | | (157) all_58_12 = e0
% 158.74/27.76 | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.76 | | | | | | | | | | | | | | (11), (12), (14), (16), (18), (19), (22), (23),
% 158.74/27.76 | | | | | | | | | | | | | | (24), (27), (28), (30), (31), (32), (33), (34),
% 158.74/27.76 | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 158.74/27.76 | | | | | | | | | | | | | | (44), (45), (46), (47), (48), (50), (51), (52),
% 158.74/27.76 | | | | | | | | | | | | | | (53), (54), (55), (57), (59), (60), (61), (63),
% 158.74/27.76 | | | | | | | | | | | | | | (68), (69), (70), (71), (72), (74), (76), (77),
% 158.74/27.76 | | | | | | | | | | | | | | (78), (79), (81), (82), (83), (85), (86), (87),
% 158.74/27.76 | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (93), (96), (97),
% 158.74/27.76 | | | | | | | | | | | | | | (98), (101), (106), (109), (121), (122), (126),
% 158.74/27.76 | | | | | | | | | | | | | | (135), (136), (141), (146), (155), (157) are
% 158.74/27.76 | | | | | | | | | | | | | | inconsistent by sub-proof #508.
% 158.74/27.76 | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | (158) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 158.74/27.76 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 158.74/27.76 | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 158.74/27.76 | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | (159) all_58_13 = e0 & op(e0, e2) = e0
% 158.74/27.76 | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 158.74/27.76 | | | | | | | | | | | | | | | (160) op(e0, e2) = e0
% 158.74/27.76 | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (10), (14), (19), (33), (35), (39),
% 158.74/27.76 | | | | | | | | | | | | | | | (42), (53), (57), (63), (70), (72), (81), (82),
% 158.74/27.76 | | | | | | | | | | | | | | | (83), (87), (89), (90), (93), (101), (121), (122),
% 158.74/27.76 | | | | | | | | | | | | | | | (146), (160) are inconsistent by sub-proof #560.
% 158.74/27.76 | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | (161) all_58_14 = e0 & op(e0, e1) = e0
% 158.74/27.76 | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 158.74/27.76 | | | | | | | | | | | | | | | (162) all_58_14 = e0
% 158.74/27.76 | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 158.74/27.76 | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | (163) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 158.74/27.76 | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 158.74/27.76 | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 158.74/27.76 | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | | (164) all_58_4 = e1 & op(e3, e1) = e1
% 158.74/27.76 | | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 158.74/27.76 | | | | | | | | | | | | | | | | | (165) all_58_4 = e1
% 158.74/27.76 | | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 158.74/27.76 | | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.76 | | | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (166) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 158.74/27.76 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 158.74/27.76 | | | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (50), (51),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (52), (53), (54), (55), (56), (57), (58), (59),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (60), (61), (62), (63), (65), (66), (67), (68),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (86),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (95), (96), (98), (99), (100), (101), (106),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (109), (121), (122), (123), (126), (135), (136),
% 158.74/27.76 | | | | | | | | | | | | | | | | | | (150), (154), (155), (162), (166) are inconsistent
% 158.74/27.76 | | | | | | | | | | | | | | | | | | by sub-proof #487.
% 158.74/27.76 | | | | | | | | | | | | | | | | | |
% 158.74/27.76 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.76 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (167) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 158.74/27.77 | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (168) all_58_8 = e1 & op(e1, e1) = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (169) all_58_8 = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (48), (169) are inconsistent by sub-proof
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | #950.
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (170) all_58_11 = e1 & op(e1, e0) = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (171) all_58_11 = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (11), (16), (18), (22), (23),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (27), (30), (31), (34), (36), (37), (40), (41),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (44), (46), (48), (51), (54), (59), (69), (71),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (74), (76), (77), (86), (88), (91), (92), (93),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (96), (98), (106), (126), (135), (136), (150),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (154), (155), (162), (165), (171) are inconsistent
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | by sub-proof #484.
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | (172) all_58_5 = e1 & op(e2, e1) = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 158.74/27.77 | | | | | | | | | | | | | | | | | (173) all_58_5 = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (174) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (50), (51),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (52), (53), (54), (55), (56), (57), (58), (59),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (60), (61), (62), (63), (65), (66), (67), (68),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (86),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (95), (96), (98), (99), (100), (101), (106),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (109), (121), (122), (123), (126), (135), (136),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (150), (154), (155), (162), (174) are inconsistent
% 158.74/27.77 | | | | | | | | | | | | | | | | | | by sub-proof #487.
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | (175) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 158.74/27.77 | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (176) all_58_8 = e1 & op(e1, e1) = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (177) all_58_8 = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (48), (177) are inconsistent by sub-proof
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | #950.
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (178) all_58_11 = e1 & op(e1, e0) = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (179) all_58_11 = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (11), (16), (18), (22),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (23), (24), (27), (30), (31), (34), (36), (37),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (40), (41), (44), (46), (48), (51), (54), (59),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (69), (71), (74), (76), (77), (86), (88), (91),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (92), (93), (96), (97), (98), (106), (126), (135),
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | (136), (150), (154), (155), (162), (173), (179)
% 158.74/27.77 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #483.
% 158.74/27.77 | | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | Case 2:
% 158.74/27.77 | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | (180) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 158.74/27.77 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 158.74/27.77 | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 158.74/27.77 | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | (181) all_58_8 = e1 & op(e1, e1) = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (48), (181) are inconsistent by sub-proof
% 158.74/27.77 | | | | | | | | | | | | | | | | | #959.
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | (182) all_58_14 = e1 & op(e0, e1) = e1
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (162), (182) are inconsistent by sub-proof
% 158.74/27.77 | | | | | | | | | | | | | | | | | #482.
% 158.74/27.77 | | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | Case 2:
% 158.74/27.77 | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | (183) all_58_12 = e0 & op(e0, e3) = e0
% 158.74/27.77 | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.77 | | | | | | | | | | | | (11), (12), (14), (16), (18), (19), (22), (23),
% 158.74/27.77 | | | | | | | | | | | | (24), (27), (28), (30), (31), (32), (33), (34),
% 158.74/27.77 | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 158.74/27.77 | | | | | | | | | | | | (44), (45), (46), (47), (48), (50), (51), (52),
% 158.74/27.77 | | | | | | | | | | | | (53), (54), (55), (57), (59), (60), (61), (63),
% 158.74/27.77 | | | | | | | | | | | | (68), (69), (70), (71), (72), (74), (76), (77),
% 158.74/27.77 | | | | | | | | | | | | (78), (79), (81), (82), (83), (85), (86), (87),
% 158.74/27.77 | | | | | | | | | | | | (88), (89), (90), (91), (92), (93), (96), (97),
% 158.74/27.77 | | | | | | | | | | | | (98), (101), (106), (109), (121), (122), (126),
% 158.74/27.77 | | | | | | | | | | | | (135), (136), (141), (146), (183) are inconsistent
% 158.74/27.77 | | | | | | | | | | | | by sub-proof #481.
% 158.74/27.77 | | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | | |
% 158.74/27.77 | | | | | | | | | End of split
% 158.74/27.77 | | | | | | | | |
% 158.74/27.77 | | | | | | | | End of split
% 158.74/27.77 | | | | | | | |
% 158.74/27.77 | | | | | | | End of split
% 158.74/27.77 | | | | | | |
% 158.74/27.77 | | | | | | End of split
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | End of split
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | End of split
% 158.74/27.77 | | | |
% 158.74/27.77 | | | End of split
% 158.74/27.77 | | |
% 158.74/27.77 | | Case 2:
% 158.74/27.77 | | |
% 158.74/27.77 | | | (184) all_58_2 = e1 & op(e2, e3) = e1
% 158.74/27.77 | | |
% 158.74/27.77 | | | ALPHA: (184) implies:
% 158.74/27.77 | | | (185) op(e2, e3) = e1
% 158.74/27.77 | | |
% 158.74/27.77 | | | REF_CLOSE: (46), (71), (93), (185) are inconsistent by sub-proof #1430.
% 158.74/27.77 | | |
% 158.74/27.77 | | End of split
% 158.74/27.77 | |
% 158.74/27.77 | Case 2:
% 158.74/27.77 | |
% 158.74/27.77 | | (186) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 158.74/27.77 | | e1)
% 158.74/27.77 | |
% 158.74/27.77 | | BETA: splitting (186) gives:
% 158.74/27.77 | |
% 158.74/27.77 | | Case 1:
% 158.74/27.77 | | |
% 158.74/27.77 | | | (187) all_58_6 = e1 & op(e1, e3) = e1
% 158.74/27.77 | | |
% 158.74/27.77 | | | ALPHA: (187) implies:
% 158.74/27.77 | | | (188) all_58_6 = e1
% 158.74/27.77 | | |
% 158.74/27.77 | | | BETA: splitting (103) gives:
% 158.74/27.77 | | |
% 158.74/27.77 | | | Case 1:
% 158.74/27.77 | | | |
% 158.74/27.77 | | | | (189) all_56_12 = e3
% 158.74/27.77 | | | |
% 158.74/27.77 | | | | REF_CLOSE: (48), (49), (189) are inconsistent by sub-proof #1191.
% 158.74/27.77 | | | |
% 158.74/27.77 | | | Case 2:
% 158.74/27.77 | | | |
% 158.74/27.77 | | | | (190) ~ (all_56_12 = e3)
% 158.74/27.77 | | | | (191) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.74/27.77 | | | |
% 158.74/27.77 | | | | REDUCE: (49), (190) imply:
% 158.74/27.77 | | | | (192) ~ (e3 = e1)
% 158.74/27.77 | | | |
% 158.74/27.77 | | | | BETA: splitting (191) gives:
% 158.74/27.77 | | | |
% 158.74/27.77 | | | | Case 1:
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | | (193) all_56_13 = e2
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | | COMBINE_EQS: (79), (193) imply:
% 158.74/27.77 | | | | | (194) e3 = e2
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | | REDUCE: (96), (194) imply:
% 158.74/27.77 | | | | | (195) $false
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | | CLOSE: (195) is inconsistent.
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | Case 2:
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | | (196) ~ (all_56_13 = e2)
% 158.74/27.77 | | | | | (197) all_56_14 = e1 | all_56_15 = e0
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | | BETA: splitting (197) gives:
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | | Case 1:
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | (198) all_56_14 = e1
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | REF_CLOSE: (2), (48), (198) are inconsistent by sub-proof #585.
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | Case 2:
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | (199) all_56_15 = e0
% 158.74/27.77 | | | | | | (200) ~ (all_56_14 = e1)
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | COMBINE_EQS: (61), (199) imply:
% 158.74/27.77 | | | | | | (201) all_4_2 = e0
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | SIMP: (201) implies:
% 158.74/27.77 | | | | | | (202) all_4_2 = e0
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | REDUCE: (84), (202) imply:
% 158.74/27.77 | | | | | | (203) ~ (all_52_7 = e0)
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | REDUCE: (64), (202) imply:
% 158.74/27.77 | | | | | | (204) ~ (all_52_13 = e0)
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | REDUCE: (102), (202) imply:
% 158.74/27.77 | | | | | | (205) ~ (all_52_14 = e0)
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | REDUCE: (28), (202) imply:
% 158.74/27.77 | | | | | | (206) ~ (e2 = e0)
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | REDUCE: (52), (202) imply:
% 158.74/27.77 | | | | | | (207) ~ (e1 = e0)
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | REDUCE: (55), (202) imply:
% 158.74/27.77 | | | | | | (208) op(e0, e0) = e0
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 158.74/27.77 | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 158.74/27.77 | | | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 158.74/27.77 | | | | | | (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 158.74/27.77 | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 158.74/27.77 | | | | | | (48), (50), (51), (52), (53), (54), (55), (56), (57),
% 158.74/27.77 | | | | | | (58), (59), (60), (61), (62), (63), (65), (66), (67),
% 158.74/27.77 | | | | | | (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 158.74/27.77 | | | | | | (77), (78), (79), (80), (81), (82), (83), (86), (87),
% 158.74/27.77 | | | | | | (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 158.74/27.77 | | | | | | (98), (99), (100), (101), (188), (191), (203), (204),
% 158.74/27.77 | | | | | | (205), (208) are inconsistent by sub-proof #490.
% 158.74/27.77 | | | | | |
% 158.74/27.77 | | | | | End of split
% 158.74/27.77 | | | | |
% 158.74/27.77 | | | | End of split
% 158.74/27.77 | | | |
% 158.74/27.77 | | | End of split
% 158.74/27.77 | | |
% 158.74/27.77 | | Case 2:
% 158.74/27.77 | | |
% 158.74/27.77 | | | (209) all_58_12 = e1 & op(e0, e3) = e1
% 158.74/27.77 | | |
% 158.74/27.77 | | | ALPHA: (209) implies:
% 158.74/27.77 | | | (210) all_58_12 = e1
% 158.74/27.77 | | |
% 158.74/27.77 | | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (16), (18), (22), (23), (24),
% 158.74/27.77 | | | (27), (28), (31), (34), (36), (37), (41), (44), (46), (48),
% 158.74/27.77 | | | (49), (50), (52), (54), (55), (59), (61), (68), (69), (71),
% 158.74/27.77 | | | (74), (76), (77), (78), (79), (86), (87), (88), (92), (93),
% 158.74/27.77 | | | (96), (98), (103), (210) are inconsistent by sub-proof #571.
% 158.74/27.77 | | |
% 158.74/27.77 | | End of split
% 158.74/27.77 | |
% 158.74/27.77 | End of split
% 158.74/27.77 |
% 158.74/27.77 End of proof
% 158.74/27.77
% 158.74/27.77 Sub-proof #481 shows that the following formulas are inconsistent:
% 158.74/27.77 ----------------------------------------------------------------
% 158.74/27.77 (1) all_56_14 = e3
% 158.74/27.77 (2) all_58_15 = e3
% 158.74/27.77 (3) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.74/27.77 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.77 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.77 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.77 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.77 (6) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.77 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.77 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.77 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.77 (8) all_54_13 = all_52_7
% 158.74/27.77 (9) op(e1, e1) = all_6_2
% 158.74/27.77 (10) ~ (all_52_7 = e3)
% 158.74/27.77 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.77 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.74/27.77 e1)
% 158.74/27.77 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.74/27.77 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.74/27.77 (13) ~ (all_52_11 = e3)
% 158.74/27.77 (14) op(e3, e3) = all_28_1
% 158.74/27.77 (15) all_58_8 = e3
% 158.74/27.77 (16) ~ (all_52_7 = all_52_11)
% 158.74/27.77 (17) all_58_0 = e1
% 158.74/27.77 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.77 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.77 (19) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.77 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.77 (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.74/27.77 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.77 (21) op(e3, e2) = all_52_4
% 158.74/27.77 (22) ~ (all_4_2 = e2)
% 158.74/27.77 (23) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.77 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.77 (24) op(e2, e3) = all_52_1
% 158.74/27.77 (25) ~ (all_52_13 = e3)
% 158.74/27.77 (26) all_54_2 = all_52_8
% 158.74/27.77 (27) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.77 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.77 (28) ~ (all_52_8 = all_52_9)
% 158.74/27.77 (29) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.74/27.77 (30) ~ (e3 = e0)
% 158.74/27.77 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.77 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.77 (32) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.74/27.77 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.74/27.77 (33) ~ (all_52_9 = all_52_13)
% 158.74/27.77 (34) op(e0, e0) = e0
% 158.74/27.77 (35) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.77 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.77 e2)
% 158.74/27.77 (36) ~ (e2 = e0)
% 158.74/27.77 (37) ~ (all_52_9 = e3)
% 158.74/27.77 (38) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.77 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.77 (39) all_58_12 = e0 & op(e0, e3) = e0
% 158.74/27.77 (40) op(e2, e0) = all_52_13
% 158.74/27.77 (41) op(e2, e3) = e2
% 158.74/27.77 (42) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.77 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.77 (43) ~ (e3 = e1)
% 158.74/27.77 (44) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.74/27.77 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.77 (45) op(e1, e2) = all_52_6
% 158.74/27.77 (46) ~ (all_4_2 = e1)
% 158.74/27.77 (47) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.74/27.77 (48) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.77 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.77 (49) ~ (all_52_7 = e0)
% 158.74/27.77 (50) op(e0, e0) = all_4_2
% 158.74/27.77 (51) all_54_7 = all_52_13
% 158.74/27.77 (52) op(e3, e3) = e1
% 158.74/27.77 (53) ~ (all_52_13 = e2)
% 158.74/27.77 (54) all_56_15 = all_4_2
% 158.74/27.77 (55) ~ (all_52_9 = all_52_11)
% 158.74/27.77 (56) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.74/27.77 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.74/27.77 (57) ~ (all_52_4 = e3)
% 158.74/27.77 (58) all_54_6 = all_52_9
% 158.74/27.77 (59) ~ (e2 = e1)
% 158.74/27.77 (60) ~ (all_52_8 = all_52_11)
% 158.74/27.77 (61) ~ (all_52_13 = e0)
% 158.74/27.77 (62) ~ (e1 = e0)
% 158.74/27.77 (63) all_58_3 = e3
% 158.74/27.77 (64) ~ (all_6_2 = e2)
% 158.74/27.77 (65) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.74/27.77 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.74/27.77 e3)
% 158.74/27.77 (66) all_56_13 = e3
% 158.74/27.77 (67) ~ (all_52_9 = e2)
% 158.74/27.77 (68) ~ (all_52_8 = e3)
% 158.74/27.77 (69) all_54_14 = all_52_11
% 158.74/27.77 (70) op(e1, e3) = e1
% 158.74/27.77 (71) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.77 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.77 (72) op(e0, e2) = all_52_7
% 158.74/27.77 (73) op(e3, e3) = all_22_1
% 158.74/27.77 (74) ~ (all_52_8 = e1)
% 158.74/27.77 (75) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.74/27.77 (76) ~ (all_52_6 = e3)
% 158.74/27.77 (77) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.77 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.77 (78) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.77 (79) ~ (e3 = e2)
% 158.74/27.77 (80) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.74/27.77 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.77 (81) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.77 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.77 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.74/27.77 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.74/27.77 (82) all_54_7 = e1 | all_54_7 = e0
% 158.74/27.77 (83) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.74/27.77 (84) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.74/27.77 (85) op(e0, e0) = e3
% 158.74/27.77
% 158.74/27.77 Begin of proof
% 158.74/27.77 |
% 158.74/27.77 | ALPHA: (39) implies:
% 158.74/27.77 | (86) all_58_12 = e0
% 158.74/27.77 |
% 158.74/27.77 | BETA: splitting (81) gives:
% 158.74/27.77 |
% 158.74/27.77 | Case 1:
% 158.74/27.77 | |
% 158.74/27.77 | | (87) all_58_15 = e0 & op(e0, e0) = e0
% 158.74/27.77 | |
% 158.74/27.77 | | ALPHA: (87) implies:
% 158.74/27.77 | | (88) all_58_15 = e0
% 158.74/27.77 | |
% 158.74/27.77 | | REF_CLOSE: (2), (30), (88) are inconsistent by sub-proof #1318.
% 158.74/27.77 | |
% 158.74/27.77 | Case 2:
% 158.74/27.77 | |
% 158.74/27.77 | | (89) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 158.74/27.77 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 158.74/27.77 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 158.74/27.77 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 158.74/27.77 | |
% 158.74/27.77 | | ALPHA: (89) implies:
% 158.74/27.77 | | (90) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 158.74/27.77 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.77 | |
% 158.74/27.77 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.74/27.77 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 158.74/27.77 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.74/27.77 | | (35), (36), (37), (38), (40), (41), (42), (43), (44), (45), (46),
% 158.74/27.77 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 158.74/27.77 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 158.74/27.77 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 158.74/27.77 | | (80), (81), (82), (83), (84), (85), (86), (90) are inconsistent
% 158.74/27.77 | | by sub-proof #508.
% 158.74/27.77 | |
% 158.74/27.77 | End of split
% 158.74/27.77 |
% 158.74/27.77 End of proof
% 158.74/27.77
% 158.74/27.77 Sub-proof #482 shows that the following formulas are inconsistent:
% 158.74/27.77 ----------------------------------------------------------------
% 158.74/27.77 (1) all_58_14 = e1 & op(e0, e1) = e1
% 158.74/27.77 (2) all_58_14 = e0
% 158.74/27.77 (3) ~ (e1 = e0)
% 158.74/27.77
% 158.74/27.77 Begin of proof
% 158.74/27.77 |
% 158.74/27.77 | ALPHA: (1) implies:
% 158.74/27.77 | (4) all_58_14 = e1
% 158.74/27.77 |
% 158.74/27.77 | COMBINE_EQS: (2), (4) imply:
% 158.74/27.77 | (5) e1 = e0
% 158.74/27.77 |
% 158.74/27.77 | REDUCE: (3), (5) imply:
% 158.74/27.77 | (6) $false
% 158.74/27.77 |
% 158.74/27.77 | CLOSE: (6) is inconsistent.
% 158.74/27.77 |
% 158.74/27.77 End of proof
% 158.74/27.77
% 158.74/27.77 Sub-proof #483 shows that the following formulas are inconsistent:
% 158.74/27.77 ----------------------------------------------------------------
% 158.74/27.77 (1) all_58_15 = e3
% 158.74/27.77 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.77 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.77 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.77 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.77 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.77 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.77 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.77 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.77 (6) all_58_11 = e1
% 158.74/27.77 (7) op(e1, e1) = all_6_2
% 158.74/27.77 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 158.74/27.77 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.77 (9) op(e3, e3) = all_28_1
% 158.74/27.77 (10) all_58_14 = e0
% 158.74/27.77 (11) all_58_8 = e3
% 158.74/27.77 (12) all_58_0 = e1
% 158.74/27.77 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.77 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.77 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.77 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.77 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.74/27.77 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.77 (16) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 158.74/27.77 (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.78 (17) op(e3, e2) = all_52_4
% 158.74/27.78 (18) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.78 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.78 (19) op(e2, e3) = all_52_1
% 158.74/27.78 (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.78 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.78 (21) ~ (e3 = e0)
% 158.74/27.78 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.78 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.78 (23) op(e0, e0) = e0
% 158.74/27.78 (24) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.78 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.78 e2)
% 158.74/27.78 (25) ~ (e2 = e0)
% 158.74/27.78 (26) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.78 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.78 (27) all_58_6 = e0
% 158.74/27.78 (28) op(e2, e3) = e2
% 158.74/27.78 (29) ~ (e3 = e1)
% 158.74/27.78 (30) all_58_5 = e1
% 158.74/27.78 (31) op(e1, e2) = all_52_6
% 158.74/27.78 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.78 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.78 (33) op(e3, e3) = e1
% 158.74/27.78 (34) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.78 | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.78 (35) ~ (all_52_4 = e3)
% 158.74/27.78 (36) ~ (e2 = e1)
% 158.74/27.78 (37) ~ (e1 = e0)
% 158.74/27.78 (38) all_58_3 = e3
% 158.74/27.78 (39) ~ (all_6_2 = e2)
% 158.74/27.78 (40) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.78 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.78 (41) op(e3, e3) = all_22_1
% 158.74/27.78 (42) ~ (all_52_6 = e3)
% 158.74/27.78 (43) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.78 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.78 (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.78 (45) ~ (e3 = e2)
% 158.74/27.78 (46) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 158.74/27.78 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.78 (47) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.78 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.78 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.74/27.78 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.74/27.78 (48) op(e0, e0) = e3
% 158.74/27.78
% 158.74/27.78 Begin of proof
% 158.74/27.78 |
% 158.74/27.78 | BETA: splitting (20) gives:
% 158.74/27.78 |
% 158.74/27.78 | Case 1:
% 158.74/27.78 | |
% 158.74/27.78 | | (49) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 158.74/27.78 | | e2)
% 158.74/27.78 | |
% 158.74/27.78 | | BETA: splitting (49) gives:
% 158.74/27.78 | |
% 158.74/27.78 | | Case 1:
% 158.74/27.78 | | |
% 158.74/27.78 | | | (50) all_58_6 = e2 & op(e1, e3) = e2
% 158.74/27.78 | | |
% 158.74/27.78 | | | ALPHA: (50) implies:
% 158.74/27.78 | | | (51) all_58_6 = e2
% 158.74/27.78 | | |
% 158.74/27.78 | | | REF_CLOSE: (13), (19), (21), (22), (25), (28), (29), (36), (37), (43),
% 158.74/27.78 | | | (44), (45), (51) are inconsistent by sub-proof #1152.
% 158.74/27.78 | | |
% 158.74/27.78 | | Case 2:
% 158.74/27.78 | | |
% 158.74/27.78 | | | (52) all_58_7 = e2 & op(e1, e2) = e2
% 158.74/27.78 | | |
% 158.74/27.78 | | | ALPHA: (52) implies:
% 158.74/27.78 | | | (53) all_58_7 = e2
% 158.74/27.78 | | |
% 158.74/27.78 | | | BETA: splitting (24) gives:
% 158.74/27.78 | | |
% 158.74/27.78 | | | Case 1:
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | (54) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 158.74/27.78 | | | | e2) = e2)
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | BETA: splitting (54) gives:
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | Case 1:
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | (55) all_58_12 = e2 & op(e0, e3) = e2
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | ALPHA: (55) implies:
% 158.74/27.78 | | | | | (56) all_58_12 = e2
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | REF_CLOSE: (12), (13), (19), (21), (27), (28), (29), (44), (45), (56)
% 158.74/27.78 | | | | | are inconsistent by sub-proof #1065.
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | Case 2:
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | (57) all_58_13 = e2 & op(e0, e2) = e2
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | ALPHA: (57) implies:
% 158.74/27.78 | | | | | (58) all_58_13 = e2
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | BETA: splitting (32) gives:
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | Case 1:
% 158.74/27.78 | | | | | |
% 158.74/27.78 | | | | | | (59) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2,
% 158.74/27.78 | | | | | | e2) = e0)
% 158.74/27.78 | | | | | |
% 158.74/27.78 | | | | | | REF_CLOSE: (21), (25), (28), (38), (44), (59) are inconsistent by
% 158.74/27.78 | | | | | | sub-proof #755.
% 158.74/27.78 | | | | | |
% 158.74/27.78 | | | | | Case 2:
% 158.74/27.78 | | | | | |
% 158.74/27.78 | | | | | | (60) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2,
% 158.74/27.78 | | | | | | e0) = e0)
% 158.74/27.78 | | | | | |
% 158.74/27.78 | | | | | | BETA: splitting (60) gives:
% 158.74/27.78 | | | | | |
% 158.74/27.78 | | | | | | Case 1:
% 158.74/27.78 | | | | | | |
% 158.74/27.78 | | | | | | | (61) all_58_5 = e0 & op(e2, e1) = e0
% 158.74/27.78 | | | | | | |
% 158.74/27.78 | | | | | | | REF_CLOSE: (30), (37), (61) are inconsistent by sub-proof #1343.
% 158.74/27.78 | | | | | | |
% 158.74/27.78 | | | | | | Case 2:
% 158.74/27.78 | | | | | | |
% 158.74/27.78 | | | | | | | (62) all_58_10 = e0 & op(e2, e0) = e0
% 158.74/27.78 | | | | | | |
% 158.74/27.78 | | | | | | | ALPHA: (62) implies:
% 158.74/27.78 | | | | | | | (63) all_58_10 = e0
% 158.74/27.78 | | | | | | |
% 158.74/27.78 | | | | | | | BETA: splitting (14) gives:
% 158.74/27.78 | | | | | | |
% 158.74/27.78 | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | |
% 158.74/27.78 | | | | | | | | (64) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 158.74/27.78 | | | | | | | | op(e2, e1) = e2)
% 158.74/27.78 | | | | | | | |
% 158.74/27.78 | | | | | | | | BETA: splitting (64) gives:
% 158.74/27.78 | | | | | | | |
% 158.74/27.78 | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | | (65) all_58_4 = e2 & op(e3, e1) = e2
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | | ALPHA: (65) implies:
% 158.74/27.78 | | | | | | | | | (66) all_58_4 = e2
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | | BETA: splitting (3) gives:
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | (67) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 158.74/27.78 | | | | | | | | | | op(e2, e2) = e1)
% 158.74/27.78 | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | BETA: splitting (67) gives:
% 158.74/27.78 | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | (68) all_58_1 = e1 & op(e3, e2) = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | ALPHA: (68) implies:
% 158.74/27.78 | | | | | | | | | | | (69) all_58_1 = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | BETA: splitting (15) gives:
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | (70) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 158.74/27.78 | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 158.74/27.78 | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | BETA: splitting (70) gives:
% 158.74/27.78 | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | (71) all_58_9 = e2 & op(e3, e0) = e2
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | ALPHA: (71) implies:
% 158.74/27.78 | | | | | | | | | | | | | (72) all_58_9 = e2
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | BETA: splitting (46) gives:
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | (73) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 158.74/27.78 | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 158.74/27.78 | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 158.74/27.78 | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | (74) all_58_0 = e0 & op(e3, e3) = e0
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (28), (29), (30), (36), (37), (38),
% 158.74/27.78 | | | | | | | | | | | | | | | (44), (63), (74) are inconsistent by sub-proof
% 158.74/27.78 | | | | | | | | | | | | | | | #797.
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | (75) all_58_1 = e0 & op(e3, e2) = e0
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | ALPHA: (75) implies:
% 158.74/27.78 | | | | | | | | | | | | | | | (76) all_58_1 = e0
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | COMBINE_EQS: (69), (76) imply:
% 158.74/27.78 | | | | | | | | | | | | | | | (77) e1 = e0
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | COMBINE_EQS: (30), (77) imply:
% 158.74/27.78 | | | | | | | | | | | | | | | (78) all_58_5 = e0
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | REF_CLOSE: (5), (28), (29), (36), (37), (38), (44), (63),
% 158.74/27.78 | | | | | | | | | | | | | | | (78) are inconsistent by sub-proof #839.
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | (79) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 158.74/27.78 | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 158.74/27.78 | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 158.74/27.78 | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | (80) all_58_4 = e0 & op(e3, e1) = e0
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 158.74/27.78 | | | | | | | | | | | | | | | (81) all_58_4 = e0
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (21), (25), (28), (29), (32), (36), (37),
% 158.74/27.78 | | | | | | | | | | | | | | | | (38), (44), (64), (81) are inconsistent by
% 158.74/27.78 | | | | | | | | | | | | | | | | sub-proof #855.
% 158.74/27.78 | | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | | (82) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 158.74/27.78 | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 158.74/27.78 | | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (8), (21), (25), (29), (36), (37), (39),
% 158.74/27.78 | | | | | | | | | | | | | | | | (44), (47), (58), (82) are inconsistent by
% 158.74/27.78 | | | | | | | | | | | | | | | | sub-proof #600.
% 158.74/27.78 | | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | (83) all_58_9 = e0 & op(e3, e0) = e0
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | | REF_CLOSE: (25), (72), (83) are inconsistent by sub-proof
% 158.74/27.78 | | | | | | | | | | | | | | | #1252.
% 158.74/27.78 | | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | (84) all_58_10 = e2 & op(e2, e0) = e2
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | ALPHA: (84) implies:
% 158.74/27.78 | | | | | | | | | | | | | (85) all_58_10 = e2
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | REF_CLOSE: (21), (25), (28), (30), (32), (37), (38), (44),
% 158.74/27.78 | | | | | | | | | | | | | (85) are inconsistent by sub-proof #907.
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | (86) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 158.74/27.78 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 158.74/27.78 | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | BETA: splitting (86) gives:
% 158.74/27.78 | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | (87) all_58_11 = e2 & op(e1, e0) = e2
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | ALPHA: (87) implies:
% 158.74/27.78 | | | | | | | | | | | | | (88) all_58_11 = e2
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (9), (11), (16), (17), (18), (21),
% 158.74/27.78 | | | | | | | | | | | | | (23), (25), (26), (29), (31), (33), (35), (36),
% 158.74/27.78 | | | | | | | | | | | | | (37), (40), (41), (42), (44), (45), (48), (66),
% 158.74/27.78 | | | | | | | | | | | | | (88) are inconsistent by sub-proof #529.
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | (89) all_58_15 = e2 & op(e0, e0) = e2
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | ALPHA: (89) implies:
% 158.74/27.78 | | | | | | | | | | | | | (90) op(e0, e0) = e2
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | | REF_CLOSE: (44), (45), (48), (90) are inconsistent by
% 158.74/27.78 | | | | | | | | | | | | | sub-proof #1382.
% 158.74/27.78 | | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | (91) all_58_3 = e1 & op(e2, e2) = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | REF_CLOSE: (29), (38), (91) are inconsistent by sub-proof
% 158.74/27.78 | | | | | | | | | | | #912.
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | (92) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1
% 158.74/27.78 | | | | | | | | | | & op(e0, e2) = e1)
% 158.74/27.78 | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | BETA: splitting (92) gives:
% 158.74/27.78 | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | Case 1:
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | (93) all_58_7 = e1 & op(e1, e2) = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | ALPHA: (93) implies:
% 158.74/27.78 | | | | | | | | | | | (94) all_58_7 = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11),
% 158.74/27.78 | | | | | | | | | | | (12), (13), (14), (16), (17), (18), (19), (20),
% 158.74/27.78 | | | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 158.74/27.78 | | | | | | | | | | | (29), (31), (32), (33), (34), (35), (36), (37),
% 158.74/27.78 | | | | | | | | | | | (38), (39), (40), (41), (42), (43), (44), (45),
% 158.74/27.78 | | | | | | | | | | | (48), (94) are inconsistent by sub-proof #488.
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | (95) all_58_13 = e1 & op(e0, e2) = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | ALPHA: (95) implies:
% 158.74/27.78 | | | | | | | | | | | (96) all_58_13 = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | COMBINE_EQS: (58), (96) imply:
% 158.74/27.78 | | | | | | | | | | | (97) e2 = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | COMBINE_EQS: (66), (97) imply:
% 158.74/27.78 | | | | | | | | | | | (98) all_58_4 = e1
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11),
% 158.74/27.78 | | | | | | | | | | | (12), (13), (14), (16), (17), (18), (19), (20),
% 158.74/27.78 | | | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 158.74/27.78 | | | | | | | | | | | (29), (31), (32), (33), (34), (35), (36), (37),
% 158.74/27.78 | | | | | | | | | | | (38), (39), (40), (41), (42), (43), (44), (45),
% 158.74/27.78 | | | | | | | | | | | (47), (48), (53), (58), (98) are inconsistent by
% 158.74/27.78 | | | | | | | | | | | sub-proof #486.
% 158.74/27.78 | | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | | |
% 158.74/27.78 | | | | | | | | | End of split
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | | (99) all_58_5 = e2 & op(e2, e1) = e2
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | | ALPHA: (99) implies:
% 158.74/27.78 | | | | | | | | | (100) all_58_5 = e2
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | | REF_CLOSE: (5), (21), (25), (28), (29), (32), (36), (37),
% 158.74/27.78 | | | | | | | | | (38), (44), (100) are inconsistent by sub-proof
% 158.74/27.78 | | | | | | | | | #898.
% 158.74/27.78 | | | | | | | | |
% 158.74/27.78 | | | | | | | | End of split
% 158.74/27.78 | | | | | | | |
% 158.74/27.78 | | | | | | | Case 2:
% 158.74/27.78 | | | | | | | |
% 158.74/27.78 | | | | | | | | (101) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 158.74/27.78 | | | | | | | | op(e0, e1) = e2)
% 158.74/27.78 | | | | | | | |
% 158.74/27.78 | | | | | | | | REF_CLOSE: (1), (7), (8), (21), (25), (29), (36), (37), (39),
% 158.74/27.78 | | | | | | | | (44), (47), (58), (101) are inconsistent by sub-proof
% 158.74/27.78 | | | | | | | | #600.
% 158.74/27.78 | | | | | | | |
% 158.74/27.78 | | | | | | | End of split
% 158.74/27.78 | | | | | | |
% 158.74/27.78 | | | | | | End of split
% 158.74/27.78 | | | | | |
% 158.74/27.78 | | | | | End of split
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | End of split
% 158.74/27.78 | | | |
% 158.74/27.78 | | | Case 2:
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | (102) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 158.74/27.78 | | | | e0) = e2)
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | REF_CLOSE: (6), (7), (10), (13), (19), (20), (21), (22), (25), (28),
% 158.74/27.78 | | | | (29), (36), (37), (39), (43), (44), (45), (48), (53), (102)
% 158.74/27.78 | | | | are inconsistent by sub-proof #485.
% 158.74/27.78 | | | |
% 158.74/27.78 | | | End of split
% 158.74/27.78 | | |
% 158.74/27.78 | | End of split
% 158.74/27.78 | |
% 158.74/27.78 | Case 2:
% 158.74/27.78 | |
% 158.74/27.78 | | (103) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 158.74/27.78 | | e2)
% 158.74/27.78 | |
% 158.74/27.78 | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.74/27.78 | | (16), (17), (18), (19), (21), (23), (24), (25), (26), (27), (28),
% 158.74/27.78 | | (29), (31), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 158.74/27.78 | | (41), (42), (44), (45), (48), (103) are inconsistent by sub-proof
% 158.74/27.78 | | #489.
% 158.74/27.78 | |
% 158.74/27.78 | End of split
% 158.74/27.78 |
% 158.74/27.78 End of proof
% 158.74/27.78
% 158.74/27.78 Sub-proof #484 shows that the following formulas are inconsistent:
% 158.74/27.78 ----------------------------------------------------------------
% 158.74/27.78 (1) all_58_15 = e3
% 158.74/27.78 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.78 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.78 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.78 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.78 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.78 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.78 (5) all_58_11 = e1
% 158.74/27.78 (6) op(e1, e1) = all_6_2
% 158.74/27.78 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 158.74/27.78 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.78 (8) op(e3, e3) = all_28_1
% 158.74/27.78 (9) all_58_14 = e0
% 158.74/27.78 (10) all_58_8 = e3
% 158.74/27.78 (11) all_58_0 = e1
% 158.74/27.78 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.78 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.78 (13) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.78 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.78 (14) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 158.74/27.78 (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.78 (15) op(e3, e2) = all_52_4
% 158.74/27.78 (16) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.78 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.78 (17) op(e2, e3) = all_52_1
% 158.74/27.78 (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.78 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.78 (19) ~ (e3 = e0)
% 158.74/27.78 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.78 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.78 (21) all_58_4 = e1
% 158.74/27.78 (22) op(e0, e0) = e0
% 158.74/27.78 (23) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.78 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.78 e2)
% 158.74/27.78 (24) ~ (e2 = e0)
% 158.74/27.78 (25) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.78 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.78 (26) all_58_6 = e0
% 158.74/27.78 (27) op(e2, e3) = e2
% 158.74/27.78 (28) ~ (e3 = e1)
% 158.74/27.78 (29) op(e1, e2) = all_52_6
% 158.74/27.78 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.78 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.78 (31) op(e3, e3) = e1
% 158.74/27.78 (32) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.78 | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.78 (33) ~ (all_52_4 = e3)
% 158.74/27.78 (34) ~ (e2 = e1)
% 158.74/27.78 (35) ~ (e1 = e0)
% 158.74/27.78 (36) all_58_3 = e3
% 158.74/27.78 (37) ~ (all_6_2 = e2)
% 158.74/27.78 (38) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.78 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.78 (39) op(e3, e3) = all_22_1
% 158.74/27.78 (40) ~ (all_52_6 = e3)
% 158.74/27.78 (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.78 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.78 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.78 (43) ~ (e3 = e2)
% 158.74/27.78 (44) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.78 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.78 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.74/27.78 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.74/27.78 (45) op(e0, e0) = e3
% 158.74/27.78
% 158.74/27.78 Begin of proof
% 158.74/27.78 |
% 158.74/27.78 | BETA: splitting (18) gives:
% 158.74/27.78 |
% 158.74/27.78 | Case 1:
% 158.74/27.78 | |
% 158.74/27.78 | | (46) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 158.74/27.78 | | e2)
% 158.74/27.78 | |
% 158.74/27.78 | | BETA: splitting (46) gives:
% 158.74/27.78 | |
% 158.74/27.78 | | Case 1:
% 158.74/27.78 | | |
% 158.74/27.78 | | | (47) all_58_6 = e2 & op(e1, e3) = e2
% 158.74/27.78 | | |
% 158.74/27.78 | | | ALPHA: (47) implies:
% 158.74/27.78 | | | (48) all_58_6 = e2
% 158.74/27.78 | | |
% 158.74/27.78 | | | REF_CLOSE: (12), (17), (19), (20), (24), (27), (28), (34), (35), (41),
% 158.74/27.78 | | | (42), (43), (48) are inconsistent by sub-proof #1152.
% 158.74/27.78 | | |
% 158.74/27.78 | | Case 2:
% 158.74/27.78 | | |
% 158.74/27.78 | | | (49) all_58_7 = e2 & op(e1, e2) = e2
% 158.74/27.78 | | |
% 158.74/27.78 | | | ALPHA: (49) implies:
% 158.74/27.78 | | | (50) all_58_7 = e2
% 158.74/27.78 | | |
% 158.74/27.78 | | | BETA: splitting (23) gives:
% 158.74/27.78 | | |
% 158.74/27.78 | | | Case 1:
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | (51) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 158.74/27.78 | | | | e2) = e2)
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | BETA: splitting (51) gives:
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | Case 1:
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | (52) all_58_12 = e2 & op(e0, e3) = e2
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | ALPHA: (52) implies:
% 158.74/27.78 | | | | | (53) all_58_12 = e2
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | REF_CLOSE: (11), (12), (17), (19), (26), (27), (28), (42), (43), (53)
% 158.74/27.78 | | | | | are inconsistent by sub-proof #1065.
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | Case 2:
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | (54) all_58_13 = e2 & op(e0, e2) = e2
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | ALPHA: (54) implies:
% 158.74/27.78 | | | | | (55) all_58_13 = e2
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 158.74/27.78 | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 158.74/27.78 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 158.74/27.78 | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 158.74/27.78 | | | | | (43), (44), (45), (50), (55) are inconsistent by sub-proof
% 158.74/27.78 | | | | | #486.
% 158.74/27.78 | | | | |
% 158.74/27.78 | | | | End of split
% 158.74/27.78 | | | |
% 158.74/27.78 | | | Case 2:
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | (56) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 158.74/27.78 | | | | e0) = e2)
% 158.74/27.78 | | | |
% 158.74/27.78 | | | | REF_CLOSE: (5), (6), (9), (12), (17), (18), (19), (20), (24), (27),
% 158.74/27.78 | | | | (28), (34), (35), (37), (41), (42), (43), (45), (50), (56)
% 158.74/27.78 | | | | are inconsistent by sub-proof #485.
% 158.74/27.78 | | | |
% 158.74/27.78 | | | End of split
% 158.74/27.78 | | |
% 158.74/27.78 | | End of split
% 158.74/27.78 | |
% 158.74/27.78 | Case 2:
% 158.74/27.78 | |
% 158.74/27.78 | | (57) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 158.74/27.78 | | e2)
% 158.74/27.78 | |
% 158.74/27.78 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 158.74/27.78 | | (14), (15), (16), (17), (19), (22), (23), (24), (25), (26), (27),
% 158.74/27.78 | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 158.74/27.78 | | (39), (40), (42), (43), (45), (57) are inconsistent by sub-proof
% 158.74/27.78 | | #489.
% 158.74/27.78 | |
% 158.74/27.78 | End of split
% 158.74/27.78 |
% 158.74/27.78 End of proof
% 158.74/27.78
% 158.74/27.78 Sub-proof #485 shows that the following formulas are inconsistent:
% 158.74/27.78 ----------------------------------------------------------------
% 158.74/27.78 (1) all_58_11 = e1
% 158.74/27.78 (2) op(e1, e1) = all_6_2
% 158.74/27.78 (3) all_58_7 = e2
% 158.74/27.78 (4) all_58_14 = e0
% 158.74/27.78 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.78 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.78 (6) op(e2, e3) = all_52_1
% 158.74/27.78 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.78 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.78 (8) ~ (e3 = e0)
% 158.74/27.78 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.78 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.78 (10) ~ (e2 = e0)
% 158.74/27.78 (11) op(e2, e3) = e2
% 158.74/27.78 (12) ~ (e3 = e1)
% 158.74/27.78 (13) ~ (e2 = e1)
% 158.74/27.78 (14) ~ (e1 = e0)
% 158.74/27.78 (15) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.78 (16) ~ (all_6_2 = e2)
% 158.74/27.78 (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.78 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.78 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.78 (19) ~ (e3 = e2)
% 158.74/27.78 (20) op(e0, e0) = e3
% 158.74/27.78
% 158.74/27.78 Begin of proof
% 158.74/27.78 |
% 158.74/27.78 | BETA: splitting (15) gives:
% 158.74/27.78 |
% 158.74/27.78 | Case 1:
% 158.74/27.78 | |
% 158.74/27.78 | | (21) all_58_14 = e2 & op(e0, e1) = e2
% 158.74/27.78 | |
% 158.74/27.78 | | ALPHA: (21) implies:
% 158.74/27.78 | | (22) all_58_14 = e2
% 158.74/27.78 | |
% 158.74/27.78 | | COMBINE_EQS: (4), (22) imply:
% 158.74/27.78 | | (23) e2 = e0
% 158.74/27.78 | |
% 158.74/27.78 | | SIMP: (23) implies:
% 158.74/27.78 | | (24) e2 = e0
% 158.74/27.78 | |
% 158.74/27.78 | | COMBINE_EQS: (3), (24) imply:
% 158.74/27.78 | | (25) all_58_7 = e0
% 158.74/27.78 | |
% 158.74/27.79 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 158.74/27.79 | | (16), (17), (18), (19), (25) are inconsistent by sub-proof #743.
% 158.74/27.79 | |
% 158.74/27.79 | Case 2:
% 158.74/27.79 | |
% 158.74/27.79 | | (26) all_58_15 = e2 & op(e0, e0) = e2
% 158.74/27.79 | |
% 158.74/27.79 | | ALPHA: (26) implies:
% 158.74/27.79 | | (27) op(e0, e0) = e2
% 158.74/27.79 | |
% 158.74/27.79 | | REF_CLOSE: (18), (19), (20), (27) are inconsistent by sub-proof #1382.
% 158.74/27.79 | |
% 158.74/27.79 | End of split
% 158.74/27.79 |
% 158.74/27.79 End of proof
% 158.74/27.79
% 158.74/27.79 Sub-proof #486 shows that the following formulas are inconsistent:
% 158.74/27.79 ----------------------------------------------------------------
% 158.74/27.79 (1) all_58_15 = e3
% 158.74/27.79 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.79 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.79 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.79 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.79 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.79 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.79 (5) op(e1, e1) = all_6_2
% 158.74/27.79 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 158.74/27.79 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.79 (7) op(e3, e3) = all_28_1
% 158.74/27.79 (8) all_58_7 = e2
% 158.74/27.79 (9) all_58_14 = e0
% 158.74/27.79 (10) all_58_8 = e3
% 158.74/27.79 (11) all_58_0 = e1
% 158.74/27.79 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.79 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.79 (13) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.79 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.79 (14) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 158.74/27.79 (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.79 (15) op(e3, e2) = all_52_4
% 158.74/27.79 (16) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.79 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.79 (17) op(e2, e3) = all_52_1
% 158.74/27.79 (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.79 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.79 (19) ~ (e3 = e0)
% 158.74/27.79 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.79 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.79 (21) all_58_4 = e1
% 158.74/27.79 (22) op(e0, e0) = e0
% 158.74/27.79 (23) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.79 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.79 e2)
% 158.74/27.79 (24) ~ (e2 = e0)
% 158.74/27.79 (25) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.79 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.79 (26) all_58_6 = e0
% 158.74/27.79 (27) op(e2, e3) = e2
% 158.74/27.79 (28) ~ (e3 = e1)
% 158.74/27.79 (29) op(e1, e2) = all_52_6
% 158.74/27.79 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.79 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.79 (31) op(e3, e3) = e1
% 158.74/27.79 (32) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.79 | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.79 (33) ~ (all_52_4 = e3)
% 158.74/27.79 (34) ~ (e2 = e1)
% 158.74/27.79 (35) ~ (e1 = e0)
% 158.74/27.79 (36) all_58_3 = e3
% 158.74/27.79 (37) ~ (all_6_2 = e2)
% 158.74/27.79 (38) all_58_13 = e2
% 158.74/27.79 (39) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.79 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.79 (40) op(e3, e3) = all_22_1
% 158.74/27.79 (41) ~ (all_52_6 = e3)
% 158.74/27.79 (42) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.79 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.79 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.79 (44) ~ (e3 = e2)
% 158.74/27.79 (45) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.79 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.79 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.74/27.79 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.74/27.79 (46) op(e0, e0) = e3
% 158.74/27.79
% 158.74/27.79 Begin of proof
% 158.74/27.79 |
% 158.74/27.79 | BETA: splitting (13) gives:
% 158.74/27.79 |
% 158.74/27.79 | Case 1:
% 158.74/27.79 | |
% 158.74/27.79 | | (47) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 158.74/27.79 | | e2)
% 158.74/27.79 | |
% 158.74/27.79 | | BETA: splitting (47) gives:
% 158.74/27.79 | |
% 158.74/27.79 | | Case 1:
% 158.74/27.79 | | |
% 158.74/27.79 | | | (48) all_58_4 = e2 & op(e3, e1) = e2
% 158.74/27.79 | | |
% 158.74/27.79 | | | ALPHA: (48) implies:
% 158.74/27.79 | | | (49) all_58_4 = e2
% 158.74/27.79 | | |
% 158.74/27.79 | | | COMBINE_EQS: (21), (49) imply:
% 158.74/27.79 | | | (50) e2 = e1
% 158.74/27.79 | | |
% 158.74/27.79 | | | SIMP: (50) implies:
% 158.74/27.79 | | | (51) e2 = e1
% 158.74/27.79 | | |
% 158.74/27.79 | | | COMBINE_EQS: (8), (51) imply:
% 158.74/27.79 | | | (52) all_58_7 = e1
% 158.74/27.79 | | |
% 158.74/27.79 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 158.74/27.79 | | | (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 158.74/27.79 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.74/27.79 | | | (35), (36), (37), (39), (40), (41), (42), (43), (44), (46),
% 158.74/27.79 | | | (52) are inconsistent by sub-proof #488.
% 158.74/27.79 | | |
% 158.74/27.79 | | Case 2:
% 158.74/27.79 | | |
% 158.74/27.79 | | | (53) all_58_5 = e2 & op(e2, e1) = e2
% 158.74/27.79 | | |
% 158.74/27.79 | | | ALPHA: (53) implies:
% 158.74/27.79 | | | (54) all_58_5 = e2
% 158.74/27.79 | | |
% 158.74/27.79 | | | REF_CLOSE: (4), (19), (24), (27), (28), (30), (34), (35), (36), (43), (54)
% 158.74/27.79 | | | are inconsistent by sub-proof #898.
% 158.74/27.79 | | |
% 158.74/27.79 | | End of split
% 158.74/27.79 | |
% 158.74/27.79 | Case 2:
% 158.74/27.79 | |
% 158.74/27.79 | | (55) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 158.74/27.79 | | e2)
% 158.74/27.79 | |
% 158.74/27.79 | | REF_CLOSE: (1), (5), (6), (19), (24), (28), (34), (35), (37), (38), (43),
% 158.74/27.79 | | (45), (55) are inconsistent by sub-proof #600.
% 158.74/27.79 | |
% 158.74/27.79 | End of split
% 158.74/27.79 |
% 158.74/27.79 End of proof
% 158.74/27.79
% 158.74/27.79 Sub-proof #487 shows that the following formulas are inconsistent:
% 158.74/27.79 ----------------------------------------------------------------
% 158.74/27.79 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.74/27.79 (2) all_56_14 = e3
% 158.74/27.79 (3) all_58_15 = e3
% 158.74/27.79 (4) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.74/27.79 (5) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.79 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.79 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.79 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.79 (7) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.79 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.79 (8) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.79 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.79 (9) all_54_13 = all_52_7
% 158.74/27.79 (10) op(e1, e1) = all_6_2
% 158.74/27.79 (11) ~ (all_52_7 = e3)
% 158.74/27.79 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.79 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.74/27.79 e1)
% 158.74/27.79 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.74/27.79 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.74/27.79 (14) ~ (all_52_6 = all_52_14)
% 158.74/27.79 (15) ~ (all_52_14 = e0)
% 158.74/27.79 (16) ~ (all_52_11 = e3)
% 158.74/27.79 (17) ~ (all_52_4 = all_52_6)
% 158.74/27.79 (18) op(e3, e3) = all_28_1
% 158.74/27.79 (19) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.74/27.79 (20) all_58_14 = e0
% 158.74/27.79 (21) all_58_8 = e3
% 158.74/27.79 (22) ~ (all_52_7 = all_52_11)
% 158.74/27.79 (23) all_58_0 = e1
% 158.74/27.79 (24) op(e1, e2) = all_14_0
% 158.74/27.79 (25) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.74/27.79 (26) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.79 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.79 (27) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.79 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.79 (28) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.74/27.79 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.79 (29) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 158.74/27.79 (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.79 (30) ~ (all_52_14 = e3)
% 158.74/27.79 (31) all_54_1 = all_52_4
% 158.74/27.79 (32) op(e3, e2) = all_52_4
% 158.74/27.79 (33) ~ (all_4_2 = e2)
% 158.74/27.79 (34) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.74/27.79 (35) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.79 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.79 (36) op(e2, e3) = all_52_1
% 158.74/27.79 (37) ~ (all_52_13 = e3)
% 158.74/27.79 (38) all_54_2 = all_52_8
% 158.74/27.79 (39) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.79 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.79 (40) ~ (all_52_8 = all_52_9)
% 158.74/27.79 (41) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.74/27.79 (42) ~ (e3 = e0)
% 158.74/27.79 (43) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.79 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.79 (44) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.74/27.79 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.74/27.79 (45) ~ (all_52_9 = all_52_13)
% 158.74/27.79 (46) op(e0, e0) = e0
% 158.74/27.79 (47) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.79 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.79 e2)
% 158.74/27.79 (48) ~ (e2 = e0)
% 158.74/27.79 (49) ~ (all_52_9 = e3)
% 158.74/27.79 (50) ~ (all_52_2 = all_52_6)
% 158.74/27.79 (51) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.79 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.79 (52) all_58_6 = e0
% 158.74/27.79 (53) op(e2, e0) = all_52_13
% 158.74/27.79 (54) op(e2, e3) = e2
% 158.74/27.79 (55) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.79 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.79 (56) ~ (e3 = e1)
% 158.74/27.79 (57) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.74/27.79 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.79 (58) op(e1, e2) = all_52_6
% 158.74/27.79 (59) ~ (all_4_2 = e1)
% 158.74/27.79 (60) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.74/27.79 (61) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.79 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.79 (62) ~ (all_52_7 = e0)
% 158.74/27.79 (63) op(e0, e0) = all_4_2
% 158.74/27.79 (64) all_54_8 = all_52_2
% 158.74/27.79 (65) all_54_7 = all_52_13
% 158.74/27.79 (66) ~ (all_52_2 = e3)
% 158.74/27.79 (67) op(e3, e3) = e1
% 158.74/27.79 (68) ~ (all_52_13 = e2)
% 158.74/27.79 (69) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.79 | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.79 (70) all_56_15 = all_4_2
% 158.74/27.79 (71) ~ (all_52_4 = e1)
% 158.74/27.79 (72) ~ (all_52_9 = all_52_11)
% 158.74/27.79 (73) ~ (all_52_2 = e1)
% 158.74/27.79 (74) ~ (all_52_2 = all_52_14)
% 158.74/27.79 (75) ~ (all_52_6 = all_52_7)
% 158.74/27.79 (76) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.74/27.79 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.74/27.79 (77) ~ (all_52_4 = e3)
% 158.74/27.79 (78) all_54_6 = all_52_9
% 158.74/27.79 (79) ~ (e2 = e1)
% 158.74/27.79 (80) ~ (all_52_8 = all_52_11)
% 158.74/27.79 (81) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.74/27.79 (82) ~ (all_52_13 = e0)
% 158.74/27.79 (83) ~ (e1 = e0)
% 158.74/27.79 (84) ~ (all_52_2 = e2)
% 158.74/27.79 (85) all_58_3 = e3
% 158.74/27.79 (86) ~ (all_6_2 = e2)
% 158.74/27.79 (87) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.74/27.79 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.74/27.79 e3)
% 158.74/27.79 (88) all_56_13 = e3
% 158.74/27.79 (89) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.74/27.79 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.74/27.79 (90) ~ (all_52_9 = e2)
% 158.74/27.79 (91) ~ (all_52_8 = e3)
% 158.74/27.79 (92) all_54_14 = all_52_11
% 158.74/27.79 (93) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.79 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.79 (94) op(e0, e2) = all_52_7
% 158.74/27.79 (95) op(e3, e3) = all_22_1
% 158.74/27.79 (96) ~ (all_52_8 = e1)
% 158.74/27.79 (97) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.74/27.79 (98) ~ (all_52_6 = e3)
% 158.74/27.79 (99) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.79 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.79 (100) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.79 (101) all_54_11 = all_52_14
% 158.74/27.79 (102) ~ (all_52_13 = all_52_14)
% 158.74/27.79 (103) ~ (e3 = e2)
% 158.74/27.79 (104) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 158.74/27.79 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 158.74/27.79 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 158.74/27.79 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.74/27.79 e0)))
% 158.74/27.79 (105) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 158.74/27.79 (106) all_54_9 = all_52_6
% 158.74/27.79 (107) ~ (all_52_4 = all_52_8)
% 158.74/27.79 (108) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.74/27.79 (109) op(e0, e0) = e3
% 158.74/27.79
% 158.74/27.79 Begin of proof
% 158.74/27.79 |
% 158.74/27.79 | BETA: splitting (105) gives:
% 158.74/27.79 |
% 158.74/27.79 | Case 1:
% 158.74/27.79 | |
% 158.74/27.79 | | (110) all_58_6 = e1 & op(e1, e3) = e1
% 158.74/27.79 | |
% 158.74/27.79 | | ALPHA: (110) implies:
% 158.74/27.79 | | (111) all_58_6 = e1
% 158.74/27.79 | |
% 158.74/27.79 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 158.74/27.79 | | (14), (15), (16), (17), (18), (19), (21), (22), (24), (25), (26),
% 158.74/27.79 | | (27), (28), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 158.74/27.79 | | (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 158.74/27.79 | | (50), (51), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 158.74/27.79 | | (62), (63), (64), (65), (66), (67), (68), (70), (71), (72), (73),
% 158.74/27.79 | | (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 158.74/27.79 | | (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 158.74/27.79 | | (96), (97), (98), (99), (100), (101), (102), (103), (104), (106),
% 158.74/27.79 | | (107), (108), (111) are inconsistent by sub-proof #490.
% 158.74/27.79 | |
% 158.74/27.79 | Case 2:
% 158.74/27.79 | |
% 158.74/27.79 | | (112) all_58_7 = e1 & op(e1, e2) = e1
% 158.74/27.79 | |
% 158.74/27.79 | | ALPHA: (112) implies:
% 158.74/27.79 | | (113) all_58_7 = e1
% 158.74/27.79 | |
% 158.74/27.79 | | REF_CLOSE: (3), (5), (7), (8), (10), (12), (18), (20), (21), (23), (26),
% 158.74/27.79 | | (27), (29), (32), (35), (36), (39), (42), (43), (46), (47), (48),
% 158.74/27.79 | | (51), (52), (54), (56), (58), (61), (67), (69), (77), (79), (83),
% 158.74/27.79 | | (85), (86), (93), (95), (98), (99), (100), (103), (109), (113)
% 158.74/27.79 | | are inconsistent by sub-proof #488.
% 158.74/27.79 | |
% 158.74/27.79 | End of split
% 158.74/27.79 |
% 158.74/27.79 End of proof
% 158.74/27.79
% 158.74/27.79 Sub-proof #488 shows that the following formulas are inconsistent:
% 158.74/27.79 ----------------------------------------------------------------
% 158.74/27.79 (1) all_58_15 = e3
% 158.74/27.79 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.79 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.79 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.79 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.79 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.79 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.79 (5) op(e1, e1) = all_6_2
% 158.74/27.79 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 158.74/27.79 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.79 (7) op(e3, e3) = all_28_1
% 158.74/27.79 (8) all_58_14 = e0
% 158.74/27.79 (9) all_58_8 = e3
% 158.74/27.79 (10) all_58_0 = e1
% 158.74/27.79 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.79 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.79 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.79 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.79 (13) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 158.74/27.79 (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.79 (14) op(e3, e2) = all_52_4
% 158.74/27.79 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.79 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.79 (16) op(e2, e3) = all_52_1
% 158.74/27.79 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.79 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.79 (18) ~ (e3 = e0)
% 158.74/27.79 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.79 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.79 (20) op(e0, e0) = e0
% 158.74/27.79 (21) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.79 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.79 e2)
% 158.74/27.79 (22) ~ (e2 = e0)
% 158.74/27.79 (23) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.79 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.79 (24) all_58_6 = e0
% 158.74/27.79 (25) op(e2, e3) = e2
% 158.74/27.79 (26) ~ (e3 = e1)
% 158.74/27.79 (27) op(e1, e2) = all_52_6
% 158.74/27.79 (28) all_58_7 = e1
% 158.74/27.79 (29) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.79 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.79 (30) op(e3, e3) = e1
% 158.74/27.79 (31) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.79 | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.79 (32) ~ (all_52_4 = e3)
% 158.74/27.79 (33) ~ (e2 = e1)
% 158.74/27.79 (34) ~ (e1 = e0)
% 158.74/27.79 (35) all_58_3 = e3
% 158.74/27.79 (36) ~ (all_6_2 = e2)
% 158.74/27.79 (37) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.79 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.79 (38) op(e3, e3) = all_22_1
% 158.74/27.79 (39) ~ (all_52_6 = e3)
% 158.74/27.79 (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.79 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.79 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.79 (42) ~ (e3 = e2)
% 158.74/27.79 (43) op(e0, e0) = e3
% 158.74/27.79
% 158.74/27.79 Begin of proof
% 158.74/27.79 |
% 158.74/27.79 | BETA: splitting (17) gives:
% 158.74/27.79 |
% 158.74/27.79 | Case 1:
% 158.74/27.79 | |
% 158.74/27.79 | | (44) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 158.74/27.79 | | e2)
% 158.74/27.79 | |
% 158.74/27.79 | | REF_CLOSE: (11), (16), (18), (19), (22), (25), (26), (28), (33), (34), (40),
% 158.74/27.79 | | (41), (42), (44) are inconsistent by sub-proof #728.
% 158.74/27.79 | |
% 158.74/27.79 | Case 2:
% 158.74/27.79 | |
% 158.74/27.79 | | (45) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 158.74/27.79 | | e2)
% 158.74/27.79 | |
% 158.74/27.79 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.74/27.79 | | (13), (14), (15), (16), (18), (20), (21), (22), (23), (24), (25),
% 158.74/27.79 | | (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 158.74/27.79 | | (38), (39), (41), (42), (43), (45) are inconsistent by sub-proof
% 158.74/27.79 | | #489.
% 158.74/27.79 | |
% 158.74/27.79 | End of split
% 158.74/27.79 |
% 158.74/27.79 End of proof
% 158.74/27.79
% 158.74/27.79 Sub-proof #489 shows that the following formulas are inconsistent:
% 158.74/27.79 ----------------------------------------------------------------
% 158.74/27.79 (1) all_58_15 = e3
% 158.74/27.79 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.79 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.80 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.80 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.80 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.80 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.80 (5) op(e1, e1) = all_6_2
% 158.74/27.80 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 158.74/27.80 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.80 (7) op(e3, e3) = all_28_1
% 158.74/27.80 (8) all_58_14 = e0
% 158.74/27.80 (9) all_58_8 = e3
% 158.74/27.80 (10) all_58_0 = e1
% 158.74/27.80 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.80 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.80 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.80 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.80 (13) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 158.74/27.80 (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.80 (14) op(e3, e2) = all_52_4
% 158.74/27.80 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.80 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.80 (16) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.80 (17) op(e2, e3) = all_52_1
% 158.74/27.80 (18) ~ (e3 = e0)
% 158.74/27.80 (19) op(e0, e0) = e0
% 158.74/27.80 (20) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.80 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.80 e2)
% 158.74/27.80 (21) ~ (e2 = e0)
% 158.74/27.80 (22) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.80 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.80 (23) all_58_6 = e0
% 158.74/27.80 (24) op(e2, e3) = e2
% 158.74/27.80 (25) ~ (e3 = e1)
% 158.74/27.80 (26) op(e1, e2) = all_52_6
% 158.74/27.80 (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.80 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.80 (28) op(e3, e3) = e1
% 158.74/27.80 (29) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.80 | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.80 (30) ~ (all_52_4 = e3)
% 158.74/27.80 (31) ~ (e2 = e1)
% 158.74/27.80 (32) ~ (e1 = e0)
% 158.74/27.80 (33) all_58_3 = e3
% 158.74/27.80 (34) ~ (all_6_2 = e2)
% 158.74/27.80 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.80 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.80 (36) op(e3, e3) = all_22_1
% 158.74/27.80 (37) ~ (all_52_6 = e3)
% 158.74/27.80 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.80 (39) ~ (e3 = e2)
% 158.74/27.80 (40) op(e0, e0) = e3
% 158.74/27.80
% 158.74/27.80 Begin of proof
% 158.74/27.80 |
% 158.74/27.80 | BETA: splitting (16) gives:
% 158.74/27.80 |
% 158.74/27.80 | Case 1:
% 158.74/27.80 | |
% 158.74/27.80 | | (41) all_58_8 = e2 & op(e1, e1) = e2
% 158.74/27.80 | |
% 158.74/27.80 | | REF_CLOSE: (5), (34), (38), (41) are inconsistent by sub-proof #1440.
% 158.74/27.80 | |
% 158.74/27.80 | Case 2:
% 158.74/27.80 | |
% 158.74/27.80 | | (42) all_58_11 = e2 & op(e1, e0) = e2
% 158.74/27.80 | |
% 158.74/27.80 | | ALPHA: (42) implies:
% 158.74/27.80 | | (43) all_58_11 = e2
% 158.74/27.80 | |
% 158.74/27.80 | | BETA: splitting (20) gives:
% 158.74/27.80 | |
% 158.74/27.80 | | Case 1:
% 158.74/27.80 | | |
% 158.74/27.80 | | | (44) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2)
% 158.74/27.80 | | | = e2)
% 158.74/27.80 | | |
% 158.74/27.80 | | | BETA: splitting (44) gives:
% 158.74/27.80 | | |
% 158.74/27.80 | | | Case 1:
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | (45) all_58_12 = e2 & op(e0, e3) = e2
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | ALPHA: (45) implies:
% 158.74/27.80 | | | | (46) all_58_12 = e2
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | REF_CLOSE: (10), (11), (17), (18), (23), (24), (25), (38), (39), (46)
% 158.74/27.80 | | | | are inconsistent by sub-proof #1065.
% 158.74/27.80 | | | |
% 158.74/27.80 | | | Case 2:
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | (47) all_58_13 = e2 & op(e0, e2) = e2
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | ALPHA: (47) implies:
% 158.74/27.80 | | | | (48) all_58_13 = e2
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | BETA: splitting (12) gives:
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | Case 1:
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | (49) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 158.74/27.80 | | | | | e1) = e2)
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | BETA: splitting (49) gives:
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | Case 1:
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | (50) all_58_4 = e2 & op(e3, e1) = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | ALPHA: (50) implies:
% 158.74/27.80 | | | | | | (51) all_58_4 = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | REF_CLOSE: (1), (2), (3), (7), (9), (13), (14), (15), (18), (19),
% 158.74/27.80 | | | | | | (21), (22), (25), (26), (28), (30), (31), (32), (35),
% 158.74/27.80 | | | | | | (36), (37), (38), (39), (40), (43), (51) are inconsistent
% 158.74/27.80 | | | | | | by sub-proof #529.
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | Case 2:
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | (52) all_58_5 = e2 & op(e2, e1) = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | ALPHA: (52) implies:
% 158.74/27.80 | | | | | | (53) all_58_5 = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | REF_CLOSE: (4), (18), (21), (24), (25), (27), (31), (32), (33),
% 158.74/27.80 | | | | | | (38), (53) are inconsistent by sub-proof #898.
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | End of split
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | Case 2:
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | (54) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 158.74/27.80 | | | | | e1) = e2)
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | BETA: splitting (54) gives:
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | Case 1:
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | (55) all_58_8 = e2 & op(e1, e1) = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | ALPHA: (55) implies:
% 158.74/27.80 | | | | | | (56) all_58_8 = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | REF_CLOSE: (2), (15), (18), (21), (22), (25), (26), (31), (32),
% 158.74/27.80 | | | | | | (37), (38), (39), (43), (56) are inconsistent by
% 158.74/27.80 | | | | | | sub-proof #1068.
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | Case 2:
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | (57) all_58_14 = e2 & op(e0, e1) = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | ALPHA: (57) implies:
% 158.74/27.80 | | | | | | (58) all_58_14 = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | REF_CLOSE: (1), (6), (21), (25), (29), (31), (32), (48), (58) are
% 158.74/27.80 | | | | | | inconsistent by sub-proof #1205.
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | End of split
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | End of split
% 158.74/27.80 | | | |
% 158.74/27.80 | | | End of split
% 158.74/27.80 | | |
% 158.74/27.80 | | Case 2:
% 158.74/27.80 | | |
% 158.74/27.80 | | | (59) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0)
% 158.74/27.80 | | | = e2)
% 158.74/27.80 | | |
% 158.74/27.80 | | | BETA: splitting (59) gives:
% 158.74/27.80 | | |
% 158.74/27.80 | | | Case 1:
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | (60) all_58_14 = e2 & op(e0, e1) = e2
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | ALPHA: (60) implies:
% 158.74/27.80 | | | | (61) all_58_14 = e2
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | REF_CLOSE: (8), (21), (61) are inconsistent by sub-proof #1408.
% 158.74/27.80 | | | |
% 158.74/27.80 | | | Case 2:
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | (62) all_58_15 = e2 & op(e0, e0) = e2
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | ALPHA: (62) implies:
% 158.74/27.80 | | | | (63) op(e0, e0) = e2
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | REF_CLOSE: (38), (39), (40), (63) are inconsistent by sub-proof #1382.
% 158.74/27.80 | | | |
% 158.74/27.80 | | | End of split
% 158.74/27.80 | | |
% 158.74/27.80 | | End of split
% 158.74/27.80 | |
% 158.74/27.80 | End of split
% 158.74/27.80 |
% 158.74/27.80 End of proof
% 158.74/27.80
% 158.74/27.80 Sub-proof #490 shows that the following formulas are inconsistent:
% 158.74/27.80 ----------------------------------------------------------------
% 158.74/27.80 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.74/27.80 (2) all_56_14 = e3
% 158.74/27.80 (3) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.74/27.80 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.80 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.80 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.80 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.80 (6) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.80 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.80 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.80 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.80 (8) all_54_13 = all_52_7
% 158.74/27.80 (9) op(e1, e1) = all_6_2
% 158.74/27.80 (10) ~ (all_52_7 = e3)
% 158.74/27.80 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.80 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.74/27.80 e1)
% 158.74/27.80 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.74/27.80 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.74/27.80 (13) ~ (all_52_6 = all_52_14)
% 158.74/27.80 (14) ~ (all_52_14 = e0)
% 158.74/27.80 (15) ~ (all_52_11 = e3)
% 158.74/27.80 (16) ~ (all_52_4 = all_52_6)
% 158.74/27.80 (17) op(e3, e3) = all_28_1
% 158.74/27.80 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.74/27.80 (19) all_58_8 = e3
% 158.74/27.80 (20) ~ (all_52_7 = all_52_11)
% 158.74/27.80 (21) op(e1, e2) = all_14_0
% 158.74/27.80 (22) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.74/27.80 (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.80 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.80 (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.80 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.80 (25) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.74/27.80 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.80 (26) ~ (all_52_14 = e3)
% 158.74/27.80 (27) all_54_1 = all_52_4
% 158.74/27.80 (28) op(e3, e2) = all_52_4
% 158.74/27.80 (29) ~ (all_4_2 = e2)
% 158.74/27.80 (30) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.74/27.80 (31) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.80 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.80 (32) all_58_6 = e1
% 158.74/27.80 (33) op(e2, e3) = all_52_1
% 158.74/27.80 (34) ~ (all_52_13 = e3)
% 158.74/27.80 (35) all_54_2 = all_52_8
% 158.74/27.80 (36) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.80 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.80 (37) ~ (all_52_8 = all_52_9)
% 158.74/27.80 (38) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 158.74/27.80 (39) ~ (e3 = e0)
% 158.74/27.80 (40) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.80 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.80 (41) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 158.74/27.80 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 158.74/27.80 (42) ~ (all_52_9 = all_52_13)
% 158.74/27.80 (43) op(e0, e0) = e0
% 158.74/27.80 (44) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 158.74/27.80 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 158.74/27.80 e2)
% 158.74/27.80 (45) ~ (e2 = e0)
% 158.74/27.80 (46) ~ (all_52_9 = e3)
% 158.74/27.80 (47) ~ (all_52_2 = all_52_6)
% 158.74/27.80 (48) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.80 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.80 (49) op(e2, e0) = all_52_13
% 158.74/27.80 (50) op(e2, e3) = e2
% 158.74/27.80 (51) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.80 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 158.74/27.80 (52) ~ (e3 = e1)
% 158.74/27.80 (53) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 158.74/27.80 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 158.74/27.80 (54) op(e1, e2) = all_52_6
% 158.74/27.80 (55) ~ (all_4_2 = e1)
% 158.74/27.80 (56) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.74/27.80 (57) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.80 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.80 (58) ~ (all_52_7 = e0)
% 158.74/27.80 (59) op(e0, e0) = all_4_2
% 158.74/27.80 (60) all_54_8 = all_52_2
% 158.74/27.80 (61) all_54_7 = all_52_13
% 158.74/27.80 (62) ~ (all_52_2 = e3)
% 158.74/27.80 (63) op(e3, e3) = e1
% 158.74/27.80 (64) ~ (all_52_13 = e2)
% 158.74/27.80 (65) all_56_15 = all_4_2
% 158.74/27.80 (66) ~ (all_52_4 = e1)
% 158.74/27.80 (67) ~ (all_52_9 = all_52_11)
% 158.74/27.80 (68) ~ (all_52_2 = e1)
% 158.74/27.80 (69) ~ (all_52_2 = all_52_14)
% 158.74/27.80 (70) ~ (all_52_6 = all_52_7)
% 158.74/27.80 (71) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.74/27.80 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.74/27.80 (72) ~ (all_52_4 = e3)
% 158.74/27.80 (73) all_54_6 = all_52_9
% 158.74/27.80 (74) ~ (e2 = e1)
% 158.74/27.80 (75) ~ (all_52_8 = all_52_11)
% 158.74/27.80 (76) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.74/27.80 (77) ~ (all_52_13 = e0)
% 158.74/27.80 (78) ~ (e1 = e0)
% 158.74/27.80 (79) ~ (all_52_2 = e2)
% 158.74/27.80 (80) all_58_3 = e3
% 158.74/27.80 (81) ~ (all_6_2 = e2)
% 158.74/27.80 (82) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 158.74/27.80 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 158.74/27.80 e3)
% 158.74/27.80 (83) all_56_13 = e3
% 158.74/27.80 (84) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.74/27.80 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.74/27.80 (85) ~ (all_52_9 = e2)
% 158.74/27.80 (86) ~ (all_52_8 = e3)
% 158.74/27.80 (87) all_54_14 = all_52_11
% 158.74/27.80 (88) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.80 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.80 (89) op(e0, e2) = all_52_7
% 158.74/27.80 (90) op(e3, e3) = all_22_1
% 158.74/27.80 (91) ~ (all_52_8 = e1)
% 158.74/27.80 (92) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 158.74/27.80 (93) ~ (all_52_6 = e3)
% 158.74/27.80 (94) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 158.74/27.80 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 158.74/27.80 (95) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.80 (96) all_54_11 = all_52_14
% 158.74/27.80 (97) ~ (all_52_13 = all_52_14)
% 158.74/27.80 (98) ~ (e3 = e2)
% 158.74/27.80 (99) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.80 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.80 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.74/27.80 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.74/27.80 (100) all_54_9 = all_52_6
% 158.74/27.80 (101) ~ (all_52_4 = all_52_8)
% 158.74/27.80 (102) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 158.74/27.80
% 158.74/27.80 Begin of proof
% 158.74/27.80 |
% 158.74/27.80 | BETA: splitting (48) gives:
% 158.74/27.80 |
% 158.74/27.80 | Case 1:
% 158.74/27.80 | |
% 158.74/27.80 | | (103) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 158.74/27.80 | | e0)
% 158.74/27.80 | |
% 158.74/27.80 | | BETA: splitting (103) gives:
% 158.74/27.80 | |
% 158.74/27.80 | | Case 1:
% 158.74/27.80 | | |
% 158.74/27.80 | | | (104) all_58_6 = e0 & op(e1, e3) = e0
% 158.74/27.80 | | |
% 158.74/27.80 | | | ALPHA: (104) implies:
% 158.74/27.80 | | | (105) all_58_6 = e0
% 158.74/27.80 | | |
% 158.74/27.80 | | | REF_CLOSE: (32), (78), (105) are inconsistent by sub-proof #735.
% 158.74/27.80 | | |
% 158.74/27.80 | | Case 2:
% 158.74/27.80 | | |
% 158.74/27.80 | | | (106) all_58_7 = e0 & op(e1, e2) = e0
% 158.74/27.80 | | |
% 158.74/27.80 | | | ALPHA: (106) implies:
% 158.74/27.80 | | | (107) all_58_7 = e0
% 158.74/27.80 | | | (108) op(e1, e2) = e0
% 158.74/27.80 | | |
% 158.74/27.80 | | | BETA: splitting (18) gives:
% 158.74/27.80 | | |
% 158.74/27.80 | | | Case 1:
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | (109) all_54_7 = e3
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | COMBINE_EQS: (61), (109) imply:
% 158.74/27.80 | | | | (110) all_52_13 = e3
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | REDUCE: (34), (110) imply:
% 158.74/27.80 | | | | (111) $false
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | CLOSE: (111) is inconsistent.
% 158.74/27.80 | | | |
% 158.74/27.80 | | | Case 2:
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | (112) ~ (all_54_7 = e3)
% 158.74/27.80 | | | | (113) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | BETA: splitting (36) gives:
% 158.74/27.80 | | | |
% 158.74/27.80 | | | | Case 1:
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | (114) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 158.74/27.80 | | | | | e2) = e2)
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | REF_CLOSE: (23), (33), (39), (40), (45), (50), (52), (74), (78), (94),
% 158.74/27.80 | | | | | (95), (98), (107), (114) are inconsistent by sub-proof
% 158.74/27.80 | | | | | #744.
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | Case 2:
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | (115) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 158.74/27.80 | | | | | e0) = e2)
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | BETA: splitting (115) gives:
% 158.74/27.80 | | | | |
% 158.74/27.80 | | | | | Case 1:
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | (116) all_58_8 = e2 & op(e1, e1) = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | REF_CLOSE: (9), (81), (95), (116) are inconsistent by sub-proof
% 158.74/27.80 | | | | | | #1440.
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | Case 2:
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | (117) all_58_11 = e2 & op(e1, e0) = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | ALPHA: (117) implies:
% 158.74/27.80 | | | | | | (118) all_58_11 = e2
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | BETA: splitting (94) gives:
% 158.74/27.80 | | | | | |
% 158.74/27.80 | | | | | | Case 1:
% 158.74/27.80 | | | | | | |
% 158.74/27.80 | | | | | | | (119) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 158.74/27.80 | | | | | | | op(e2, e3) = e0)
% 158.74/27.80 | | | | | | |
% 158.74/27.80 | | | | | | | BETA: splitting (119) gives:
% 158.74/27.80 | | | | | | |
% 158.74/27.80 | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | |
% 158.74/27.80 | | | | | | | | (120) all_58_0 = e0 & op(e3, e3) = e0
% 158.74/27.80 | | | | | | | |
% 158.74/27.80 | | | | | | | | ALPHA: (120) implies:
% 158.74/27.80 | | | | | | | | (121) all_58_0 = e0
% 158.74/27.80 | | | | | | | |
% 158.74/27.80 | | | | | | | | BETA: splitting (99) gives:
% 158.74/27.80 | | | | | | | |
% 158.74/27.80 | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | |
% 158.74/27.80 | | | | | | | | | (122) all_58_15 = e0 & op(e0, e0) = e0
% 158.74/27.80 | | | | | | | | |
% 158.74/27.80 | | | | | | | | | ALPHA: (122) implies:
% 158.74/27.80 | | | | | | | | | (123) all_58_15 = e0
% 158.74/27.80 | | | | | | | | |
% 158.74/27.80 | | | | | | | | | BETA: splitting (22) gives:
% 158.74/27.80 | | | | | | | | |
% 158.74/27.80 | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | (124) all_54_8 = e3
% 158.74/27.80 | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | REF_CLOSE: (60), (62), (124) are inconsistent by sub-proof
% 158.74/27.80 | | | | | | | | | | #1425.
% 158.74/27.80 | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | Case 2:
% 158.74/27.80 | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | (125) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.74/27.80 | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | BETA: splitting (82) gives:
% 158.74/27.80 | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | (126) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 158.74/27.80 | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 158.74/27.80 | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | BETA: splitting (126) gives:
% 158.74/27.80 | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | (127) all_58_12 = e3 & op(e0, e3) = e3
% 158.74/27.80 | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | ALPHA: (127) implies:
% 158.74/27.80 | | | | | | | | | | | | (128) all_58_12 = e3
% 158.74/27.80 | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | BETA: splitting (84) gives:
% 158.74/27.80 | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | (129) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 158.74/27.80 | | | | | | | | | | | | | & op(e3, e2) = e1)
% 158.74/27.80 | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | BETA: splitting (129) gives:
% 158.74/27.80 | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | (130) all_58_0 = e1 & op(e3, e3) = e1
% 158.74/27.80 | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | REF_CLOSE: (32), (40), (50), (52), (74), (78), (95), (121),
% 158.74/27.80 | | | | | | | | | | | | | | (128), (130) are inconsistent by sub-proof #694.
% 158.74/27.80 | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | Case 2:
% 158.74/27.80 | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | (131) all_58_1 = e1 & op(e3, e2) = e1
% 158.74/27.80 | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | ALPHA: (131) implies:
% 158.74/27.80 | | | | | | | | | | | | | | (132) all_58_1 = e1
% 158.74/27.80 | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 158.74/27.80 | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | (133) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 158.74/27.80 | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 158.74/27.80 | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 158.74/27.80 | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | (134) all_58_9 = e3 & op(e3, e0) = e3
% 158.74/27.80 | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 158.74/27.80 | | | | | | | | | | | | | | | | (135) all_58_9 = e3
% 158.74/27.80 | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 158.74/27.80 | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | (136) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 158.74/27.80 | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 158.74/27.80 | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 158.74/27.80 | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (137) all_58_0 = e2 & op(e3, e3) = e2
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (138) all_58_0 = e2
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (138) imply:
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (139) e2 = e0
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (11), (12), (15), (17), (19), (20), (23), (24),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (25), (28), (29), (32), (33), (34), (35), (36),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (63), (64), (65),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (67), (71), (72), (73), (74), (75), (77), (78),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (94), (95), (98),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (99), (102), (113), (118), (139) are inconsistent
% 158.74/27.80 | | | | | | | | | | | | | | | | | | by sub-proof #503.
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (140) all_58_1 = e2 & op(e3, e2) = e2
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (132), (140) are inconsistent by sub-proof
% 158.74/27.80 | | | | | | | | | | | | | | | | | | #1213.
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.80 | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.80 | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | (141) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 158.74/27.80 | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 158.74/27.80 | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 158.74/27.80 | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (142) all_58_4 = e2 & op(e3, e1) = e2
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (143) all_58_4 = e2
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (8), (10), (13), (15), (20), (21), (26),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (32), (35), (37), (40), (42), (46), (47), (50),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (54), (56), (58), (60), (61), (64), (67), (68),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (69), (70), (73), (75), (76), (77), (79), (84),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (85), (86), (87), (91), (92), (93), (95), (96),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (100), (102), (108), (113), (121), (125), (128),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (132), (135), (143) are inconsistent by sub-proof
% 158.74/27.80 | | | | | | | | | | | | | | | | | | #501.
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (144) all_58_9 = e2 & op(e3, e0) = e2
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (31), (39), (45), (48), (52), (54),
% 158.74/27.80 | | | | | | | | | | | | | | | | | | (74), (78), (93), (95), (98), (118), (135), (144)
% 158.74/27.80 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #500.
% 158.74/27.80 | | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.80 | | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | End of split
% 158.74/27.80 | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | Case 2:
% 158.74/27.80 | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | (145) all_58_10 = e3 & op(e2, e0) = e3
% 158.74/27.80 | | | | | | | | | | | | | | | |
% 158.74/27.80 | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 158.74/27.80 | | | | | | | | | | | | | | | | (146) op(e2, e0) = e3
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | REF_CLOSE: (34), (49), (95), (146) are inconsistent by
% 158.74/27.81 | | | | | | | | | | | | | | | | sub-proof #1364.
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | (147) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 158.74/27.81 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (19), (23), (31), (32), (33), (39),
% 158.74/27.81 | | | | | | | | | | | | | | | (43), (45), (48), (50), (52), (54), (63), (74),
% 158.74/27.81 | | | | | | | | | | | | | | | (78), (90), (93), (95), (98), (118), (123), (128),
% 158.74/27.81 | | | | | | | | | | | | | | | (147) are inconsistent by sub-proof #499.
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | (148) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 158.74/27.81 | | | | | | | | | | | | | & op(e3, e0) = e1)
% 158.74/27.81 | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | BETA: splitting (148) gives:
% 158.74/27.81 | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | (149) all_58_4 = e1 & op(e3, e1) = e1
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | ALPHA: (149) implies:
% 158.74/27.81 | | | | | | | | | | | | | | (150) all_58_4 = e1
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | (151) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 158.74/27.81 | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | (152) all_58_9 = e3 & op(e3, e0) = e3
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | (153) all_58_9 = e3
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | (154) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (155) all_58_0 = e2 & op(e3, e3) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (156) all_58_0 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (156) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (157) e2 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (11), (12), (15), (17), (19), (20), (23), (24),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (25), (28), (29), (32), (33), (34), (35), (36),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (63), (64), (65),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (67), (71), (72), (73), (74), (75), (77), (78),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (94), (95), (98),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (99), (102), (113), (118), (157) are inconsistent
% 158.74/27.81 | | | | | | | | | | | | | | | | | | by sub-proof #503.
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (158) all_58_1 = e2 & op(e3, e2) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (159) all_58_1 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (160) op(e3, e2) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | (161) all_54_7 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (161) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | #1427.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | (162) ~ (all_54_7 = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | (163) all_54_7 = e1 | all_54_7 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (164) all_54_7 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (164) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (165) all_52_13 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | SIMP: (165) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (166) all_52_13 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (166) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (167) ~ (all_52_9 = e1)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (166) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (168) ~ (all_52_14 = e1)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | SIMP: (168) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (169) ~ (all_52_14 = e1)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | (170) all_54_6 = e3
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (73), (170) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | #1193.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | (171) ~ (all_54_6 = e3)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | (172) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | (173) all_54_6 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (85), (173) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | #1192.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | (174) ~ (all_54_6 = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | (175) all_54_6 = e1 | all_54_6 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | (176) all_54_6 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (167), (176) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | #562.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | (177) all_54_6 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (177) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | (178) all_52_9 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (178) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | (179) all_52_9 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (179) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | (180) ~ (all_52_8 = e0)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | (181) all_54_11 = e3
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (96), (181) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | #1415.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | (182) ~ (all_54_11 = e3)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | (183) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_54_2 = e3
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (86), (184) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | #1210.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | (185) ~ (all_54_2 = e3)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_54_2 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (187) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_52_8 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (188) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_52_8 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (189) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (190) ~ (all_52_4 = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_54_1 = e3
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (191) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_52_4 = e3
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (192) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) $false
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (193) is inconsistent.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) ~ (all_54_1 = e3)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_54_11 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (196) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_52_14 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_52_14 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (198) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) ~ (all_52_6 = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (198) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) ~ (e3 = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_54_9 = e3
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (93), (100), (201) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1181.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) ~ (all_54_9 = e3)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_54_1 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (204) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_52_4 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (205) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) $false
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) ~ (all_54_1 = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_54_1 = e1 | all_54_1 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_1 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (209) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_52_4 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (210) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) $false
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_54_1 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (212) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_52_4 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (213) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) ~ (all_52_6 = e0)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) ~ (all_52_6 = e0)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (213) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) ~ (e3 = e0)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (213) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) ~ (e2 = e0)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (213) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) op(e3, e2) = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_54_9 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (199), (219) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1180.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_54_9 = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_54_9 = e1 | all_54_9 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_54_9 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (222) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_52_6 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (223) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_52_6 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (224) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) ~ (e3 = e1)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (224) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) ~ (e2 = e1)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (95) with e0, e2, e2, e3,
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (160), (218) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) e2 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (227) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_58_1 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_58_0 = e2 & op(e3, e3) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_0 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (230) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) e2 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (15), (17), (19), (20), (23), (24),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (25), (28), (29), (32), (33), (34), (35), (36),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (63), (64), (65),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (67), (71), (72), (73), (74), (75), (77), (78),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (94), (95), (98),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (102), (113), (118), (231) are inconsistent
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #503.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (228) imply:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) e2 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (15), (17), (19), (20), (23), (24),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (25), (28), (29), (32), (33), (34), (35), (36),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (63), (64), (65),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (67), (71), (72), (73), (74), (75), (77), (78),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (94), (95), (98),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (102), (113), (118), (232) are inconsistent
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #503.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_4 = e2 & op(e3, e1) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_58_4 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (50), (52), (74), (78), (84), (95), (121),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (128), (153), (228), (235) are inconsistent by
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #498.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_58_9 = e2 & op(e3, e0) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (31), (39), (45), (48), (52), (54),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (74), (78), (93), (95), (98), (118), (153), (236)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #500.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_54_9 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (215), (237) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1170.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_54_11 = e1 | all_54_11 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (96), (169), (238) are inconsistent by
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1227.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_54_2 = e1 | all_54_2 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (91), (180), (239) are inconsistent by
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #561.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (240) all_54_7 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (77), (240) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | #1112.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | (241) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (242) all_58_4 = e2 & op(e3, e1) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (243) all_58_4 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (150), (243) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | | | | | | | #1311.
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (244) all_58_9 = e2 & op(e3, e0) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (31), (39), (45), (48), (52), (54),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (74), (78), (93), (95), (98), (118), (153), (244)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #500.
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | (245) all_58_10 = e3 & op(e2, e0) = e3
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | ALPHA: (245) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | (246) op(e2, e0) = e3
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | REF_CLOSE: (34), (49), (95), (246) are inconsistent by
% 158.74/27.81 | | | | | | | | | | | | | | | | sub-proof #1364.
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | (247) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 158.74/27.81 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (19), (23), (31), (32), (33), (39),
% 158.74/27.81 | | | | | | | | | | | | | | | (43), (45), (48), (50), (52), (54), (63), (74),
% 158.74/27.81 | | | | | | | | | | | | | | | (78), (90), (93), (95), (98), (118), (123), (128),
% 158.74/27.81 | | | | | | | | | | | | | | | (247) are inconsistent by sub-proof #499.
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | (248) all_58_9 = e1 & op(e3, e0) = e1
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | ALPHA: (248) implies:
% 158.74/27.81 | | | | | | | | | | | | | | (249) all_58_9 = e1
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | (250) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 158.74/27.81 | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (17), (19), (23),
% 158.74/27.81 | | | | | | | | | | | | | | | (24), (25), (28), (29), (33), (34), (36), (38),
% 158.74/27.81 | | | | | | | | | | | | | | | (39), (40), (45), (48), (49), (50), (52), (53),
% 158.74/27.81 | | | | | | | | | | | | | | | (55), (57), (59), (63), (65), (71), (72), (74),
% 158.74/27.81 | | | | | | | | | | | | | | | (78), (80), (81), (82), (83), (88), (89), (90),
% 158.74/27.81 | | | | | | | | | | | | | | | (94), (95), (98), (99), (128), (249), (250) are
% 158.74/27.81 | | | | | | | | | | | | | | | inconsistent by sub-proof #496.
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | (251) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 158.74/27.81 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (19), (23), (31), (32), (33), (39),
% 158.74/27.81 | | | | | | | | | | | | | | | (43), (45), (48), (50), (52), (54), (63), (74),
% 158.74/27.81 | | | | | | | | | | | | | | | (78), (90), (93), (95), (98), (118), (123), (128),
% 158.74/27.81 | | | | | | | | | | | | | | | (251) are inconsistent by sub-proof #499.
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | (252) all_58_13 = e3 & op(e0, e2) = e3
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | REF_CLOSE: (10), (89), (95), (252) are inconsistent by
% 158.74/27.81 | | | | | | | | | | | | sub-proof #1449.
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | (253) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 158.74/27.81 | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | BETA: splitting (253) gives:
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | (254) all_58_14 = e3 & op(e0, e1) = e3
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | ALPHA: (254) implies:
% 158.74/27.81 | | | | | | | | | | | | (255) all_58_14 = e3
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | REF_CLOSE: (7), (9), (19), (24), (39), (45), (50), (52),
% 158.74/27.81 | | | | | | | | | | | | (53), (57), (71), (74), (78), (80), (81), (95),
% 158.74/27.81 | | | | | | | | | | | | (98), (255) are inconsistent by sub-proof #780.
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | (256) all_58_15 = e3 & op(e0, e0) = e3
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | ALPHA: (256) implies:
% 158.74/27.81 | | | | | | | | | | | | (257) all_58_15 = e3
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | REF_CLOSE: (39), (123), (257) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | #1318.
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | End of split
% 158.74/27.81 | | | | | | | | |
% 158.74/27.81 | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | |
% 158.74/27.81 | | | | | | | | | (258) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 158.74/27.81 | | | | | | | | | & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.81 | | | | | | | | | = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 158.74/27.81 | | | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 158.74/27.81 | | | | | | | | | e0 & op(e0, e1) = e0))
% 158.74/27.81 | | | | | | | | |
% 158.74/27.81 | | | | | | | | | ALPHA: (258) implies:
% 158.74/27.81 | | | | | | | | | (259) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0
% 158.74/27.81 | | | | | | | | | & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 158.74/27.81 | | | | | | | | | e0)
% 158.74/27.81 | | | | | | | | | (260) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 158.74/27.81 | | | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 158.74/27.81 | | | | | | | | | e0)
% 158.74/27.81 | | | | | | | | |
% 158.74/27.81 | | | | | | | | | BETA: splitting (259) gives:
% 158.74/27.81 | | | | | | | | |
% 158.74/27.81 | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | (261) all_58_12 = e0 & op(e0, e3) = e0
% 158.74/27.81 | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | ALPHA: (261) implies:
% 158.74/27.81 | | | | | | | | | | (262) all_58_12 = e0
% 158.74/27.81 | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | REF_CLOSE: (7), (9), (10), (17), (19), (23), (24), (32),
% 158.74/27.81 | | | | | | | | | | (33), (39), (43), (45), (50), (52), (53), (57),
% 158.74/27.81 | | | | | | | | | | (63), (71), (74), (78), (80), (81), (82), (89),
% 158.74/27.81 | | | | | | | | | | (90), (95), (98), (262) are inconsistent by
% 158.74/27.81 | | | | | | | | | | sub-proof #523.
% 158.74/27.81 | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | (263) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 158.74/27.81 | | | | | | | | | | e0 & op(e0, e1) = e0)
% 158.74/27.81 | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | BETA: splitting (263) gives:
% 158.74/27.81 | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | (264) all_58_13 = e0 & op(e0, e2) = e0
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | ALPHA: (264) implies:
% 158.74/27.81 | | | | | | | | | | | (265) op(e0, e2) = e0
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | REF_CLOSE: (3), (8), (10), (15), (20), (35), (37), (42),
% 158.74/27.81 | | | | | | | | | | | (46), (56), (58), (61), (64), (67), (73), (75),
% 158.74/27.81 | | | | | | | | | | | (77), (85), (86), (87), (89), (91), (92), (95),
% 158.74/27.81 | | | | | | | | | | | (102), (113), (265) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | #559.
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | (266) all_58_14 = e0 & op(e0, e1) = e0
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | ALPHA: (266) implies:
% 158.74/27.81 | | | | | | | | | | | (267) all_58_14 = e0
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | BETA: splitting (22) gives:
% 158.74/27.81 | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | (268) all_54_8 = e3
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | REF_CLOSE: (60), (62), (268) are inconsistent by sub-proof
% 158.74/27.81 | | | | | | | | | | | | #1425.
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | (269) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | BETA: splitting (24) gives:
% 158.74/27.81 | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | (270) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 158.74/27.81 | | | | | | | | | | | | | & op(e2, e1) = e2)
% 158.74/27.81 | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | BETA: splitting (270) gives:
% 158.74/27.81 | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | (271) all_58_4 = e2 & op(e3, e1) = e2
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | ALPHA: (271) implies:
% 158.74/27.81 | | | | | | | | | | | | | | (272) all_58_4 = e2
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 158.74/27.81 | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | (273) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 158.74/27.81 | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 158.74/27.81 | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | (274) all_58_12 = e2 & op(e0, e3) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | (275) all_58_12 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | REF_CLOSE: (23), (32), (33), (39), (50), (52), (95), (98),
% 158.74/27.81 | | | | | | | | | | | | | | | | (121), (275) are inconsistent by sub-proof #1067.
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | (276) all_58_13 = e2 & op(e0, e2) = e2
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | (277) all_58_13 = e2
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | (278) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 158.74/27.81 | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (279) all_58_12 = e3 & op(e0, e3) = e3
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | (280) all_58_12 = e3
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | (281) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (17), (19), (23), (24), (32),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | (33), (39), (43), (45), (50), (52), (53), (57),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | (63), (71), (74), (78), (80), (81), (82), (89),
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | (90), (95), (98), (280), (281) are inconsistent by
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | sub-proof #519.
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | (282) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (283) all_58_5 = e0 & op(e2, e1) = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | (284) all_58_5 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | (285) all_58_9 = e0 & op(e3, e0) = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | (286) all_58_9 = e0
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | (287) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 158.74/27.81 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (17), (19), (20), (21),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (23), (24), (25), (26), (28), (31), (32), (33),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (34), (35), (36), (37), (39), (40), (42), (43),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (54),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (60), (61), (63), (64), (67),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (68), (69), (70), (71), (72), (73), (74), (75),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (76), (77), (78), (79), (80), (81), (84), (85),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (95),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (96), (98), (99), (100), (102), (107), (108),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (113), (118), (121), (267), (269), (272), (277),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (280), (287) are inconsistent by sub-proof #494.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (288) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (289) all_58_4 = e1 & op(e3, e1) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (272), (289) are inconsistent by sub-proof
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | #1476.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_9 = e1 & op(e3, e0) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (291) all_58_9 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (291) imply:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (292) e1 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (292) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (293) e1 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (293) imply:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_6 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (50), (52), (74), (78), (95), (121), (280),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (294) are inconsistent by sub-proof #733.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (295) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (296) all_58_10 = e0 & op(e2, e0) = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (297) all_58_10 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (298) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_2 = e1 & op(e2, e3) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (300) op(e2, e3) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (74), (95), (300) are inconsistent by
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1430.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_3 = e1 & op(e2, e2) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_3 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (302) imply:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (303) e3 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (17), (19), (23),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (24), (25), (28), (29), (33), (36), (38), (39),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (40), (45), (48), (50), (52), (53), (55), (57),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (59), (63), (65), (71), (72), (74), (78), (80),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (81), (82), (83), (88), (89), (90), (94), (95),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (98), (99), (280), (303) are inconsistent by
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #497.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (304) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (305) all_58_5 = e1 & op(e2, e1) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (40), (50), (52), (74), (78), (95), (121),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (280), (284), (305) are inconsistent by sub-proof
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | #518.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (306) all_58_10 = e1 & op(e2, e0) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (40), (50), (52), (74), (78), (95), (121),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (280), (297), (306) are inconsistent by sub-proof
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | #689.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (307) all_58_11 = e0 & op(e1, e0) = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (308) all_58_11 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (11), (12), (15), (17), (19), (20), (23), (24),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (25), (28), (29), (32), (33), (34), (35), (36),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (63), (64), (65),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (67), (71), (72), (73), (74), (75), (77), (78),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (94), (95), (98),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (99), (102), (113), (308) are inconsistent by
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | sub-proof #504.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (309) all_58_10 = e0 & op(e2, e0) = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (310) all_58_10 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (311) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (17), (19), (20), (21),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (23), (24), (25), (26), (28), (31), (32), (33),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (34), (35), (36), (37), (39), (40), (42), (43),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (54),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (60), (61), (63), (64), (67),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (68), (69), (70), (71), (72), (73), (74), (75),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (76), (77), (78), (79), (80), (81), (84), (85),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (86), (87), (88), (90), (91), (92), (93), (95),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (96), (98), (99), (100), (102), (107), (108),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (113), (118), (121), (267), (269), (272), (277),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (280), (311) are inconsistent by sub-proof #494.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (312) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (313) all_58_4 = e1 & op(e3, e1) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (272), (313) are inconsistent by sub-proof
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | #1476.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (314) all_58_9 = e1 & op(e3, e0) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (315) all_58_9 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (316) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (17), (19), (23),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (24), (25), (28), (29), (33), (34), (36), (38),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (39), (40), (45), (48), (49), (50), (52), (53),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (55), (57), (59), (63), (65), (71), (72), (74),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (78), (80), (81), (82), (83), (88), (89), (90),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (94), (95), (98), (99), (280), (315), (316) are
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #496.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | (317) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (318) all_58_11 = e3 & op(e1, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (31), (39), (45), (48), (52), (54),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (74), (78), (93), (95), (98), (118), (318) are
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #933.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (319) all_58_15 = e3 & op(e0, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_15 = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (321) op(e0, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (11), (17), (19), (23),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (24), (25), (28), (33), (36), (39), (40), (43),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (45), (48), (50), (52), (57), (63), (71), (72),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (84), (88), (90), (95),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (98), (99), (107), (118), (121), (267), (272),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | (277), (310), (315), (320), (321) are inconsistent
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #493.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (322) all_58_13 = e3 & op(e0, e2) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (89), (95), (322) are inconsistent by
% 158.74/27.82 | | | | | | | | | | | | | | | | | | sub-proof #1449.
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | (323) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 158.74/27.82 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (324) all_58_14 = e3 & op(e0, e1) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (325) all_58_14 = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (19), (24), (39), (45), (50), (52),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (53), (57), (71), (74), (78), (80), (81), (95),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (98), (325) are inconsistent by sub-proof #780.
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (326) all_58_15 = e3 & op(e0, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (327) all_58_15 = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (328) op(e0, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | (329) all_58_9 = e0 & op(e3, e0) = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | (330) all_58_9 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (331) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (11), (17), (19), (23),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (24), (25), (28), (33), (36), (39), (40), (43),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (45), (48), (50), (52), (57), (63), (71), (72),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (88), (90), (95), (98),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (99), (107), (121), (267), (277), (327), (328),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (331) are inconsistent by sub-proof #492.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (332) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (78), (272), (330), (332) are inconsistent
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | by sub-proof #1100.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | (333) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (334) all_58_10 = e0 & op(e2, e0) = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (335) all_58_10 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (336) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (11), (17), (19), (23),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (24), (25), (28), (33), (36), (39), (40), (43),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (45), (48), (50), (52), (57), (63), (71), (72),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (88), (90), (95), (98),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (99), (107), (121), (267), (277), (327), (328),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (336) are inconsistent by sub-proof #492.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | (337) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (338) all_58_4 = e1 & op(e3, e1) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (272), (338) are inconsistent by sub-proof
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | #1476.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (339) all_58_9 = e1 & op(e3, e0) = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (340) all_58_9 = e1
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (11), (17), (19), (23),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (24), (25), (28), (33), (36), (39), (40), (43),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (45), (48), (50), (52), (57), (63), (71), (72),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (84), (88), (90), (95),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (98), (99), (107), (118), (121), (267), (272),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | (277), (327), (328), (335), (340) are inconsistent
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #493.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (341) all_58_11 = e0 & op(e1, e0) = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (342) all_58_11 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (11), (12), (15), (17), (19), (20), (23), (24),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (25), (28), (29), (32), (33), (34), (35), (36),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (63), (64), (65),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (67), (71), (72), (73), (74), (75), (77), (78),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (94), (95), (98),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | (99), (102), (113), (342) are inconsistent by
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | | sub-proof #504.
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | (343) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 158.74/27.82 | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 158.74/27.82 | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | BETA: splitting (343) gives:
% 158.74/27.82 | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | (344) all_58_14 = e2 & op(e0, e1) = e2
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | (345) all_58_14 = e2
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (345) imply:
% 158.74/27.82 | | | | | | | | | | | | | | | | (346) e2 = e0
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.82 | | | | | | | | | | | | | | | | (11), (12), (15), (17), (19), (20), (23), (24),
% 158.74/27.82 | | | | | | | | | | | | | | | | (25), (28), (29), (32), (33), (34), (35), (36),
% 158.74/27.82 | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 158.74/27.82 | | | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.82 | | | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (63), (64), (65),
% 158.74/27.82 | | | | | | | | | | | | | | | | (67), (71), (72), (73), (74), (75), (77), (78),
% 158.74/27.82 | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 158.74/27.82 | | | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (94), (95), (98),
% 158.74/27.82 | | | | | | | | | | | | | | | | (99), (102), (113), (118), (346) are inconsistent
% 158.74/27.82 | | | | | | | | | | | | | | | | by sub-proof #503.
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | (347) all_58_15 = e2 & op(e0, e0) = e2
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | ALPHA: (347) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | (348) op(e0, e0) = e2
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | (349) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 158.74/27.82 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | BETA: splitting (349) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (350) all_58_9 = e3 & op(e3, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (45), (52), (74), (78), (95), (118),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (260), (348), (350) are inconsistent by sub-proof
% 158.74/27.82 | | | | | | | | | | | | | | | | | | #491.
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (351) all_58_10 = e3 & op(e2, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | ALPHA: (351) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (352) op(e2, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (49), (95), (352) are inconsistent by
% 158.74/27.82 | | | | | | | | | | | | | | | | | | sub-proof #1364.
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | (353) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 158.74/27.82 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | BETA: splitting (353) gives:
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (354) all_58_11 = e3 & op(e1, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (31), (39), (45), (48), (52), (54),
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (74), (78), (93), (95), (98), (118), (354) are
% 158.74/27.82 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #933.
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (355) all_58_15 = e3 & op(e0, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | ALPHA: (355) implies:
% 158.74/27.82 | | | | | | | | | | | | | | | | | | (356) op(e0, e0) = e3
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (98), (348), (356) are inconsistent by
% 158.74/27.82 | | | | | | | | | | | | | | | | | | sub-proof #1382.
% 158.74/27.82 | | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | (357) all_58_5 = e2 & op(e2, e1) = e2
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | ALPHA: (357) implies:
% 158.74/27.82 | | | | | | | | | | | | | | (358) all_58_5 = e2
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (45), (50), (52), (57), (74), (78),
% 158.74/27.82 | | | | | | | | | | | | | | (80), (95), (358) are inconsistent by sub-proof
% 158.74/27.82 | | | | | | | | | | | | | | #898.
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | (359) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 158.74/27.82 | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 158.74/27.82 | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | BETA: splitting (359) gives:
% 158.74/27.82 | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | Case 1:
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | (360) all_58_8 = e2 & op(e1, e1) = e2
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | ALPHA: (360) implies:
% 158.74/27.82 | | | | | | | | | | | | | | (361) all_58_8 = e2
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | REF_CLOSE: (4), (31), (39), (45), (48), (52), (54), (74),
% 158.74/27.82 | | | | | | | | | | | | | | (78), (93), (95), (98), (118), (361) are
% 158.74/27.82 | | | | | | | | | | | | | | inconsistent by sub-proof #1068.
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | (362) all_58_14 = e2 & op(e0, e1) = e2
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | ALPHA: (362) implies:
% 158.74/27.82 | | | | | | | | | | | | | | (363) all_58_14 = e2
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | COMBINE_EQS: (267), (363) imply:
% 158.74/27.82 | | | | | | | | | | | | | | (364) e2 = e0
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 158.74/27.82 | | | | | | | | | | | | | | (11), (12), (15), (17), (19), (20), (23), (24),
% 158.74/27.82 | | | | | | | | | | | | | | (25), (28), (29), (32), (33), (34), (35), (36),
% 158.74/27.82 | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (44), (45),
% 158.74/27.82 | | | | | | | | | | | | | | (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.82 | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (63), (64), (65),
% 158.74/27.82 | | | | | | | | | | | | | | (67), (71), (72), (73), (74), (75), (77), (78),
% 158.74/27.82 | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87),
% 158.74/27.82 | | | | | | | | | | | | | | (88), (89), (90), (91), (92), (94), (95), (98),
% 158.74/27.82 | | | | | | | | | | | | | | (99), (102), (113), (118), (364) are inconsistent
% 158.74/27.82 | | | | | | | | | | | | | | by sub-proof #503.
% 158.74/27.82 | | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | | |
% 158.74/27.82 | | | | | | | | | End of split
% 158.74/27.82 | | | | | | | | |
% 158.74/27.82 | | | | | | | | End of split
% 158.74/27.82 | | | | | | | |
% 158.74/27.82 | | | | | | | Case 2:
% 158.74/27.82 | | | | | | | |
% 158.74/27.82 | | | | | | | | (365) all_58_2 = e0 & op(e2, e3) = e0
% 158.74/27.82 | | | | | | | |
% 158.74/27.82 | | | | | | | | ALPHA: (365) implies:
% 158.74/27.82 | | | | | | | | (366) op(e2, e3) = e0
% 158.74/27.82 | | | | | | | |
% 158.74/27.82 | | | | | | | | REF_CLOSE: (45), (50), (95), (366) are inconsistent by sub-proof
% 158.74/27.82 | | | | | | | | #1156.
% 158.74/27.82 | | | | | | | |
% 158.74/27.82 | | | | | | | End of split
% 158.74/27.82 | | | | | | |
% 158.74/27.82 | | | | | | Case 2:
% 158.74/27.82 | | | | | | |
% 158.74/27.82 | | | | | | | (367) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 158.74/27.82 | | | | | | | op(e0, e3) = e0)
% 158.74/27.82 | | | | | | |
% 158.74/27.82 | | | | | | | REF_CLOSE: (7), (9), (10), (17), (19), (23), (24), (32), (33),
% 158.74/27.82 | | | | | | | (39), (43), (45), (50), (52), (53), (57), (63), (71),
% 158.74/27.82 | | | | | | | (74), (78), (80), (81), (82), (89), (90), (95), (98),
% 158.74/27.82 | | | | | | | (367) are inconsistent by sub-proof #510.
% 158.74/27.82 | | | | | | |
% 158.74/27.82 | | | | | | End of split
% 158.74/27.82 | | | | | |
% 158.74/27.82 | | | | | End of split
% 158.74/27.82 | | | | |
% 158.74/27.82 | | | | End of split
% 158.74/27.82 | | | |
% 158.74/27.82 | | | End of split
% 158.74/27.82 | | |
% 158.74/27.82 | | End of split
% 158.74/27.82 | |
% 158.74/27.82 | Case 2:
% 158.74/27.82 | |
% 158.74/27.82 | | (368) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 158.74/27.82 | | e0)
% 158.74/27.82 | |
% 158.74/27.82 | | BETA: splitting (368) gives:
% 158.74/27.82 | |
% 158.74/27.82 | | Case 1:
% 158.74/27.82 | | |
% 158.74/27.82 | | | (369) all_58_8 = e0 & op(e1, e1) = e0
% 158.74/27.82 | | |
% 158.74/27.82 | | | REF_CLOSE: (19), (39), (369) are inconsistent by sub-proof #598.
% 158.74/27.82 | | |
% 158.74/27.82 | | Case 2:
% 158.74/27.82 | | |
% 158.74/27.82 | | | (370) all_58_11 = e0 & op(e1, e0) = e0
% 158.74/27.82 | | |
% 158.74/27.82 | | | ALPHA: (370) implies:
% 158.74/27.82 | | | (371) all_58_11 = e0
% 158.74/27.82 | | |
% 158.74/27.82 | | | BETA: splitting (18) gives:
% 158.74/27.82 | | |
% 158.74/27.82 | | | Case 1:
% 158.74/27.82 | | | |
% 158.74/27.82 | | | | (372) all_54_7 = e3
% 158.74/27.82 | | | |
% 158.74/27.82 | | | | COMBINE_EQS: (61), (372) imply:
% 158.74/27.82 | | | | (373) all_52_13 = e3
% 158.74/27.82 | | | |
% 158.74/27.82 | | | | REDUCE: (34), (373) imply:
% 158.74/27.82 | | | | (374) $false
% 158.74/27.82 | | | |
% 158.74/27.82 | | | | CLOSE: (374) is inconsistent.
% 158.74/27.82 | | | |
% 158.74/27.82 | | | Case 2:
% 158.74/27.82 | | | |
% 158.74/27.82 | | | | (375) ~ (all_54_7 = e3)
% 158.74/27.82 | | | | (376) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 158.74/27.82 | | | |
% 158.74/27.82 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.74/27.82 | | | | (15), (17), (19), (20), (23), (24), (25), (28), (29), (32),
% 158.74/27.82 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (42), (43),
% 158.74/27.82 | | | | (44), (45), (46), (48), (49), (50), (51), (52), (53), (55),
% 158.74/27.82 | | | | (56), (57), (58), (59), (61), (63), (64), (65), (67), (71),
% 158.74/27.82 | | | | (72), (73), (74), (75), (77), (78), (80), (81), (82), (83),
% 158.74/27.82 | | | | (84), (85), (86), (87), (88), (89), (90), (91), (92), (94),
% 158.74/27.82 | | | | (95), (98), (99), (102), (371), (376) are inconsistent by
% 158.74/27.82 | | | | sub-proof #504.
% 158.74/27.82 | | | |
% 158.74/27.82 | | | End of split
% 158.74/27.82 | | |
% 158.74/27.82 | | End of split
% 158.74/27.82 | |
% 158.74/27.82 | End of split
% 158.74/27.82 |
% 158.74/27.82 End of proof
% 158.74/27.82
% 158.74/27.82 Sub-proof #491 shows that the following formulas are inconsistent:
% 158.74/27.82 ----------------------------------------------------------------
% 158.74/27.82 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.82 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.82 (2) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 158.74/27.82 (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.82 (3) ~ (e3 = e0)
% 158.74/27.82 (4) ~ (e2 = e0)
% 158.74/27.82 (5) ~ (e3 = e1)
% 158.74/27.82 (6) op(e0, e0) = e2
% 158.74/27.82 (7) all_58_11 = e2
% 158.74/27.82 (8) ~ (e2 = e1)
% 158.74/27.82 (9) ~ (e1 = e0)
% 158.74/27.82 (10) all_58_9 = e3 & op(e3, e0) = e3
% 158.74/27.82 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.82
% 158.74/27.82 Begin of proof
% 158.74/27.82 |
% 158.74/27.82 | ALPHA: (10) implies:
% 158.74/27.82 | (12) all_58_9 = e3
% 158.74/27.82 |
% 158.74/27.82 | BETA: splitting (1) gives:
% 158.74/27.82 |
% 158.74/27.82 | Case 1:
% 158.74/27.82 | |
% 158.74/27.82 | | (13) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 158.74/27.82 | | e1)
% 158.74/27.82 | |
% 158.74/27.82 | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (12), (13) are inconsistent by
% 158.74/27.82 | | sub-proof #1456.
% 158.74/27.82 | |
% 158.74/27.82 | Case 2:
% 158.74/27.82 | |
% 158.74/27.82 | | (14) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.74/27.82 | | e1)
% 158.74/27.82 | |
% 158.74/27.82 | | REF_CLOSE: (6), (7), (8), (11), (14) are inconsistent by sub-proof #895.
% 158.74/27.82 | |
% 158.74/27.82 | End of split
% 158.74/27.82 |
% 158.74/27.82 End of proof
% 158.74/27.82
% 158.74/27.82 Sub-proof #492 shows that the following formulas are inconsistent:
% 158.74/27.82 ----------------------------------------------------------------
% 158.74/27.82 (1) all_58_15 = e3
% 158.74/27.82 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.82 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.82 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.82 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.82 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.82 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.82 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.82 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.82 (6) op(e1, e1) = all_6_2
% 158.74/27.83 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 158.74/27.83 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.83 (8) op(e3, e3) = all_28_1
% 158.74/27.83 (9) all_58_14 = e0
% 158.74/27.83 (10) all_58_8 = e3
% 158.74/27.83 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.83 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.83 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.83 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.83 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.74/27.83 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.83 (14) op(e3, e2) = all_52_4
% 158.74/27.83 (15) all_58_7 = e0
% 158.74/27.83 (16) op(e2, e3) = all_52_1
% 158.74/27.83 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.83 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.83 (18) ~ (e3 = e0)
% 158.74/27.83 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.83 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.83 (20) op(e0, e0) = e0
% 158.74/27.83 (21) ~ (e2 = e0)
% 158.74/27.83 (22) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.83 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.83 (23) op(e2, e3) = e2
% 158.74/27.83 (24) ~ (e3 = e1)
% 158.74/27.83 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.83 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.83 (26) op(e3, e3) = e1
% 158.74/27.83 (27) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.74/27.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.74/27.83 (28) ~ (all_52_4 = e3)
% 158.74/27.83 (29) ~ (e2 = e1)
% 158.74/27.83 (30) ~ (e1 = e0)
% 158.74/27.83 (31) all_58_3 = e3
% 158.74/27.83 (32) ~ (all_6_2 = e2)
% 158.74/27.83 (33) all_58_13 = e2
% 158.74/27.83 (34) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.83 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.83 (35) op(e3, e3) = all_22_1
% 158.74/27.83 (36) all_58_0 = e0
% 158.74/27.83 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.83 (38) ~ (e3 = e2)
% 158.74/27.83 (39) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.83 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.83 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.74/27.83 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.74/27.83 (40) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 158.74/27.83 (41) op(e0, e0) = e3
% 158.74/27.83
% 158.74/27.83 Begin of proof
% 158.74/27.83 |
% 158.74/27.83 | BETA: splitting (40) gives:
% 158.74/27.83 |
% 158.74/27.83 | Case 1:
% 158.74/27.83 | |
% 158.74/27.83 | | (42) all_58_0 = e1 & op(e3, e3) = e1
% 158.74/27.83 | |
% 158.74/27.83 | | REF_CLOSE: (30), (36), (42) are inconsistent by sub-proof #1495.
% 158.74/27.83 | |
% 158.74/27.83 | Case 2:
% 158.74/27.83 | |
% 158.74/27.83 | | (43) all_58_1 = e1 & op(e3, e2) = e1
% 158.74/27.83 | |
% 158.74/27.83 | | ALPHA: (43) implies:
% 158.74/27.83 | | (44) all_58_1 = e1
% 158.74/27.83 | |
% 158.74/27.83 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.74/27.83 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 158.74/27.83 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 158.74/27.83 | | (35), (36), (37), (38), (39), (41), (44) are inconsistent by
% 158.74/27.83 | | sub-proof #495.
% 158.74/27.83 | |
% 158.74/27.83 | End of split
% 158.74/27.83 |
% 158.74/27.83 End of proof
% 158.74/27.83
% 158.74/27.83 Sub-proof #493 shows that the following formulas are inconsistent:
% 158.74/27.83 ----------------------------------------------------------------
% 158.74/27.83 (1) all_58_15 = e3
% 158.74/27.83 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.83 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.83 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.83 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.83 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.83 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.83 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.83 (6) op(e1, e1) = all_6_2
% 158.74/27.83 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 158.74/27.83 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.83 (8) op(e3, e3) = all_28_1
% 158.74/27.83 (9) all_58_14 = e0
% 158.74/27.83 (10) all_58_8 = e3
% 158.74/27.83 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.83 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.83 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.83 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.83 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.74/27.83 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.83 (14) op(e3, e2) = all_52_4
% 158.74/27.83 (15) all_58_7 = e0
% 158.74/27.83 (16) op(e2, e3) = all_52_1
% 158.74/27.83 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.83 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.83 (18) ~ (e3 = e0)
% 158.74/27.83 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.83 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.83 (20) op(e0, e0) = e0
% 158.74/27.83 (21) ~ (e2 = e0)
% 158.74/27.83 (22) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.83 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.83 (23) op(e2, e3) = e2
% 158.74/27.83 (24) ~ (e3 = e1)
% 158.74/27.83 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.83 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.83 (26) op(e3, e3) = e1
% 158.74/27.83 (27) all_58_11 = e2
% 158.74/27.83 (28) all_58_4 = e2
% 158.74/27.83 (29) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 158.74/27.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 158.74/27.83 (30) ~ (all_52_4 = e3)
% 158.74/27.83 (31) ~ (e2 = e1)
% 158.74/27.83 (32) ~ (e1 = e0)
% 158.74/27.83 (33) all_58_3 = e3
% 158.74/27.83 (34) all_58_9 = e1
% 158.74/27.83 (35) ~ (all_6_2 = e2)
% 158.74/27.83 (36) all_58_13 = e2
% 158.74/27.83 (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 158.74/27.83 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 158.74/27.83 (38) all_58_10 = e0
% 158.74/27.83 (39) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 158.74/27.83 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 158.74/27.83 (40) op(e3, e3) = all_22_1
% 158.74/27.83 (41) all_58_0 = e0
% 158.74/27.83 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 158.74/27.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 158.74/27.83 (43) ~ (e3 = e2)
% 158.74/27.83 (44) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 158.74/27.83 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 158.74/27.83 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 158.74/27.83 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 158.74/27.83 (45) op(e0, e0) = e3
% 158.74/27.83
% 158.74/27.83 Begin of proof
% 158.74/27.83 |
% 158.74/27.83 | BETA: splitting (3) gives:
% 158.74/27.83 |
% 158.74/27.83 | Case 1:
% 158.74/27.83 | |
% 158.74/27.83 | | (46) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 158.74/27.83 | | e1)
% 158.74/27.83 | |
% 158.74/27.83 | | BETA: splitting (46) gives:
% 158.74/27.83 | |
% 158.74/27.83 | | Case 1:
% 158.74/27.83 | | |
% 158.74/27.83 | | | (47) all_58_1 = e1 & op(e3, e2) = e1
% 158.74/27.83 | | |
% 158.74/27.83 | | | ALPHA: (47) implies:
% 158.74/27.83 | | | (48) all_58_1 = e1
% 158.74/27.83 | | |
% 158.74/27.83 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 158.74/27.83 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 158.74/27.83 | | | (23), (24), (25), (26), (29), (30), (31), (32), (33), (35),
% 158.74/27.83 | | | (36), (39), (40), (41), (42), (43), (44), (45), (48) are
% 158.74/27.83 | | | inconsistent by sub-proof #495.
% 158.74/27.83 | | |
% 158.74/27.83 | | Case 2:
% 158.74/27.83 | | |
% 158.74/27.83 | | | (49) all_58_3 = e1 & op(e2, e2) = e1
% 158.74/27.83 | | |
% 158.74/27.83 | | | REF_CLOSE: (24), (33), (49) are inconsistent by sub-proof #912.
% 158.74/27.83 | | |
% 158.74/27.83 | | End of split
% 158.74/27.83 | |
% 158.74/27.83 | Case 2:
% 158.74/27.83 | |
% 158.74/27.83 | | (50) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 158.74/27.83 | | e1)
% 158.74/27.83 | |
% 158.74/27.83 | | BETA: splitting (50) gives:
% 158.74/27.83 | |
% 158.74/27.83 | | Case 1:
% 158.74/27.83 | | |
% 158.74/27.83 | | | (51) all_58_7 = e1 & op(e1, e2) = e1
% 158.74/27.83 | | |
% 158.74/27.83 | | | ALPHA: (51) implies:
% 158.74/27.83 | | | (52) all_58_7 = e1
% 158.74/27.83 | | |
% 158.74/27.83 | | | COMBINE_EQS: (15), (52) imply:
% 158.74/27.83 | | | (53) e1 = e0
% 158.74/27.83 | | |
% 158.74/27.83 | | | COMBINE_EQS: (34), (53) imply:
% 158.74/27.83 | | | (54) all_58_9 = e0
% 158.74/27.83 | | |
% 158.74/27.83 | | | BETA: splitting (37) gives:
% 158.74/27.83 | | |
% 158.74/27.83 | | | Case 1:
% 158.74/27.83 | | | |
% 158.74/27.83 | | | | (55) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 158.74/27.83 | | | | = e1)
% 158.74/27.83 | | | |
% 158.74/27.83 | | | | BETA: splitting (55) gives:
% 158.74/27.83 | | | |
% 158.74/27.83 | | | | Case 1:
% 158.74/27.83 | | | | |
% 158.74/27.83 | | | | | (56) all_58_0 = e1 & op(e3, e3) = e1
% 158.74/27.83 | | | | |
% 158.74/27.83 | | | | | REF_CLOSE: (32), (41), (56) are inconsistent by sub-proof #1495.
% 158.74/27.83 | | | | |
% 158.74/27.83 | | | | Case 2:
% 158.74/27.83 | | | | |
% 158.74/27.83 | | | | | (57) all_58_1 = e1 & op(e3, e2) = e1
% 158.74/27.83 | | | | |
% 158.74/27.83 | | | | | ALPHA: (57) implies:
% 158.74/27.83 | | | | | (58) all_58_1 = e1
% 158.74/27.83 | | | | |
% 158.74/27.83 | | | | | BETA: splitting (4) gives:
% 158.74/27.83 | | | | |
% 158.74/27.83 | | | | | Case 1:
% 158.74/27.83 | | | | | |
% 158.74/27.83 | | | | | | (59) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 158.74/27.83 | | | | | | e0) = e1)
% 158.74/27.83 | | | | | |
% 158.74/27.83 | | | | | | BETA: splitting (59) gives:
% 158.74/27.83 | | | | | |
% 158.74/27.83 | | | | | | Case 1:
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | | (60) all_58_9 = e1 & op(e3, e0) = e1
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | | REF_CLOSE: (3), (15), (24), (31), (32), (33), (36), (54), (58),
% 158.74/27.83 | | | | | | | (60) are inconsistent by sub-proof #595.
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | Case 2:
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | | (61) all_58_10 = e1 & op(e2, e0) = e1
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | | ALPHA: (61) implies:
% 158.74/27.83 | | | | | | | (62) all_58_10 = e1
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | | COMBINE_EQS: (38), (62) imply:
% 158.74/27.83 | | | | | | | (63) e1 = e0
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | | COMBINE_EQS: (53), (58) imply:
% 158.74/27.83 | | | | | | | (64) all_58_1 = e0
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | | REF_CLOSE: (3), (15), (24), (31), (32), (33), (36), (64) are
% 158.74/27.83 | | | | | | | inconsistent by sub-proof #752.
% 158.74/27.83 | | | | | | |
% 158.74/27.83 | | | | | | End of split
% 158.74/27.83 | | | | | |
% 158.74/27.83 | | | | | Case 2:
% 158.74/27.83 | | | | | |
% 158.74/27.83 | | | | | | (65) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 158.74/27.83 | | | | | | op(e0, e0) = e1)
% 158.74/27.83 | | | | | |
% 158.74/27.83 | | | | | | REF_CLOSE: (1), (24), (27), (31), (65) are inconsistent by sub-proof
% 158.74/27.83 | | | | | | #1317.
% 158.74/27.83 | | | | | |
% 158.74/27.83 | | | | | End of split
% 158.74/27.83 | | | | |
% 158.74/27.83 | | | | End of split
% 158.74/27.83 | | | |
% 158.74/27.83 | | | Case 2:
% 158.74/27.83 | | | |
% 158.74/27.83 | | | | (66) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 158.74/27.83 | | | | = e1)
% 158.74/27.83 | | | |
% 158.74/27.83 | | | | REF_CLOSE: (28), (31), (32), (54), (66) are inconsistent by sub-proof
% 158.74/27.83 | | | | #1100.
% 158.74/27.83 | | | |
% 158.74/27.83 | | | End of split
% 158.74/27.83 | | |
% 158.74/27.83 | | Case 2:
% 158.74/27.83 | | |
% 158.74/27.83 | | | (67) all_58_13 = e1 & op(e0, e2) = e1
% 158.74/27.83 | | |
% 158.74/27.83 | | | REF_CLOSE: (31), (36), (67) are inconsistent by sub-proof #1206.
% 158.74/27.83 | | |
% 158.74/27.83 | | End of split
% 158.74/27.83 | |
% 158.74/27.83 | End of split
% 158.74/27.83 |
% 158.74/27.83 End of proof
% 158.74/27.83
% 158.74/27.83 Sub-proof #494 shows that the following formulas are inconsistent:
% 158.74/27.83 ----------------------------------------------------------------
% 158.74/27.83 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 158.74/27.83 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 158.74/27.83 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 158.74/27.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 158.74/27.83 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.83 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.83 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 158.74/27.83 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 158.74/27.83 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 158.74/27.83 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 158.74/27.83 (7) all_54_13 = all_52_7
% 158.74/27.83 (8) op(e1, e1) = all_6_2
% 158.74/27.83 (9) ~ (all_52_7 = e3)
% 158.74/27.83 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 158.74/27.83 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 158.74/27.83 e1)
% 158.74/27.83 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 158.74/27.83 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 158.74/27.83 (12) ~ (all_52_6 = all_52_14)
% 158.74/27.83 (13) ~ (all_52_11 = e3)
% 158.74/27.83 (14) all_58_12 = e3
% 158.74/27.83 (15) op(e3, e3) = all_28_1
% 158.74/27.83 (16) all_58_14 = e0
% 158.74/27.83 (17) all_58_8 = e3
% 158.74/27.83 (18) ~ (all_52_7 = all_52_11)
% 158.74/27.83 (19) op(e1, e2) = all_14_0
% 158.74/27.83 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 158.74/27.83 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 158.74/27.83 (21) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 158.74/27.83 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 158.74/27.83 (22) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 158.74/27.83 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 158.74/27.83 (23) ~ (all_52_14 = e3)
% 158.74/27.83 (24) op(e3, e2) = all_52_4
% 158.74/27.83 (25) all_58_7 = e0
% 158.74/27.83 (26) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 158.74/27.83 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 158.74/27.83 (27) all_58_6 = e1
% 158.74/27.83 (28) op(e1, e2) = e0
% 158.74/27.83 (29) op(e2, e3) = all_52_1
% 158.74/27.83 (30) ~ (all_52_13 = e3)
% 158.74/27.83 (31) all_54_2 = all_52_8
% 158.74/27.83 (32) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 158.74/27.83 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 158.74/27.83 (33) ~ (all_52_8 = all_52_9)
% 158.74/27.83 (34) ~ (e3 = e0)
% 158.74/27.83 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 158.74/27.83 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 158.74/27.83 (36) ~ (all_52_9 = all_52_13)
% 158.74/27.83 (37) op(e0, e0) = e0
% 158.74/27.83 (38) ~ (e2 = e0)
% 158.74/27.83 (39) ~ (all_52_9 = e3)
% 158.74/27.83 (40) ~ (all_52_2 = all_52_6)
% 158.74/27.83 (41) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 158.74/27.83 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 158.74/27.83 (42) op(e2, e0) = all_52_13
% 158.74/27.83 (43) op(e2, e3) = e2
% 158.74/27.83 (44) ~ (e3 = e1)
% 158.74/27.83 (45) op(e1, e2) = all_52_6
% 158.74/27.83 (46) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 158.74/27.83 (47) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 158.74/27.83 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 158.74/27.83 (48) ~ (all_52_7 = e0)
% 158.74/27.83 (49) all_54_8 = all_52_2
% 158.74/27.83 (50) all_54_7 = all_52_13
% 159.05/27.83 (51) op(e3, e3) = e1
% 159.05/27.83 (52) ~ (all_52_13 = e2)
% 159.05/27.83 (53) ~ (all_52_9 = all_52_11)
% 159.05/27.83 (54) all_58_11 = e2
% 159.05/27.83 (55) ~ (all_52_2 = e1)
% 159.05/27.83 (56) all_58_4 = e2
% 159.05/27.83 (57) ~ (all_52_2 = all_52_14)
% 159.05/27.83 (58) ~ (all_52_6 = all_52_7)
% 159.05/27.83 (59) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.83 (60) ~ (all_52_4 = e3)
% 159.05/27.83 (61) all_54_6 = all_52_9
% 159.05/27.83 (62) ~ (e2 = e1)
% 159.05/27.83 (63) ~ (all_52_8 = all_52_11)
% 159.05/27.83 (64) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.83 (65) ~ (all_52_13 = e0)
% 159.05/27.83 (66) ~ (e1 = e0)
% 159.05/27.83 (67) ~ (all_52_2 = e2)
% 159.05/27.83 (68) all_58_3 = e3
% 159.05/27.83 (69) ~ (all_6_2 = e2)
% 159.05/27.83 (70) all_58_13 = e2
% 159.05/27.83 (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/27.83 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/27.83 (72) ~ (all_52_9 = e2)
% 159.05/27.83 (73) ~ (all_52_8 = e3)
% 159.05/27.83 (74) all_54_14 = all_52_11
% 159.05/27.83 (75) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.83 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.83 (76) op(e3, e3) = all_22_1
% 159.05/27.83 (77) all_58_0 = e0
% 159.05/27.83 (78) ~ (all_52_8 = e1)
% 159.05/27.83 (79) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 159.05/27.83 (80) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.83 (81) ~ (all_52_6 = e3)
% 159.05/27.83 (82) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.83 (83) all_54_11 = all_52_14
% 159.05/27.83 (84) ~ (e3 = e2)
% 159.05/27.83 (85) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.83 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.83 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.83 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.83 (86) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 159.05/27.83 (87) all_54_9 = all_52_6
% 159.05/27.83 (88) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.83 (89) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.83
% 159.05/27.83 Begin of proof
% 159.05/27.83 |
% 159.05/27.83 | BETA: splitting (86) gives:
% 159.05/27.83 |
% 159.05/27.83 | Case 1:
% 159.05/27.83 | |
% 159.05/27.83 | | (90) all_58_0 = e1 & op(e3, e3) = e1
% 159.05/27.83 | |
% 159.05/27.83 | | REF_CLOSE: (14), (27), (35), (43), (44), (62), (66), (77), (82), (90) are
% 159.05/27.83 | | inconsistent by sub-proof #694.
% 159.05/27.83 | |
% 159.05/27.83 | Case 2:
% 159.05/27.83 | |
% 159.05/27.83 | | (91) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/27.83 | |
% 159.05/27.83 | | ALPHA: (91) implies:
% 159.05/27.83 | | (92) all_58_1 = e1
% 159.05/27.83 | |
% 159.05/27.83 | | BETA: splitting (11) gives:
% 159.05/27.83 | |
% 159.05/27.83 | | Case 1:
% 159.05/27.83 | | |
% 159.05/27.83 | | | (93) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 159.05/27.83 | | | e3)
% 159.05/27.83 | | |
% 159.05/27.83 | | | BETA: splitting (93) gives:
% 159.05/27.83 | | |
% 159.05/27.83 | | | Case 1:
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | (94) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | ALPHA: (94) implies:
% 159.05/27.83 | | | | (95) all_58_9 = e3
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | REF_CLOSE: (1), (2), (7), (9), (12), (13), (14), (18), (19), (23), (27),
% 159.05/27.83 | | | | (28), (31), (33), (35), (36), (39), (40), (43), (45), (46),
% 159.05/27.83 | | | | (48), (49), (50), (52), (53), (55), (56), (57), (58), (61),
% 159.05/27.83 | | | | (63), (64), (65), (67), (71), (72), (73), (74), (77), (78),
% 159.05/27.83 | | | | (79), (80), (81), (82), (83), (87), (88), (89), (92), (95)
% 159.05/27.83 | | | | are inconsistent by sub-proof #501.
% 159.05/27.83 | | | |
% 159.05/27.83 | | | Case 2:
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | (96) all_58_10 = e3 & op(e2, e0) = e3
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | ALPHA: (96) implies:
% 159.05/27.83 | | | | (97) op(e2, e0) = e3
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | REF_CLOSE: (30), (42), (82), (97) are inconsistent by sub-proof #1364.
% 159.05/27.83 | | | |
% 159.05/27.83 | | | End of split
% 159.05/27.83 | | |
% 159.05/27.83 | | Case 2:
% 159.05/27.83 | | |
% 159.05/27.83 | | | (98) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0)
% 159.05/27.83 | | | = e3)
% 159.05/27.83 | | |
% 159.05/27.83 | | | BETA: splitting (98) gives:
% 159.05/27.83 | | |
% 159.05/27.83 | | | Case 1:
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | (99) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | REF_CLOSE: (3), (17), (26), (34), (38), (41), (44), (45), (54), (62),
% 159.05/27.83 | | | | (66), (81), (82), (84), (99) are inconsistent by sub-proof
% 159.05/27.83 | | | | #933.
% 159.05/27.83 | | | |
% 159.05/27.83 | | | Case 2:
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | (100) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | ALPHA: (100) implies:
% 159.05/27.83 | | | | (101) all_58_15 = e3
% 159.05/27.83 | | | | (102) op(e0, e0) = e3
% 159.05/27.83 | | | |
% 159.05/27.83 | | | | REF_CLOSE: (3), (4), (5), (6), (8), (10), (15), (16), (17), (20), (21),
% 159.05/27.83 | | | | (22), (24), (25), (29), (32), (34), (35), (37), (38), (41),
% 159.05/27.83 | | | | (43), (44), (47), (51), (59), (60), (62), (66), (68), (69),
% 159.05/27.83 | | | | (70), (75), (76), (77), (82), (84), (85), (92), (101), (102)
% 159.05/27.83 | | | | are inconsistent by sub-proof #495.
% 159.05/27.83 | | | |
% 159.05/27.83 | | | End of split
% 159.05/27.83 | | |
% 159.05/27.83 | | End of split
% 159.05/27.83 | |
% 159.05/27.83 | End of split
% 159.05/27.83 |
% 159.05/27.83 End of proof
% 159.05/27.83
% 159.05/27.83 Sub-proof #495 shows that the following formulas are inconsistent:
% 159.05/27.83 ----------------------------------------------------------------
% 159.05/27.83 (1) all_58_15 = e3
% 159.05/27.83 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.84 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.84 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.84 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.84 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.84 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.84 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.84 (6) op(e1, e1) = all_6_2
% 159.05/27.84 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.05/27.84 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.84 (8) op(e3, e3) = all_28_1
% 159.05/27.84 (9) all_58_14 = e0
% 159.05/27.84 (10) all_58_8 = e3
% 159.05/27.84 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.84 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.84 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.84 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.84 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.84 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.84 (14) op(e3, e2) = all_52_4
% 159.05/27.84 (15) all_58_7 = e0
% 159.05/27.84 (16) op(e2, e3) = all_52_1
% 159.05/27.84 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.84 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.84 (18) ~ (e3 = e0)
% 159.05/27.84 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.84 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.84 (20) op(e0, e0) = e0
% 159.05/27.84 (21) ~ (e2 = e0)
% 159.05/27.84 (22) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.84 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.84 (23) op(e2, e3) = e2
% 159.05/27.84 (24) ~ (e3 = e1)
% 159.05/27.84 (25) all_58_1 = e1
% 159.05/27.84 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.84 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.84 (27) op(e3, e3) = e1
% 159.05/27.84 (28) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.84 (29) ~ (all_52_4 = e3)
% 159.05/27.84 (30) ~ (e2 = e1)
% 159.05/27.84 (31) ~ (e1 = e0)
% 159.05/27.84 (32) all_58_3 = e3
% 159.05/27.84 (33) ~ (all_6_2 = e2)
% 159.05/27.84 (34) all_58_13 = e2
% 159.05/27.84 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.84 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.84 (36) op(e3, e3) = all_22_1
% 159.05/27.84 (37) all_58_0 = e0
% 159.05/27.84 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.84 (39) ~ (e3 = e2)
% 159.05/27.84 (40) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.84 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.84 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.84 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.84 (41) op(e0, e0) = e3
% 159.05/27.84
% 159.05/27.84 Begin of proof
% 159.05/27.84 |
% 159.05/27.84 | BETA: splitting (7) gives:
% 159.05/27.84 |
% 159.05/27.84 | Case 1:
% 159.05/27.84 | |
% 159.05/27.84 | | (42) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 159.05/27.84 | | e1)
% 159.05/27.84 | |
% 159.05/27.84 | | BETA: splitting (42) gives:
% 159.05/27.84 | |
% 159.05/27.84 | | Case 1:
% 159.05/27.84 | | |
% 159.05/27.84 | | | (43) all_58_12 = e1 & op(e0, e3) = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | ALPHA: (43) implies:
% 159.05/27.84 | | | (44) all_58_12 = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 159.05/27.84 | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 159.05/27.84 | | | (27), (28), (29), (30), (31), (32), (33), (35), (36), (37),
% 159.05/27.84 | | | (38), (39), (40), (41), (44) are inconsistent by sub-proof
% 159.05/27.84 | | | #575.
% 159.05/27.84 | | |
% 159.05/27.84 | | Case 2:
% 159.05/27.84 | | |
% 159.05/27.84 | | | (45) all_58_13 = e1 & op(e0, e2) = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | ALPHA: (45) implies:
% 159.05/27.84 | | | (46) all_58_13 = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | REF_CLOSE: (30), (34), (46) are inconsistent by sub-proof #807.
% 159.05/27.84 | | |
% 159.05/27.84 | | End of split
% 159.05/27.84 | |
% 159.05/27.84 | Case 2:
% 159.05/27.84 | |
% 159.05/27.84 | | (47) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.84 | | e1)
% 159.05/27.84 | |
% 159.05/27.84 | | BETA: splitting (47) gives:
% 159.05/27.84 | |
% 159.05/27.84 | | Case 1:
% 159.05/27.84 | | |
% 159.05/27.84 | | | (48) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | ALPHA: (48) implies:
% 159.05/27.84 | | | (49) all_58_14 = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | COMBINE_EQS: (9), (49) imply:
% 159.05/27.84 | | | (50) e1 = e0
% 159.05/27.84 | | |
% 159.05/27.84 | | | COMBINE_EQS: (25), (50) imply:
% 159.05/27.84 | | | (51) all_58_1 = e0
% 159.05/27.84 | | |
% 159.05/27.84 | | | REF_CLOSE: (3), (15), (24), (30), (31), (32), (34), (51) are inconsistent
% 159.05/27.84 | | | by sub-proof #752.
% 159.05/27.84 | | |
% 159.05/27.84 | | Case 2:
% 159.05/27.84 | | |
% 159.05/27.84 | | | (52) all_58_15 = e1 & op(e0, e0) = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | ALPHA: (52) implies:
% 159.05/27.84 | | | (53) all_58_15 = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | REF_CLOSE: (1), (24), (53) are inconsistent by sub-proof #1404.
% 159.05/27.84 | | |
% 159.05/27.84 | | End of split
% 159.05/27.84 | |
% 159.05/27.84 | End of split
% 159.05/27.84 |
% 159.05/27.84 End of proof
% 159.05/27.84
% 159.05/27.84 Sub-proof #496 shows that the following formulas are inconsistent:
% 159.05/27.84 ----------------------------------------------------------------
% 159.05/27.84 (1) all_56_14 = e3
% 159.05/27.84 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.84 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.84 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.84 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.84 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.84 (5) op(e1, e1) = all_6_2
% 159.05/27.84 (6) ~ (all_52_7 = e3)
% 159.05/27.84 (7) all_58_12 = e3
% 159.05/27.84 (8) op(e3, e3) = all_28_1
% 159.05/27.84 (9) all_58_8 = e3
% 159.05/27.84 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.84 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.84 (11) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.84 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.84 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.84 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.84 (13) op(e3, e2) = all_52_4
% 159.05/27.84 (14) ~ (all_4_2 = e2)
% 159.05/27.84 (15) op(e2, e3) = all_52_1
% 159.05/27.84 (16) ~ (all_52_13 = e3)
% 159.05/27.84 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.84 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.84 (18) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.84 (19) ~ (e3 = e0)
% 159.05/27.84 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.84 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.84 (21) ~ (e2 = e0)
% 159.05/27.84 (22) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.84 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.84 (23) op(e2, e0) = all_52_13
% 159.05/27.84 (24) op(e2, e3) = e2
% 159.05/27.84 (25) ~ (e3 = e1)
% 159.05/27.84 (26) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.84 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.84 (27) ~ (all_4_2 = e1)
% 159.05/27.84 (28) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.84 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.84 (29) op(e0, e0) = all_4_2
% 159.05/27.84 (30) op(e3, e3) = e1
% 159.05/27.84 (31) all_56_15 = all_4_2
% 159.05/27.84 (32) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.84 (33) ~ (all_52_4 = e3)
% 159.05/27.84 (34) ~ (e2 = e1)
% 159.05/27.84 (35) ~ (e1 = e0)
% 159.05/27.84 (36) all_58_3 = e3
% 159.05/27.84 (37) all_58_9 = e1
% 159.05/27.84 (38) ~ (all_6_2 = e2)
% 159.05/27.84 (39) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 159.05/27.84 (40) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.84 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.84 e3)
% 159.05/27.84 (41) all_56_13 = e3
% 159.05/27.84 (42) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.84 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.84 (43) op(e0, e2) = all_52_7
% 159.05/27.84 (44) op(e3, e3) = all_22_1
% 159.05/27.84 (45) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.84 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.84 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.84 (47) ~ (e3 = e2)
% 159.05/27.84 (48) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.84 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.84 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.84 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.84
% 159.05/27.84 Begin of proof
% 159.05/27.84 |
% 159.05/27.84 | BETA: splitting (39) gives:
% 159.05/27.84 |
% 159.05/27.84 | Case 1:
% 159.05/27.84 | |
% 159.05/27.84 | | (49) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.84 | |
% 159.05/27.84 | | ALPHA: (49) implies:
% 159.05/27.84 | | (50) all_58_9 = e3
% 159.05/27.84 | |
% 159.05/27.84 | | COMBINE_EQS: (37), (50) imply:
% 159.05/27.84 | | (51) e3 = e1
% 159.05/27.84 | |
% 159.05/27.84 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/27.84 | | (13), (14), (15), (17), (18), (19), (20), (21), (22), (24), (25),
% 159.05/27.84 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 159.05/27.84 | | (38), (40), (41), (42), (43), (44), (45), (46), (47), (48), (51)
% 159.05/27.84 | | are inconsistent by sub-proof #497.
% 159.05/27.84 | |
% 159.05/27.84 | Case 2:
% 159.05/27.84 | |
% 159.05/27.84 | | (52) all_58_10 = e3 & op(e2, e0) = e3
% 159.05/27.84 | |
% 159.05/27.84 | | ALPHA: (52) implies:
% 159.05/27.84 | | (53) op(e2, e0) = e3
% 159.05/27.84 | |
% 159.05/27.84 | | REF_CLOSE: (16), (23), (46), (53) are inconsistent by sub-proof #1364.
% 159.05/27.84 | |
% 159.05/27.84 | End of split
% 159.05/27.84 |
% 159.05/27.84 End of proof
% 159.05/27.84
% 159.05/27.84 Sub-proof #497 shows that the following formulas are inconsistent:
% 159.05/27.84 ----------------------------------------------------------------
% 159.05/27.84 (1) all_56_14 = e3
% 159.05/27.84 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.84 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.84 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.84 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.84 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.84 (5) op(e1, e1) = all_6_2
% 159.05/27.84 (6) ~ (all_52_7 = e3)
% 159.05/27.84 (7) all_58_12 = e3
% 159.05/27.84 (8) op(e3, e3) = all_28_1
% 159.05/27.84 (9) all_58_8 = e3
% 159.05/27.84 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.84 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.84 (11) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.84 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.84 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.84 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.84 (13) op(e3, e2) = all_52_4
% 159.05/27.84 (14) ~ (all_4_2 = e2)
% 159.05/27.84 (15) op(e2, e3) = all_52_1
% 159.05/27.84 (16) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.84 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.84 (17) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.84 (18) ~ (e3 = e0)
% 159.05/27.84 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.84 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.84 (20) ~ (e2 = e0)
% 159.05/27.84 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.84 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.84 (22) op(e2, e3) = e2
% 159.05/27.84 (23) ~ (e3 = e1)
% 159.05/27.84 (24) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.84 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.84 (25) ~ (all_4_2 = e1)
% 159.05/27.84 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.84 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.84 (27) op(e0, e0) = all_4_2
% 159.05/27.84 (28) op(e3, e3) = e1
% 159.05/27.84 (29) e3 = e1
% 159.05/27.84 (30) all_56_15 = all_4_2
% 159.05/27.84 (31) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.84 (32) ~ (all_52_4 = e3)
% 159.05/27.84 (33) ~ (e2 = e1)
% 159.05/27.84 (34) ~ (e1 = e0)
% 159.05/27.84 (35) all_58_3 = e3
% 159.05/27.84 (36) ~ (all_6_2 = e2)
% 159.05/27.84 (37) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.84 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.84 e3)
% 159.05/27.84 (38) all_56_13 = e3
% 159.05/27.84 (39) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.84 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.84 (40) op(e0, e2) = all_52_7
% 159.05/27.84 (41) op(e3, e3) = all_22_1
% 159.05/27.84 (42) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.84 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.84 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.84 (44) ~ (e3 = e2)
% 159.05/27.84 (45) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.84 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.84 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.84 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.84
% 159.05/27.84 Begin of proof
% 159.05/27.84 |
% 159.05/27.84 | SIMP: (29) implies:
% 159.05/27.84 | (46) e3 = e1
% 159.05/27.84 |
% 159.05/27.84 | COMBINE_EQS: (7), (46) imply:
% 159.05/27.84 | (47) all_58_12 = e1
% 159.05/27.84 |
% 159.05/27.84 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 159.05/27.84 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 159.05/27.84 | (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 159.05/27.84 | (37), (38), (39), (40), (41), (42), (43), (44), (45), (47) are
% 159.05/27.84 | inconsistent by sub-proof #572.
% 159.05/27.84 |
% 159.05/27.84 End of proof
% 159.05/27.84
% 159.05/27.84 Sub-proof #498 shows that the following formulas are inconsistent:
% 159.05/27.84 ----------------------------------------------------------------
% 159.05/27.84 (1) all_58_1 = e0
% 159.05/27.84 (2) all_58_12 = e3
% 159.05/27.84 (3) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.84 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.84 (4) all_58_9 = e3
% 159.05/27.84 (5) op(e2, e3) = e2
% 159.05/27.84 (6) ~ (e3 = e1)
% 159.05/27.84 (7) all_58_4 = e2
% 159.05/27.84 (8) ~ (e2 = e1)
% 159.05/27.84 (9) ~ (e1 = e0)
% 159.05/27.84 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/27.84 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/27.84 (11) all_58_0 = e0
% 159.05/27.84 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.84
% 159.05/27.84 Begin of proof
% 159.05/27.84 |
% 159.05/27.84 | BETA: splitting (3) gives:
% 159.05/27.84 |
% 159.05/27.84 | Case 1:
% 159.05/27.84 | |
% 159.05/27.84 | | (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 159.05/27.84 | | e1)
% 159.05/27.84 | |
% 159.05/27.84 | | REF_CLOSE: (5), (8), (9), (11), (12), (13) are inconsistent by sub-proof
% 159.05/27.84 | | #1160.
% 159.05/27.84 | |
% 159.05/27.84 | Case 2:
% 159.05/27.84 | |
% 159.05/27.84 | | (14) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 159.05/27.84 | | e1)
% 159.05/27.84 | |
% 159.05/27.84 | | BETA: splitting (14) gives:
% 159.05/27.84 | |
% 159.05/27.84 | | Case 1:
% 159.05/27.84 | | |
% 159.05/27.84 | | | (15) all_58_6 = e1 & op(e1, e3) = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | ALPHA: (15) implies:
% 159.05/27.84 | | | (16) all_58_6 = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/27.84 | | | (16) are inconsistent by sub-proof #502.
% 159.05/27.84 | | |
% 159.05/27.84 | | Case 2:
% 159.05/27.84 | | |
% 159.05/27.84 | | | (17) all_58_12 = e1 & op(e0, e3) = e1
% 159.05/27.84 | | |
% 159.05/27.84 | | | REF_CLOSE: (2), (6), (17) are inconsistent by sub-proof #1388.
% 159.05/27.84 | | |
% 159.05/27.84 | | End of split
% 159.05/27.84 | |
% 159.05/27.84 | End of split
% 159.05/27.84 |
% 159.05/27.84 End of proof
% 159.05/27.84
% 159.05/27.84 Sub-proof #499 shows that the following formulas are inconsistent:
% 159.05/27.84 ----------------------------------------------------------------
% 159.05/27.84 (1) all_58_15 = e0
% 159.05/27.84 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.84 (3) all_58_12 = e3
% 159.05/27.84 (4) op(e3, e3) = all_28_1
% 159.05/27.84 (5) all_58_8 = e3
% 159.05/27.84 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.84 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.84 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/27.84 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/27.84 (8) all_58_6 = e1
% 159.05/27.84 (9) op(e2, e3) = all_52_1
% 159.05/27.84 (10) ~ (e3 = e0)
% 159.05/27.84 (11) op(e0, e0) = e0
% 159.05/27.84 (12) ~ (e2 = e0)
% 159.05/27.84 (13) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.84 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.84 (14) op(e2, e3) = e2
% 159.05/27.84 (15) ~ (e3 = e1)
% 159.05/27.84 (16) op(e1, e2) = all_52_6
% 159.05/27.84 (17) op(e3, e3) = e1
% 159.05/27.84 (18) all_58_11 = e2
% 159.05/27.84 (19) ~ (e2 = e1)
% 159.05/27.84 (20) ~ (e1 = e0)
% 159.05/27.84 (21) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.84 (22) op(e3, e3) = all_22_1
% 159.05/27.84 (23) ~ (all_52_6 = e3)
% 159.05/27.84 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.84 (25) ~ (e3 = e2)
% 159.05/27.84
% 159.05/27.84 Begin of proof
% 159.05/27.84 |
% 159.05/27.84 | BETA: splitting (21) gives:
% 159.05/27.84 |
% 159.05/27.84 | Case 1:
% 159.05/27.84 | |
% 159.05/27.84 | | (26) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.84 | |
% 159.05/27.84 | | REF_CLOSE: (2), (5), (7), (10), (12), (13), (15), (16), (18), (19), (20),
% 159.05/27.84 | | (23), (24), (25), (26) are inconsistent by sub-proof #933.
% 159.05/27.84 | |
% 159.05/27.84 | Case 2:
% 159.05/27.84 | |
% 159.05/27.84 | | (27) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.84 | |
% 159.05/27.84 | | ALPHA: (27) implies:
% 159.05/27.84 | | (28) all_58_15 = e3
% 159.05/27.84 | | (29) op(e0, e0) = e3
% 159.05/27.84 | |
% 159.05/27.84 | | COMBINE_EQS: (1), (28) imply:
% 159.05/27.84 | | (30) e3 = e0
% 159.05/27.84 | |
% 159.05/27.84 | | COMBINE_EQS: (3), (30) imply:
% 159.05/27.84 | | (31) all_58_12 = e0
% 159.05/27.84 | |
% 159.05/27.84 | | REF_CLOSE: (4), (6), (8), (9), (10), (11), (14), (15), (17), (20), (22),
% 159.05/27.84 | | (24), (25), (29), (31) are inconsistent by sub-proof #546.
% 159.05/27.84 | |
% 159.05/27.84 | End of split
% 159.05/27.84 |
% 159.05/27.84 End of proof
% 159.05/27.84
% 159.05/27.84 Sub-proof #500 shows that the following formulas are inconsistent:
% 159.05/27.84 ----------------------------------------------------------------
% 159.05/27.84 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.84 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.85 (2) all_58_8 = e3
% 159.05/27.85 (3) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/27.85 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/27.85 (4) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.85 (5) ~ (e3 = e0)
% 159.05/27.85 (6) ~ (e2 = e0)
% 159.05/27.85 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.85 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.85 (8) all_58_9 = e3
% 159.05/27.85 (9) ~ (e3 = e1)
% 159.05/27.85 (10) op(e1, e2) = all_52_6
% 159.05/27.85 (11) all_58_11 = e2
% 159.05/27.85 (12) ~ (e2 = e1)
% 159.05/27.85 (13) ~ (e1 = e0)
% 159.05/27.85 (14) ~ (all_52_6 = e3)
% 159.05/27.85 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.85 (16) ~ (e3 = e2)
% 159.05/27.85
% 159.05/27.85 Begin of proof
% 159.05/27.85 |
% 159.05/27.85 | ALPHA: (4) implies:
% 159.05/27.85 | (17) all_58_9 = e2
% 159.05/27.85 |
% 159.05/27.85 | COMBINE_EQS: (8), (17) imply:
% 159.05/27.85 | (18) e3 = e2
% 159.05/27.85 |
% 159.05/27.85 | COMBINE_EQS: (2), (18) imply:
% 159.05/27.85 | (19) all_58_8 = e2
% 159.05/27.85 |
% 159.05/27.85 | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 159.05/27.85 | (16), (19) are inconsistent by sub-proof #1068.
% 159.05/27.85 |
% 159.05/27.85 End of proof
% 159.05/27.85
% 159.05/27.85 Sub-proof #501 shows that the following formulas are inconsistent:
% 159.05/27.85 ----------------------------------------------------------------
% 159.05/27.85 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.05/27.85 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.85 (3) all_54_13 = all_52_7
% 159.05/27.85 (4) ~ (all_52_7 = e3)
% 159.05/27.85 (5) ~ (all_52_6 = all_52_14)
% 159.05/27.85 (6) ~ (all_52_11 = e3)
% 159.05/27.85 (7) all_58_12 = e3
% 159.05/27.85 (8) ~ (all_52_7 = all_52_11)
% 159.05/27.85 (9) op(e1, e2) = all_14_0
% 159.05/27.85 (10) ~ (all_52_14 = e3)
% 159.05/27.85 (11) all_58_6 = e1
% 159.05/27.85 (12) op(e1, e2) = e0
% 159.05/27.85 (13) all_54_2 = all_52_8
% 159.05/27.85 (14) ~ (all_52_8 = all_52_9)
% 159.05/27.85 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.85 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.85 (16) ~ (all_52_9 = all_52_13)
% 159.05/27.85 (17) ~ (all_52_9 = e3)
% 159.05/27.85 (18) ~ (all_52_2 = all_52_6)
% 159.05/27.85 (19) all_58_9 = e3
% 159.05/27.85 (20) op(e2, e3) = e2
% 159.05/27.85 (21) op(e1, e2) = all_52_6
% 159.05/27.85 (22) all_58_1 = e1
% 159.05/27.85 (23) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.85 (24) ~ (all_52_7 = e0)
% 159.05/27.85 (25) all_54_8 = all_52_2
% 159.05/27.85 (26) all_54_7 = all_52_13
% 159.05/27.85 (27) ~ (all_52_13 = e2)
% 159.05/27.85 (28) ~ (all_52_9 = all_52_11)
% 159.05/27.85 (29) ~ (all_52_2 = e1)
% 159.05/27.85 (30) all_58_4 = e2
% 159.05/27.85 (31) ~ (all_52_2 = all_52_14)
% 159.05/27.85 (32) ~ (all_52_6 = all_52_7)
% 159.05/27.85 (33) all_54_6 = all_52_9
% 159.05/27.85 (34) ~ (all_52_8 = all_52_11)
% 159.05/27.85 (35) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.85 (36) ~ (all_52_13 = e0)
% 159.05/27.85 (37) ~ (all_52_2 = e2)
% 159.05/27.85 (38) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/27.85 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/27.85 (39) ~ (all_52_9 = e2)
% 159.05/27.85 (40) ~ (all_52_8 = e3)
% 159.05/27.85 (41) all_54_14 = all_52_11
% 159.05/27.85 (42) all_58_0 = e0
% 159.05/27.85 (43) ~ (all_52_8 = e1)
% 159.05/27.85 (44) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 159.05/27.85 (45) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.85 (46) ~ (all_52_6 = e3)
% 159.05/27.85 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.85 (48) all_54_11 = all_52_14
% 159.05/27.85 (49) all_54_9 = all_52_6
% 159.05/27.85 (50) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.85 (51) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.85
% 159.05/27.85 Begin of proof
% 159.05/27.85 |
% 159.05/27.85 | BETA: splitting (50) gives:
% 159.05/27.85 |
% 159.05/27.85 | Case 1:
% 159.05/27.85 | |
% 159.05/27.85 | | (52) all_54_7 = e2
% 159.05/27.85 | |
% 159.05/27.85 | | COMBINE_EQS: (26), (52) imply:
% 159.05/27.85 | | (53) all_52_13 = e2
% 159.05/27.85 | |
% 159.05/27.85 | | REDUCE: (27), (53) imply:
% 159.05/27.85 | | (54) $false
% 159.05/27.85 | |
% 159.05/27.85 | | CLOSE: (54) is inconsistent.
% 159.05/27.85 | |
% 159.05/27.85 | Case 2:
% 159.05/27.85 | |
% 159.05/27.85 | | (55) all_54_7 = e1 | all_54_7 = e0
% 159.05/27.85 | |
% 159.05/27.85 | | BETA: splitting (55) gives:
% 159.05/27.85 | |
% 159.05/27.85 | | Case 1:
% 159.05/27.85 | | |
% 159.05/27.85 | | | (56) all_54_7 = e1
% 159.05/27.85 | | |
% 159.05/27.85 | | | COMBINE_EQS: (26), (56) imply:
% 159.05/27.85 | | | (57) all_52_13 = e1
% 159.05/27.85 | | |
% 159.05/27.85 | | | REDUCE: (16), (57) imply:
% 159.05/27.85 | | | (58) ~ (all_52_9 = e1)
% 159.05/27.85 | | |
% 159.05/27.85 | | | BETA: splitting (2) gives:
% 159.05/27.85 | | |
% 159.05/27.85 | | | Case 1:
% 159.05/27.85 | | | |
% 159.05/27.85 | | | | (59) all_54_6 = e3
% 159.05/27.85 | | | |
% 159.05/27.85 | | | | REF_CLOSE: (17), (33), (59) are inconsistent by sub-proof #1193.
% 159.05/27.85 | | | |
% 159.05/27.85 | | | Case 2:
% 159.05/27.85 | | | |
% 159.05/27.85 | | | | (60) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.85 | | | |
% 159.05/27.85 | | | | BETA: splitting (60) gives:
% 159.05/27.85 | | | |
% 159.05/27.85 | | | | Case 1:
% 159.05/27.85 | | | | |
% 159.05/27.85 | | | | | (61) all_54_6 = e2
% 159.05/27.85 | | | | |
% 159.05/27.85 | | | | | REF_CLOSE: (33), (39), (61) are inconsistent by sub-proof #1192.
% 159.05/27.85 | | | | |
% 159.05/27.85 | | | | Case 2:
% 159.05/27.85 | | | | |
% 159.05/27.85 | | | | | (62) all_54_6 = e1 | all_54_6 = e0
% 159.05/27.85 | | | | |
% 159.05/27.85 | | | | | BETA: splitting (35) gives:
% 159.05/27.85 | | | | |
% 159.05/27.85 | | | | | Case 1:
% 159.05/27.85 | | | | | |
% 159.05/27.85 | | | | | | (63) all_54_11 = e3
% 159.05/27.85 | | | | | |
% 159.05/27.85 | | | | | | REF_CLOSE: (10), (48), (63) are inconsistent by sub-proof #1415.
% 159.05/27.85 | | | | | |
% 159.05/27.85 | | | | | Case 2:
% 159.05/27.85 | | | | | |
% 159.05/27.85 | | | | | | (64) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.85 | | | | | |
% 159.05/27.85 | | | | | | BETA: splitting (62) gives:
% 159.05/27.85 | | | | | |
% 159.05/27.85 | | | | | | Case 1:
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | (65) all_54_6 = e1
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | REF_CLOSE: (33), (58), (65) are inconsistent by sub-proof #562.
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | Case 2:
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | (66) all_54_6 = e0
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | COMBINE_EQS: (33), (66) imply:
% 159.05/27.85 | | | | | | | (67) all_52_9 = e0
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | SIMP: (67) implies:
% 159.05/27.85 | | | | | | | (68) all_52_9 = e0
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | REDUCE: (14), (68) imply:
% 159.05/27.85 | | | | | | | (69) ~ (all_52_8 = e0)
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | REDUCE: (28), (68) imply:
% 159.05/27.85 | | | | | | | (70) ~ (all_52_11 = e0)
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | SIMP: (70) implies:
% 159.05/27.85 | | | | | | | (71) ~ (all_52_11 = e0)
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | BETA: splitting (23) gives:
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | |
% 159.05/27.85 | | | | | | | | (72) all_54_2 = e3
% 159.05/27.85 | | | | | | | |
% 159.05/27.85 | | | | | | | | REF_CLOSE: (13), (40), (72) are inconsistent by sub-proof #1210.
% 159.05/27.85 | | | | | | | |
% 159.05/27.85 | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | |
% 159.05/27.85 | | | | | | | | (73) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.85 | | | | | | | |
% 159.05/27.85 | | | | | | | | BETA: splitting (44) gives:
% 159.05/27.85 | | | | | | | |
% 159.05/27.85 | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | |
% 159.05/27.85 | | | | | | | | | (74) all_54_8 = e2
% 159.05/27.85 | | | | | | | | |
% 159.05/27.85 | | | | | | | | | REF_CLOSE: (25), (37), (74) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | #1231.
% 159.05/27.85 | | | | | | | | |
% 159.05/27.85 | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | |
% 159.05/27.85 | | | | | | | | | (75) all_54_8 = e1 | all_54_8 = e0
% 159.05/27.85 | | | | | | | | |
% 159.05/27.85 | | | | | | | | | BETA: splitting (75) gives:
% 159.05/27.85 | | | | | | | | |
% 159.05/27.85 | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | (76) all_54_8 = e1
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | REF_CLOSE: (25), (29), (76) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | | #1379.
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | (77) all_54_8 = e0
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | COMBINE_EQS: (25), (77) imply:
% 159.05/27.85 | | | | | | | | | | (78) all_52_2 = e0
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | SIMP: (78) implies:
% 159.05/27.85 | | | | | | | | | | (79) all_52_2 = e0
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | REDUCE: (18), (79) imply:
% 159.05/27.85 | | | | | | | | | | (80) ~ (all_52_6 = e0)
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | SIMP: (80) implies:
% 159.05/27.85 | | | | | | | | | | (81) ~ (all_52_6 = e0)
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | REDUCE: (31), (79) imply:
% 159.05/27.85 | | | | | | | | | | (82) ~ (all_52_14 = e0)
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | SIMP: (82) implies:
% 159.05/27.85 | | | | | | | | | | (83) ~ (all_52_14 = e0)
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | BETA: splitting (73) gives:
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | (84) all_54_2 = e2
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | COMBINE_EQS: (13), (84) imply:
% 159.05/27.85 | | | | | | | | | | | (85) all_52_8 = e2
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | SIMP: (85) implies:
% 159.05/27.85 | | | | | | | | | | | (86) all_52_8 = e2
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | REDUCE: (34), (86) imply:
% 159.05/27.85 | | | | | | | | | | | (87) ~ (all_52_11 = e2)
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | SIMP: (87) implies:
% 159.05/27.85 | | | | | | | | | | | (88) ~ (all_52_11 = e2)
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | BETA: splitting (51) gives:
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | (89) all_54_14 = e3
% 159.05/27.85 | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | REF_CLOSE: (6), (41), (89) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | | | | #1413.
% 159.05/27.85 | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | (90) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.85 | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | BETA: splitting (90) gives:
% 159.05/27.85 | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | (91) all_54_14 = e2
% 159.05/27.85 | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | REF_CLOSE: (41), (88), (91) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | | | | | #1232.
% 159.05/27.85 | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | (92) all_54_14 = e1 | all_54_14 = e0
% 159.05/27.85 | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | BETA: splitting (92) gives:
% 159.05/27.85 | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | (93) all_54_14 = e1
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | COMBINE_EQS: (41), (93) imply:
% 159.05/27.85 | | | | | | | | | | | | | | (94) all_52_11 = e1
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | SIMP: (94) implies:
% 159.05/27.85 | | | | | | | | | | | | | | (95) all_52_11 = e1
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | REDUCE: (8), (95) imply:
% 159.05/27.85 | | | | | | | | | | | | | | (96) ~ (all_52_7 = e1)
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | (97) all_54_13 = e3
% 159.05/27.85 | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (97) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | | | | | | | #1435.
% 159.05/27.85 | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | (98) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.85 | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 159.05/27.85 | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | (99) all_54_13 = e2
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (99) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | (100) all_52_7 = e2
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | SIMP: (100) implies:
% 159.05/27.85 | | | | | | | | | | | | | | | | (101) all_52_7 = e2
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | REDUCE: (32), (101) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | (102) ~ (all_52_6 = e2)
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | (103) all_54_9 = e3
% 159.05/27.85 | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (49), (103) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | | | | | | | | | #1181.
% 159.05/27.85 | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | (104) ~ (all_54_9 = e3)
% 159.05/27.85 | | | | | | | | | | | | | | | | | (105) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.05/27.85 | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 159.05/27.85 | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | (106) all_54_9 = e2
% 159.05/27.85 | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (102), (106) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | | | | | | | | | | #1180.
% 159.05/27.85 | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | (107) all_54_9 = e1 | all_54_9 = e0
% 159.05/27.85 | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 159.05/27.85 | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (108) all_54_9 = e1
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (108) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (109) all_52_6 = e1
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | SIMP: (109) implies:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (110) all_52_6 = e1
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | REDUCE: (5), (110) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (111) ~ (all_52_14 = e1)
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | SIMP: (111) implies:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (112) ~ (all_52_14 = e1)
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | REDUCE: (46), (110) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (113) ~ (e3 = e1)
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | SIMP: (113) implies:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (114) ~ (e3 = e1)
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | REDUCE: (81), (110) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (115) ~ (e1 = e0)
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | REDUCE: (21), (110) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (116) op(e1, e2) = e1
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (117) all_54_11 = e2
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (117) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (118) all_52_14 = e2
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | SIMP: (118) implies:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (119) all_52_14 = e2
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (119) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (120) ~ (e2 = e1)
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e1, all_14_0, e2, e1,
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | simplifying with (9), (116) gives:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (121) all_14_0 = e1
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e0, all_14_0, e2, e1,
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | simplifying with (9), (12) gives:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (122) all_14_0 = e0
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (122) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (123) e1 = e0
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (123) imply:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (124) all_58_1 = e0
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (15), (19), (20), (30), (38), (42),
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (47), (114), (115), (120), (124) are inconsistent
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | by sub-proof #502.
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | (125) all_54_11 = e1 | all_54_11 = e0
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (83), (112), (125) are inconsistent by
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | | sub-proof #1227.
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | (126) all_54_9 = e0
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (81), (126) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | | | | | | | | | | | #1170.
% 159.05/27.85 | | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | (127) all_54_13 = e1 | all_54_13 = e0
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (24), (96), (127) are inconsistent by
% 159.05/27.85 | | | | | | | | | | | | | | | | sub-proof #875.
% 159.05/27.85 | | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | (128) all_54_14 = e0
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | | REF_CLOSE: (41), (71), (128) are inconsistent by sub-proof
% 159.05/27.85 | | | | | | | | | | | | | | #1400.
% 159.05/27.85 | | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | Case 2:
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | (129) all_54_2 = e1 | all_54_2 = e0
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | | REF_CLOSE: (13), (43), (69), (129) are inconsistent by
% 159.05/27.85 | | | | | | | | | | | sub-proof #561.
% 159.05/27.85 | | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | | |
% 159.05/27.85 | | | | | | | | | End of split
% 159.05/27.85 | | | | | | | | |
% 159.05/27.85 | | | | | | | | End of split
% 159.05/27.85 | | | | | | | |
% 159.05/27.85 | | | | | | | End of split
% 159.05/27.85 | | | | | | |
% 159.05/27.85 | | | | | | End of split
% 159.05/27.85 | | | | | |
% 159.05/27.85 | | | | | End of split
% 159.05/27.85 | | | | |
% 159.05/27.85 | | | | End of split
% 159.05/27.85 | | | |
% 159.05/27.85 | | | End of split
% 159.05/27.85 | | |
% 159.05/27.85 | | Case 2:
% 159.05/27.85 | | |
% 159.05/27.85 | | | (130) all_54_7 = e0
% 159.05/27.85 | | |
% 159.05/27.85 | | | COMBINE_EQS: (26), (130) imply:
% 159.05/27.85 | | | (131) all_52_13 = e0
% 159.05/27.85 | | |
% 159.05/27.85 | | | REDUCE: (36), (131) imply:
% 159.05/27.85 | | | (132) $false
% 159.05/27.85 | | |
% 159.05/27.85 | | | CLOSE: (132) is inconsistent.
% 159.05/27.85 | | |
% 159.05/27.85 | | End of split
% 159.05/27.85 | |
% 159.05/27.85 | End of split
% 159.05/27.85 |
% 159.05/27.85 End of proof
% 159.05/27.85
% 159.05/27.85 Sub-proof #502 shows that the following formulas are inconsistent:
% 159.05/27.85 ----------------------------------------------------------------
% 159.05/27.85 (1) all_58_1 = e0
% 159.05/27.85 (2) all_58_12 = e3
% 159.05/27.85 (3) all_58_6 = e1
% 159.05/27.85 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.85 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.85 (5) all_58_9 = e3
% 159.05/27.85 (6) op(e2, e3) = e2
% 159.05/27.85 (7) ~ (e3 = e1)
% 159.05/27.85 (8) all_58_4 = e2
% 159.05/27.85 (9) ~ (e2 = e1)
% 159.05/27.85 (10) ~ (e1 = e0)
% 159.05/27.85 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/27.85 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/27.85 (12) all_58_0 = e0
% 159.05/27.85 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.85
% 159.05/27.85 Begin of proof
% 159.05/27.85 |
% 159.05/27.85 | BETA: splitting (11) gives:
% 159.05/27.85 |
% 159.05/27.85 | Case 1:
% 159.05/27.85 | |
% 159.05/27.85 | | (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 159.05/27.85 | | e1)
% 159.05/27.85 | |
% 159.05/27.85 | | BETA: splitting (14) gives:
% 159.05/27.85 | |
% 159.05/27.85 | | Case 1:
% 159.05/27.85 | | |
% 159.05/27.85 | | | (15) all_58_0 = e1 & op(e3, e3) = e1
% 159.05/27.85 | | |
% 159.05/27.85 | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (12), (13), (15) are
% 159.05/27.85 | | | inconsistent by sub-proof #694.
% 159.05/27.85 | | |
% 159.05/27.85 | | Case 2:
% 159.05/27.85 | | |
% 159.05/27.85 | | | (16) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/27.85 | | |
% 159.05/27.85 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (12), (13), (16) are
% 159.05/27.85 | | | inconsistent by sub-proof #517.
% 159.05/27.85 | | |
% 159.05/27.85 | | End of split
% 159.05/27.85 | |
% 159.05/27.85 | Case 2:
% 159.05/27.85 | |
% 159.05/27.85 | | (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 159.05/27.85 | | e1)
% 159.05/27.85 | |
% 159.05/27.85 | | BETA: splitting (17) gives:
% 159.05/27.85 | |
% 159.05/27.85 | | Case 1:
% 159.05/27.85 | | |
% 159.05/27.85 | | | (18) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/27.85 | | |
% 159.05/27.85 | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #1476.
% 159.05/27.85 | | |
% 159.05/27.85 | | Case 2:
% 159.05/27.85 | | |
% 159.05/27.85 | | | (19) all_58_9 = e1 & op(e3, e0) = e1
% 159.05/27.85 | | |
% 159.05/27.85 | | | REF_CLOSE: (5), (7), (19) are inconsistent by sub-proof #1078.
% 159.05/27.85 | | |
% 159.05/27.85 | | End of split
% 159.05/27.85 | |
% 159.05/27.85 | End of split
% 159.05/27.85 |
% 159.05/27.85 End of proof
% 159.05/27.85
% 159.05/27.85 Sub-proof #503 shows that the following formulas are inconsistent:
% 159.05/27.85 ----------------------------------------------------------------
% 159.05/27.85 (1) all_56_14 = e3
% 159.05/27.85 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.85 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.85 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.85 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.85 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.85 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.85 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.85 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.85 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.85 (7) all_54_13 = all_52_7
% 159.05/27.85 (8) op(e1, e1) = all_6_2
% 159.05/27.85 (9) ~ (all_52_7 = e3)
% 159.05/27.85 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.85 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.85 e1)
% 159.05/27.85 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/27.85 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.85 (12) ~ (all_52_11 = e3)
% 159.05/27.85 (13) op(e3, e3) = all_28_1
% 159.05/27.85 (14) all_58_8 = e3
% 159.05/27.85 (15) ~ (all_52_7 = all_52_11)
% 159.05/27.85 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.85 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.85 (17) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.85 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.85 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.85 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.85 (19) op(e3, e2) = all_52_4
% 159.05/27.85 (20) ~ (all_4_2 = e2)
% 159.05/27.85 (21) all_58_6 = e1
% 159.05/27.85 (22) op(e2, e3) = all_52_1
% 159.05/27.85 (23) ~ (all_52_13 = e3)
% 159.05/27.85 (24) all_54_2 = all_52_8
% 159.05/27.85 (25) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.85 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.85 (26) ~ (all_52_8 = all_52_9)
% 159.05/27.85 (27) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.85 (28) ~ (e3 = e0)
% 159.05/27.85 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.85 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.85 (30) ~ (all_52_9 = all_52_13)
% 159.05/27.85 (31) op(e0, e0) = e0
% 159.05/27.85 (32) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/27.85 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/27.85 e2)
% 159.05/27.85 (33) ~ (e2 = e0)
% 159.05/27.85 (34) ~ (all_52_9 = e3)
% 159.05/27.85 (35) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.85 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.85 (36) op(e2, e0) = all_52_13
% 159.05/27.85 (37) op(e2, e3) = e2
% 159.05/27.85 (38) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.85 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.85 (39) ~ (e3 = e1)
% 159.05/27.85 (40) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.85 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.85 (41) ~ (all_4_2 = e1)
% 159.05/27.85 (42) e2 = e0
% 159.05/27.85 (43) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.85 (44) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.85 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.85 (45) ~ (all_52_7 = e0)
% 159.05/27.85 (46) op(e0, e0) = all_4_2
% 159.05/27.85 (47) all_54_7 = all_52_13
% 159.05/27.85 (48) op(e3, e3) = e1
% 159.05/27.85 (49) ~ (all_52_13 = e2)
% 159.05/27.85 (50) all_56_15 = all_4_2
% 159.05/27.85 (51) ~ (all_52_9 = all_52_11)
% 159.05/27.85 (52) all_58_11 = e2
% 159.05/27.85 (53) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.85 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.85 (54) ~ (all_52_4 = e3)
% 159.05/27.85 (55) all_54_6 = all_52_9
% 159.05/27.85 (56) ~ (e2 = e1)
% 159.05/27.85 (57) ~ (all_52_8 = all_52_11)
% 159.05/27.85 (58) ~ (all_52_13 = e0)
% 159.05/27.85 (59) ~ (e1 = e0)
% 159.05/27.85 (60) all_58_3 = e3
% 159.05/27.85 (61) ~ (all_6_2 = e2)
% 159.05/27.85 (62) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.85 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.85 e3)
% 159.05/27.85 (63) all_56_13 = e3
% 159.05/27.85 (64) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/27.85 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/27.85 (65) ~ (all_52_9 = e2)
% 159.05/27.85 (66) ~ (all_52_8 = e3)
% 159.05/27.85 (67) all_54_14 = all_52_11
% 159.05/27.85 (68) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.85 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.85 (69) op(e0, e2) = all_52_7
% 159.05/27.85 (70) op(e3, e3) = all_22_1
% 159.05/27.85 (71) ~ (all_52_8 = e1)
% 159.05/27.85 (72) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.86 (73) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.86 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.86 (74) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.86 (75) ~ (e3 = e2)
% 159.05/27.86 (76) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.86 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.86 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.86 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.86 (77) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.86 (78) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.86
% 159.05/27.86 Begin of proof
% 159.05/27.86 |
% 159.05/27.86 | SIMP: (42) implies:
% 159.05/27.86 | (79) e2 = e0
% 159.05/27.86 |
% 159.05/27.86 | COMBINE_EQS: (52), (79) imply:
% 159.05/27.86 | (80) all_58_11 = e0
% 159.05/27.86 |
% 159.05/27.86 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/27.86 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.05/27.86 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 159.05/27.86 | (35), (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 159.05/27.86 | (47), (48), (49), (50), (51), (53), (54), (55), (56), (57), (58),
% 159.05/27.86 | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 159.05/27.86 | (70), (71), (72), (73), (74), (75), (76), (77), (78), (80) are
% 159.05/27.86 | inconsistent by sub-proof #504.
% 159.05/27.86 |
% 159.05/27.86 End of proof
% 159.05/27.86
% 159.05/27.86 Sub-proof #504 shows that the following formulas are inconsistent:
% 159.05/27.86 ----------------------------------------------------------------
% 159.05/27.86 (1) all_56_14 = e3
% 159.05/27.86 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.86 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.86 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.86 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.86 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.86 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.86 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.86 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.86 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.86 (7) all_54_13 = all_52_7
% 159.05/27.86 (8) op(e1, e1) = all_6_2
% 159.05/27.86 (9) ~ (all_52_7 = e3)
% 159.05/27.86 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.86 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.86 e1)
% 159.05/27.86 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/27.86 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.86 (12) ~ (all_52_11 = e3)
% 159.05/27.86 (13) op(e3, e3) = all_28_1
% 159.05/27.86 (14) all_58_8 = e3
% 159.05/27.86 (15) ~ (all_52_7 = all_52_11)
% 159.05/27.86 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.86 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.86 (17) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.86 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.86 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.86 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.86 (19) op(e3, e2) = all_52_4
% 159.05/27.86 (20) ~ (all_4_2 = e2)
% 159.05/27.86 (21) all_58_6 = e1
% 159.05/27.86 (22) op(e2, e3) = all_52_1
% 159.05/27.86 (23) ~ (all_52_13 = e3)
% 159.05/27.86 (24) all_54_2 = all_52_8
% 159.05/27.86 (25) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.86 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.86 (26) ~ (all_52_8 = all_52_9)
% 159.05/27.86 (27) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.86 (28) ~ (e3 = e0)
% 159.05/27.86 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.86 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.86 (30) ~ (all_52_9 = all_52_13)
% 159.05/27.86 (31) op(e0, e0) = e0
% 159.05/27.86 (32) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/27.86 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/27.86 e2)
% 159.05/27.86 (33) ~ (e2 = e0)
% 159.05/27.86 (34) ~ (all_52_9 = e3)
% 159.05/27.86 (35) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.86 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.86 (36) op(e2, e0) = all_52_13
% 159.05/27.86 (37) op(e2, e3) = e2
% 159.05/27.86 (38) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.86 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.86 (39) ~ (e3 = e1)
% 159.05/27.86 (40) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.86 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.86 (41) ~ (all_4_2 = e1)
% 159.05/27.86 (42) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.86 (43) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.86 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.86 (44) ~ (all_52_7 = e0)
% 159.05/27.86 (45) op(e0, e0) = all_4_2
% 159.05/27.86 (46) all_54_7 = all_52_13
% 159.05/27.86 (47) op(e3, e3) = e1
% 159.05/27.86 (48) ~ (all_52_13 = e2)
% 159.05/27.86 (49) all_56_15 = all_4_2
% 159.05/27.86 (50) ~ (all_52_9 = all_52_11)
% 159.05/27.86 (51) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.86 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.86 (52) ~ (all_52_4 = e3)
% 159.05/27.86 (53) all_54_6 = all_52_9
% 159.05/27.86 (54) ~ (e2 = e1)
% 159.05/27.86 (55) ~ (all_52_8 = all_52_11)
% 159.05/27.86 (56) ~ (all_52_13 = e0)
% 159.05/27.86 (57) ~ (e1 = e0)
% 159.05/27.86 (58) all_58_3 = e3
% 159.05/27.86 (59) ~ (all_6_2 = e2)
% 159.05/27.86 (60) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.86 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.86 e3)
% 159.05/27.86 (61) all_56_13 = e3
% 159.05/27.86 (62) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/27.86 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/27.86 (63) ~ (all_52_9 = e2)
% 159.05/27.86 (64) ~ (all_52_8 = e3)
% 159.05/27.86 (65) all_54_14 = all_52_11
% 159.05/27.86 (66) all_58_11 = e0
% 159.05/27.86 (67) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.86 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.86 (68) op(e0, e2) = all_52_7
% 159.05/27.86 (69) op(e3, e3) = all_22_1
% 159.05/27.86 (70) ~ (all_52_8 = e1)
% 159.05/27.86 (71) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.86 (72) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.86 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.86 (73) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.86 (74) ~ (e3 = e2)
% 159.05/27.86 (75) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.86 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.86 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.86 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.86 (76) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.86 (77) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.86
% 159.05/27.86 Begin of proof
% 159.05/27.86 |
% 159.05/27.86 | BETA: splitting (25) gives:
% 159.05/27.86 |
% 159.05/27.86 | Case 1:
% 159.05/27.86 | |
% 159.05/27.86 | | (78) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 159.05/27.86 | | e2)
% 159.05/27.86 | |
% 159.05/27.86 | | BETA: splitting (78) gives:
% 159.05/27.86 | |
% 159.05/27.86 | | Case 1:
% 159.05/27.86 | | |
% 159.05/27.86 | | | (79) all_58_6 = e2 & op(e1, e3) = e2
% 159.05/27.86 | | |
% 159.05/27.86 | | | ALPHA: (79) implies:
% 159.05/27.86 | | | (80) all_58_6 = e2
% 159.05/27.86 | | |
% 159.05/27.86 | | | REF_CLOSE: (16), (22), (28), (29), (33), (37), (39), (54), (57), (72),
% 159.05/27.86 | | | (73), (74), (80) are inconsistent by sub-proof #1152.
% 159.05/27.86 | | |
% 159.05/27.86 | | Case 2:
% 159.05/27.86 | | |
% 159.05/27.86 | | | (81) all_58_7 = e2 & op(e1, e2) = e2
% 159.05/27.86 | | |
% 159.05/27.86 | | | ALPHA: (81) implies:
% 159.05/27.86 | | | (82) all_58_7 = e2
% 159.05/27.86 | | |
% 159.05/27.86 | | | BETA: splitting (18) gives:
% 159.05/27.86 | | |
% 159.05/27.86 | | | Case 1:
% 159.05/27.86 | | | |
% 159.05/27.86 | | | | (83) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 159.05/27.86 | | | | = e2)
% 159.05/27.86 | | | |
% 159.05/27.86 | | | | BETA: splitting (83) gives:
% 159.05/27.86 | | | |
% 159.05/27.86 | | | | Case 1:
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | (84) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | ALPHA: (84) implies:
% 159.05/27.86 | | | | | (85) all_58_9 = e2
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.05/27.86 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 159.05/27.86 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 159.05/27.86 | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 159.05/27.86 | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 159.05/27.86 | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 159.05/27.86 | | | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 159.05/27.86 | | | | | (73), (74), (75), (76), (77), (82), (85) are inconsistent
% 159.05/27.86 | | | | | by sub-proof #509.
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | Case 2:
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | (86) all_58_10 = e2 & op(e2, e0) = e2
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | ALPHA: (86) implies:
% 159.05/27.86 | | | | | (87) all_58_10 = e2
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | REF_CLOSE: (6), (28), (33), (37), (39), (43), (54), (57), (58), (73),
% 159.05/27.86 | | | | | (87) are inconsistent by sub-proof #906.
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | End of split
% 159.05/27.86 | | | |
% 159.05/27.86 | | | Case 2:
% 159.05/27.86 | | | |
% 159.05/27.86 | | | | (88) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 159.05/27.86 | | | | e0) = e2)
% 159.05/27.86 | | | |
% 159.05/27.86 | | | | BETA: splitting (88) gives:
% 159.05/27.86 | | | |
% 159.05/27.86 | | | | Case 1:
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | (89) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | REF_CLOSE: (33), (66), (89) are inconsistent by sub-proof #507.
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | Case 2:
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | (90) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | ALPHA: (90) implies:
% 159.05/27.86 | | | | | (91) all_58_15 = e2
% 159.05/27.86 | | | | | (92) op(e0, e0) = e2
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | BETA: splitting (72) gives:
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | | Case 1:
% 159.05/27.86 | | | | | |
% 159.05/27.86 | | | | | | (93) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 159.05/27.86 | | | | | | e3) = e0)
% 159.05/27.86 | | | | | |
% 159.05/27.86 | | | | | | BETA: splitting (93) gives:
% 159.05/27.86 | | | | | |
% 159.05/27.86 | | | | | | Case 1:
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | | (94) all_58_0 = e0 & op(e3, e3) = e0
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | | ALPHA: (94) implies:
% 159.05/27.86 | | | | | | | (95) all_58_0 = e0
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | | BETA: splitting (75) gives:
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | |
% 159.05/27.86 | | | | | | | | (96) all_58_15 = e0 & op(e0, e0) = e0
% 159.05/27.86 | | | | | | | |
% 159.05/27.86 | | | | | | | | REF_CLOSE: (33), (91), (96) are inconsistent by sub-proof #885.
% 159.05/27.86 | | | | | | | |
% 159.05/27.86 | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | |
% 159.05/27.86 | | | | | | | | (97) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 159.05/27.86 | | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.05/27.86 | | | | | | | | e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 159.05/27.86 | | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 159.05/27.86 | | | | | | | | op(e0, e1) = e0))
% 159.05/27.86 | | | | | | | |
% 159.05/27.86 | | | | | | | | ALPHA: (97) implies:
% 159.05/27.86 | | | | | | | | (98) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.86 | | | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.86 | | | | | | | |
% 159.05/27.86 | | | | | | | | BETA: splitting (60) gives:
% 159.05/27.86 | | | | | | | |
% 159.05/27.86 | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | |
% 159.05/27.86 | | | | | | | | | (99) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 159.05/27.86 | | | | | | | | | op(e0, e2) = e3)
% 159.05/27.86 | | | | | | | | |
% 159.05/27.86 | | | | | | | | | BETA: splitting (99) gives:
% 159.05/27.86 | | | | | | | | |
% 159.05/27.86 | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | (100) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.86 | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | ALPHA: (100) implies:
% 159.05/27.86 | | | | | | | | | | (101) all_58_12 = e3
% 159.05/27.86 | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | BETA: splitting (38) gives:
% 159.05/27.86 | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | (102) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 159.05/27.86 | | | | | | | | | | | & op(e2, e2) = e0)
% 159.05/27.86 | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | BETA: splitting (102) gives:
% 159.05/27.86 | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | (103) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.86 | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | ALPHA: (103) implies:
% 159.05/27.86 | | | | | | | | | | | | (104) all_58_1 = e0
% 159.05/27.86 | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | BETA: splitting (11) gives:
% 159.05/27.86 | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | (105) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 159.05/27.86 | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 159.05/27.86 | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | BETA: splitting (105) gives:
% 159.05/27.86 | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | (106) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | ALPHA: (106) implies:
% 159.05/27.86 | | | | | | | | | | | | | | (107) all_58_9 = e3
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | (108) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 159.05/27.86 | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.05/27.86 | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 159.05/27.86 | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | (109) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | REF_CLOSE: (21), (29), (37), (39), (54), (57), (73), (95),
% 159.05/27.86 | | | | | | | | | | | | | | | | (101), (104), (109) are inconsistent by sub-proof
% 159.05/27.86 | | | | | | | | | | | | | | | | #517.
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | (110) all_58_3 = e1 & op(e2, e2) = e1
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (13), (14), (16),
% 159.05/27.86 | | | | | | | | | | | | | | | | (17), (18), (19), (20), (22), (25), (27), (28),
% 159.05/27.86 | | | | | | | | | | | | | | | | (29), (33), (35), (37), (39), (40), (41), (43),
% 159.05/27.86 | | | | | | | | | | | | | | | | (45), (47), (49), (51), (52), (54), (57), (58),
% 159.05/27.86 | | | | | | | | | | | | | | | | (59), (60), (61), (67), (68), (69), (72), (73),
% 159.05/27.86 | | | | | | | | | | | | | | | | (74), (75), (101), (110) are inconsistent by
% 159.05/27.86 | | | | | | | | | | | | | | | | sub-proof #513.
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | (111) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 159.05/27.86 | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.05/27.86 | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 159.05/27.86 | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | (112) all_58_7 = e1 & op(e1, e2) = e1
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 159.05/27.86 | | | | | | | | | | | | | | | | (113) all_58_7 = e1
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | REF_CLOSE: (54), (82), (113) are inconsistent by sub-proof
% 159.05/27.86 | | | | | | | | | | | | | | | | #721.
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | (114) all_58_13 = e1 & op(e0, e2) = e1
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 159.05/27.86 | | | | | | | | | | | | | | | | (115) all_58_13 = e1
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | (116) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 159.05/27.86 | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 159.05/27.86 | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 159.05/27.86 | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | | (117) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/27.86 | | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 159.05/27.86 | | | | | | | | | | | | | | | | | | (118) all_58_4 = e2
% 159.05/27.86 | | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (54), (57), (58), (62), (82), (95),
% 159.05/27.86 | | | | | | | | | | | | | | | | | | (104), (107), (115), (118) are inconsistent by
% 159.05/27.86 | | | | | | | | | | | | | | | | | | sub-proof #641.
% 159.05/27.86 | | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | | (119) all_58_5 = e2 & op(e2, e1) = e2
% 159.05/27.86 | | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 159.05/27.86 | | | | | | | | | | | | | | | | | | (120) all_58_5 = e2
% 159.05/27.86 | | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (28), (33), (37), (39), (43), (54), (57),
% 159.05/27.86 | | | | | | | | | | | | | | | | | | (58), (73), (120) are inconsistent by sub-proof
% 159.05/27.86 | | | | | | | | | | | | | | | | | | #898.
% 159.05/27.86 | | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | (121) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 159.05/27.86 | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 159.05/27.86 | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (28), (33), (39), (54), (57), (59),
% 159.05/27.86 | | | | | | | | | | | | | | | | | (73), (92), (98), (101), (121) are inconsistent by
% 159.05/27.86 | | | | | | | | | | | | | | | | | sub-proof #506.
% 159.05/27.86 | | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | (122) all_58_10 = e3 & op(e2, e0) = e3
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | ALPHA: (122) implies:
% 159.05/27.86 | | | | | | | | | | | | | | (123) op(e2, e0) = e3
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | REF_CLOSE: (23), (36), (73), (123) are inconsistent by
% 159.05/27.86 | | | | | | | | | | | | | | sub-proof #1364.
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | (124) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 159.05/27.86 | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 159.05/27.86 | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | BETA: splitting (124) gives:
% 159.05/27.86 | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | Case 1:
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | (125) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (13), (14), (16), (17), (21), (22),
% 159.05/27.86 | | | | | | | | | | | | | | (28), (31), (33), (37), (39), (40), (43), (47),
% 159.05/27.86 | | | | | | | | | | | | | | (51), (54), (57), (58), (59), (60), (66), (68),
% 159.05/27.86 | | | | | | | | | | | | | | (69), (73), (74), (101), (125) are inconsistent by
% 159.05/27.86 | | | | | | | | | | | | | | sub-proof #522.
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | (126) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | ALPHA: (126) implies:
% 159.05/27.86 | | | | | | | | | | | | | | (127) op(e0, e0) = e3
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | | REF_CLOSE: (73), (74), (92), (127) are inconsistent by
% 159.05/27.86 | | | | | | | | | | | | | | sub-proof #1382.
% 159.05/27.86 | | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | (128) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.86 | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (13), (14), (16), (17), (21), (22),
% 159.05/27.86 | | | | | | | | | | | | (28), (31), (33), (37), (39), (40), (43), (47),
% 159.05/27.86 | | | | | | | | | | | | (51), (54), (57), (58), (59), (60), (68), (69),
% 159.05/27.86 | | | | | | | | | | | | (73), (74), (101), (128) are inconsistent by
% 159.05/27.86 | | | | | | | | | | | | sub-proof #520.
% 159.05/27.86 | | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | (129) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 159.05/27.86 | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 159.05/27.86 | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | | REF_CLOSE: (2), (7), (9), (12), (15), (24), (26), (30), (33),
% 159.05/27.86 | | | | | | | | | | | (34), (42), (44), (46), (48), (50), (53), (55),
% 159.05/27.86 | | | | | | | | | | | (56), (63), (64), (65), (68), (70), (71), (73),
% 159.05/27.86 | | | | | | | | | | | (76), (77), (82), (129) are inconsistent by
% 159.05/27.86 | | | | | | | | | | | sub-proof #512.
% 159.05/27.86 | | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | (130) all_58_13 = e3 & op(e0, e2) = e3
% 159.05/27.86 | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | | REF_CLOSE: (9), (68), (73), (130) are inconsistent by
% 159.05/27.86 | | | | | | | | | | sub-proof #1449.
% 159.05/27.86 | | | | | | | | | |
% 159.05/27.86 | | | | | | | | | End of split
% 159.05/27.86 | | | | | | | | |
% 159.05/27.86 | | | | | | | | Case 2:
% 159.05/27.86 | | | | | | | | |
% 159.05/27.86 | | | | | | | | | (131) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3
% 159.05/27.86 | | | | | | | | | & op(e0, e0) = e3)
% 159.05/27.86 | | | | | | | | |
% 159.05/27.86 | | | | | | | | | REF_CLOSE: (6), (8), (14), (17), (28), (33), (37), (39), (40),
% 159.05/27.86 | | | | | | | | | (43), (51), (54), (57), (58), (59), (73), (74),
% 159.05/27.86 | | | | | | | | | (92), (131) are inconsistent by sub-proof #505.
% 159.05/27.86 | | | | | | | | |
% 159.05/27.86 | | | | | | | | End of split
% 159.05/27.86 | | | | | | | |
% 159.05/27.86 | | | | | | | End of split
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | Case 2:
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | | (132) all_58_2 = e0 & op(e2, e3) = e0
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | | ALPHA: (132) implies:
% 159.05/27.86 | | | | | | | (133) op(e2, e3) = e0
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | | REF_CLOSE: (33), (37), (73), (133) are inconsistent by sub-proof
% 159.05/27.86 | | | | | | | #1156.
% 159.05/27.86 | | | | | | |
% 159.05/27.86 | | | | | | End of split
% 159.05/27.86 | | | | | |
% 159.05/27.86 | | | | | Case 2:
% 159.05/27.86 | | | | | |
% 159.05/27.86 | | | | | | (134) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 159.05/27.86 | | | | | | op(e0, e3) = e0)
% 159.05/27.86 | | | | | |
% 159.05/27.86 | | | | | | REF_CLOSE: (6), (8), (9), (13), (14), (16), (17), (21), (22), (28),
% 159.05/27.86 | | | | | | (31), (33), (37), (39), (40), (43), (47), (51), (54),
% 159.05/27.86 | | | | | | (57), (58), (59), (60), (68), (69), (73), (74), (134) are
% 159.05/27.86 | | | | | | inconsistent by sub-proof #510.
% 159.05/27.86 | | | | | |
% 159.05/27.86 | | | | | End of split
% 159.05/27.86 | | | | |
% 159.05/27.86 | | | | End of split
% 159.05/27.86 | | | |
% 159.05/27.86 | | | End of split
% 159.05/27.86 | | |
% 159.05/27.86 | | End of split
% 159.05/27.86 | |
% 159.05/27.86 | Case 2:
% 159.05/27.86 | |
% 159.05/27.86 | | (135) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 159.05/27.86 | | e2)
% 159.05/27.86 | |
% 159.05/27.86 | | BETA: splitting (135) gives:
% 159.05/27.86 | |
% 159.05/27.86 | | Case 1:
% 159.05/27.86 | | |
% 159.05/27.86 | | | (136) all_58_8 = e2 & op(e1, e1) = e2
% 159.05/27.86 | | |
% 159.05/27.86 | | | REF_CLOSE: (8), (59), (73), (136) are inconsistent by sub-proof #1440.
% 159.05/27.86 | | |
% 159.05/27.86 | | Case 2:
% 159.05/27.86 | | |
% 159.05/27.86 | | | (137) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.86 | | |
% 159.05/27.86 | | | REF_CLOSE: (33), (66), (137) are inconsistent by sub-proof #507.
% 159.05/27.86 | | |
% 159.05/27.86 | | End of split
% 159.05/27.86 | |
% 159.05/27.86 | End of split
% 159.05/27.86 |
% 159.05/27.86 End of proof
% 159.05/27.86
% 159.05/27.86 Sub-proof #505 shows that the following formulas are inconsistent:
% 159.05/27.86 ----------------------------------------------------------------
% 159.05/27.86 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.86 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.86 (2) op(e1, e1) = all_6_2
% 159.05/27.86 (3) all_58_8 = e3
% 159.05/27.86 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.86 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.86 (5) ~ (e3 = e0)
% 159.05/27.86 (6) ~ (e2 = e0)
% 159.05/27.86 (7) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.86 (8) op(e2, e3) = e2
% 159.05/27.86 (9) ~ (e3 = e1)
% 159.05/27.86 (10) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.86 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.86 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.86 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.86 (12) op(e0, e0) = e2
% 159.05/27.86 (13) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.86 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.86 (14) ~ (e2 = e1)
% 159.05/27.86 (15) ~ (e1 = e0)
% 159.05/27.86 (16) all_58_3 = e3
% 159.05/27.86 (17) ~ (all_6_2 = e2)
% 159.05/27.86 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.86 (19) ~ (e3 = e2)
% 159.05/27.86
% 159.05/27.86 Begin of proof
% 159.05/27.86 |
% 159.05/27.86 | BETA: splitting (7) gives:
% 159.05/27.86 |
% 159.05/27.86 | Case 1:
% 159.05/27.86 | |
% 159.05/27.86 | | (20) all_58_14 = e3 & op(e0, e1) = e3
% 159.05/27.86 | |
% 159.05/27.86 | | ALPHA: (20) implies:
% 159.05/27.86 | | (21) all_58_14 = e3
% 159.05/27.86 | |
% 159.05/27.86 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 159.05/27.86 | | (15), (16), (17), (18), (19), (21) are inconsistent by sub-proof
% 159.05/27.86 | | #780.
% 159.05/27.86 | |
% 159.05/27.86 | Case 2:
% 159.05/27.86 | |
% 159.05/27.86 | | (22) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.86 | |
% 159.05/27.86 | | ALPHA: (22) implies:
% 159.05/27.86 | | (23) op(e0, e0) = e3
% 159.05/27.86 | |
% 159.05/27.87 | | REF_CLOSE: (12), (18), (19), (23) are inconsistent by sub-proof #1382.
% 159.05/27.87 | |
% 159.05/27.87 | End of split
% 159.05/27.87 |
% 159.05/27.87 End of proof
% 159.05/27.87
% 159.05/27.87 Sub-proof #506 shows that the following formulas are inconsistent:
% 159.05/27.87 ----------------------------------------------------------------
% 159.05/27.87 (1) op(e1, e1) = all_6_2
% 159.05/27.87 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.05/27.87 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.87 (3) all_58_12 = e3
% 159.05/27.87 (4) ~ (e3 = e0)
% 159.05/27.87 (5) ~ (e2 = e0)
% 159.05/27.87 (6) ~ (e3 = e1)
% 159.05/27.87 (7) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.87 (8) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 159.05/27.87 (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.87 (9) op(e0, e0) = e2
% 159.05/27.87 (10) ~ (e2 = e1)
% 159.05/27.87 (11) ~ (e1 = e0)
% 159.05/27.87 (12) ~ (all_6_2 = e2)
% 159.05/27.87 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.87
% 159.05/27.87 Begin of proof
% 159.05/27.87 |
% 159.05/27.87 | BETA: splitting (7) gives:
% 159.05/27.87 |
% 159.05/27.87 | Case 1:
% 159.05/27.87 | |
% 159.05/27.87 | | (14) all_58_8 = e2 & op(e1, e1) = e2
% 159.05/27.87 | |
% 159.05/27.87 | | REF_CLOSE: (1), (12), (13), (14) are inconsistent by sub-proof #1440.
% 159.05/27.87 | |
% 159.05/27.87 | Case 2:
% 159.05/27.87 | |
% 159.05/27.87 | | (15) all_58_14 = e2 & op(e0, e1) = e2
% 159.05/27.87 | |
% 159.05/27.87 | | ALPHA: (15) implies:
% 159.05/27.87 | | (16) all_58_14 = e2
% 159.05/27.87 | |
% 159.05/27.87 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (16) are
% 159.05/27.87 | | inconsistent by sub-proof #1384.
% 159.05/27.87 | |
% 159.05/27.87 | End of split
% 159.05/27.87 |
% 159.05/27.87 End of proof
% 159.05/27.87
% 159.05/27.87 Sub-proof #507 shows that the following formulas are inconsistent:
% 159.05/27.87 ----------------------------------------------------------------
% 159.05/27.87 (1) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.87 (2) all_58_11 = e0
% 159.05/27.87 (3) ~ (e2 = e0)
% 159.05/27.87
% 159.05/27.87 Begin of proof
% 159.05/27.87 |
% 159.05/27.87 | ALPHA: (1) implies:
% 159.05/27.87 | (4) all_58_11 = e2
% 159.05/27.87 |
% 159.05/27.87 | COMBINE_EQS: (2), (4) imply:
% 159.05/27.87 | (5) e2 = e0
% 159.05/27.87 |
% 159.05/27.87 | REDUCE: (3), (5) imply:
% 159.05/27.87 | (6) $false
% 159.05/27.87 |
% 159.05/27.87 | CLOSE: (6) is inconsistent.
% 159.05/27.87 |
% 159.05/27.87 End of proof
% 159.05/27.87
% 159.05/27.87 Sub-proof #508 shows that the following formulas are inconsistent:
% 159.05/27.87 ----------------------------------------------------------------
% 159.05/27.87 (1) all_56_14 = e3
% 159.05/27.87 (2) all_58_15 = e3
% 159.05/27.87 (3) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.87 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.87 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.87 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.87 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.87 (6) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.87 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.87 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.87 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.87 (8) all_54_13 = all_52_7
% 159.05/27.87 (9) op(e1, e1) = all_6_2
% 159.05/27.87 (10) ~ (all_52_7 = e3)
% 159.05/27.87 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.87 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.87 e1)
% 159.05/27.87 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/27.87 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.87 (13) ~ (all_52_11 = e3)
% 159.05/27.87 (14) op(e3, e3) = all_28_1
% 159.05/27.87 (15) all_58_8 = e3
% 159.05/27.87 (16) ~ (all_52_7 = all_52_11)
% 159.05/27.87 (17) all_58_0 = e1
% 159.05/27.87 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.87 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.87 (19) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.87 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.87 (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.87 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.87 (21) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.87 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.87 (22) all_58_12 = e0
% 159.05/27.87 (23) op(e3, e2) = all_52_4
% 159.05/27.87 (24) ~ (all_4_2 = e2)
% 159.05/27.87 (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/27.87 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/27.87 (26) op(e2, e3) = all_52_1
% 159.05/27.87 (27) ~ (all_52_13 = e3)
% 159.05/27.87 (28) all_54_2 = all_52_8
% 159.05/27.87 (29) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.87 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.87 (30) ~ (all_52_8 = all_52_9)
% 159.05/27.87 (31) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.87 (32) ~ (e3 = e0)
% 159.05/27.87 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.87 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.87 (34) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.87 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.87 (35) ~ (all_52_9 = all_52_13)
% 159.05/27.87 (36) op(e0, e0) = e0
% 159.05/27.87 (37) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/27.87 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/27.87 e2)
% 159.05/27.87 (38) ~ (e2 = e0)
% 159.05/27.87 (39) ~ (all_52_9 = e3)
% 159.05/27.87 (40) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.87 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.87 (41) op(e2, e0) = all_52_13
% 159.05/27.87 (42) op(e2, e3) = e2
% 159.05/27.87 (43) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.87 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.87 (44) ~ (e3 = e1)
% 159.05/27.87 (45) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.87 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.87 (46) op(e1, e2) = all_52_6
% 159.05/27.87 (47) ~ (all_4_2 = e1)
% 159.05/27.87 (48) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.87 (49) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.87 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.87 (50) ~ (all_52_7 = e0)
% 159.05/27.87 (51) op(e0, e0) = all_4_2
% 159.05/27.87 (52) all_54_7 = all_52_13
% 159.05/27.87 (53) op(e3, e3) = e1
% 159.05/27.87 (54) ~ (all_52_13 = e2)
% 159.05/27.87 (55) all_56_15 = all_4_2
% 159.05/27.87 (56) ~ (all_52_9 = all_52_11)
% 159.05/27.87 (57) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.87 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.87 (58) ~ (all_52_4 = e3)
% 159.05/27.87 (59) all_54_6 = all_52_9
% 159.05/27.87 (60) ~ (e2 = e1)
% 159.05/27.87 (61) ~ (all_52_8 = all_52_11)
% 159.05/27.87 (62) ~ (all_52_13 = e0)
% 159.05/27.87 (63) ~ (e1 = e0)
% 159.05/27.87 (64) all_58_3 = e3
% 159.05/27.87 (65) ~ (all_6_2 = e2)
% 159.05/27.87 (66) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.87 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.87 e3)
% 159.05/27.87 (67) all_56_13 = e3
% 159.05/27.87 (68) ~ (all_52_9 = e2)
% 159.05/27.87 (69) ~ (all_52_8 = e3)
% 159.05/27.87 (70) all_54_14 = all_52_11
% 159.05/27.87 (71) op(e1, e3) = e1
% 159.05/27.87 (72) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.87 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.87 (73) op(e0, e2) = all_52_7
% 159.05/27.87 (74) op(e3, e3) = all_22_1
% 159.05/27.87 (75) ~ (all_52_8 = e1)
% 159.05/27.87 (76) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.87 (77) ~ (all_52_6 = e3)
% 159.05/27.87 (78) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.87 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.87 (79) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.87 (80) ~ (e3 = e2)
% 159.05/27.87 (81) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/27.87 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.87 (82) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.87 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.87 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.87 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.87 (83) all_54_7 = e1 | all_54_7 = e0
% 159.05/27.87 (84) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.87 (85) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.87 (86) op(e0, e0) = e3
% 159.05/27.87
% 159.05/27.87 Begin of proof
% 159.05/27.87 |
% 159.05/27.87 | BETA: splitting (21) gives:
% 159.05/27.87 |
% 159.05/27.87 | Case 1:
% 159.05/27.87 | |
% 159.05/27.87 | | (87) all_58_9 = e0 & op(e3, e0) = e0
% 159.05/27.87 | |
% 159.05/27.87 | | ALPHA: (87) implies:
% 159.05/27.87 | | (88) all_58_9 = e0
% 159.05/27.87 | |
% 159.05/27.87 | | BETA: splitting (49) gives:
% 159.05/27.87 | |
% 159.05/27.87 | | Case 1:
% 159.05/27.87 | | |
% 159.05/27.87 | | | (89) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 159.05/27.87 | | | e0)
% 159.05/27.87 | | |
% 159.05/27.87 | | | REF_CLOSE: (32), (38), (42), (64), (79), (89) are inconsistent by
% 159.05/27.87 | | | sub-proof #755.
% 159.05/27.87 | | |
% 159.05/27.87 | | Case 2:
% 159.05/27.87 | | |
% 159.05/27.87 | | | (90) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 159.05/27.87 | | | e0)
% 159.05/27.87 | | |
% 159.05/27.87 | | | BETA: splitting (90) gives:
% 159.05/27.87 | | |
% 159.05/27.87 | | | Case 1:
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | (91) all_58_5 = e0 & op(e2, e1) = e0
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | ALPHA: (91) implies:
% 159.05/27.87 | | | | (92) all_58_5 = e0
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | BETA: splitting (20) gives:
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | Case 1:
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | (93) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 159.05/27.87 | | | | | e0) = e2)
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | REF_CLOSE: (7), (32), (38), (42), (44), (49), (60), (63), (64), (79),
% 159.05/27.87 | | | | | (88), (93) are inconsistent by sub-proof #537.
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | Case 2:
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | (94) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 159.05/27.87 | | | | | e0) = e2)
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | BETA: splitting (94) gives:
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | Case 1:
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | (95) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | ALPHA: (95) implies:
% 159.05/27.87 | | | | | | (96) all_58_11 = e2
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (13), (14), (15), (17),
% 159.05/27.87 | | | | | | (18), (20), (21), (22), (23), (25), (26), (28), (29),
% 159.05/27.87 | | | | | | (30), (32), (33), (34), (35), (36), (38), (39), (40),
% 159.05/27.87 | | | | | | (42), (44), (46), (48), (49), (52), (53), (56), (58),
% 159.05/27.87 | | | | | | (59), (60), (61), (62), (63), (64), (65), (68), (69),
% 159.05/27.87 | | | | | | (70), (71), (72), (74), (75), (77), (78), (79), (80),
% 159.05/27.87 | | | | | | (81), (83), (85), (86), (92), (96) are inconsistent by
% 159.05/27.87 | | | | | | sub-proof #526.
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | Case 2:
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | (97) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | ALPHA: (97) implies:
% 159.05/27.87 | | | | | | (98) op(e0, e0) = e2
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | REF_CLOSE: (79), (80), (86), (98) are inconsistent by sub-proof
% 159.05/27.87 | | | | | | #1382.
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | End of split
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | End of split
% 159.05/27.87 | | | |
% 159.05/27.87 | | | Case 2:
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | (99) all_58_10 = e0 & op(e2, e0) = e0
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (13), (14), (15), (17), (18),
% 159.05/27.87 | | | | (20), (21), (22), (23), (25), (26), (28), (29), (30), (32),
% 159.05/27.87 | | | | (33), (34), (35), (36), (38), (39), (40), (42), (44), (46),
% 159.05/27.87 | | | | (48), (49), (52), (53), (56), (58), (59), (60), (61), (62),
% 159.05/27.87 | | | | (63), (64), (65), (68), (69), (70), (71), (72), (74), (75),
% 159.05/27.87 | | | | (77), (78), (79), (80), (81), (83), (85), (86), (99) are
% 159.05/27.87 | | | | inconsistent by sub-proof #525.
% 159.05/27.87 | | | |
% 159.05/27.87 | | | End of split
% 159.05/27.87 | | |
% 159.05/27.87 | | End of split
% 159.05/27.87 | |
% 159.05/27.87 | Case 2:
% 159.05/27.87 | |
% 159.05/27.87 | | (100) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.05/27.87 | | e0)
% 159.05/27.87 | |
% 159.05/27.87 | | BETA: splitting (100) gives:
% 159.05/27.87 | |
% 159.05/27.87 | | Case 1:
% 159.05/27.87 | | |
% 159.05/27.87 | | | (101) all_58_10 = e0 & op(e2, e0) = e0
% 159.05/27.87 | | |
% 159.05/27.87 | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (13), (14), (15), (17), (18),
% 159.05/27.87 | | | (20), (21), (22), (23), (25), (26), (28), (29), (30), (32),
% 159.05/27.87 | | | (33), (34), (35), (36), (38), (39), (40), (42), (44), (46),
% 159.05/27.87 | | | (48), (49), (52), (53), (56), (58), (59), (60), (61), (62),
% 159.05/27.87 | | | (63), (64), (65), (68), (69), (70), (71), (72), (74), (75),
% 159.05/27.87 | | | (77), (78), (79), (80), (81), (83), (85), (86), (101) are
% 159.05/27.87 | | | inconsistent by sub-proof #525.
% 159.05/27.87 | | |
% 159.05/27.87 | | Case 2:
% 159.05/27.87 | | |
% 159.05/27.87 | | | (102) all_58_11 = e0 & op(e1, e0) = e0
% 159.05/27.87 | | |
% 159.05/27.87 | | | ALPHA: (102) implies:
% 159.05/27.87 | | | (103) all_58_11 = e0
% 159.05/27.87 | | |
% 159.05/27.87 | | | BETA: splitting (49) gives:
% 159.05/27.87 | | |
% 159.05/27.87 | | | Case 1:
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | (104) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 159.05/27.87 | | | | = e0)
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | REF_CLOSE: (32), (38), (42), (64), (79), (104) are inconsistent by
% 159.05/27.87 | | | | sub-proof #755.
% 159.05/27.87 | | | |
% 159.05/27.87 | | | Case 2:
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | (105) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2,
% 159.05/27.87 | | | | e0) = e0)
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | BETA: splitting (105) gives:
% 159.05/27.87 | | | |
% 159.05/27.87 | | | | Case 1:
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | (106) all_58_5 = e0 & op(e2, e1) = e0
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | ALPHA: (106) implies:
% 159.05/27.87 | | | | | (107) all_58_5 = e0
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | BETA: splitting (20) gives:
% 159.05/27.87 | | | | |
% 159.05/27.87 | | | | | Case 1:
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | (108) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 159.05/27.87 | | | | | | op(e2, e0) = e2)
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | BETA: splitting (108) gives:
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | Case 1:
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | (109) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | ALPHA: (109) implies:
% 159.05/27.87 | | | | | | | (110) all_58_9 = e2
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | BETA: splitting (7) gives:
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | |
% 159.05/27.87 | | | | | | | | (111) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 159.05/27.87 | | | | | | | | op(e2, e2) = e1)
% 159.05/27.87 | | | | | | | |
% 159.05/27.87 | | | | | | | | REF_CLOSE: (42), (44), (60), (64), (79), (111) are inconsistent
% 159.05/27.87 | | | | | | | | by sub-proof #840.
% 159.05/27.87 | | | | | | | |
% 159.05/27.87 | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | |
% 159.05/27.87 | | | | | | | | (112) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 159.05/27.87 | | | | | | | | op(e2, e0) = e1)
% 159.05/27.87 | | | | | | | |
% 159.05/27.87 | | | | | | | | BETA: splitting (112) gives:
% 159.05/27.87 | | | | | | | |
% 159.05/27.87 | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | | (113) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | | ALPHA: (113) implies:
% 159.05/27.87 | | | | | | | | | (114) all_58_5 = e1
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | | REF_CLOSE: (63), (107), (114) are inconsistent by sub-proof
% 159.05/27.87 | | | | | | | | | #935.
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | | (115) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | | ALPHA: (115) implies:
% 159.05/27.87 | | | | | | | | | (116) all_58_10 = e1
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | | BETA: splitting (18) gives:
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | (117) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 159.05/27.87 | | | | | | | | | | & op(e2, e3) = e3)
% 159.05/27.87 | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | REF_CLOSE: (14), (26), (36), (42), (53), (63), (74), (79),
% 159.05/27.87 | | | | | | | | | | (80), (86), (117) are inconsistent by sub-proof
% 159.05/27.87 | | | | | | | | | | #583.
% 159.05/27.87 | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | (118) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3
% 159.05/27.87 | | | | | | | | | | & op(e0, e3) = e3)
% 159.05/27.87 | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | BETA: splitting (118) gives:
% 159.05/27.87 | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | (119) all_58_6 = e3 & op(e1, e3) = e3
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | ALPHA: (119) implies:
% 159.05/27.87 | | | | | | | | | | | (120) all_58_6 = e3
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | BETA: splitting (29) gives:
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | (121) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 159.05/27.87 | | | | | | | | | | | | & op(e1, e2) = e2)
% 159.05/27.87 | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | BETA: splitting (121) gives:
% 159.05/27.87 | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | (122) all_58_6 = e2 & op(e1, e3) = e2
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | ALPHA: (122) implies:
% 159.05/27.87 | | | | | | | | | | | | | (123) all_58_6 = e2
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | REF_CLOSE: (17), (18), (22), (26), (32), (42), (44), (79),
% 159.05/27.87 | | | | | | | | | | | | | (80), (123) are inconsistent by sub-proof #1154.
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | (124) all_58_7 = e2 & op(e1, e2) = e2
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | ALPHA: (124) implies:
% 159.05/27.87 | | | | | | | | | | | | | (125) all_58_7 = e2
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | BETA: splitting (4) gives:
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | (126) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 159.05/27.87 | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 159.05/27.87 | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 159.05/27.87 | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | (127) all_58_6 = e1 & op(e1, e3) = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 159.05/27.87 | | | | | | | | | | | | | | | (128) all_58_6 = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.05/27.87 | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (18), (19),
% 159.05/27.87 | | | | | | | | | | | | | | | (20), (23), (24), (26), (27), (28), (29), (30),
% 159.05/27.87 | | | | | | | | | | | | | | | (31), (32), (33), (35), (36), (37), (38), (39),
% 159.05/27.87 | | | | | | | | | | | | | | | (40), (41), (42), (43), (44), (45), (47), (48),
% 159.05/27.87 | | | | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 159.05/27.87 | | | | | | | | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64),
% 159.05/27.87 | | | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (72), (73),
% 159.05/27.87 | | | | | | | | | | | | | | | (74), (75), (76), (78), (79), (80), (82), (84),
% 159.05/27.87 | | | | | | | | | | | | | | | (85), (103), (110), (125), (128) are inconsistent
% 159.05/27.87 | | | | | | | | | | | | | | | by sub-proof #509.
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | (129) all_58_7 = e1 & op(e1, e2) = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 159.05/27.87 | | | | | | | | | | | | | | | (130) all_58_7 = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | REF_CLOSE: (60), (125), (130) are inconsistent by sub-proof
% 159.05/27.87 | | | | | | | | | | | | | | | #721.
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | End of split
% 159.05/27.87 | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | (131) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 159.05/27.87 | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 159.05/27.87 | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 159.05/27.87 | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | (132) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 159.05/27.87 | | | | | | | | | | | | | | | (133) all_58_8 = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | COMBINE_EQS: (15), (133) imply:
% 159.05/27.87 | | | | | | | | | | | | | | | (134) e3 = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | COMBINE_EQS: (120), (134) imply:
% 159.05/27.87 | | | | | | | | | | | | | | | (135) all_58_6 = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.05/27.87 | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (18), (19),
% 159.05/27.87 | | | | | | | | | | | | | | | (20), (23), (24), (26), (27), (28), (29), (30),
% 159.05/27.87 | | | | | | | | | | | | | | | (31), (32), (33), (35), (36), (37), (38), (39),
% 159.05/27.87 | | | | | | | | | | | | | | | (40), (41), (42), (43), (44), (45), (47), (48),
% 159.05/27.87 | | | | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 159.05/27.87 | | | | | | | | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64),
% 159.05/27.87 | | | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (72), (73),
% 159.05/27.87 | | | | | | | | | | | | | | | (74), (75), (76), (78), (79), (80), (82), (84),
% 159.05/27.87 | | | | | | | | | | | | | | | (85), (103), (110), (125), (135) are inconsistent
% 159.05/27.87 | | | | | | | | | | | | | | | by sub-proof #509.
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | (136) all_58_11 = e1 & op(e1, e0) = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 159.05/27.87 | | | | | | | | | | | | | | | (137) all_58_11 = e1
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | COMBINE_EQS: (103), (137) imply:
% 159.05/27.87 | | | | | | | | | | | | | | | (138) e1 = e0
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | SIMP: (138) implies:
% 159.05/27.87 | | | | | | | | | | | | | | | (139) e1 = e0
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | COMBINE_EQS: (116), (139) imply:
% 159.05/27.87 | | | | | | | | | | | | | | | (140) all_58_10 = e0
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (14), (15), (17), (18),
% 159.05/27.87 | | | | | | | | | | | | | | | (20), (21), (22), (23), (25), (26), (29), (32),
% 159.05/27.87 | | | | | | | | | | | | | | | (33), (34), (36), (38), (40), (42), (44), (46),
% 159.05/27.87 | | | | | | | | | | | | | | | (49), (53), (58), (60), (63), (64), (65), (72),
% 159.05/27.87 | | | | | | | | | | | | | | | (74), (77), (78), (79), (80), (81), (86), (120),
% 159.05/27.87 | | | | | | | | | | | | | | | (140) are inconsistent by sub-proof #528.
% 159.05/27.87 | | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | | End of split
% 159.05/27.87 | | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | End of split
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | End of split
% 159.05/27.87 | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | (141) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 159.05/27.87 | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 159.05/27.87 | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | BETA: splitting (141) gives:
% 159.05/27.87 | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | Case 1:
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | (142) all_58_8 = e2 & op(e1, e1) = e2
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | REF_CLOSE: (9), (65), (79), (142) are inconsistent by
% 159.05/27.87 | | | | | | | | | | | | | sub-proof #1440.
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | (143) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | ALPHA: (143) implies:
% 159.05/27.87 | | | | | | | | | | | | | (144) all_58_11 = e2
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (14), (15), (17), (18),
% 159.05/27.87 | | | | | | | | | | | | | (20), (21), (22), (23), (25), (26), (29), (32),
% 159.05/27.87 | | | | | | | | | | | | | (33), (34), (36), (38), (40), (42), (44), (46),
% 159.05/27.87 | | | | | | | | | | | | | (49), (53), (58), (60), (63), (64), (65), (72),
% 159.05/27.87 | | | | | | | | | | | | | (74), (77), (78), (79), (80), (81), (86), (116),
% 159.05/27.87 | | | | | | | | | | | | | (120), (144) are inconsistent by sub-proof #527.
% 159.05/27.87 | | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | | End of split
% 159.05/27.87 | | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | End of split
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | Case 2:
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | (145) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | ALPHA: (145) implies:
% 159.05/27.87 | | | | | | | | | | | (146) all_58_12 = e3
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | | REF_CLOSE: (3), (13), (17), (28), (30), (32), (33), (35),
% 159.05/27.87 | | | | | | | | | | | (38), (39), (42), (48), (52), (56), (59), (61),
% 159.05/27.87 | | | | | | | | | | | (62), (63), (68), (69), (70), (71), (75), (78),
% 159.05/27.87 | | | | | | | | | | | (79), (83), (85), (146) are inconsistent by
% 159.05/27.87 | | | | | | | | | | | sub-proof #533.
% 159.05/27.87 | | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | | End of split
% 159.05/27.87 | | | | | | | | | |
% 159.05/27.87 | | | | | | | | | End of split
% 159.05/27.87 | | | | | | | | |
% 159.05/27.87 | | | | | | | | End of split
% 159.05/27.87 | | | | | | | |
% 159.05/27.87 | | | | | | | End of split
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | Case 2:
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | (147) all_58_10 = e2 & op(e2, e0) = e2
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | ALPHA: (147) implies:
% 159.05/27.87 | | | | | | | (148) all_58_10 = e2
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | REF_CLOSE: (7), (32), (38), (42), (44), (49), (60), (63), (64),
% 159.05/27.87 | | | | | | | (79), (148) are inconsistent by sub-proof #906.
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | End of split
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | Case 2:
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | (149) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 159.05/27.87 | | | | | | op(e0, e0) = e2)
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | BETA: splitting (149) gives:
% 159.05/27.87 | | | | | |
% 159.05/27.87 | | | | | | Case 1:
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | (150) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.87 | | | | | | |
% 159.05/27.87 | | | | | | | ALPHA: (150) implies:
% 159.05/27.87 | | | | | | | (151) all_58_11 = e2
% 159.05/27.87 | | | | | | |
% 159.05/27.88 | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (13), (14), (15), (17),
% 159.05/27.88 | | | | | | | (18), (20), (21), (22), (23), (25), (26), (28), (29),
% 159.05/27.88 | | | | | | | (30), (32), (33), (34), (35), (36), (38), (39), (40),
% 159.05/27.88 | | | | | | | (42), (44), (46), (48), (49), (52), (53), (56), (58),
% 159.05/27.88 | | | | | | | (59), (60), (61), (62), (63), (64), (65), (68), (69),
% 159.05/27.88 | | | | | | | (70), (71), (72), (74), (75), (77), (78), (79), (80),
% 159.05/27.88 | | | | | | | (81), (83), (85), (86), (107), (151) are inconsistent
% 159.05/27.88 | | | | | | | by sub-proof #526.
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | Case 2:
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | (152) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | ALPHA: (152) implies:
% 159.05/27.88 | | | | | | | (153) op(e0, e0) = e2
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | REF_CLOSE: (79), (80), (86), (153) are inconsistent by sub-proof
% 159.05/27.88 | | | | | | | #1382.
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | End of split
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | End of split
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | Case 2:
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | | (154) all_58_10 = e0 & op(e2, e0) = e0
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (13), (14), (15), (17), (18),
% 159.05/27.88 | | | | | (20), (21), (22), (23), (25), (26), (28), (29), (30), (32),
% 159.05/27.88 | | | | | (33), (34), (35), (36), (38), (39), (40), (42), (44), (46),
% 159.05/27.88 | | | | | (48), (49), (52), (53), (56), (58), (59), (60), (61), (62),
% 159.05/27.88 | | | | | (63), (64), (65), (68), (69), (70), (71), (72), (74), (75),
% 159.05/27.88 | | | | | (77), (78), (79), (80), (81), (83), (85), (86), (154) are
% 159.05/27.88 | | | | | inconsistent by sub-proof #525.
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | End of split
% 159.05/27.88 | | | |
% 159.05/27.88 | | | End of split
% 159.05/27.88 | | |
% 159.05/27.88 | | End of split
% 159.05/27.88 | |
% 159.05/27.88 | End of split
% 159.05/27.88 |
% 159.05/27.88 End of proof
% 159.05/27.88
% 159.05/27.88 Sub-proof #509 shows that the following formulas are inconsistent:
% 159.05/27.88 ----------------------------------------------------------------
% 159.05/27.88 (1) all_56_14 = e3
% 159.05/27.88 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.88 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.88 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.88 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.88 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.88 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.88 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.88 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.88 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.88 (7) all_54_13 = all_52_7
% 159.05/27.88 (8) op(e1, e1) = all_6_2
% 159.05/27.88 (9) ~ (all_52_7 = e3)
% 159.05/27.88 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.88 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.88 e1)
% 159.05/27.88 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/27.88 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.88 (12) ~ (all_52_11 = e3)
% 159.05/27.88 (13) op(e3, e3) = all_28_1
% 159.05/27.88 (14) all_58_7 = e2
% 159.05/27.88 (15) all_58_8 = e3
% 159.05/27.88 (16) ~ (all_52_7 = all_52_11)
% 159.05/27.88 (17) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.88 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.88 (18) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.88 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.88 (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.88 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.88 (20) op(e3, e2) = all_52_4
% 159.05/27.88 (21) ~ (all_4_2 = e2)
% 159.05/27.88 (22) all_58_6 = e1
% 159.05/27.88 (23) op(e2, e3) = all_52_1
% 159.05/27.88 (24) ~ (all_52_13 = e3)
% 159.05/27.88 (25) all_54_2 = all_52_8
% 159.05/27.88 (26) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.88 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.88 (27) ~ (all_52_8 = all_52_9)
% 159.05/27.88 (28) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.88 (29) ~ (e3 = e0)
% 159.05/27.88 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.88 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.88 (31) ~ (all_52_9 = all_52_13)
% 159.05/27.88 (32) op(e0, e0) = e0
% 159.05/27.88 (33) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/27.88 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/27.88 e2)
% 159.05/27.88 (34) ~ (e2 = e0)
% 159.05/27.88 (35) ~ (all_52_9 = e3)
% 159.05/27.88 (36) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.88 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.88 (37) op(e2, e0) = all_52_13
% 159.05/27.88 (38) op(e2, e3) = e2
% 159.05/27.88 (39) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.88 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.88 (40) ~ (e3 = e1)
% 159.05/27.88 (41) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.88 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.88 (42) ~ (all_4_2 = e1)
% 159.05/27.88 (43) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.88 (44) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.88 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.88 (45) ~ (all_52_7 = e0)
% 159.05/27.88 (46) op(e0, e0) = all_4_2
% 159.05/27.88 (47) all_54_7 = all_52_13
% 159.05/27.88 (48) op(e3, e3) = e1
% 159.05/27.88 (49) ~ (all_52_13 = e2)
% 159.05/27.88 (50) all_56_15 = all_4_2
% 159.05/27.88 (51) ~ (all_52_9 = all_52_11)
% 159.05/27.88 (52) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.88 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.88 (53) ~ (all_52_4 = e3)
% 159.05/27.88 (54) all_54_6 = all_52_9
% 159.05/27.88 (55) ~ (e2 = e1)
% 159.05/27.88 (56) ~ (all_52_8 = all_52_11)
% 159.05/27.88 (57) ~ (all_52_13 = e0)
% 159.05/27.88 (58) ~ (e1 = e0)
% 159.05/27.88 (59) all_58_3 = e3
% 159.05/27.88 (60) ~ (all_6_2 = e2)
% 159.05/27.88 (61) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.88 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.88 e3)
% 159.05/27.88 (62) all_56_13 = e3
% 159.05/27.88 (63) ~ (all_52_9 = e2)
% 159.05/27.88 (64) ~ (all_52_8 = e3)
% 159.05/27.88 (65) all_54_14 = all_52_11
% 159.05/27.88 (66) all_58_11 = e0
% 159.05/27.88 (67) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.88 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.88 (68) all_58_9 = e2
% 159.05/27.88 (69) op(e0, e2) = all_52_7
% 159.05/27.88 (70) op(e3, e3) = all_22_1
% 159.05/27.88 (71) ~ (all_52_8 = e1)
% 159.05/27.88 (72) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.88 (73) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.88 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.88 (74) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.88 (75) ~ (e3 = e2)
% 159.05/27.88 (76) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.88 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.88 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.88 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.88 (77) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.88 (78) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.88
% 159.05/27.88 Begin of proof
% 159.05/27.88 |
% 159.05/27.88 | BETA: splitting (73) gives:
% 159.05/27.88 |
% 159.05/27.88 | Case 1:
% 159.05/27.88 | |
% 159.05/27.88 | | (79) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.05/27.88 | | e0)
% 159.05/27.88 | |
% 159.05/27.88 | | BETA: splitting (79) gives:
% 159.05/27.88 | |
% 159.05/27.88 | | Case 1:
% 159.05/27.88 | | |
% 159.05/27.88 | | | (80) all_58_0 = e0 & op(e3, e3) = e0
% 159.05/27.88 | | |
% 159.05/27.88 | | | ALPHA: (80) implies:
% 159.05/27.88 | | | (81) all_58_0 = e0
% 159.05/27.88 | | |
% 159.05/27.88 | | | BETA: splitting (76) gives:
% 159.05/27.88 | | |
% 159.05/27.88 | | | Case 1:
% 159.05/27.88 | | | |
% 159.05/27.88 | | | | (82) all_58_15 = e0 & op(e0, e0) = e0
% 159.05/27.88 | | | |
% 159.05/27.88 | | | | ALPHA: (82) implies:
% 159.05/27.88 | | | | (83) all_58_15 = e0
% 159.05/27.88 | | | |
% 159.05/27.88 | | | | REF_CLOSE: (6), (8), (9), (11), (13), (15), (17), (18), (22), (23),
% 159.05/27.88 | | | | (24), (29), (32), (34), (37), (38), (40), (41), (44), (48),
% 159.05/27.88 | | | | (52), (55), (58), (59), (60), (61), (66), (68), (69), (70),
% 159.05/27.88 | | | | (74), (75), (81), (83) are inconsistent by sub-proof #521.
% 159.05/27.88 | | | |
% 159.05/27.88 | | | Case 2:
% 159.05/27.88 | | | |
% 159.05/27.88 | | | | (84) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 159.05/27.88 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 159.05/27.88 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 159.05/27.88 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.05/27.88 | | | |
% 159.05/27.88 | | | | ALPHA: (84) implies:
% 159.05/27.88 | | | | (85) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 159.05/27.88 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.88 | | | |
% 159.05/27.88 | | | | BETA: splitting (61) gives:
% 159.05/27.88 | | | |
% 159.05/27.88 | | | | Case 1:
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | | (86) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 159.05/27.88 | | | | | e2) = e3)
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | | BETA: splitting (86) gives:
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | | Case 1:
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | (87) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | ALPHA: (87) implies:
% 159.05/27.88 | | | | | | (88) all_58_12 = e3
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | BETA: splitting (44) gives:
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | Case 1:
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | (89) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 159.05/27.88 | | | | | | | op(e2, e2) = e0)
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | REF_CLOSE: (6), (8), (9), (13), (15), (17), (18), (22), (23),
% 159.05/27.88 | | | | | | | (29), (32), (34), (38), (40), (41), (44), (48), (52),
% 159.05/27.88 | | | | | | | (55), (58), (59), (60), (61), (69), (70), (74), (75),
% 159.05/27.88 | | | | | | | (88), (89) are inconsistent by sub-proof #519.
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | Case 2:
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | (90) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 159.05/27.88 | | | | | | | op(e2, e0) = e0)
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | BETA: splitting (90) gives:
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | Case 1:
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | (91) all_58_5 = e0 & op(e2, e1) = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | ALPHA: (91) implies:
% 159.05/27.88 | | | | | | | | (92) all_58_5 = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 159.05/27.88 | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 159.05/27.88 | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 159.05/27.88 | | | | | | | | (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 159.05/27.88 | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 159.05/27.88 | | | | | | | | (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 159.05/27.88 | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 159.05/27.88 | | | | | | | | (66), (67), (68), (69), (70), (71), (72), (74), (75),
% 159.05/27.88 | | | | | | | | (76), (77), (78), (81), (85), (88), (92) are
% 159.05/27.88 | | | | | | | | inconsistent by sub-proof #514.
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | Case 2:
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | (93) all_58_10 = e0 & op(e2, e0) = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | ALPHA: (93) implies:
% 159.05/27.88 | | | | | | | | (94) all_58_10 = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.05/27.88 | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 159.05/27.88 | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 159.05/27.88 | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 159.05/27.88 | | | | | | | | (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 159.05/27.88 | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 159.05/27.88 | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 159.05/27.88 | | | | | | | | (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 159.05/27.88 | | | | | | | | (74), (75), (76), (77), (78), (81), (85), (88), (94)
% 159.05/27.88 | | | | | | | | are inconsistent by sub-proof #511.
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | End of split
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | End of split
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | Case 2:
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | (95) all_58_13 = e3 & op(e0, e2) = e3
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | REF_CLOSE: (9), (69), (74), (95) are inconsistent by sub-proof
% 159.05/27.88 | | | | | | #1449.
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | End of split
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | Case 2:
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | | (96) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 159.05/27.88 | | | | | e0) = e3)
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | | BETA: splitting (96) gives:
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | | Case 1:
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | (97) all_58_14 = e3 & op(e0, e1) = e3
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | ALPHA: (97) implies:
% 159.05/27.88 | | | | | | (98) all_58_14 = e3
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | REF_CLOSE: (6), (8), (15), (18), (29), (34), (38), (40), (41), (44),
% 159.05/27.88 | | | | | | (52), (55), (58), (59), (60), (74), (75), (98) are
% 159.05/27.88 | | | | | | inconsistent by sub-proof #780.
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | Case 2:
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | (99) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | ALPHA: (99) implies:
% 159.05/27.88 | | | | | | (100) all_58_15 = e3
% 159.05/27.88 | | | | | | (101) op(e0, e0) = e3
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | BETA: splitting (44) gives:
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | | Case 1:
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | (102) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 159.05/27.88 | | | | | | | op(e2, e2) = e0)
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | BETA: splitting (102) gives:
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | Case 1:
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | (103) all_58_2 = e0 & op(e2, e3) = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | ALPHA: (103) implies:
% 159.05/27.88 | | | | | | | | (104) op(e2, e3) = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | REF_CLOSE: (34), (38), (74), (104) are inconsistent by sub-proof
% 159.05/27.88 | | | | | | | | #1156.
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | Case 2:
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | (105) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | ALPHA: (105) implies:
% 159.05/27.88 | | | | | | | | (106) all_58_3 = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | COMBINE_EQS: (59), (106) imply:
% 159.05/27.88 | | | | | | | | (107) e3 = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | SIMP: (107) implies:
% 159.05/27.88 | | | | | | | | (108) e3 = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | COMBINE_EQS: (100), (108) imply:
% 159.05/27.88 | | | | | | | | (109) all_58_15 = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | REF_CLOSE: (6), (8), (9), (11), (13), (15), (17), (18), (22),
% 159.05/27.88 | | | | | | | | (23), (24), (29), (32), (34), (37), (38), (40), (41),
% 159.05/27.88 | | | | | | | | (44), (48), (52), (55), (58), (59), (60), (61), (66),
% 159.05/27.88 | | | | | | | | (68), (69), (70), (74), (75), (81), (109) are
% 159.05/27.88 | | | | | | | | inconsistent by sub-proof #521.
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | End of split
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | Case 2:
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | (110) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 159.05/27.88 | | | | | | | op(e2, e0) = e0)
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | BETA: splitting (110) gives:
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | | Case 1:
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | (111) all_58_5 = e0 & op(e2, e1) = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | ALPHA: (111) implies:
% 159.05/27.88 | | | | | | | | (112) all_58_5 = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | BETA: splitting (17) gives:
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | Case 1:
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | (113) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 159.05/27.88 | | | | | | | | | op(e2, e3) = e3)
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | REF_CLOSE: (13), (23), (32), (38), (48), (58), (70), (74),
% 159.05/27.88 | | | | | | | | | (75), (101), (113) are inconsistent by sub-proof
% 159.05/27.88 | | | | | | | | | #583.
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | Case 2:
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | (114) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 159.05/27.88 | | | | | | | | | op(e0, e3) = e3)
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | BETA: splitting (114) gives:
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | Case 1:
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | (115) all_58_6 = e3 & op(e1, e3) = e3
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | ALPHA: (115) implies:
% 159.05/27.88 | | | | | | | | | | (116) all_58_6 = e3
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | REF_CLOSE: (22), (40), (116) are inconsistent by sub-proof
% 159.05/27.88 | | | | | | | | | | #1073.
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | Case 2:
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | (117) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | ALPHA: (117) implies:
% 159.05/27.88 | | | | | | | | | | (118) all_58_12 = e3
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 159.05/27.88 | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19),
% 159.05/27.88 | | | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27),
% 159.05/27.88 | | | | | | | | | | (28), (29), (30), (31), (32), (33), (34), (35),
% 159.05/27.88 | | | | | | | | | | (36), (37), (38), (39), (40), (41), (42), (43),
% 159.05/27.88 | | | | | | | | | | (44), (45), (46), (47), (48), (49), (50), (51),
% 159.05/27.88 | | | | | | | | | | (52), (53), (54), (55), (56), (57), (58), (59),
% 159.05/27.88 | | | | | | | | | | (60), (61), (62), (63), (64), (65), (66), (67),
% 159.05/27.88 | | | | | | | | | | (68), (69), (70), (71), (72), (74), (75), (76),
% 159.05/27.88 | | | | | | | | | | (77), (78), (81), (85), (112), (118) are
% 159.05/27.88 | | | | | | | | | | inconsistent by sub-proof #514.
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | End of split
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | End of split
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | Case 2:
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | (119) all_58_10 = e0 & op(e2, e0) = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | ALPHA: (119) implies:
% 159.05/27.88 | | | | | | | | (120) all_58_10 = e0
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | BETA: splitting (17) gives:
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | | Case 1:
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | (121) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 159.05/27.88 | | | | | | | | | op(e2, e3) = e3)
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | REF_CLOSE: (13), (23), (32), (38), (48), (58), (70), (74),
% 159.05/27.88 | | | | | | | | | (75), (101), (121) are inconsistent by sub-proof
% 159.05/27.88 | | | | | | | | | #583.
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | Case 2:
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | (122) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 159.05/27.88 | | | | | | | | | op(e0, e3) = e3)
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | BETA: splitting (122) gives:
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | | Case 1:
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | (123) all_58_6 = e3 & op(e1, e3) = e3
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | ALPHA: (123) implies:
% 159.05/27.88 | | | | | | | | | | (124) all_58_6 = e3
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | REF_CLOSE: (22), (40), (124) are inconsistent by sub-proof
% 159.05/27.88 | | | | | | | | | | #1073.
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | Case 2:
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | (125) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | ALPHA: (125) implies:
% 159.05/27.88 | | | | | | | | | | (126) all_58_12 = e3
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.05/27.88 | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 159.05/27.88 | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 159.05/27.88 | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 159.05/27.88 | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.05/27.88 | | | | | | | | | | (43), (44), (45), (46), (47), (48), (49), (50),
% 159.05/27.88 | | | | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58),
% 159.05/27.88 | | | | | | | | | | (59), (60), (61), (62), (63), (64), (65), (66),
% 159.05/27.88 | | | | | | | | | | (67), (68), (69), (70), (71), (72), (73), (74),
% 159.05/27.88 | | | | | | | | | | (75), (76), (77), (78), (81), (85), (120), (126)
% 159.05/27.88 | | | | | | | | | | are inconsistent by sub-proof #511.
% 159.05/27.88 | | | | | | | | | |
% 159.05/27.88 | | | | | | | | | End of split
% 159.05/27.88 | | | | | | | | |
% 159.05/27.88 | | | | | | | | End of split
% 159.05/27.88 | | | | | | | |
% 159.05/27.88 | | | | | | | End of split
% 159.05/27.88 | | | | | | |
% 159.05/27.88 | | | | | | End of split
% 159.05/27.88 | | | | | |
% 159.05/27.88 | | | | | End of split
% 159.05/27.88 | | | | |
% 159.05/27.88 | | | | End of split
% 159.05/27.88 | | | |
% 159.05/27.88 | | | End of split
% 159.05/27.88 | | |
% 159.05/27.88 | | Case 2:
% 159.05/27.88 | | |
% 159.05/27.88 | | | (127) all_58_2 = e0 & op(e2, e3) = e0
% 159.05/27.88 | | |
% 159.05/27.88 | | | ALPHA: (127) implies:
% 159.05/27.88 | | | (128) op(e2, e3) = e0
% 159.05/27.88 | | |
% 159.05/27.88 | | | REF_CLOSE: (34), (38), (74), (128) are inconsistent by sub-proof #1156.
% 159.05/27.88 | | |
% 159.05/27.88 | | End of split
% 159.05/27.88 | |
% 159.05/27.88 | Case 2:
% 159.05/27.88 | |
% 159.05/27.88 | | (129) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.05/27.88 | | e0)
% 159.05/27.88 | |
% 159.05/27.88 | | REF_CLOSE: (6), (8), (9), (13), (15), (17), (18), (22), (23), (29), (32),
% 159.05/27.88 | | (34), (38), (40), (41), (44), (48), (52), (55), (58), (59), (60),
% 159.05/27.88 | | (61), (69), (70), (74), (75), (129) are inconsistent by sub-proof
% 159.05/27.88 | | #510.
% 159.05/27.88 | |
% 159.05/27.88 | End of split
% 159.05/27.88 |
% 159.05/27.88 End of proof
% 159.05/27.88
% 159.05/27.88 Sub-proof #510 shows that the following formulas are inconsistent:
% 159.05/27.88 ----------------------------------------------------------------
% 159.05/27.88 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.88 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.88 (2) op(e1, e1) = all_6_2
% 159.05/27.88 (3) ~ (all_52_7 = e3)
% 159.05/27.88 (4) op(e3, e3) = all_28_1
% 159.05/27.88 (5) all_58_8 = e3
% 159.05/27.88 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.88 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.88 (7) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.88 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.88 (8) all_58_6 = e1
% 159.05/27.88 (9) op(e2, e3) = all_52_1
% 159.05/27.88 (10) ~ (e3 = e0)
% 159.05/27.88 (11) op(e0, e0) = e0
% 159.05/27.88 (12) ~ (e2 = e0)
% 159.05/27.88 (13) op(e2, e3) = e2
% 159.05/27.88 (14) ~ (e3 = e1)
% 159.05/27.88 (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.88 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.88 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.88 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.88 (17) op(e3, e3) = e1
% 159.05/27.88 (18) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.88 (19) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.88 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.88 (20) ~ (e2 = e1)
% 159.05/27.88 (21) ~ (e1 = e0)
% 159.05/27.88 (22) all_58_3 = e3
% 159.05/27.88 (23) ~ (all_6_2 = e2)
% 159.05/27.88 (24) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.88 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.88 e3)
% 159.05/27.88 (25) op(e0, e2) = all_52_7
% 159.05/27.88 (26) op(e3, e3) = all_22_1
% 159.05/27.88 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.88 (28) ~ (e3 = e2)
% 159.05/27.88
% 159.05/27.88 Begin of proof
% 159.05/27.88 |
% 159.05/27.88 | BETA: splitting (18) gives:
% 159.05/27.88 |
% 159.05/27.88 | Case 1:
% 159.05/27.88 | |
% 159.05/27.88 | | (29) all_58_6 = e0 & op(e1, e3) = e0
% 159.05/27.88 | |
% 159.05/27.88 | | ALPHA: (29) implies:
% 159.05/27.88 | | (30) all_58_6 = e0
% 159.05/27.88 | |
% 159.05/27.88 | | REF_CLOSE: (8), (21), (30) are inconsistent by sub-proof #735.
% 159.05/27.88 | |
% 159.05/27.88 | Case 2:
% 159.05/27.88 | |
% 159.05/27.88 | | (31) all_58_12 = e0 & op(e0, e3) = e0
% 159.05/27.88 | |
% 159.05/27.88 | | ALPHA: (31) implies:
% 159.05/27.88 | | (32) all_58_12 = e0
% 159.05/27.88 | |
% 159.05/27.88 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/27.88 | | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 159.05/27.88 | | (25), (26), (27), (28), (32) are inconsistent by sub-proof #523.
% 159.05/27.88 | |
% 159.05/27.88 | End of split
% 159.05/27.88 |
% 159.05/27.88 End of proof
% 159.05/27.88
% 159.05/27.88 Sub-proof #511 shows that the following formulas are inconsistent:
% 159.05/27.88 ----------------------------------------------------------------
% 159.05/27.88 (1) all_56_14 = e3
% 159.05/27.88 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.89 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.89 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.89 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.89 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.89 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.89 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.89 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.89 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.89 (7) all_54_13 = all_52_7
% 159.05/27.89 (8) op(e1, e1) = all_6_2
% 159.05/27.89 (9) ~ (all_52_7 = e3)
% 159.05/27.89 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.89 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.89 e1)
% 159.05/27.89 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/27.89 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.89 (12) ~ (all_52_11 = e3)
% 159.05/27.89 (13) all_58_12 = e3
% 159.05/27.89 (14) op(e3, e3) = all_28_1
% 159.05/27.89 (15) all_58_7 = e2
% 159.05/27.89 (16) all_58_8 = e3
% 159.05/27.89 (17) ~ (all_52_7 = all_52_11)
% 159.05/27.89 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.89 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.89 (19) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.89 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.89 (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.89 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.89 (21) op(e3, e2) = all_52_4
% 159.05/27.89 (22) ~ (all_4_2 = e2)
% 159.05/27.89 (23) all_58_6 = e1
% 159.05/27.89 (24) op(e2, e3) = all_52_1
% 159.05/27.89 (25) ~ (all_52_13 = e3)
% 159.05/27.89 (26) all_54_2 = all_52_8
% 159.05/27.89 (27) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.89 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.89 (28) ~ (all_52_8 = all_52_9)
% 159.05/27.89 (29) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.89 (30) ~ (e3 = e0)
% 159.05/27.89 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.89 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.89 (32) ~ (all_52_9 = all_52_13)
% 159.05/27.89 (33) op(e0, e0) = e0
% 159.05/27.89 (34) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/27.89 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/27.89 e2)
% 159.05/27.89 (35) ~ (e2 = e0)
% 159.05/27.89 (36) ~ (all_52_9 = e3)
% 159.05/27.89 (37) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.89 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.89 (38) op(e2, e0) = all_52_13
% 159.05/27.89 (39) op(e2, e3) = e2
% 159.05/27.89 (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.89 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.89 (41) ~ (e3 = e1)
% 159.05/27.89 (42) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.89 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.89 (43) ~ (all_4_2 = e1)
% 159.05/27.89 (44) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.89 (45) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.89 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.89 (46) ~ (all_52_7 = e0)
% 159.05/27.89 (47) op(e0, e0) = all_4_2
% 159.05/27.89 (48) all_54_7 = all_52_13
% 159.05/27.89 (49) op(e3, e3) = e1
% 159.05/27.89 (50) ~ (all_52_13 = e2)
% 159.05/27.89 (51) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.89 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.89 (52) all_56_15 = all_4_2
% 159.05/27.89 (53) ~ (all_52_9 = all_52_11)
% 159.05/27.89 (54) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.89 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.89 (55) ~ (all_52_4 = e3)
% 159.05/27.89 (56) all_54_6 = all_52_9
% 159.05/27.89 (57) ~ (e2 = e1)
% 159.05/27.89 (58) ~ (all_52_8 = all_52_11)
% 159.05/27.89 (59) ~ (all_52_13 = e0)
% 159.05/27.89 (60) ~ (e1 = e0)
% 159.05/27.89 (61) all_58_3 = e3
% 159.05/27.89 (62) ~ (all_6_2 = e2)
% 159.05/27.89 (63) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.89 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.89 e3)
% 159.05/27.89 (64) all_56_13 = e3
% 159.05/27.89 (65) ~ (all_52_9 = e2)
% 159.05/27.89 (66) ~ (all_52_8 = e3)
% 159.05/27.89 (67) all_54_14 = all_52_11
% 159.05/27.89 (68) all_58_11 = e0
% 159.05/27.89 (69) all_58_10 = e0
% 159.05/27.89 (70) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.89 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.89 (71) all_58_9 = e2
% 159.05/27.89 (72) op(e0, e2) = all_52_7
% 159.05/27.89 (73) op(e3, e3) = all_22_1
% 159.05/27.89 (74) all_58_0 = e0
% 159.05/27.89 (75) ~ (all_52_8 = e1)
% 159.05/27.89 (76) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.89 (77) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.89 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.89 (78) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.89 (79) ~ (e3 = e2)
% 159.05/27.89 (80) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.89 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.89 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.89 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.89 (81) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.89 (82) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.89
% 159.05/27.89 Begin of proof
% 159.05/27.89 |
% 159.05/27.89 | BETA: splitting (40) gives:
% 159.05/27.89 |
% 159.05/27.89 | Case 1:
% 159.05/27.89 | |
% 159.05/27.89 | | (83) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 159.05/27.89 | | e0)
% 159.05/27.89 | |
% 159.05/27.89 | | BETA: splitting (83) gives:
% 159.05/27.89 | |
% 159.05/27.89 | | Case 1:
% 159.05/27.89 | | |
% 159.05/27.89 | | | (84) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.89 | | |
% 159.05/27.89 | | | ALPHA: (84) implies:
% 159.05/27.89 | | | (85) all_58_1 = e0
% 159.05/27.89 | | |
% 159.05/27.89 | | | BETA: splitting (6) gives:
% 159.05/27.89 | | |
% 159.05/27.89 | | | Case 1:
% 159.05/27.89 | | | |
% 159.05/27.89 | | | | (86) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 159.05/27.89 | | | | = e1)
% 159.05/27.89 | | | |
% 159.05/27.89 | | | | BETA: splitting (86) gives:
% 159.05/27.89 | | | |
% 159.05/27.89 | | | | Case 1:
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | (87) all_58_2 = e1 & op(e2, e3) = e1
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | ALPHA: (87) implies:
% 159.05/27.89 | | | | | (88) op(e2, e3) = e1
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | REF_CLOSE: (39), (57), (78), (88) are inconsistent by sub-proof #1430.
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | Case 2:
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | (89) all_58_3 = e1 & op(e2, e2) = e1
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (13), (14), (16), (18), (19),
% 159.05/27.89 | | | | | (20), (21), (22), (24), (27), (29), (30), (31), (35), (37),
% 159.05/27.89 | | | | | (39), (41), (42), (43), (45), (47), (49), (52), (54), (55),
% 159.05/27.89 | | | | | (57), (60), (61), (62), (63), (64), (70), (72), (73), (77),
% 159.05/27.89 | | | | | (78), (79), (80), (89) are inconsistent by sub-proof #513.
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | End of split
% 159.05/27.89 | | | |
% 159.05/27.89 | | | Case 2:
% 159.05/27.89 | | | |
% 159.05/27.89 | | | | (90) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 159.05/27.89 | | | | = e1)
% 159.05/27.89 | | | |
% 159.05/27.89 | | | | BETA: splitting (90) gives:
% 159.05/27.89 | | | |
% 159.05/27.89 | | | | Case 1:
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | (91) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | ALPHA: (91) implies:
% 159.05/27.89 | | | | | (92) all_58_5 = e1
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | BETA: splitting (11) gives:
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | Case 1:
% 159.05/27.89 | | | | | |
% 159.05/27.89 | | | | | | (93) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2,
% 159.05/27.89 | | | | | | e0) = e3)
% 159.05/27.89 | | | | | |
% 159.05/27.89 | | | | | | REF_CLOSE: (13), (18), (23), (24), (25), (30), (38), (39), (41),
% 159.05/27.89 | | | | | | (71), (74), (78), (79), (93) are inconsistent by
% 159.05/27.89 | | | | | | sub-proof #524.
% 159.05/27.89 | | | | | |
% 159.05/27.89 | | | | | Case 2:
% 159.05/27.89 | | | | | |
% 159.05/27.89 | | | | | | (94) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 159.05/27.89 | | | | | | op(e0, e0) = e3)
% 159.05/27.89 | | | | | |
% 159.05/27.89 | | | | | | BETA: splitting (94) gives:
% 159.05/27.89 | | | | | |
% 159.05/27.89 | | | | | | Case 1:
% 159.05/27.89 | | | | | | |
% 159.05/27.89 | | | | | | | (95) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.89 | | | | | | |
% 159.05/27.89 | | | | | | | REF_CLOSE: (6), (8), (9), (13), (14), (16), (18), (19), (23),
% 159.05/27.89 | | | | | | | (24), (30), (33), (35), (39), (41), (42), (45), (49),
% 159.05/27.89 | | | | | | | (54), (57), (60), (61), (62), (63), (68), (72), (73),
% 159.05/27.89 | | | | | | | (78), (79), (95) are inconsistent by sub-proof #522.
% 159.05/27.89 | | | | | | |
% 159.05/27.89 | | | | | | Case 2:
% 159.05/27.89 | | | | | | |
% 159.05/27.89 | | | | | | | (96) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.89 | | | | | | |
% 159.05/27.89 | | | | | | | ALPHA: (96) implies:
% 159.05/27.89 | | | | | | | (97) all_58_15 = e3
% 159.05/27.89 | | | | | | | (98) op(e0, e0) = e3
% 159.05/27.89 | | | | | | |
% 159.05/27.89 | | | | | | | BETA: splitting (70) gives:
% 159.05/27.89 | | | | | | |
% 159.05/27.89 | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | |
% 159.05/27.89 | | | | | | | | (99) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 159.05/27.89 | | | | | | | | op(e3, e2) = e3)
% 159.05/27.89 | | | | | | | |
% 159.05/27.89 | | | | | | | | REF_CLOSE: (14), (21), (33), (49), (55), (60), (73), (78), (98),
% 159.05/27.89 | | | | | | | | (99) are inconsistent by sub-proof #581.
% 159.05/27.89 | | | | | | | |
% 159.05/27.89 | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | |
% 159.05/27.89 | | | | | | | | (100) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 159.05/27.89 | | | | | | | | op(e3, e0) = e3)
% 159.05/27.89 | | | | | | | |
% 159.05/27.89 | | | | | | | | BETA: splitting (100) gives:
% 159.05/27.89 | | | | | | | |
% 159.05/27.89 | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | | (101) all_58_4 = e3 & op(e3, e1) = e3
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | | ALPHA: (101) implies:
% 159.05/27.89 | | | | | | | | | (102) all_58_4 = e3
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | | BETA: splitting (42) gives:
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | (103) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 159.05/27.89 | | | | | | | | | | & op(e2, e1) = e0)
% 159.05/27.89 | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | BETA: splitting (103) gives:
% 159.05/27.89 | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | (104) all_58_4 = e0 & op(e3, e1) = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | ALPHA: (104) implies:
% 159.05/27.89 | | | | | | | | | | | (105) all_58_4 = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | COMBINE_EQS: (102), (105) imply:
% 159.05/27.89 | | | | | | | | | | | (106) e3 = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | COMBINE_EQS: (13), (106) imply:
% 159.05/27.89 | | | | | | | | | | | (107) all_58_12 = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | REF_CLOSE: (14), (18), (23), (24), (30), (33), (39), (41),
% 159.05/27.89 | | | | | | | | | | | (49), (60), (73), (78), (79), (98), (107) are
% 159.05/27.89 | | | | | | | | | | | inconsistent by sub-proof #546.
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | (108) all_58_5 = e0 & op(e2, e1) = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | ALPHA: (108) implies:
% 159.05/27.89 | | | | | | | | | | | (109) all_58_5 = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (13), (14), (15),
% 159.05/27.89 | | | | | | | | | | | (16), (18), (19), (20), (21), (22), (23), (24),
% 159.05/27.89 | | | | | | | | | | | (27), (29), (30), (31), (34), (35), (37), (39),
% 159.05/27.89 | | | | | | | | | | | (41), (43), (45), (47), (49), (51), (52), (54),
% 159.05/27.89 | | | | | | | | | | | (55), (57), (60), (61), (62), (64), (70), (72),
% 159.05/27.89 | | | | | | | | | | | (73), (74), (78), (79), (80), (85), (97), (98),
% 159.05/27.89 | | | | | | | | | | | (102), (109) are inconsistent by sub-proof #515.
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | (110) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0
% 159.05/27.89 | | | | | | | | | | & op(e0, e1) = e0)
% 159.05/27.89 | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | BETA: splitting (110) gives:
% 159.05/27.89 | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | (111) all_58_8 = e0 & op(e1, e1) = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | ALPHA: (111) implies:
% 159.05/27.89 | | | | | | | | | | | (112) all_58_8 = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | COMBINE_EQS: (16), (112) imply:
% 159.05/27.89 | | | | | | | | | | | (113) e3 = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | COMBINE_EQS: (13), (113) imply:
% 159.05/27.89 | | | | | | | | | | | (114) all_58_12 = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | REF_CLOSE: (14), (18), (23), (24), (30), (33), (39), (41),
% 159.05/27.89 | | | | | | | | | | | (49), (60), (73), (78), (79), (98), (114) are
% 159.05/27.89 | | | | | | | | | | | inconsistent by sub-proof #546.
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | (115) all_58_14 = e0 & op(e0, e1) = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | ALPHA: (115) implies:
% 159.05/27.89 | | | | | | | | | | | (116) all_58_14 = e0
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | BETA: splitting (34) gives:
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | (117) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 159.05/27.89 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.05/27.89 | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | BETA: splitting (117) gives:
% 159.05/27.89 | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | (118) all_58_12 = e2 & op(e0, e3) = e2
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | ALPHA: (118) implies:
% 159.05/27.89 | | | | | | | | | | | | | (119) all_58_12 = e2
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | REF_CLOSE: (18), (23), (24), (30), (39), (41), (74), (78),
% 159.05/27.89 | | | | | | | | | | | | | (79), (119) are inconsistent by sub-proof #1067.
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | (120) all_58_13 = e2 & op(e0, e2) = e2
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | ALPHA: (120) implies:
% 159.05/27.89 | | | | | | | | | | | | | (121) all_58_13 = e2
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | BETA: splitting (4) gives:
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | (122) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 159.05/27.89 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | (123) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | (124) all_58_1 = e1
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | COMBINE_EQS: (85), (124) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | (125) e1 = e0
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | SIMP: (125) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | (126) e1 = e0
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | COMBINE_EQS: (92), (126) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | (127) all_58_5 = e0
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (13), (14), (15),
% 159.05/27.89 | | | | | | | | | | | | | | | (16), (18), (19), (20), (21), (22), (23), (24),
% 159.05/27.89 | | | | | | | | | | | | | | | (27), (29), (30), (31), (34), (35), (37), (39),
% 159.05/27.89 | | | | | | | | | | | | | | | (41), (43), (45), (47), (49), (51), (52), (54),
% 159.05/27.89 | | | | | | | | | | | | | | | (55), (57), (60), (61), (62), (64), (70), (72),
% 159.05/27.89 | | | | | | | | | | | | | | | (73), (74), (78), (79), (80), (85), (97), (98),
% 159.05/27.89 | | | | | | | | | | | | | | | (102), (127) are inconsistent by sub-proof #515.
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | (128) all_58_3 = e1 & op(e2, e2) = e1
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | (129) all_58_3 = e1
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | COMBINE_EQS: (61), (129) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | (130) e3 = e1
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | COMBINE_EQS: (13), (130) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | (131) all_58_12 = e1
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (14), (16), (18), (19), (20),
% 159.05/27.89 | | | | | | | | | | | | | | | (21), (24), (27), (30), (31), (33), (35), (37),
% 159.05/27.89 | | | | | | | | | | | | | | | (39), (41), (45), (49), (54), (55), (57), (60),
% 159.05/27.89 | | | | | | | | | | | | | | | (61), (62), (70), (73), (74), (78), (79), (80),
% 159.05/27.89 | | | | | | | | | | | | | | | (97), (98), (131) are inconsistent by sub-proof
% 159.05/27.89 | | | | | | | | | | | | | | | #575.
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | (132) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 159.05/27.89 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | REF_CLOSE: (15), (57), (121), (132) are inconsistent by
% 159.05/27.89 | | | | | | | | | | | | | | sub-proof #516.
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | (133) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 159.05/27.89 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.05/27.89 | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | BETA: splitting (133) gives:
% 159.05/27.89 | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | (134) all_58_14 = e2 & op(e0, e1) = e2
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | ALPHA: (134) implies:
% 159.05/27.89 | | | | | | | | | | | | | (135) all_58_14 = e2
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | COMBINE_EQS: (116), (135) imply:
% 159.05/27.89 | | | | | | | | | | | | | (136) e2 = e0
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | REDUCE: (35), (136) imply:
% 159.05/27.89 | | | | | | | | | | | | | (137) $false
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | CLOSE: (137) is inconsistent.
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | (138) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | ALPHA: (138) implies:
% 159.05/27.89 | | | | | | | | | | | | | (139) all_58_15 = e2
% 159.05/27.89 | | | | | | | | | | | | | (140) op(e0, e0) = e2
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | BETA: splitting (70) gives:
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | (141) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 159.05/27.89 | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | (142) all_58_0 = e3 & op(e3, e3) = e3
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | (143) all_58_0 = e3
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | COMBINE_EQS: (74), (143) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | (144) e3 = e0
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | SIMP: (144) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | (145) e3 = e0
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | COMBINE_EQS: (13), (145) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | (146) all_58_12 = e0
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (14), (16), (18), (19), (23), (24),
% 159.05/27.89 | | | | | | | | | | | | | | | (30), (33), (35), (39), (41), (42), (45), (49),
% 159.05/27.89 | | | | | | | | | | | | | | | (54), (57), (60), (61), (62), (63), (72), (73),
% 159.05/27.89 | | | | | | | | | | | | | | | (78), (79), (146) are inconsistent by sub-proof
% 159.05/27.89 | | | | | | | | | | | | | | | #523.
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | (147) all_58_1 = e3 & op(e3, e2) = e3
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | (148) op(e3, e2) = e3
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | REF_CLOSE: (21), (55), (78), (148) are inconsistent by
% 159.05/27.89 | | | | | | | | | | | | | | | sub-proof #1540.
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | (149) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 159.05/27.89 | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 159.05/27.89 | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (18), (23), (24), (25), (30), (38), (39),
% 159.05/27.89 | | | | | | | | | | | | | | | | (41), (71), (74), (78), (79), (149) are
% 159.05/27.89 | | | | | | | | | | | | | | | | inconsistent by sub-proof #524.
% 159.05/27.89 | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 159.05/27.89 | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | | (150) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | | | (151) all_58_11 = e3
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (151) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | | | (152) e3 = e0
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | | SIMP: (152) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | | | (153) e3 = e0
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (153) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | | | (154) all_58_4 = e0
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (19), (30), (35), (39), (41),
% 159.05/27.89 | | | | | | | | | | | | | | | | | (45), (57), (60), (61), (62), (63), (72), (78),
% 159.05/27.89 | | | | | | | | | | | | | | | | | (79), (80), (139), (140), (154) are inconsistent
% 159.05/27.89 | | | | | | | | | | | | | | | | | by sub-proof #847.
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (79), (98), (140) are inconsistent by
% 159.05/27.89 | | | | | | | | | | | | | | | | | sub-proof #1382.
% 159.05/27.89 | | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | (155) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 159.05/27.89 | | | | | | | | | | | | | | | (156) all_58_9 = e3
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | COMBINE_EQS: (71), (156) imply:
% 159.05/27.89 | | | | | | | | | | | | | | | (157) e3 = e2
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | | REF_CLOSE: (13), (18), (23), (24), (30), (39), (41), (74),
% 159.05/27.89 | | | | | | | | | | | | | | | (78), (79), (157) are inconsistent by sub-proof
% 159.05/27.89 | | | | | | | | | | | | | | | #698.
% 159.05/27.89 | | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | | |
% 159.05/27.89 | | | | | | | | | End of split
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | Case 2:
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | | (158) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | | ALPHA: (158) implies:
% 159.05/27.89 | | | | | | | | | (159) all_58_9 = e3
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | | COMBINE_EQS: (71), (159) imply:
% 159.05/27.89 | | | | | | | | | (160) e3 = e2
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | | REF_CLOSE: (13), (18), (23), (24), (30), (39), (41), (74),
% 159.05/27.89 | | | | | | | | | (78), (79), (160) are inconsistent by sub-proof
% 159.05/27.89 | | | | | | | | | #698.
% 159.05/27.89 | | | | | | | | |
% 159.05/27.89 | | | | | | | | End of split
% 159.05/27.89 | | | | | | | |
% 159.05/27.89 | | | | | | | End of split
% 159.05/27.89 | | | | | | |
% 159.05/27.89 | | | | | | End of split
% 159.05/27.89 | | | | | |
% 159.05/27.89 | | | | | End of split
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | Case 2:
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | (161) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | | REF_CLOSE: (13), (23), (31), (39), (41), (57), (60), (69), (74), (78),
% 159.05/27.89 | | | | | (161) are inconsistent by sub-proof #689.
% 159.05/27.89 | | | | |
% 159.05/27.89 | | | | End of split
% 159.05/27.89 | | | |
% 159.05/27.89 | | | End of split
% 159.05/27.89 | | |
% 159.05/27.89 | | Case 2:
% 159.05/27.89 | | |
% 159.05/27.89 | | | (162) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.89 | | |
% 159.05/27.89 | | | REF_CLOSE: (6), (8), (9), (13), (14), (16), (18), (19), (23), (24), (30),
% 159.05/27.89 | | | (33), (35), (39), (41), (42), (45), (49), (54), (57), (60),
% 159.05/27.89 | | | (61), (62), (63), (72), (73), (78), (79), (162) are
% 159.05/27.89 | | | inconsistent by sub-proof #520.
% 159.05/27.89 | | |
% 159.05/27.89 | | End of split
% 159.05/27.89 | |
% 159.05/27.89 | Case 2:
% 159.05/27.89 | |
% 159.05/27.89 | | (163) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.05/27.89 | | e0)
% 159.05/27.89 | |
% 159.05/27.89 | | REF_CLOSE: (2), (7), (9), (12), (15), (17), (26), (28), (32), (35), (36),
% 159.05/27.89 | | (44), (46), (48), (50), (53), (56), (58), (59), (65), (66), (67),
% 159.05/27.89 | | (72), (75), (76), (78), (81), (82), (163) are inconsistent by
% 159.05/27.89 | | sub-proof #512.
% 159.05/27.89 | |
% 159.05/27.89 | End of split
% 159.05/27.89 |
% 159.05/27.89 End of proof
% 159.05/27.89
% 159.05/27.89 Sub-proof #512 shows that the following formulas are inconsistent:
% 159.05/27.89 ----------------------------------------------------------------
% 159.05/27.89 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.89 (2) all_54_13 = all_52_7
% 159.05/27.89 (3) ~ (all_52_7 = e3)
% 159.05/27.89 (4) ~ (all_52_11 = e3)
% 159.05/27.89 (5) all_58_7 = e2
% 159.05/27.89 (6) ~ (all_52_7 = all_52_11)
% 159.05/27.89 (7) all_54_2 = all_52_8
% 159.05/27.89 (8) ~ (all_52_8 = all_52_9)
% 159.05/27.89 (9) ~ (all_52_9 = all_52_13)
% 159.05/27.89 (10) ~ (e2 = e0)
% 159.05/27.89 (11) ~ (all_52_9 = e3)
% 159.05/27.89 (12) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.89 (13) ~ (all_52_7 = e0)
% 159.05/27.89 (14) all_54_7 = all_52_13
% 159.05/27.89 (15) ~ (all_52_13 = e2)
% 159.05/27.89 (16) ~ (all_52_9 = all_52_11)
% 159.05/27.89 (17) all_54_6 = all_52_9
% 159.05/27.89 (18) ~ (all_52_8 = all_52_11)
% 159.05/27.89 (19) ~ (all_52_13 = e0)
% 159.05/27.89 (20) ~ (all_52_9 = e2)
% 159.05/27.89 (21) ~ (all_52_8 = e3)
% 159.05/27.89 (22) all_54_14 = all_52_11
% 159.05/27.89 (23) op(e0, e2) = all_52_7
% 159.05/27.89 (24) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.89 (25) ~ (all_52_8 = e1)
% 159.05/27.89 (26) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.89 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.89 (28) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.89 (29) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.89
% 159.05/27.89 Begin of proof
% 159.05/27.89 |
% 159.05/27.89 | BETA: splitting (24) gives:
% 159.05/27.89 |
% 159.05/27.89 | Case 1:
% 159.05/27.89 | |
% 159.05/27.89 | | (30) all_58_7 = e0 & op(e1, e2) = e0
% 159.05/27.89 | |
% 159.05/27.89 | | REF_CLOSE: (5), (10), (30) are inconsistent by sub-proof #1468.
% 159.05/27.89 | |
% 159.05/27.89 | Case 2:
% 159.05/27.89 | |
% 159.05/27.89 | | (31) all_58_13 = e0 & op(e0, e2) = e0
% 159.05/27.89 | |
% 159.05/27.89 | | ALPHA: (31) implies:
% 159.05/27.90 | | (32) op(e0, e2) = e0
% 159.05/27.90 | |
% 159.05/27.90 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14),
% 159.05/27.90 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 159.05/27.90 | | (27), (28), (29), (32) are inconsistent by sub-proof #559.
% 159.05/27.90 | |
% 159.05/27.90 | End of split
% 159.05/27.90 |
% 159.05/27.90 End of proof
% 159.05/27.90
% 159.05/27.90 Sub-proof #513 shows that the following formulas are inconsistent:
% 159.05/27.90 ----------------------------------------------------------------
% 159.05/27.90 (1) all_56_14 = e3
% 159.05/27.90 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.90 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.90 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.90 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.90 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.90 (5) op(e1, e1) = all_6_2
% 159.05/27.90 (6) ~ (all_52_7 = e3)
% 159.05/27.90 (7) all_58_12 = e3
% 159.05/27.90 (8) op(e3, e3) = all_28_1
% 159.05/27.90 (9) all_58_8 = e3
% 159.05/27.90 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.90 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.90 (11) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.90 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.90 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.90 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.90 (13) op(e3, e2) = all_52_4
% 159.05/27.90 (14) ~ (all_4_2 = e2)
% 159.05/27.90 (15) op(e2, e3) = all_52_1
% 159.05/27.90 (16) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.90 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.90 (17) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.90 (18) ~ (e3 = e0)
% 159.05/27.90 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.90 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.90 (20) ~ (e2 = e0)
% 159.05/27.90 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.90 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.90 (22) op(e2, e3) = e2
% 159.05/27.90 (23) ~ (e3 = e1)
% 159.05/27.90 (24) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.90 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.90 (25) ~ (all_4_2 = e1)
% 159.05/27.90 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.90 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.90 (27) op(e0, e0) = all_4_2
% 159.05/27.90 (28) all_58_3 = e1 & op(e2, e2) = e1
% 159.05/27.90 (29) op(e3, e3) = e1
% 159.05/27.90 (30) all_56_15 = all_4_2
% 159.05/27.90 (31) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.90 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.90 (32) ~ (all_52_4 = e3)
% 159.05/27.90 (33) ~ (e2 = e1)
% 159.05/27.90 (34) ~ (e1 = e0)
% 159.05/27.90 (35) all_58_3 = e3
% 159.05/27.90 (36) ~ (all_6_2 = e2)
% 159.05/27.90 (37) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.90 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.90 e3)
% 159.05/27.90 (38) all_56_13 = e3
% 159.05/27.90 (39) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.90 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.90 (40) op(e0, e2) = all_52_7
% 159.05/27.90 (41) op(e3, e3) = all_22_1
% 159.05/27.90 (42) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.90 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.90 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.90 (44) ~ (e3 = e2)
% 159.05/27.90 (45) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.90 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.90 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.90 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.90
% 159.05/27.90 Begin of proof
% 159.05/27.90 |
% 159.05/27.90 | ALPHA: (28) implies:
% 159.05/27.90 | (46) all_58_3 = e1
% 159.05/27.90 |
% 159.05/27.90 | COMBINE_EQS: (35), (46) imply:
% 159.05/27.90 | (47) e3 = e1
% 159.05/27.90 |
% 159.05/27.90 | COMBINE_EQS: (7), (47) imply:
% 159.05/27.90 | (48) all_58_12 = e1
% 159.05/27.90 |
% 159.05/27.90 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 159.05/27.90 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 159.05/27.90 | (25), (26), (27), (29), (30), (31), (32), (33), (34), (35), (36),
% 159.05/27.90 | (37), (38), (39), (40), (41), (42), (43), (44), (45), (48) are
% 159.05/27.90 | inconsistent by sub-proof #572.
% 159.05/27.90 |
% 159.05/27.90 End of proof
% 159.05/27.90
% 159.05/27.90 Sub-proof #514 shows that the following formulas are inconsistent:
% 159.05/27.90 ----------------------------------------------------------------
% 159.05/27.90 (1) all_56_14 = e3
% 159.05/27.90 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.90 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.90 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.90 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.90 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.90 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.90 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.90 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.90 (7) all_54_13 = all_52_7
% 159.05/27.90 (8) op(e1, e1) = all_6_2
% 159.05/27.90 (9) ~ (all_52_7 = e3)
% 159.05/27.90 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/27.90 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.90 (11) ~ (all_52_11 = e3)
% 159.05/27.90 (12) all_58_12 = e3
% 159.05/27.90 (13) op(e3, e3) = all_28_1
% 159.05/27.90 (14) all_58_7 = e2
% 159.05/27.90 (15) all_58_8 = e3
% 159.05/27.90 (16) ~ (all_52_7 = all_52_11)
% 159.05/27.90 (17) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.90 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.90 (18) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.90 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.90 (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.90 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.90 (20) op(e3, e2) = all_52_4
% 159.05/27.90 (21) ~ (all_4_2 = e2)
% 159.05/27.90 (22) all_58_6 = e1
% 159.05/27.90 (23) op(e2, e3) = all_52_1
% 159.05/27.90 (24) ~ (all_52_13 = e3)
% 159.05/27.90 (25) all_54_2 = all_52_8
% 159.05/27.90 (26) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.90 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.90 (27) ~ (all_52_8 = all_52_9)
% 159.05/27.90 (28) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.90 (29) ~ (e3 = e0)
% 159.05/27.90 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.90 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.90 (31) ~ (all_52_9 = all_52_13)
% 159.05/27.90 (32) op(e0, e0) = e0
% 159.05/27.90 (33) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/27.90 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/27.90 e2)
% 159.05/27.90 (34) ~ (e2 = e0)
% 159.05/27.90 (35) ~ (all_52_9 = e3)
% 159.05/27.90 (36) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.90 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.90 (37) op(e2, e0) = all_52_13
% 159.05/27.90 (38) op(e2, e3) = e2
% 159.05/27.90 (39) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.90 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.90 (40) ~ (e3 = e1)
% 159.05/27.90 (41) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.90 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.90 (42) ~ (all_4_2 = e1)
% 159.05/27.90 (43) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.90 (44) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.90 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.90 (45) ~ (all_52_7 = e0)
% 159.05/27.90 (46) op(e0, e0) = all_4_2
% 159.05/27.90 (47) all_54_7 = all_52_13
% 159.05/27.90 (48) op(e3, e3) = e1
% 159.05/27.90 (49) ~ (all_52_13 = e2)
% 159.05/27.90 (50) all_58_5 = e0
% 159.05/27.90 (51) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.90 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.90 (52) all_56_15 = all_4_2
% 159.05/27.90 (53) ~ (all_52_9 = all_52_11)
% 159.05/27.90 (54) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.90 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.90 (55) ~ (all_52_4 = e3)
% 159.05/27.90 (56) all_54_6 = all_52_9
% 159.05/27.90 (57) ~ (e2 = e1)
% 159.05/27.90 (58) ~ (all_52_8 = all_52_11)
% 159.05/27.90 (59) ~ (all_52_13 = e0)
% 159.05/27.90 (60) ~ (e1 = e0)
% 159.05/27.90 (61) all_58_3 = e3
% 159.05/27.90 (62) ~ (all_6_2 = e2)
% 159.05/27.90 (63) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.90 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.90 e3)
% 159.05/27.90 (64) all_56_13 = e3
% 159.05/27.90 (65) ~ (all_52_9 = e2)
% 159.05/27.90 (66) ~ (all_52_8 = e3)
% 159.05/27.90 (67) all_54_14 = all_52_11
% 159.05/27.90 (68) all_58_11 = e0
% 159.05/27.90 (69) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.90 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.90 (70) all_58_9 = e2
% 159.05/27.90 (71) op(e0, e2) = all_52_7
% 159.05/27.90 (72) op(e3, e3) = all_22_1
% 159.05/27.90 (73) all_58_0 = e0
% 159.05/27.90 (74) ~ (all_52_8 = e1)
% 159.05/27.90 (75) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.90 (76) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.90 (77) ~ (e3 = e2)
% 159.05/27.90 (78) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.90 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.90 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.90 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.90 (79) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.90 (80) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.90
% 159.05/27.90 Begin of proof
% 159.05/27.90 |
% 159.05/27.90 | BETA: splitting (39) gives:
% 159.05/27.90 |
% 159.05/27.90 | Case 1:
% 159.05/27.90 | |
% 159.05/27.90 | | (81) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 159.05/27.90 | | e0)
% 159.05/27.90 | |
% 159.05/27.90 | | BETA: splitting (81) gives:
% 159.05/27.90 | |
% 159.05/27.90 | | Case 1:
% 159.05/27.90 | | |
% 159.05/27.90 | | | (82) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.90 | | |
% 159.05/27.90 | | | ALPHA: (82) implies:
% 159.05/27.90 | | | (83) all_58_1 = e0
% 159.05/27.90 | | |
% 159.05/27.90 | | | BETA: splitting (10) gives:
% 159.05/27.90 | | |
% 159.05/27.90 | | | Case 1:
% 159.05/27.90 | | | |
% 159.05/27.90 | | | | (84) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 159.05/27.90 | | | | = e3)
% 159.05/27.90 | | | |
% 159.05/27.90 | | | | REF_CLOSE: (12), (17), (22), (23), (24), (29), (37), (38), (40), (70),
% 159.05/27.90 | | | | (73), (76), (77), (84) are inconsistent by sub-proof #524.
% 159.05/27.90 | | | |
% 159.05/27.90 | | | Case 2:
% 159.05/27.90 | | | |
% 159.05/27.90 | | | | (85) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 159.05/27.90 | | | | e0) = e3)
% 159.05/27.90 | | | |
% 159.05/27.90 | | | | BETA: splitting (85) gives:
% 159.05/27.90 | | | |
% 159.05/27.90 | | | | Case 1:
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | | (86) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | | REF_CLOSE: (6), (8), (9), (12), (13), (15), (17), (18), (22), (23),
% 159.05/27.90 | | | | | (29), (32), (34), (38), (40), (41), (44), (48), (54), (57),
% 159.05/27.90 | | | | | (60), (61), (62), (63), (68), (71), (72), (76), (77), (86)
% 159.05/27.90 | | | | | are inconsistent by sub-proof #522.
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | Case 2:
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | | (87) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | | ALPHA: (87) implies:
% 159.05/27.90 | | | | | (88) all_58_15 = e3
% 159.05/27.90 | | | | | (89) op(e0, e0) = e3
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | | BETA: splitting (69) gives:
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | | Case 1:
% 159.05/27.90 | | | | | |
% 159.05/27.90 | | | | | | (90) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 159.05/27.90 | | | | | | e2) = e3)
% 159.05/27.90 | | | | | |
% 159.05/27.90 | | | | | | REF_CLOSE: (13), (20), (32), (48), (55), (60), (72), (76), (89),
% 159.05/27.90 | | | | | | (90) are inconsistent by sub-proof #581.
% 159.05/27.90 | | | | | |
% 159.05/27.90 | | | | | Case 2:
% 159.05/27.90 | | | | | |
% 159.05/27.90 | | | | | | (91) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 159.05/27.90 | | | | | | e0) = e3)
% 159.05/27.90 | | | | | |
% 159.05/27.90 | | | | | | BETA: splitting (91) gives:
% 159.05/27.90 | | | | | |
% 159.05/27.90 | | | | | | Case 1:
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | | (92) all_58_4 = e3 & op(e3, e1) = e3
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | | ALPHA: (92) implies:
% 159.05/27.90 | | | | | | | (93) all_58_4 = e3
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (12), (13), (14), (15),
% 159.05/27.90 | | | | | | | (17), (18), (19), (20), (21), (22), (23), (26), (28),
% 159.05/27.90 | | | | | | | (29), (30), (33), (34), (36), (38), (40), (42), (44),
% 159.05/27.90 | | | | | | | (46), (48), (50), (51), (52), (54), (55), (57), (60),
% 159.05/27.90 | | | | | | | (61), (62), (64), (69), (71), (72), (73), (76), (77),
% 159.05/27.90 | | | | | | | (78), (83), (88), (89), (93) are inconsistent by
% 159.05/27.90 | | | | | | | sub-proof #515.
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | Case 2:
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | | (94) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | | ALPHA: (94) implies:
% 159.05/27.90 | | | | | | | (95) all_58_9 = e3
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | | COMBINE_EQS: (70), (95) imply:
% 159.05/27.90 | | | | | | | (96) e3 = e2
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | | REF_CLOSE: (12), (17), (22), (23), (29), (38), (40), (73), (76),
% 159.05/27.90 | | | | | | | (77), (96) are inconsistent by sub-proof #698.
% 159.05/27.90 | | | | | | |
% 159.05/27.90 | | | | | | End of split
% 159.05/27.90 | | | | | |
% 159.05/27.90 | | | | | End of split
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | End of split
% 159.05/27.90 | | | |
% 159.05/27.90 | | | End of split
% 159.05/27.90 | | |
% 159.05/27.90 | | Case 2:
% 159.05/27.90 | | |
% 159.05/27.90 | | | (97) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.90 | | |
% 159.05/27.90 | | | REF_CLOSE: (6), (8), (9), (12), (13), (15), (17), (18), (22), (23), (29),
% 159.05/27.90 | | | (32), (34), (38), (40), (41), (44), (48), (54), (57), (60),
% 159.05/27.90 | | | (61), (62), (63), (71), (72), (76), (77), (97) are inconsistent
% 159.05/27.90 | | | by sub-proof #520.
% 159.05/27.90 | | |
% 159.05/27.90 | | End of split
% 159.05/27.90 | |
% 159.05/27.90 | Case 2:
% 159.05/27.90 | |
% 159.05/27.90 | | (98) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.05/27.90 | | e0)
% 159.05/27.90 | |
% 159.05/27.90 | | BETA: splitting (98) gives:
% 159.05/27.90 | |
% 159.05/27.90 | | Case 1:
% 159.05/27.90 | | |
% 159.05/27.90 | | | (99) all_58_7 = e0 & op(e1, e2) = e0
% 159.05/27.90 | | |
% 159.05/27.90 | | | ALPHA: (99) implies:
% 159.05/27.90 | | | (100) all_58_7 = e0
% 159.05/27.90 | | |
% 159.05/27.90 | | | REF_CLOSE: (14), (34), (100) are inconsistent by sub-proof #1086.
% 159.05/27.90 | | |
% 159.05/27.90 | | Case 2:
% 159.05/27.90 | | |
% 159.05/27.90 | | | (101) all_58_13 = e0 & op(e0, e2) = e0
% 159.05/27.90 | | |
% 159.05/27.90 | | | ALPHA: (101) implies:
% 159.05/27.90 | | | (102) op(e0, e2) = e0
% 159.05/27.90 | | |
% 159.05/27.90 | | | REF_CLOSE: (2), (7), (9), (11), (16), (25), (27), (31), (35), (43), (45),
% 159.05/27.90 | | | (47), (49), (53), (56), (58), (59), (65), (66), (67), (71),
% 159.05/27.90 | | | (74), (75), (76), (79), (80), (102) are inconsistent by
% 159.05/27.90 | | | sub-proof #559.
% 159.05/27.90 | | |
% 159.05/27.90 | | End of split
% 159.05/27.90 | |
% 159.05/27.90 | End of split
% 159.05/27.90 |
% 159.05/27.90 End of proof
% 159.05/27.90
% 159.05/27.90 Sub-proof #515 shows that the following formulas are inconsistent:
% 159.05/27.90 ----------------------------------------------------------------
% 159.05/27.90 (1) all_56_14 = e3
% 159.05/27.90 (2) all_58_15 = e3
% 159.05/27.90 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.90 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.90 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.90 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.90 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.90 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.90 (6) all_58_1 = e0
% 159.05/27.90 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.90 (8) op(e1, e1) = all_6_2
% 159.05/27.90 (9) all_58_12 = e3
% 159.05/27.90 (10) op(e3, e3) = all_28_1
% 159.05/27.90 (11) all_58_7 = e2
% 159.05/27.90 (12) all_58_8 = e3
% 159.05/27.90 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.90 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.90 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.90 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.90 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.90 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.90 (16) op(e3, e2) = all_52_4
% 159.05/27.90 (17) ~ (all_4_2 = e2)
% 159.05/27.90 (18) all_58_6 = e1
% 159.05/27.90 (19) op(e2, e3) = all_52_1
% 159.05/27.90 (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.90 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.90 (21) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.90 (22) ~ (e3 = e0)
% 159.05/27.90 (23) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.90 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.90 (24) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/27.90 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/27.90 e2)
% 159.05/27.90 (25) ~ (e2 = e0)
% 159.05/27.90 (26) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.90 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.90 (27) op(e2, e3) = e2
% 159.05/27.90 (28) ~ (e3 = e1)
% 159.05/27.90 (29) ~ (all_4_2 = e1)
% 159.05/27.90 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.90 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.90 (31) op(e0, e0) = all_4_2
% 159.05/27.90 (32) op(e3, e3) = e1
% 159.05/27.90 (33) all_58_5 = e0
% 159.05/27.90 (34) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.90 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.90 (35) all_56_15 = all_4_2
% 159.05/27.90 (36) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.90 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.90 (37) ~ (all_52_4 = e3)
% 159.05/27.90 (38) ~ (e2 = e1)
% 159.05/27.90 (39) ~ (e1 = e0)
% 159.05/27.90 (40) all_58_4 = e3
% 159.05/27.90 (41) all_58_3 = e3
% 159.05/27.90 (42) ~ (all_6_2 = e2)
% 159.05/27.90 (43) all_56_13 = e3
% 159.05/27.90 (44) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.90 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.90 (45) op(e0, e2) = all_52_7
% 159.05/27.90 (46) op(e3, e3) = all_22_1
% 159.05/27.90 (47) all_58_0 = e0
% 159.05/27.90 (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.90 (49) ~ (e3 = e2)
% 159.05/27.90 (50) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.90 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.90 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.90 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.90 (51) op(e0, e0) = e3
% 159.05/27.90
% 159.05/27.90 Begin of proof
% 159.05/27.90 |
% 159.05/27.90 | BETA: splitting (36) gives:
% 159.05/27.90 |
% 159.05/27.90 | Case 1:
% 159.05/27.90 | |
% 159.05/27.90 | | (52) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 159.05/27.90 | | e1)
% 159.05/27.90 | |
% 159.05/27.90 | | BETA: splitting (52) gives:
% 159.05/27.90 | |
% 159.05/27.90 | | Case 1:
% 159.05/27.90 | | |
% 159.05/27.90 | | | (53) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | ALPHA: (53) implies:
% 159.05/27.90 | | | (54) all_58_4 = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | COMBINE_EQS: (40), (54) imply:
% 159.05/27.90 | | | (55) e3 = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | COMBINE_EQS: (9), (55) imply:
% 159.05/27.90 | | | (56) all_58_12 = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (12), (13), (14), (15),
% 159.05/27.90 | | | (16), (17), (19), (20), (21), (22), (23), (26), (27), (28),
% 159.05/27.90 | | | (29), (30), (31), (32), (35), (36), (37), (38), (41), (42),
% 159.05/27.90 | | | (43), (44), (46), (47), (48), (49), (50), (51), (56) are
% 159.05/27.90 | | | inconsistent by sub-proof #574.
% 159.05/27.90 | | |
% 159.05/27.90 | | Case 2:
% 159.05/27.90 | | |
% 159.05/27.90 | | | (57) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | REF_CLOSE: (9), (18), (23), (27), (28), (33), (38), (39), (47), (48), (57)
% 159.05/27.90 | | | are inconsistent by sub-proof #518.
% 159.05/27.90 | | |
% 159.05/27.90 | | End of split
% 159.05/27.90 | |
% 159.05/27.90 | Case 2:
% 159.05/27.90 | |
% 159.05/27.90 | | (58) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 159.05/27.90 | | e1)
% 159.05/27.90 | |
% 159.05/27.90 | | BETA: splitting (58) gives:
% 159.05/27.90 | |
% 159.05/27.90 | | Case 1:
% 159.05/27.90 | | |
% 159.05/27.90 | | | (59) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | ALPHA: (59) implies:
% 159.05/27.90 | | | (60) all_58_8 = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | COMBINE_EQS: (12), (60) imply:
% 159.05/27.90 | | | (61) e3 = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | COMBINE_EQS: (9), (61) imply:
% 159.05/27.90 | | | (62) all_58_12 = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (12), (13), (14), (15),
% 159.05/27.90 | | | (16), (17), (19), (20), (21), (22), (23), (26), (27), (28),
% 159.05/27.90 | | | (29), (30), (31), (32), (35), (36), (37), (38), (41), (42),
% 159.05/27.90 | | | (43), (44), (46), (47), (48), (49), (50), (51), (62) are
% 159.05/27.90 | | | inconsistent by sub-proof #574.
% 159.05/27.90 | | |
% 159.05/27.90 | | Case 2:
% 159.05/27.90 | | |
% 159.05/27.90 | | | (63) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | ALPHA: (63) implies:
% 159.05/27.90 | | | (64) all_58_14 = e1
% 159.05/27.90 | | |
% 159.05/27.90 | | | BETA: splitting (24) gives:
% 159.05/27.90 | | |
% 159.05/27.90 | | | Case 1:
% 159.05/27.90 | | | |
% 159.05/27.90 | | | | (65) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 159.05/27.90 | | | | e2) = e2)
% 159.05/27.90 | | | |
% 159.05/27.90 | | | | BETA: splitting (65) gives:
% 159.05/27.90 | | | |
% 159.05/27.90 | | | | Case 1:
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | | (66) all_58_12 = e2 & op(e0, e3) = e2
% 159.05/27.90 | | | | |
% 159.05/27.90 | | | | | ALPHA: (66) implies:
% 159.05/27.90 | | | | | (67) all_58_12 = e2
% 159.05/27.90 | | | | |
% 159.05/27.91 | | | | | REF_CLOSE: (13), (18), (19), (22), (27), (28), (47), (48), (49), (67)
% 159.05/27.91 | | | | | are inconsistent by sub-proof #1067.
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | Case 2:
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | (68) all_58_13 = e2 & op(e0, e2) = e2
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | ALPHA: (68) implies:
% 159.05/27.91 | | | | | (69) all_58_13 = e2
% 159.05/27.91 | | | | | (70) op(e0, e2) = e2
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | BETA: splitting (4) gives:
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | Case 1:
% 159.05/27.91 | | | | | |
% 159.05/27.91 | | | | | | (71) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 159.05/27.91 | | | | | | e2) = e1)
% 159.05/27.91 | | | | | |
% 159.05/27.91 | | | | | | BETA: splitting (71) gives:
% 159.05/27.91 | | | | | |
% 159.05/27.91 | | | | | | Case 1:
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | | (72) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | | REF_CLOSE: (6), (9), (18), (23), (27), (28), (38), (39), (47),
% 159.05/27.91 | | | | | | | (48), (72) are inconsistent by sub-proof #517.
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | Case 2:
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | | (73) all_58_3 = e1 & op(e2, e2) = e1
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | | ALPHA: (73) implies:
% 159.05/27.91 | | | | | | | (74) all_58_3 = e1
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | | COMBINE_EQS: (41), (74) imply:
% 159.05/27.91 | | | | | | | (75) e3 = e1
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | | COMBINE_EQS: (9), (75) imply:
% 159.05/27.91 | | | | | | | (76) all_58_12 = e1
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | | REF_CLOSE: (25), (34), (39), (45), (48), (64), (70), (76) are
% 159.05/27.91 | | | | | | | inconsistent by sub-proof #613.
% 159.05/27.91 | | | | | | |
% 159.05/27.91 | | | | | | End of split
% 159.05/27.91 | | | | | |
% 159.05/27.91 | | | | | Case 2:
% 159.05/27.91 | | | | | |
% 159.05/27.91 | | | | | | (77) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 159.05/27.91 | | | | | | e2) = e1)
% 159.05/27.91 | | | | | |
% 159.05/27.91 | | | | | | REF_CLOSE: (11), (38), (69), (77) are inconsistent by sub-proof
% 159.05/27.91 | | | | | | #516.
% 159.05/27.91 | | | | | |
% 159.05/27.91 | | | | | End of split
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | End of split
% 159.05/27.91 | | | |
% 159.05/27.91 | | | Case 2:
% 159.05/27.91 | | | |
% 159.05/27.91 | | | | (78) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 159.05/27.91 | | | | e0) = e2)
% 159.05/27.91 | | | |
% 159.05/27.91 | | | | BETA: splitting (78) gives:
% 159.05/27.91 | | | |
% 159.05/27.91 | | | | Case 1:
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | (79) all_58_14 = e2 & op(e0, e1) = e2
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | REF_CLOSE: (38), (64), (79) are inconsistent by sub-proof #703.
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | Case 2:
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | (80) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | ALPHA: (80) implies:
% 159.05/27.91 | | | | | (81) op(e0, e0) = e2
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | REF_CLOSE: (48), (49), (51), (81) are inconsistent by sub-proof #1382.
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | End of split
% 159.05/27.91 | | | |
% 159.05/27.91 | | | End of split
% 159.05/27.91 | | |
% 159.05/27.91 | | End of split
% 159.05/27.91 | |
% 159.05/27.91 | End of split
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #516 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.91 (2) all_58_7 = e2
% 159.05/27.91 (3) ~ (e2 = e1)
% 159.05/27.91 (4) all_58_13 = e2
% 159.05/27.91
% 159.05/27.91 Begin of proof
% 159.05/27.91 |
% 159.05/27.91 | BETA: splitting (1) gives:
% 159.05/27.91 |
% 159.05/27.91 | Case 1:
% 159.05/27.91 | |
% 159.05/27.91 | | (5) all_58_7 = e1 & op(e1, e2) = e1
% 159.05/27.91 | |
% 159.05/27.91 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1045.
% 159.05/27.91 | |
% 159.05/27.91 | Case 2:
% 159.05/27.91 | |
% 159.05/27.91 | | (6) all_58_13 = e1 & op(e0, e2) = e1
% 159.05/27.91 | |
% 159.05/27.91 | | ALPHA: (6) implies:
% 159.05/27.91 | | (7) all_58_13 = e1
% 159.05/27.91 | |
% 159.05/27.91 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #807.
% 159.05/27.91 | |
% 159.05/27.91 | End of split
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #517 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) all_58_1 = e0
% 159.05/27.91 (2) all_58_12 = e3
% 159.05/27.91 (3) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/27.91 (4) all_58_6 = e1
% 159.05/27.91 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.91 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.91 (6) op(e2, e3) = e2
% 159.05/27.91 (7) ~ (e3 = e1)
% 159.05/27.91 (8) ~ (e2 = e1)
% 159.05/27.91 (9) ~ (e1 = e0)
% 159.05/27.91 (10) all_58_0 = e0
% 159.05/27.91 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.91
% 159.05/27.91 Begin of proof
% 159.05/27.91 |
% 159.05/27.91 | ALPHA: (3) implies:
% 159.05/27.91 | (12) all_58_1 = e1
% 159.05/27.91 |
% 159.05/27.91 | COMBINE_EQS: (1), (12) imply:
% 159.05/27.91 | (13) e1 = e0
% 159.05/27.91 |
% 159.05/27.91 | SIMP: (13) implies:
% 159.05/27.91 | (14) e1 = e0
% 159.05/27.91 |
% 159.05/27.91 | COMBINE_EQS: (4), (14) imply:
% 159.05/27.91 | (15) all_58_6 = e0
% 159.05/27.91 |
% 159.05/27.91 | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (11), (15) are inconsistent by
% 159.05/27.91 | sub-proof #733.
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #518 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) all_58_12 = e3
% 159.05/27.91 (2) all_58_6 = e1
% 159.05/27.91 (3) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.91 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.91 (4) op(e2, e3) = e2
% 159.05/27.91 (5) ~ (e3 = e1)
% 159.05/27.91 (6) all_58_5 = e0
% 159.05/27.91 (7) ~ (e2 = e1)
% 159.05/27.91 (8) ~ (e1 = e0)
% 159.05/27.91 (9) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.91 (10) all_58_0 = e0
% 159.05/27.91 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.91
% 159.05/27.91 Begin of proof
% 159.05/27.91 |
% 159.05/27.91 | ALPHA: (9) implies:
% 159.05/27.91 | (12) all_58_5 = e1
% 159.05/27.91 |
% 159.05/27.91 | COMBINE_EQS: (6), (12) imply:
% 159.05/27.91 | (13) e1 = e0
% 159.05/27.91 |
% 159.05/27.91 | SIMP: (13) implies:
% 159.05/27.91 | (14) e1 = e0
% 159.05/27.91 |
% 159.05/27.91 | COMBINE_EQS: (2), (14) imply:
% 159.05/27.91 | (15) all_58_6 = e0
% 159.05/27.91 |
% 159.05/27.91 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (15) are inconsistent by
% 159.05/27.91 | sub-proof #733.
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #519 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.91 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.91 (2) op(e1, e1) = all_6_2
% 159.05/27.91 (3) ~ (all_52_7 = e3)
% 159.05/27.91 (4) all_58_12 = e3
% 159.05/27.91 (5) op(e3, e3) = all_28_1
% 159.05/27.91 (6) all_58_8 = e3
% 159.05/27.91 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.91 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.91 (8) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.91 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.91 (9) all_58_6 = e1
% 159.05/27.91 (10) op(e2, e3) = all_52_1
% 159.05/27.91 (11) ~ (e3 = e0)
% 159.05/27.91 (12) op(e0, e0) = e0
% 159.05/27.91 (13) ~ (e2 = e0)
% 159.05/27.91 (14) op(e2, e3) = e2
% 159.05/27.91 (15) ~ (e3 = e1)
% 159.05/27.91 (16) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.91 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.91 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.91 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.91 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 159.05/27.91 (19) op(e3, e3) = e1
% 159.05/27.91 (20) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.91 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.91 (21) ~ (e2 = e1)
% 159.05/27.91 (22) ~ (e1 = e0)
% 159.05/27.91 (23) all_58_3 = e3
% 159.05/27.91 (24) ~ (all_6_2 = e2)
% 159.05/27.91 (25) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.91 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.91 e3)
% 159.05/27.91 (26) op(e0, e2) = all_52_7
% 159.05/27.91 (27) op(e3, e3) = all_22_1
% 159.05/27.91 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.91 (29) ~ (e3 = e2)
% 159.05/27.91
% 159.05/27.91 Begin of proof
% 159.05/27.91 |
% 159.05/27.91 | BETA: splitting (18) gives:
% 159.05/27.91 |
% 159.05/27.91 | Case 1:
% 159.05/27.91 | |
% 159.05/27.91 | | (30) all_58_2 = e0 & op(e2, e3) = e0
% 159.05/27.91 | |
% 159.05/27.91 | | ALPHA: (30) implies:
% 159.05/27.91 | | (31) op(e2, e3) = e0
% 159.05/27.91 | |
% 159.05/27.91 | | REF_CLOSE: (13), (14), (28), (31) are inconsistent by sub-proof #1156.
% 159.05/27.91 | |
% 159.05/27.91 | Case 2:
% 159.05/27.91 | |
% 159.05/27.91 | | (32) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.91 | |
% 159.05/27.91 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/27.91 | | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 159.05/27.91 | | (25), (26), (27), (28), (29), (32) are inconsistent by sub-proof
% 159.05/27.91 | | #520.
% 159.05/27.91 | |
% 159.05/27.91 | End of split
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #520 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.91 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.91 (2) op(e1, e1) = all_6_2
% 159.05/27.91 (3) ~ (all_52_7 = e3)
% 159.05/27.91 (4) all_58_12 = e3
% 159.05/27.91 (5) op(e3, e3) = all_28_1
% 159.05/27.91 (6) all_58_8 = e3
% 159.05/27.91 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.91 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.91 (8) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.91 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.91 (9) all_58_6 = e1
% 159.05/27.91 (10) op(e2, e3) = all_52_1
% 159.05/27.91 (11) ~ (e3 = e0)
% 159.05/27.91 (12) op(e0, e0) = e0
% 159.05/27.91 (13) ~ (e2 = e0)
% 159.05/27.91 (14) op(e2, e3) = e2
% 159.05/27.91 (15) ~ (e3 = e1)
% 159.05/27.91 (16) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.91 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.91 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.91 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.91 (18) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.91 (19) op(e3, e3) = e1
% 159.05/27.91 (20) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.91 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.91 (21) ~ (e2 = e1)
% 159.05/27.91 (22) ~ (e1 = e0)
% 159.05/27.91 (23) all_58_3 = e3
% 159.05/27.91 (24) ~ (all_6_2 = e2)
% 159.05/27.91 (25) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.91 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.91 e3)
% 159.05/27.91 (26) op(e0, e2) = all_52_7
% 159.05/27.91 (27) op(e3, e3) = all_22_1
% 159.05/27.91 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.91 (29) ~ (e3 = e2)
% 159.05/27.91
% 159.05/27.91 Begin of proof
% 159.05/27.91 |
% 159.05/27.91 | ALPHA: (18) implies:
% 159.05/27.91 | (30) all_58_3 = e0
% 159.05/27.91 |
% 159.05/27.91 | COMBINE_EQS: (23), (30) imply:
% 159.05/27.91 | (31) e3 = e0
% 159.05/27.91 |
% 159.05/27.91 | SIMP: (31) implies:
% 159.05/27.91 | (32) e3 = e0
% 159.05/27.91 |
% 159.05/27.91 | COMBINE_EQS: (4), (32) imply:
% 159.05/27.91 | (33) all_58_12 = e0
% 159.05/27.91 |
% 159.05/27.91 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.05/27.91 | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 159.05/27.91 | (26), (27), (28), (29), (33) are inconsistent by sub-proof #523.
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #521 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) all_58_15 = e0
% 159.05/27.91 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.91 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.91 (3) op(e1, e1) = all_6_2
% 159.05/27.91 (4) ~ (all_52_7 = e3)
% 159.05/27.91 (5) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/27.91 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.91 (6) op(e3, e3) = all_28_1
% 159.05/27.91 (7) all_58_8 = e3
% 159.05/27.91 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.91 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.91 (9) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.91 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.91 (10) all_58_6 = e1
% 159.05/27.91 (11) op(e2, e3) = all_52_1
% 159.05/27.91 (12) ~ (all_52_13 = e3)
% 159.05/27.91 (13) ~ (e3 = e0)
% 159.05/27.91 (14) op(e0, e0) = e0
% 159.05/27.91 (15) ~ (e2 = e0)
% 159.05/27.91 (16) op(e2, e0) = all_52_13
% 159.05/27.91 (17) op(e2, e3) = e2
% 159.05/27.91 (18) ~ (e3 = e1)
% 159.05/27.91 (19) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.91 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.91 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.91 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.91 (21) op(e3, e3) = e1
% 159.05/27.91 (22) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.91 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.91 (23) ~ (e2 = e1)
% 159.05/27.91 (24) ~ (e1 = e0)
% 159.05/27.91 (25) all_58_3 = e3
% 159.05/27.91 (26) ~ (all_6_2 = e2)
% 159.05/27.91 (27) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.91 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.91 e3)
% 159.05/27.91 (28) all_58_11 = e0
% 159.05/27.91 (29) all_58_9 = e2
% 159.05/27.91 (30) op(e0, e2) = all_52_7
% 159.05/27.91 (31) op(e3, e3) = all_22_1
% 159.05/27.91 (32) all_58_0 = e0
% 159.05/27.91 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.91 (34) ~ (e3 = e2)
% 159.05/27.91
% 159.05/27.91 Begin of proof
% 159.05/27.91 |
% 159.05/27.91 | BETA: splitting (8) gives:
% 159.05/27.91 |
% 159.05/27.91 | Case 1:
% 159.05/27.91 | |
% 159.05/27.91 | | (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 159.05/27.91 | | e3)
% 159.05/27.91 | |
% 159.05/27.91 | | REF_CLOSE: (11), (13), (17), (32), (33), (34), (35) are inconsistent by
% 159.05/27.91 | | sub-proof #1158.
% 159.05/27.91 | |
% 159.05/27.91 | Case 2:
% 159.05/27.91 | |
% 159.05/27.91 | | (36) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 159.05/27.91 | | e3)
% 159.05/27.91 | |
% 159.05/27.91 | | BETA: splitting (36) gives:
% 159.05/27.91 | |
% 159.05/27.91 | | Case 1:
% 159.05/27.91 | | |
% 159.05/27.91 | | | (37) all_58_6 = e3 & op(e1, e3) = e3
% 159.05/27.91 | | |
% 159.05/27.91 | | | REF_CLOSE: (10), (18), (37) are inconsistent by sub-proof #1335.
% 159.05/27.91 | | |
% 159.05/27.91 | | Case 2:
% 159.05/27.91 | | |
% 159.05/27.91 | | | (38) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.91 | | |
% 159.05/27.91 | | | ALPHA: (38) implies:
% 159.05/27.91 | | | (39) all_58_12 = e3
% 159.05/27.91 | | |
% 159.05/27.91 | | | BETA: splitting (5) gives:
% 159.05/27.91 | | |
% 159.05/27.91 | | | Case 1:
% 159.05/27.91 | | | |
% 159.05/27.91 | | | | (40) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 159.05/27.91 | | | | = e3)
% 159.05/27.91 | | | |
% 159.05/27.91 | | | | REF_CLOSE: (8), (10), (11), (12), (13), (16), (17), (18), (29), (32),
% 159.05/27.91 | | | | (33), (34), (39), (40) are inconsistent by sub-proof #524.
% 159.05/27.91 | | | |
% 159.05/27.91 | | | Case 2:
% 159.05/27.91 | | | |
% 159.05/27.91 | | | | (41) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 159.05/27.91 | | | | e0) = e3)
% 159.05/27.91 | | | |
% 159.05/27.91 | | | | BETA: splitting (41) gives:
% 159.05/27.91 | | | |
% 159.05/27.91 | | | | Case 1:
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | (42) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 159.05/27.91 | | | | | (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 159.05/27.91 | | | | | (26), (27), (28), (30), (31), (33), (34), (39), (42) are
% 159.05/27.91 | | | | | inconsistent by sub-proof #522.
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | Case 2:
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | (43) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | ALPHA: (43) implies:
% 159.05/27.91 | | | | | (44) all_58_15 = e3
% 159.05/27.91 | | | | | (45) op(e0, e0) = e3
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | COMBINE_EQS: (1), (44) imply:
% 159.05/27.91 | | | | | (46) e3 = e0
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | SIMP: (46) implies:
% 159.05/27.91 | | | | | (47) e3 = e0
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | COMBINE_EQS: (39), (47) imply:
% 159.05/27.91 | | | | | (48) all_58_12 = e0
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | | REF_CLOSE: (6), (8), (10), (11), (13), (14), (17), (18), (21), (24),
% 159.05/27.91 | | | | | (31), (33), (34), (45), (48) are inconsistent by sub-proof
% 159.05/27.91 | | | | | #546.
% 159.05/27.91 | | | | |
% 159.05/27.91 | | | | End of split
% 159.05/27.91 | | | |
% 159.05/27.91 | | | End of split
% 159.05/27.91 | | |
% 159.05/27.91 | | End of split
% 159.05/27.91 | |
% 159.05/27.91 | End of split
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #522 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.91 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.91 (2) op(e1, e1) = all_6_2
% 159.05/27.91 (3) ~ (all_52_7 = e3)
% 159.05/27.91 (4) all_58_12 = e3
% 159.05/27.91 (5) op(e3, e3) = all_28_1
% 159.05/27.91 (6) all_58_8 = e3
% 159.05/27.91 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.91 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.91 (8) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.91 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.91 (9) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.91 (10) all_58_6 = e1
% 159.05/27.91 (11) op(e2, e3) = all_52_1
% 159.05/27.91 (12) ~ (e3 = e0)
% 159.05/27.91 (13) op(e0, e0) = e0
% 159.05/27.91 (14) ~ (e2 = e0)
% 159.05/27.91 (15) op(e2, e3) = e2
% 159.05/27.91 (16) ~ (e3 = e1)
% 159.05/27.91 (17) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.91 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.91 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.91 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.91 (19) op(e3, e3) = e1
% 159.05/27.91 (20) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.91 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.91 (21) ~ (e2 = e1)
% 159.05/27.91 (22) ~ (e1 = e0)
% 159.05/27.91 (23) all_58_3 = e3
% 159.05/27.91 (24) ~ (all_6_2 = e2)
% 159.05/27.91 (25) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.91 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.91 e3)
% 159.05/27.91 (26) all_58_11 = e0
% 159.05/27.91 (27) op(e0, e2) = all_52_7
% 159.05/27.91 (28) op(e3, e3) = all_22_1
% 159.05/27.91 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.91 (30) ~ (e3 = e2)
% 159.05/27.91
% 159.05/27.91 Begin of proof
% 159.05/27.91 |
% 159.05/27.91 | ALPHA: (9) implies:
% 159.05/27.91 | (31) all_58_11 = e3
% 159.05/27.91 |
% 159.05/27.91 | COMBINE_EQS: (26), (31) imply:
% 159.05/27.91 | (32) e3 = e0
% 159.05/27.91 |
% 159.05/27.91 | SIMP: (32) implies:
% 159.05/27.91 | (33) e3 = e0
% 159.05/27.91 |
% 159.05/27.91 | COMBINE_EQS: (4), (33) imply:
% 159.05/27.91 | (34) all_58_12 = e0
% 159.05/27.91 |
% 159.05/27.91 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 159.05/27.91 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 159.05/27.91 | (27), (28), (29), (30), (34) are inconsistent by sub-proof #523.
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #523 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.91 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.91 (2) op(e1, e1) = all_6_2
% 159.05/27.91 (3) ~ (all_52_7 = e3)
% 159.05/27.91 (4) op(e3, e3) = all_28_1
% 159.05/27.91 (5) all_58_8 = e3
% 159.05/27.91 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.91 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.91 (7) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.91 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.91 (8) all_58_12 = e0
% 159.05/27.91 (9) all_58_6 = e1
% 159.05/27.91 (10) op(e2, e3) = all_52_1
% 159.05/27.91 (11) ~ (e3 = e0)
% 159.05/27.91 (12) op(e0, e0) = e0
% 159.05/27.91 (13) ~ (e2 = e0)
% 159.05/27.91 (14) op(e2, e3) = e2
% 159.05/27.91 (15) ~ (e3 = e1)
% 159.05/27.91 (16) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.91 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.91 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.91 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.91 (18) op(e3, e3) = e1
% 159.05/27.91 (19) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.91 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.91 (20) ~ (e2 = e1)
% 159.05/27.91 (21) ~ (e1 = e0)
% 159.05/27.91 (22) all_58_3 = e3
% 159.05/27.91 (23) ~ (all_6_2 = e2)
% 159.05/27.91 (24) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.91 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.91 e3)
% 159.05/27.91 (25) op(e0, e2) = all_52_7
% 159.05/27.91 (26) op(e3, e3) = all_22_1
% 159.05/27.91 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.91 (28) ~ (e3 = e2)
% 159.05/27.91
% 159.05/27.91 Begin of proof
% 159.05/27.91 |
% 159.05/27.91 | BETA: splitting (24) gives:
% 159.05/27.91 |
% 159.05/27.91 | Case 1:
% 159.05/27.91 | |
% 159.05/27.91 | | (29) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 159.05/27.91 | | e3)
% 159.05/27.91 | |
% 159.05/27.91 | | REF_CLOSE: (3), (8), (11), (25), (27), (29) are inconsistent by sub-proof
% 159.05/27.91 | | #967.
% 159.05/27.91 | |
% 159.05/27.91 | Case 2:
% 159.05/27.91 | |
% 159.05/27.91 | | (30) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.91 | | e3)
% 159.05/27.91 | |
% 159.05/27.91 | | BETA: splitting (30) gives:
% 159.05/27.91 | |
% 159.05/27.91 | | Case 1:
% 159.05/27.91 | | |
% 159.05/27.91 | | | (31) all_58_14 = e3 & op(e0, e1) = e3
% 159.05/27.91 | | |
% 159.05/27.91 | | | ALPHA: (31) implies:
% 159.05/27.91 | | | (32) all_58_14 = e3
% 159.05/27.91 | | |
% 159.05/27.91 | | | REF_CLOSE: (1), (2), (5), (7), (11), (13), (14), (15), (16), (17), (19),
% 159.05/27.91 | | | (20), (21), (22), (23), (27), (28), (32) are inconsistent by
% 159.05/27.91 | | | sub-proof #780.
% 159.05/27.91 | | |
% 159.05/27.91 | | Case 2:
% 159.05/27.91 | | |
% 159.05/27.91 | | | (33) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.91 | | |
% 159.05/27.91 | | | ALPHA: (33) implies:
% 159.05/27.91 | | | (34) op(e0, e0) = e3
% 159.05/27.91 | | |
% 159.05/27.91 | | | REF_CLOSE: (4), (6), (8), (9), (10), (11), (12), (14), (15), (18), (21),
% 159.05/27.91 | | | (26), (27), (28), (34) are inconsistent by sub-proof #546.
% 159.05/27.91 | | |
% 159.05/27.91 | | End of split
% 159.05/27.91 | |
% 159.05/27.91 | End of split
% 159.05/27.91 |
% 159.05/27.91 End of proof
% 159.05/27.91
% 159.05/27.91 Sub-proof #524 shows that the following formulas are inconsistent:
% 159.05/27.91 ----------------------------------------------------------------
% 159.05/27.91 (1) all_58_12 = e3
% 159.05/27.92 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.92 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.92 (3) all_58_6 = e1
% 159.05/27.92 (4) op(e2, e3) = all_52_1
% 159.05/27.92 (5) ~ (all_52_13 = e3)
% 159.05/27.92 (6) ~ (e3 = e0)
% 159.05/27.92 (7) op(e2, e0) = all_52_13
% 159.05/27.92 (8) op(e2, e3) = e2
% 159.05/27.92 (9) ~ (e3 = e1)
% 159.05/27.92 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 159.05/27.92 (11) all_58_9 = e2
% 159.05/27.92 (12) all_58_0 = e0
% 159.05/27.92 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.92 (14) ~ (e3 = e2)
% 159.05/27.92
% 159.05/27.92 Begin of proof
% 159.05/27.92 |
% 159.05/27.92 | BETA: splitting (10) gives:
% 159.05/27.92 |
% 159.05/27.92 | Case 1:
% 159.05/27.92 | |
% 159.05/27.92 | | (15) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.92 | |
% 159.05/27.92 | | ALPHA: (15) implies:
% 159.05/27.92 | | (16) all_58_9 = e3
% 159.05/27.92 | |
% 159.05/27.92 | | COMBINE_EQS: (11), (16) imply:
% 159.05/27.92 | | (17) e3 = e2
% 159.05/27.92 | |
% 159.05/27.92 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (12), (13), (14), (17) are
% 159.05/27.92 | | inconsistent by sub-proof #698.
% 159.05/27.92 | |
% 159.05/27.92 | Case 2:
% 159.05/27.92 | |
% 159.05/27.92 | | (18) all_58_10 = e3 & op(e2, e0) = e3
% 159.05/27.92 | |
% 159.05/27.92 | | ALPHA: (18) implies:
% 159.05/27.92 | | (19) op(e2, e0) = e3
% 159.05/27.92 | |
% 159.05/27.92 | | REF_CLOSE: (5), (7), (13), (19) are inconsistent by sub-proof #1364.
% 159.05/27.92 | |
% 159.05/27.92 | End of split
% 159.05/27.92 |
% 159.05/27.92 End of proof
% 159.05/27.92
% 159.05/27.92 Sub-proof #525 shows that the following formulas are inconsistent:
% 159.05/27.92 ----------------------------------------------------------------
% 159.05/27.92 (1) all_58_15 = e3
% 159.05/27.92 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.92 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.92 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.92 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.92 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.92 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.92 (6) op(e1, e1) = all_6_2
% 159.05/27.92 (7) ~ (all_52_11 = e3)
% 159.05/27.92 (8) op(e3, e3) = all_28_1
% 159.05/27.92 (9) all_58_8 = e3
% 159.05/27.92 (10) all_58_0 = e1
% 159.05/27.92 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.92 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.92 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.92 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.92 (13) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.92 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.92 (14) all_58_12 = e0
% 159.05/27.92 (15) op(e3, e2) = all_52_4
% 159.05/27.92 (16) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/27.92 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/27.92 (17) op(e2, e3) = all_52_1
% 159.05/27.92 (18) all_54_2 = all_52_8
% 159.05/27.92 (19) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.92 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.92 (20) ~ (all_52_8 = all_52_9)
% 159.05/27.92 (21) ~ (e3 = e0)
% 159.05/27.92 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.92 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.92 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.92 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.92 (24) ~ (all_52_9 = all_52_13)
% 159.05/27.92 (25) op(e0, e0) = e0
% 159.05/27.92 (26) ~ (e2 = e0)
% 159.05/27.92 (27) ~ (all_52_9 = e3)
% 159.05/27.92 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.92 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.92 (29) op(e2, e3) = e2
% 159.05/27.92 (30) ~ (e3 = e1)
% 159.05/27.92 (31) op(e1, e2) = all_52_6
% 159.05/27.92 (32) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.92 (33) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.92 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.92 (34) all_54_7 = all_52_13
% 159.05/27.92 (35) op(e3, e3) = e1
% 159.05/27.92 (36) ~ (all_52_9 = all_52_11)
% 159.05/27.92 (37) ~ (all_52_4 = e3)
% 159.05/27.92 (38) all_54_6 = all_52_9
% 159.05/27.92 (39) ~ (e2 = e1)
% 159.05/27.92 (40) ~ (all_52_8 = all_52_11)
% 159.05/27.92 (41) ~ (all_52_13 = e0)
% 159.05/27.92 (42) ~ (e1 = e0)
% 159.05/27.92 (43) all_58_3 = e3
% 159.05/27.92 (44) ~ (all_6_2 = e2)
% 159.05/27.92 (45) ~ (all_52_9 = e2)
% 159.05/27.92 (46) ~ (all_52_8 = e3)
% 159.05/27.92 (47) all_54_14 = all_52_11
% 159.05/27.92 (48) op(e1, e3) = e1
% 159.05/27.92 (49) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.92 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.92 (50) op(e3, e3) = all_22_1
% 159.05/27.92 (51) ~ (all_52_8 = e1)
% 159.05/27.92 (52) ~ (all_52_6 = e3)
% 159.05/27.92 (53) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.92 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.92 (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.92 (55) ~ (e3 = e2)
% 159.05/27.92 (56) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/27.92 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.92 (57) all_54_7 = e1 | all_54_7 = e0
% 159.05/27.92 (58) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.92 (59) op(e0, e0) = e3
% 159.05/27.92 (60) all_58_10 = e0 & op(e2, e0) = e0
% 159.05/27.92
% 159.05/27.92 Begin of proof
% 159.05/27.92 |
% 159.05/27.92 | ALPHA: (60) implies:
% 159.05/27.92 | (61) all_58_10 = e0
% 159.05/27.92 |
% 159.05/27.92 | BETA: splitting (11) gives:
% 159.05/27.92 |
% 159.05/27.92 | Case 1:
% 159.05/27.92 | |
% 159.05/27.92 | | (62) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 159.05/27.92 | | e3)
% 159.05/27.92 | |
% 159.05/27.92 | | REF_CLOSE: (8), (17), (25), (29), (35), (42), (50), (54), (55), (59), (62)
% 159.05/27.92 | | are inconsistent by sub-proof #583.
% 159.05/27.92 | |
% 159.05/27.92 | Case 2:
% 159.05/27.92 | |
% 159.05/27.92 | | (63) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 159.05/27.92 | | e3)
% 159.05/27.92 | |
% 159.05/27.92 | | BETA: splitting (63) gives:
% 159.05/27.92 | |
% 159.05/27.92 | | Case 1:
% 159.05/27.92 | | |
% 159.05/27.92 | | | (64) all_58_6 = e3 & op(e1, e3) = e3
% 159.05/27.92 | | |
% 159.05/27.92 | | | ALPHA: (64) implies:
% 159.05/27.92 | | | (65) all_58_6 = e3
% 159.05/27.92 | | |
% 159.05/27.92 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 159.05/27.92 | | | (14), (15), (16), (17), (19), (21), (22), (23), (25), (26),
% 159.05/27.92 | | | (28), (29), (30), (31), (33), (35), (37), (39), (42), (43),
% 159.05/27.92 | | | (44), (49), (50), (52), (53), (54), (55), (56), (59), (61),
% 159.05/27.92 | | | (65) are inconsistent by sub-proof #528.
% 159.05/27.92 | | |
% 159.05/27.92 | | Case 2:
% 159.05/27.92 | | |
% 159.05/27.92 | | | (66) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.92 | | |
% 159.05/27.92 | | | ALPHA: (66) implies:
% 159.05/27.92 | | | (67) all_58_12 = e3
% 159.05/27.92 | | |
% 159.05/27.92 | | | REF_CLOSE: (2), (7), (10), (18), (20), (21), (22), (24), (26), (27), (29),
% 159.05/27.92 | | | (32), (34), (36), (38), (40), (41), (42), (45), (46), (47),
% 159.05/27.92 | | | (48), (51), (53), (54), (57), (58), (67) are inconsistent by
% 159.05/27.92 | | | sub-proof #533.
% 159.05/27.92 | | |
% 159.05/27.92 | | End of split
% 159.05/27.92 | |
% 159.05/27.92 | End of split
% 159.05/27.92 |
% 159.05/27.92 End of proof
% 159.05/27.92
% 159.05/27.92 Sub-proof #526 shows that the following formulas are inconsistent:
% 159.05/27.92 ----------------------------------------------------------------
% 159.05/27.92 (1) all_58_15 = e3
% 159.05/27.92 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.92 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.92 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.92 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.92 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.92 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.92 (6) op(e1, e1) = all_6_2
% 159.05/27.92 (7) ~ (all_52_11 = e3)
% 159.05/27.92 (8) op(e3, e3) = all_28_1
% 159.05/27.92 (9) all_58_8 = e3
% 159.05/27.92 (10) all_58_0 = e1
% 159.05/27.92 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.92 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.92 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.92 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.92 (13) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.92 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.92 (14) all_58_12 = e0
% 159.05/27.92 (15) op(e3, e2) = all_52_4
% 159.05/27.92 (16) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/27.92 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/27.92 (17) op(e2, e3) = all_52_1
% 159.05/27.92 (18) all_54_2 = all_52_8
% 159.05/27.92 (19) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.92 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.92 (20) ~ (all_52_8 = all_52_9)
% 159.05/27.92 (21) ~ (e3 = e0)
% 159.05/27.92 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.92 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.92 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.92 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.92 (24) ~ (all_52_9 = all_52_13)
% 159.05/27.92 (25) op(e0, e0) = e0
% 159.05/27.92 (26) ~ (e2 = e0)
% 159.05/27.92 (27) ~ (all_52_9 = e3)
% 159.05/27.92 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.92 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.92 (29) op(e2, e3) = e2
% 159.05/27.92 (30) ~ (e3 = e1)
% 159.05/27.92 (31) op(e1, e2) = all_52_6
% 159.05/27.92 (32) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.92 (33) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.92 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.92 (34) all_54_7 = all_52_13
% 159.05/27.92 (35) op(e3, e3) = e1
% 159.05/27.92 (36) all_58_5 = e0
% 159.05/27.92 (37) ~ (all_52_9 = all_52_11)
% 159.05/27.92 (38) all_58_11 = e2
% 159.05/27.92 (39) ~ (all_52_4 = e3)
% 159.05/27.92 (40) all_54_6 = all_52_9
% 159.05/27.92 (41) ~ (e2 = e1)
% 159.05/27.92 (42) ~ (all_52_8 = all_52_11)
% 159.05/27.92 (43) ~ (all_52_13 = e0)
% 159.05/27.92 (44) ~ (e1 = e0)
% 159.05/27.92 (45) all_58_3 = e3
% 159.05/27.92 (46) ~ (all_6_2 = e2)
% 159.05/27.92 (47) ~ (all_52_9 = e2)
% 159.05/27.92 (48) ~ (all_52_8 = e3)
% 159.05/27.92 (49) all_54_14 = all_52_11
% 159.05/27.92 (50) op(e1, e3) = e1
% 159.05/27.92 (51) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.92 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.92 (52) op(e3, e3) = all_22_1
% 159.05/27.92 (53) ~ (all_52_8 = e1)
% 159.05/27.92 (54) ~ (all_52_6 = e3)
% 159.05/27.92 (55) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.92 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.92 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.92 (57) ~ (e3 = e2)
% 159.05/27.92 (58) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/27.92 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.92 (59) all_54_7 = e1 | all_54_7 = e0
% 159.05/27.92 (60) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.92 (61) op(e0, e0) = e3
% 159.05/27.92
% 159.05/27.92 Begin of proof
% 159.05/27.92 |
% 159.05/27.92 | BETA: splitting (5) gives:
% 159.05/27.92 |
% 159.05/27.92 | Case 1:
% 159.05/27.92 | |
% 159.05/27.92 | | (62) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 159.05/27.92 | | e1)
% 159.05/27.92 | |
% 159.05/27.92 | | REF_CLOSE: (29), (30), (41), (45), (56), (62) are inconsistent by sub-proof
% 159.05/27.92 | | #840.
% 159.05/27.92 | |
% 159.05/27.92 | Case 2:
% 159.05/27.92 | |
% 159.05/27.92 | | (63) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 159.05/27.92 | | e1)
% 159.05/27.92 | |
% 159.05/27.92 | | BETA: splitting (63) gives:
% 159.05/27.92 | |
% 159.05/27.92 | | Case 1:
% 159.05/27.92 | | |
% 159.05/27.92 | | | (64) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | ALPHA: (64) implies:
% 159.05/27.92 | | | (65) all_58_5 = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | REF_CLOSE: (36), (44), (65) are inconsistent by sub-proof #935.
% 159.05/27.92 | | |
% 159.05/27.92 | | Case 2:
% 159.05/27.92 | | |
% 159.05/27.92 | | | (66) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | ALPHA: (66) implies:
% 159.05/27.92 | | | (67) all_58_10 = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | BETA: splitting (11) gives:
% 159.05/27.92 | | |
% 159.05/27.92 | | | Case 1:
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | (68) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 159.05/27.92 | | | | = e3)
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | REF_CLOSE: (8), (17), (25), (29), (35), (44), (52), (56), (57), (61),
% 159.05/27.92 | | | | (68) are inconsistent by sub-proof #583.
% 159.05/27.92 | | | |
% 159.05/27.92 | | | Case 2:
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | (69) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 159.05/27.92 | | | | = e3)
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | BETA: splitting (69) gives:
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | Case 1:
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | (70) all_58_6 = e3 & op(e1, e3) = e3
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | ALPHA: (70) implies:
% 159.05/27.92 | | | | | (71) all_58_6 = e3
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 159.05/27.92 | | | | | (14), (15), (16), (17), (19), (21), (22), (23), (25), (26),
% 159.05/27.92 | | | | | (28), (29), (30), (31), (33), (35), (38), (39), (41), (44),
% 159.05/27.92 | | | | | (45), (46), (51), (52), (54), (55), (56), (57), (58), (61),
% 159.05/27.92 | | | | | (67), (71) are inconsistent by sub-proof #527.
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | Case 2:
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | (72) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | ALPHA: (72) implies:
% 159.05/27.92 | | | | | (73) all_58_12 = e3
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | REF_CLOSE: (2), (7), (10), (18), (20), (21), (22), (24), (26), (27),
% 159.05/27.92 | | | | | (29), (32), (34), (37), (40), (42), (43), (44), (47), (48),
% 159.05/27.92 | | | | | (49), (50), (53), (55), (56), (59), (60), (73) are
% 159.05/27.92 | | | | | inconsistent by sub-proof #533.
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | End of split
% 159.05/27.92 | | | |
% 159.05/27.92 | | | End of split
% 159.05/27.92 | | |
% 159.05/27.92 | | End of split
% 159.05/27.92 | |
% 159.05/27.92 | End of split
% 159.05/27.92 |
% 159.05/27.92 End of proof
% 159.05/27.92
% 159.05/27.92 Sub-proof #527 shows that the following formulas are inconsistent:
% 159.05/27.92 ----------------------------------------------------------------
% 159.05/27.92 (1) all_58_15 = e3
% 159.05/27.92 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.92 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.92 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.92 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.92 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.92 (5) op(e1, e1) = all_6_2
% 159.05/27.92 (6) op(e3, e3) = all_28_1
% 159.05/27.92 (7) all_58_8 = e3
% 159.05/27.92 (8) all_58_0 = e1
% 159.05/27.92 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.92 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.92 (10) all_58_6 = e3
% 159.05/27.92 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.92 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.92 (12) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.92 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.92 (13) all_58_12 = e0
% 159.05/27.92 (14) op(e3, e2) = all_52_4
% 159.05/27.92 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/27.92 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/27.92 (16) op(e2, e3) = all_52_1
% 159.05/27.92 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.92 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.92 (18) ~ (e3 = e0)
% 159.05/27.92 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.92 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.92 (20) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.92 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.92 (21) op(e0, e0) = e0
% 159.05/27.92 (22) ~ (e2 = e0)
% 159.05/27.92 (23) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.92 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.92 (24) op(e2, e3) = e2
% 159.05/27.92 (25) ~ (e3 = e1)
% 159.05/27.92 (26) op(e1, e2) = all_52_6
% 159.05/27.92 (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.92 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.92 (28) all_58_10 = e1
% 159.05/27.92 (29) op(e3, e3) = e1
% 159.05/27.92 (30) all_58_11 = e2
% 159.05/27.92 (31) ~ (all_52_4 = e3)
% 159.05/27.92 (32) ~ (e2 = e1)
% 159.05/27.92 (33) ~ (e1 = e0)
% 159.05/27.92 (34) all_58_3 = e3
% 159.05/27.92 (35) ~ (all_6_2 = e2)
% 159.05/27.92 (36) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.92 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.92 (37) op(e3, e3) = all_22_1
% 159.05/27.92 (38) ~ (all_52_6 = e3)
% 159.05/27.92 (39) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.92 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.92 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.92 (41) ~ (e3 = e2)
% 159.05/27.92 (42) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/27.92 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.92 (43) op(e0, e0) = e3
% 159.05/27.92
% 159.05/27.92 Begin of proof
% 159.05/27.92 |
% 159.05/27.92 | BETA: splitting (2) gives:
% 159.05/27.92 |
% 159.05/27.92 | Case 1:
% 159.05/27.92 | |
% 159.05/27.92 | | (44) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 159.05/27.92 | | e1)
% 159.05/27.92 | |
% 159.05/27.92 | | BETA: splitting (44) gives:
% 159.05/27.92 | |
% 159.05/27.92 | | Case 1:
% 159.05/27.92 | | |
% 159.05/27.92 | | | (45) all_58_6 = e1 & op(e1, e3) = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | ALPHA: (45) implies:
% 159.05/27.92 | | | (46) all_58_6 = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | REF_CLOSE: (6), (9), (13), (16), (18), (21), (24), (25), (29), (33), (37),
% 159.05/27.92 | | | (40), (41), (43), (46) are inconsistent by sub-proof #546.
% 159.05/27.92 | | |
% 159.05/27.92 | | Case 2:
% 159.05/27.92 | | |
% 159.05/27.92 | | | (47) all_58_7 = e1 & op(e1, e2) = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | ALPHA: (47) implies:
% 159.05/27.92 | | | (48) all_58_7 = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | BETA: splitting (23) gives:
% 159.05/27.92 | | |
% 159.05/27.92 | | | Case 1:
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | (49) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 159.05/27.92 | | | | = e0)
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | BETA: splitting (49) gives:
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | Case 1:
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | (50) all_58_6 = e0 & op(e1, e3) = e0
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | ALPHA: (50) implies:
% 159.05/27.92 | | | | | (51) all_58_6 = e0
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | REF_CLOSE: (10), (18), (51) are inconsistent by sub-proof #1321.
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | Case 2:
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | (52) all_58_7 = e0 & op(e1, e2) = e0
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | ALPHA: (52) implies:
% 159.05/27.92 | | | | | (53) all_58_7 = e0
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | COMBINE_EQS: (48), (53) imply:
% 159.05/27.92 | | | | | (54) e1 = e0
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | COMBINE_EQS: (28), (54) imply:
% 159.05/27.92 | | | | | (55) all_58_10 = e0
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.05/27.92 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 159.05/27.92 | | | | | (22), (23), (24), (25), (26), (27), (29), (31), (32), (33),
% 159.05/27.92 | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 159.05/27.92 | | | | | (55) are inconsistent by sub-proof #528.
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | End of split
% 159.05/27.92 | | | |
% 159.05/27.92 | | | Case 2:
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | (56) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.92 | | | | = e0)
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | BETA: splitting (56) gives:
% 159.05/27.92 | | | |
% 159.05/27.92 | | | | Case 1:
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | (57) all_58_8 = e0 & op(e1, e1) = e0
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | REF_CLOSE: (7), (18), (57) are inconsistent by sub-proof #598.
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | Case 2:
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | (58) all_58_11 = e0 & op(e1, e0) = e0
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | | REF_CLOSE: (22), (30), (58) are inconsistent by sub-proof #1470.
% 159.05/27.92 | | | | |
% 159.05/27.92 | | | | End of split
% 159.05/27.92 | | | |
% 159.05/27.92 | | | End of split
% 159.05/27.92 | | |
% 159.05/27.92 | | End of split
% 159.05/27.92 | |
% 159.05/27.92 | Case 2:
% 159.05/27.92 | |
% 159.05/27.92 | | (59) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 159.05/27.92 | | e1)
% 159.05/27.92 | |
% 159.05/27.92 | | BETA: splitting (59) gives:
% 159.05/27.92 | |
% 159.05/27.92 | | Case 1:
% 159.05/27.92 | | |
% 159.05/27.92 | | | (60) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | ALPHA: (60) implies:
% 159.05/27.92 | | | (61) all_58_8 = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | COMBINE_EQS: (7), (61) imply:
% 159.05/27.92 | | | (62) e3 = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | COMBINE_EQS: (10), (62) imply:
% 159.05/27.92 | | | (63) all_58_6 = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | REF_CLOSE: (6), (9), (13), (16), (18), (21), (24), (25), (29), (33), (37),
% 159.05/27.92 | | | (40), (41), (43), (63) are inconsistent by sub-proof #546.
% 159.05/27.92 | | |
% 159.05/27.92 | | Case 2:
% 159.05/27.92 | | |
% 159.05/27.92 | | | (64) all_58_11 = e1 & op(e1, e0) = e1
% 159.05/27.92 | | |
% 159.05/27.92 | | | REF_CLOSE: (30), (32), (64) are inconsistent by sub-proof #1455.
% 159.05/27.92 | | |
% 159.05/27.92 | | End of split
% 159.05/27.92 | |
% 159.05/27.92 | End of split
% 159.05/27.92 |
% 159.05/27.92 End of proof
% 159.05/27.92
% 159.05/27.92 Sub-proof #528 shows that the following formulas are inconsistent:
% 159.05/27.92 ----------------------------------------------------------------
% 159.05/27.92 (1) all_58_15 = e3
% 159.05/27.92 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.92 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.92 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.92 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.92 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.93 (5) op(e1, e1) = all_6_2
% 159.05/27.93 (6) op(e3, e3) = all_28_1
% 159.05/27.93 (7) all_58_8 = e3
% 159.05/27.93 (8) all_58_0 = e1
% 159.05/27.93 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.93 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.93 (10) all_58_6 = e3
% 159.05/27.93 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.93 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.93 (12) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.93 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.93 (13) all_58_12 = e0
% 159.05/27.93 (14) op(e3, e2) = all_52_4
% 159.05/27.93 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/27.93 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/27.93 (16) op(e2, e3) = all_52_1
% 159.05/27.93 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.93 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.93 (18) ~ (e3 = e0)
% 159.05/27.93 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.93 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.93 (20) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.93 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.93 (21) op(e0, e0) = e0
% 159.05/27.93 (22) ~ (e2 = e0)
% 159.05/27.93 (23) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.93 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.93 (24) op(e2, e3) = e2
% 159.05/27.93 (25) ~ (e3 = e1)
% 159.05/27.93 (26) op(e1, e2) = all_52_6
% 159.05/27.93 (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.93 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.93 (28) op(e3, e3) = e1
% 159.05/27.93 (29) ~ (all_52_4 = e3)
% 159.05/27.93 (30) ~ (e2 = e1)
% 159.05/27.93 (31) ~ (e1 = e0)
% 159.05/27.93 (32) all_58_3 = e3
% 159.05/27.93 (33) ~ (all_6_2 = e2)
% 159.05/27.93 (34) all_58_10 = e0
% 159.05/27.93 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.93 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.93 (36) op(e3, e3) = all_22_1
% 159.05/27.93 (37) ~ (all_52_6 = e3)
% 159.05/27.93 (38) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.93 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.93 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.93 (40) ~ (e3 = e2)
% 159.05/27.93 (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/27.93 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.93 (42) op(e0, e0) = e3
% 159.05/27.93
% 159.05/27.93 Begin of proof
% 159.05/27.93 |
% 159.05/27.93 | BETA: splitting (4) gives:
% 159.05/27.93 |
% 159.05/27.93 | Case 1:
% 159.05/27.93 | |
% 159.05/27.93 | | (43) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 159.05/27.93 | | e1)
% 159.05/27.93 | |
% 159.05/27.93 | | BETA: splitting (43) gives:
% 159.05/27.93 | |
% 159.05/27.93 | | Case 1:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (44) all_58_2 = e1 & op(e2, e3) = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | ALPHA: (44) implies:
% 159.05/27.93 | | | (45) op(e2, e3) = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (24), (30), (39), (45) are inconsistent by sub-proof #1430.
% 159.05/27.93 | | |
% 159.05/27.93 | | Case 2:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (46) all_58_3 = e1 & op(e2, e2) = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | ALPHA: (46) implies:
% 159.05/27.93 | | | (47) all_58_3 = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | COMBINE_EQS: (32), (47) imply:
% 159.05/27.93 | | | (48) e3 = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | SIMP: (48) implies:
% 159.05/27.93 | | | (49) e3 = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | COMBINE_EQS: (10), (49) imply:
% 159.05/27.93 | | | (50) all_58_6 = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (6), (9), (13), (16), (18), (21), (24), (25), (28), (31), (36),
% 159.05/27.93 | | | (39), (40), (42), (50) are inconsistent by sub-proof #546.
% 159.05/27.93 | | |
% 159.05/27.93 | | End of split
% 159.05/27.93 | |
% 159.05/27.93 | Case 2:
% 159.05/27.93 | |
% 159.05/27.93 | | (51) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 159.05/27.93 | | e1)
% 159.05/27.93 | |
% 159.05/27.93 | | BETA: splitting (51) gives:
% 159.05/27.93 | |
% 159.05/27.93 | | Case 1:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (52) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | ALPHA: (52) implies:
% 159.05/27.93 | | | (53) all_58_5 = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | BETA: splitting (3) gives:
% 159.05/27.93 | | |
% 159.05/27.93 | | | Case 1:
% 159.05/27.93 | | | |
% 159.05/27.93 | | | | (54) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 159.05/27.93 | | | | = e1)
% 159.05/27.93 | | | |
% 159.05/27.93 | | | | BETA: splitting (54) gives:
% 159.05/27.93 | | | |
% 159.05/27.93 | | | | Case 1:
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | (55) all_58_9 = e1 & op(e3, e0) = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | ALPHA: (55) implies:
% 159.05/27.93 | | | | | (56) all_58_9 = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | BETA: splitting (11) gives:
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | Case 1:
% 159.05/27.93 | | | | | |
% 159.05/27.93 | | | | | | (57) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 159.05/27.93 | | | | | | e0) = e2)
% 159.05/27.93 | | | | | |
% 159.05/27.93 | | | | | | REF_CLOSE: (18), (22), (24), (27), (30), (31), (32), (39), (53),
% 159.05/27.93 | | | | | | (56), (57) are inconsistent by sub-proof #580.
% 159.05/27.93 | | | | | |
% 159.05/27.93 | | | | | Case 2:
% 159.05/27.93 | | | | | |
% 159.05/27.93 | | | | | | (58) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 159.05/27.93 | | | | | | op(e0, e0) = e2)
% 159.05/27.93 | | | | | |
% 159.05/27.93 | | | | | | BETA: splitting (58) gives:
% 159.05/27.93 | | | | | |
% 159.05/27.93 | | | | | | Case 1:
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | | (59) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | | ALPHA: (59) implies:
% 159.05/27.93 | | | | | | | (60) all_58_11 = e2
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | | BETA: splitting (35) gives:
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | | Case 1:
% 159.05/27.93 | | | | | | | |
% 159.05/27.93 | | | | | | | | (61) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 159.05/27.93 | | | | | | | | op(e3, e2) = e3)
% 159.05/27.93 | | | | | | | |
% 159.05/27.93 | | | | | | | | REF_CLOSE: (6), (14), (21), (28), (29), (31), (36), (39), (42),
% 159.05/27.93 | | | | | | | | (61) are inconsistent by sub-proof #581.
% 159.05/27.93 | | | | | | | |
% 159.05/27.93 | | | | | | | Case 2:
% 159.05/27.93 | | | | | | | |
% 159.05/27.93 | | | | | | | | (62) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 159.05/27.93 | | | | | | | | op(e3, e0) = e3)
% 159.05/27.93 | | | | | | | |
% 159.05/27.93 | | | | | | | | BETA: splitting (62) gives:
% 159.05/27.93 | | | | | | | |
% 159.05/27.93 | | | | | | | | Case 1:
% 159.05/27.93 | | | | | | | | |
% 159.05/27.93 | | | | | | | | | (63) all_58_4 = e3 & op(e3, e1) = e3
% 159.05/27.93 | | | | | | | | |
% 159.05/27.93 | | | | | | | | | ALPHA: (63) implies:
% 159.05/27.93 | | | | | | | | | (64) all_58_4 = e3
% 159.05/27.93 | | | | | | | | |
% 159.05/27.93 | | | | | | | | | BETA: splitting (41) gives:
% 159.05/27.93 | | | | | | | | |
% 159.05/27.93 | | | | | | | | | Case 1:
% 159.05/27.93 | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | (65) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 159.05/27.93 | | | | | | | | | | op(e3, e2) = e0)
% 159.05/27.93 | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | BETA: splitting (65) gives:
% 159.05/27.93 | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | Case 1:
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | (66) all_58_0 = e0 & op(e3, e3) = e0
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | REF_CLOSE: (4), (8), (24), (25), (30), (31), (32), (34),
% 159.05/27.93 | | | | | | | | | | | (39), (53), (66) are inconsistent by sub-proof
% 159.05/27.93 | | | | | | | | | | | #797.
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | Case 2:
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | (67) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | ALPHA: (67) implies:
% 159.05/27.93 | | | | | | | | | | | (68) all_58_1 = e0
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | BETA: splitting (20) gives:
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | Case 1:
% 159.05/27.93 | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | (69) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 159.05/27.93 | | | | | | | | | | | | & op(e3, e2) = e2)
% 159.05/27.93 | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | BETA: splitting (69) gives:
% 159.05/27.93 | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | Case 1:
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | (70) all_58_0 = e2 & op(e3, e3) = e2
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | ALPHA: (70) implies:
% 159.05/27.93 | | | | | | | | | | | | | (71) all_58_0 = e2
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | COMBINE_EQS: (8), (71) imply:
% 159.05/27.93 | | | | | | | | | | | | | (72) e2 = e1
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | SIMP: (72) implies:
% 159.05/27.93 | | | | | | | | | | | | | (73) e2 = e1
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | COMBINE_EQS: (60), (73) imply:
% 159.05/27.93 | | | | | | | | | | | | | (74) all_58_11 = e1
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (10), (16), (17), (18), (19),
% 159.05/27.93 | | | | | | | | | | | | | (22), (23), (24), (25), (30), (31), (32), (33),
% 159.05/27.93 | | | | | | | | | | | | | (34), (38), (39), (40), (53), (74) are
% 159.05/27.93 | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | Case 2:
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | (75) all_58_1 = e2 & op(e3, e2) = e2
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | REF_CLOSE: (22), (68), (75) are inconsistent by sub-proof
% 159.05/27.93 | | | | | | | | | | | | | #801.
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | End of split
% 159.05/27.93 | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | Case 2:
% 159.05/27.93 | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | (76) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 159.05/27.93 | | | | | | | | | | | | & op(e3, e0) = e2)
% 159.05/27.93 | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | BETA: splitting (76) gives:
% 159.05/27.93 | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | Case 1:
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | (77) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | ALPHA: (77) implies:
% 159.05/27.93 | | | | | | | | | | | | | (78) all_58_4 = e2
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (12), (14), (15), (18),
% 159.05/27.93 | | | | | | | | | | | | | (21), (22), (23), (25), (26), (28), (29), (30),
% 159.05/27.93 | | | | | | | | | | | | | (31), (35), (36), (37), (39), (40), (42), (60),
% 159.05/27.93 | | | | | | | | | | | | | (78) are inconsistent by sub-proof #529.
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | Case 2:
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | (79) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | ALPHA: (79) implies:
% 159.05/27.93 | | | | | | | | | | | | | (80) all_58_9 = e2
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | COMBINE_EQS: (56), (80) imply:
% 159.05/27.93 | | | | | | | | | | | | | (81) e2 = e1
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | SIMP: (81) implies:
% 159.05/27.93 | | | | | | | | | | | | | (82) e2 = e1
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | COMBINE_EQS: (60), (82) imply:
% 159.05/27.93 | | | | | | | | | | | | | (83) all_58_11 = e1
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (10), (16), (17), (18), (19),
% 159.05/27.93 | | | | | | | | | | | | | (22), (23), (24), (25), (30), (31), (32), (33),
% 159.05/27.93 | | | | | | | | | | | | | (34), (38), (39), (40), (53), (83) are
% 159.05/27.93 | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 159.05/27.93 | | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | | End of split
% 159.05/27.93 | | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | End of split
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | End of split
% 159.05/27.93 | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | Case 2:
% 159.05/27.93 | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | (84) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 159.05/27.93 | | | | | | | | | | op(e3, e0) = e0)
% 159.05/27.93 | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | BETA: splitting (84) gives:
% 159.05/27.93 | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | Case 1:
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | (85) all_58_4 = e0 & op(e3, e1) = e0
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | REF_CLOSE: (18), (64), (85) are inconsistent by sub-proof
% 159.05/27.93 | | | | | | | | | | | #1344.
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | Case 2:
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | (86) all_58_9 = e0 & op(e3, e0) = e0
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | | REF_CLOSE: (4), (24), (25), (30), (31), (32), (34), (39),
% 159.05/27.93 | | | | | | | | | | | (53), (56), (86) are inconsistent by sub-proof
% 159.05/27.93 | | | | | | | | | | | #795.
% 159.05/27.93 | | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | | End of split
% 159.05/27.93 | | | | | | | | | |
% 159.05/27.93 | | | | | | | | | End of split
% 159.05/27.93 | | | | | | | | |
% 159.05/27.93 | | | | | | | | Case 2:
% 159.05/27.93 | | | | | | | | |
% 159.05/27.93 | | | | | | | | | (87) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.93 | | | | | | | | |
% 159.05/27.93 | | | | | | | | | REF_CLOSE: (1), (3), (12), (18), (22), (25), (30), (31), (60),
% 159.05/27.93 | | | | | | | | | (87) are inconsistent by sub-proof #530.
% 159.05/27.93 | | | | | | | | |
% 159.05/27.93 | | | | | | | | End of split
% 159.05/27.93 | | | | | | | |
% 159.05/27.93 | | | | | | | End of split
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | Case 2:
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | | (88) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | | ALPHA: (88) implies:
% 159.05/27.93 | | | | | | | (89) op(e0, e0) = e2
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | | REF_CLOSE: (39), (40), (42), (89) are inconsistent by sub-proof
% 159.05/27.93 | | | | | | | #1382.
% 159.05/27.93 | | | | | | |
% 159.05/27.93 | | | | | | End of split
% 159.05/27.93 | | | | | |
% 159.05/27.93 | | | | | End of split
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | Case 2:
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | (90) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | ALPHA: (90) implies:
% 159.05/27.93 | | | | | (91) all_58_10 = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | COMBINE_EQS: (34), (91) imply:
% 159.05/27.93 | | | | | (92) e1 = e0
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | SIMP: (92) implies:
% 159.05/27.93 | | | | | (93) e1 = e0
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | COMBINE_EQS: (53), (93) imply:
% 159.05/27.93 | | | | | (94) all_58_5 = e0
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | REF_CLOSE: (4), (24), (25), (30), (31), (32), (34), (39), (94) are
% 159.05/27.93 | | | | | inconsistent by sub-proof #839.
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | End of split
% 159.05/27.93 | | | |
% 159.05/27.93 | | | Case 2:
% 159.05/27.93 | | | |
% 159.05/27.93 | | | | (95) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 159.05/27.93 | | | | e0) = e1)
% 159.05/27.93 | | | |
% 159.05/27.93 | | | | BETA: splitting (95) gives:
% 159.05/27.93 | | | |
% 159.05/27.93 | | | | Case 1:
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | (96) all_58_11 = e1 & op(e1, e0) = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | ALPHA: (96) implies:
% 159.05/27.93 | | | | | (97) all_58_11 = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | REF_CLOSE: (4), (5), (7), (9), (10), (16), (17), (18), (19), (22),
% 159.05/27.93 | | | | | (23), (24), (25), (30), (31), (32), (33), (34), (38), (39),
% 159.05/27.93 | | | | | (40), (53), (97) are inconsistent by sub-proof #531.
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | Case 2:
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | (98) all_58_15 = e1 & op(e0, e0) = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | ALPHA: (98) implies:
% 159.05/27.93 | | | | | (99) all_58_15 = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | COMBINE_EQS: (1), (99) imply:
% 159.05/27.93 | | | | | (100) e3 = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | COMBINE_EQS: (10), (100) imply:
% 159.05/27.93 | | | | | (101) all_58_6 = e1
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | | REF_CLOSE: (6), (9), (13), (16), (18), (21), (24), (25), (28), (31),
% 159.05/27.93 | | | | | (36), (39), (40), (42), (101) are inconsistent by sub-proof
% 159.05/27.93 | | | | | #546.
% 159.05/27.93 | | | | |
% 159.05/27.93 | | | | End of split
% 159.05/27.93 | | | |
% 159.05/27.93 | | | End of split
% 159.05/27.93 | | |
% 159.05/27.93 | | Case 2:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (102) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (31), (34), (102) are inconsistent by sub-proof #1373.
% 159.05/27.93 | | |
% 159.05/27.93 | | End of split
% 159.05/27.93 | |
% 159.05/27.93 | End of split
% 159.05/27.93 |
% 159.05/27.93 End of proof
% 159.05/27.93
% 159.05/27.93 Sub-proof #529 shows that the following formulas are inconsistent:
% 159.05/27.93 ----------------------------------------------------------------
% 159.05/27.93 (1) all_58_15 = e3
% 159.05/27.93 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.93 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.93 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.93 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.93 (4) op(e3, e3) = all_28_1
% 159.05/27.93 (5) all_58_8 = e3
% 159.05/27.93 (6) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.93 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.93 (7) op(e3, e2) = all_52_4
% 159.05/27.93 (8) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/27.93 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/27.93 (9) ~ (e3 = e0)
% 159.05/27.93 (10) op(e0, e0) = e0
% 159.05/27.93 (11) ~ (e2 = e0)
% 159.05/27.93 (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.93 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.93 (13) ~ (e3 = e1)
% 159.05/27.93 (14) op(e1, e2) = all_52_6
% 159.05/27.93 (15) op(e3, e3) = e1
% 159.05/27.93 (16) all_58_11 = e2
% 159.05/27.93 (17) all_58_4 = e2
% 159.05/27.93 (18) ~ (all_52_4 = e3)
% 159.05/27.93 (19) ~ (e2 = e1)
% 159.05/27.93 (20) ~ (e1 = e0)
% 159.05/27.93 (21) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/27.93 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/27.93 (22) op(e3, e3) = all_22_1
% 159.05/27.93 (23) ~ (all_52_6 = e3)
% 159.05/27.93 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.93 (25) ~ (e3 = e2)
% 159.05/27.93 (26) op(e0, e0) = e3
% 159.05/27.93
% 159.05/27.93 Begin of proof
% 159.05/27.93 |
% 159.05/27.93 | BETA: splitting (21) gives:
% 159.05/27.93 |
% 159.05/27.93 | Case 1:
% 159.05/27.93 | |
% 159.05/27.93 | | (27) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 159.05/27.93 | | e3)
% 159.05/27.93 | |
% 159.05/27.93 | | REF_CLOSE: (4), (7), (10), (15), (18), (20), (22), (24), (26), (27) are
% 159.05/27.93 | | inconsistent by sub-proof #581.
% 159.05/27.93 | |
% 159.05/27.93 | Case 2:
% 159.05/27.93 | |
% 159.05/27.93 | | (28) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 159.05/27.93 | | e3)
% 159.05/27.93 | |
% 159.05/27.93 | | BETA: splitting (28) gives:
% 159.05/27.93 | |
% 159.05/27.93 | | Case 1:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (29) all_58_4 = e3 & op(e3, e1) = e3
% 159.05/27.93 | | |
% 159.05/27.93 | | | ALPHA: (29) implies:
% 159.05/27.93 | | | (30) all_58_4 = e3
% 159.05/27.93 | | |
% 159.05/27.93 | | | COMBINE_EQS: (17), (30) imply:
% 159.05/27.93 | | | (31) e3 = e2
% 159.05/27.93 | | |
% 159.05/27.93 | | | SIMP: (31) implies:
% 159.05/27.93 | | | (32) e3 = e2
% 159.05/27.93 | | |
% 159.05/27.93 | | | COMBINE_EQS: (5), (32) imply:
% 159.05/27.93 | | | (33) all_58_8 = e2
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (2), (8), (9), (11), (12), (13), (14), (16), (19), (20), (23),
% 159.05/27.93 | | | (24), (25), (33) are inconsistent by sub-proof #1068.
% 159.05/27.93 | | |
% 159.05/27.93 | | Case 2:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (34) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (1), (3), (6), (9), (11), (13), (16), (19), (20), (34) are
% 159.05/27.93 | | | inconsistent by sub-proof #530.
% 159.05/27.93 | | |
% 159.05/27.93 | | End of split
% 159.05/27.93 | |
% 159.05/27.93 | End of split
% 159.05/27.93 |
% 159.05/27.93 End of proof
% 159.05/27.93
% 159.05/27.93 Sub-proof #530 shows that the following formulas are inconsistent:
% 159.05/27.93 ----------------------------------------------------------------
% 159.05/27.93 (1) all_58_15 = e3
% 159.05/27.93 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.93 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.93 (3) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.93 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.93 (4) ~ (e3 = e0)
% 159.05/27.93 (5) ~ (e2 = e0)
% 159.05/27.93 (6) ~ (e3 = e1)
% 159.05/27.93 (7) all_58_11 = e2
% 159.05/27.93 (8) ~ (e2 = e1)
% 159.05/27.93 (9) ~ (e1 = e0)
% 159.05/27.93 (10) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.93
% 159.05/27.93 Begin of proof
% 159.05/27.93 |
% 159.05/27.93 | ALPHA: (10) implies:
% 159.05/27.93 | (11) all_58_9 = e3
% 159.05/27.93 |
% 159.05/27.93 | BETA: splitting (2) gives:
% 159.05/27.93 |
% 159.05/27.93 | Case 1:
% 159.05/27.93 | |
% 159.05/27.93 | | (12) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 159.05/27.93 | | e1)
% 159.05/27.93 | |
% 159.05/27.93 | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (11), (12) are inconsistent by
% 159.05/27.93 | | sub-proof #1456.
% 159.05/27.93 | |
% 159.05/27.93 | Case 2:
% 159.05/27.93 | |
% 159.05/27.93 | | (13) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.93 | | e1)
% 159.05/27.93 | |
% 159.05/27.93 | | REF_CLOSE: (1), (6), (7), (8), (13) are inconsistent by sub-proof #1317.
% 159.05/27.93 | |
% 159.05/27.93 | End of split
% 159.05/27.93 |
% 159.05/27.93 End of proof
% 159.05/27.93
% 159.05/27.93 Sub-proof #531 shows that the following formulas are inconsistent:
% 159.05/27.93 ----------------------------------------------------------------
% 159.05/27.93 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.93 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.93 (2) all_58_11 = e1
% 159.05/27.93 (3) op(e1, e1) = all_6_2
% 159.05/27.93 (4) all_58_8 = e3
% 159.05/27.93 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.93 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.93 (6) all_58_6 = e3
% 159.05/27.93 (7) op(e2, e3) = all_52_1
% 159.05/27.93 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.93 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.93 (9) ~ (e3 = e0)
% 159.05/27.93 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.93 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.93 (11) ~ (e2 = e0)
% 159.05/27.93 (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.93 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.93 (13) op(e2, e3) = e2
% 159.05/27.93 (14) ~ (e3 = e1)
% 159.05/27.93 (15) all_58_5 = e1
% 159.05/27.93 (16) ~ (e2 = e1)
% 159.05/27.93 (17) ~ (e1 = e0)
% 159.05/27.93 (18) all_58_3 = e3
% 159.05/27.93 (19) ~ (all_6_2 = e2)
% 159.05/27.93 (20) all_58_10 = e0
% 159.05/27.93 (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.93 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.93 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.93 (23) ~ (e3 = e2)
% 159.05/27.93
% 159.05/27.93 Begin of proof
% 159.05/27.93 |
% 159.05/27.93 | BETA: splitting (12) gives:
% 159.05/27.93 |
% 159.05/27.93 | Case 1:
% 159.05/27.93 | |
% 159.05/27.93 | | (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 159.05/27.93 | | e0)
% 159.05/27.93 | |
% 159.05/27.93 | | BETA: splitting (24) gives:
% 159.05/27.93 | |
% 159.05/27.93 | | Case 1:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (25) all_58_6 = e0 & op(e1, e3) = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (6), (9), (25) are inconsistent by sub-proof #1350.
% 159.05/27.93 | | |
% 159.05/27.93 | | Case 2:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (26) all_58_7 = e0 & op(e1, e2) = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | ALPHA: (26) implies:
% 159.05/27.93 | | | (27) all_58_7 = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (13), (14), (16),
% 159.05/27.93 | | | (17), (19), (21), (22), (23), (27) are inconsistent by
% 159.05/27.93 | | | sub-proof #743.
% 159.05/27.93 | | |
% 159.05/27.93 | | End of split
% 159.05/27.93 | |
% 159.05/27.93 | Case 2:
% 159.05/27.93 | |
% 159.05/27.93 | | (28) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.05/27.93 | | e0)
% 159.05/27.93 | |
% 159.05/27.93 | | BETA: splitting (28) gives:
% 159.05/27.93 | |
% 159.05/27.93 | | Case 1:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (29) all_58_8 = e0 & op(e1, e1) = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | ALPHA: (29) implies:
% 159.05/27.93 | | | (30) all_58_8 = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (4), (9), (30) are inconsistent by sub-proof #781.
% 159.05/27.93 | | |
% 159.05/27.93 | | Case 2:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (31) all_58_11 = e0 & op(e1, e0) = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | ALPHA: (31) implies:
% 159.05/27.93 | | | (32) all_58_11 = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | COMBINE_EQS: (2), (32) imply:
% 159.05/27.93 | | | (33) e1 = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | COMBINE_EQS: (15), (33) imply:
% 159.05/27.93 | | | (34) all_58_5 = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (1), (13), (14), (16), (17), (18), (20), (22), (34) are
% 159.05/27.93 | | | inconsistent by sub-proof #839.
% 159.05/27.93 | | |
% 159.05/27.93 | | End of split
% 159.05/27.93 | |
% 159.05/27.93 | End of split
% 159.05/27.93 |
% 159.05/27.93 End of proof
% 159.05/27.93
% 159.05/27.93 Sub-proof #532 shows that the following formulas are inconsistent:
% 159.05/27.93 ----------------------------------------------------------------
% 159.05/27.93 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.93 (2) ~ (all_52_11 = e3)
% 159.05/27.93 (3) all_58_12 = e3
% 159.05/27.93 (4) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.93 (5) all_58_0 = e1
% 159.05/27.93 (6) ~ (all_52_13 = e3)
% 159.05/27.93 (7) all_54_2 = all_52_8
% 159.05/27.93 (8) ~ (all_52_8 = all_52_9)
% 159.05/27.93 (9) ~ (e3 = e0)
% 159.05/27.93 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.93 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.93 (11) ~ (all_52_9 = all_52_13)
% 159.05/27.93 (12) ~ (e2 = e0)
% 159.05/27.93 (13) ~ (all_52_9 = e3)
% 159.05/27.93 (14) op(e2, e3) = e2
% 159.05/27.93 (15) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.93 (16) all_54_7 = all_52_13
% 159.05/27.93 (17) ~ (all_52_13 = e2)
% 159.05/27.93 (18) ~ (all_52_9 = all_52_11)
% 159.05/27.93 (19) all_54_6 = all_52_9
% 159.05/27.93 (20) ~ (all_52_8 = all_52_11)
% 159.05/27.93 (21) ~ (all_52_13 = e0)
% 159.05/27.93 (22) ~ (e1 = e0)
% 159.05/27.93 (23) ~ (all_52_9 = e2)
% 159.05/27.93 (24) ~ (all_52_8 = e3)
% 159.05/27.93 (25) all_54_14 = all_52_11
% 159.05/27.93 (26) op(e1, e3) = e1
% 159.05/27.93 (27) ~ (all_52_8 = e1)
% 159.05/27.93 (28) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.93 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.93 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.93 (30) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.93
% 159.05/27.93 Begin of proof
% 159.05/27.93 |
% 159.05/27.93 | BETA: splitting (4) gives:
% 159.05/27.93 |
% 159.05/27.93 | Case 1:
% 159.05/27.93 | |
% 159.05/27.93 | | (31) all_54_7 = e3
% 159.05/27.93 | |
% 159.05/27.93 | | COMBINE_EQS: (16), (31) imply:
% 159.05/27.93 | | (32) all_52_13 = e3
% 159.05/27.93 | |
% 159.05/27.93 | | REDUCE: (6), (32) imply:
% 159.05/27.93 | | (33) $false
% 159.05/27.93 | |
% 159.05/27.93 | | CLOSE: (33) is inconsistent.
% 159.05/27.93 | |
% 159.05/27.93 | Case 2:
% 159.05/27.93 | |
% 159.05/27.93 | | (34) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.93 | |
% 159.05/27.93 | | BETA: splitting (34) gives:
% 159.05/27.93 | |
% 159.05/27.93 | | Case 1:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (35) all_54_7 = e2
% 159.05/27.93 | | |
% 159.05/27.93 | | | COMBINE_EQS: (16), (35) imply:
% 159.05/27.93 | | | (36) all_52_13 = e2
% 159.05/27.93 | | |
% 159.05/27.93 | | | REDUCE: (17), (36) imply:
% 159.05/27.93 | | | (37) $false
% 159.05/27.93 | | |
% 159.05/27.93 | | | CLOSE: (37) is inconsistent.
% 159.05/27.93 | | |
% 159.05/27.93 | | Case 2:
% 159.05/27.93 | | |
% 159.05/27.93 | | | (38) all_54_7 = e1 | all_54_7 = e0
% 159.05/27.93 | | |
% 159.05/27.93 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 159.05/27.93 | | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 159.05/27.93 | | | (25), (26), (27), (28), (29), (30), (38) are inconsistent by
% 159.05/27.93 | | | sub-proof #533.
% 159.05/27.93 | | |
% 159.05/27.93 | | End of split
% 159.05/27.93 | |
% 159.05/27.93 | End of split
% 159.05/27.93 |
% 159.05/27.93 End of proof
% 159.05/27.93
% 159.05/27.93 Sub-proof #533 shows that the following formulas are inconsistent:
% 159.05/27.93 ----------------------------------------------------------------
% 159.05/27.93 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.93 (2) ~ (all_52_11 = e3)
% 159.05/27.93 (3) all_58_12 = e3
% 159.05/27.93 (4) all_58_0 = e1
% 159.05/27.93 (5) all_54_2 = all_52_8
% 159.05/27.93 (6) ~ (all_52_8 = all_52_9)
% 159.05/27.93 (7) ~ (e3 = e0)
% 159.05/27.93 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.93 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.93 (9) ~ (all_52_9 = all_52_13)
% 159.05/27.93 (10) ~ (e2 = e0)
% 159.05/27.94 (11) ~ (all_52_9 = e3)
% 159.05/27.94 (12) op(e2, e3) = e2
% 159.05/27.94 (13) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.94 (14) all_54_7 = all_52_13
% 159.05/27.94 (15) ~ (all_52_9 = all_52_11)
% 159.05/27.94 (16) all_54_6 = all_52_9
% 159.05/27.94 (17) ~ (all_52_8 = all_52_11)
% 159.05/27.94 (18) ~ (all_52_13 = e0)
% 159.05/27.94 (19) ~ (e1 = e0)
% 159.05/27.94 (20) ~ (all_52_9 = e2)
% 159.05/27.94 (21) ~ (all_52_8 = e3)
% 159.05/27.94 (22) all_54_14 = all_52_11
% 159.05/27.94 (23) op(e1, e3) = e1
% 159.05/27.94 (24) ~ (all_52_8 = e1)
% 159.05/27.94 (25) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.94 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.94 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.94 (27) all_54_7 = e1 | all_54_7 = e0
% 159.05/27.94 (28) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.94
% 159.05/27.94 Begin of proof
% 159.05/27.94 |
% 159.05/27.94 | BETA: splitting (25) gives:
% 159.05/27.94 |
% 159.05/27.94 | Case 1:
% 159.05/27.94 | |
% 159.05/27.94 | | (29) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.05/27.94 | | e0)
% 159.05/27.94 | |
% 159.05/27.94 | | REF_CLOSE: (4), (10), (12), (19), (26), (29) are inconsistent by sub-proof
% 159.05/27.94 | | #534.
% 159.05/27.94 | |
% 159.05/27.94 | Case 2:
% 159.05/27.94 | |
% 159.05/27.94 | | (30) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.05/27.94 | | e0)
% 159.05/27.94 | |
% 159.05/27.94 | | BETA: splitting (30) gives:
% 159.05/27.94 | |
% 159.05/27.94 | | Case 1:
% 159.05/27.94 | | |
% 159.05/27.94 | | | (31) all_58_6 = e0 & op(e1, e3) = e0
% 159.05/27.94 | | |
% 159.05/27.94 | | | ALPHA: (31) implies:
% 159.05/27.94 | | | (32) all_58_6 = e0
% 159.05/27.94 | | | (33) op(e1, e3) = e0
% 159.05/27.94 | | |
% 159.05/27.94 | | | BETA: splitting (27) gives:
% 159.05/27.94 | | |
% 159.05/27.94 | | | Case 1:
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | (34) all_54_7 = e1
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | COMBINE_EQS: (14), (34) imply:
% 159.05/27.94 | | | | (35) all_52_13 = e1
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | SIMP: (35) implies:
% 159.05/27.94 | | | | (36) all_52_13 = e1
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | REDUCE: (9), (36) imply:
% 159.05/27.94 | | | | (37) ~ (all_52_9 = e1)
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | BETA: splitting (1) gives:
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | Case 1:
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | (38) all_54_6 = e3
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | REF_CLOSE: (11), (16), (38) are inconsistent by sub-proof #1193.
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | Case 2:
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | (39) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | BETA: splitting (39) gives:
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | Case 1:
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | (40) all_54_6 = e2
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | REF_CLOSE: (16), (20), (40) are inconsistent by sub-proof #1192.
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | Case 2:
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | (41) all_54_6 = e1 | all_54_6 = e0
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | BETA: splitting (41) gives:
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | Case 1:
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | (42) all_54_6 = e1
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | REF_CLOSE: (16), (37), (42) are inconsistent by sub-proof #562.
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | Case 2:
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | (43) all_54_6 = e0
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | COMBINE_EQS: (16), (43) imply:
% 159.05/27.94 | | | | | | | (44) all_52_9 = e0
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | SIMP: (44) implies:
% 159.05/27.94 | | | | | | | (45) all_52_9 = e0
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | REDUCE: (6), (45) imply:
% 159.05/27.94 | | | | | | | (46) ~ (all_52_8 = e0)
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | REDUCE: (15), (45) imply:
% 159.05/27.94 | | | | | | | (47) ~ (all_52_11 = e0)
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | SIMP: (47) implies:
% 159.05/27.94 | | | | | | | (48) ~ (all_52_11 = e0)
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | BETA: splitting (13) gives:
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | (49) all_54_2 = e3
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | COMBINE_EQS: (5), (49) imply:
% 159.05/27.94 | | | | | | | | (50) all_52_8 = e3
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | REDUCE: (21), (50) imply:
% 159.05/27.94 | | | | | | | | (51) $false
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | CLOSE: (51) is inconsistent.
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | (52) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | BETA: splitting (52) gives:
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | (53) all_54_2 = e2
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | COMBINE_EQS: (5), (53) imply:
% 159.05/27.94 | | | | | | | | | (54) all_52_8 = e2
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | REDUCE: (17), (54) imply:
% 159.05/27.94 | | | | | | | | | (55) ~ (all_52_11 = e2)
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | SIMP: (55) implies:
% 159.05/27.94 | | | | | | | | | (56) ~ (all_52_11 = e2)
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | BETA: splitting (28) gives:
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | (57) all_54_14 = e3
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | REF_CLOSE: (2), (22), (57) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | #1413.
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | (58) ~ (all_54_14 = e3)
% 159.05/27.94 | | | | | | | | | | (59) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | BETA: splitting (59) gives:
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | (60) all_54_14 = e2
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | REF_CLOSE: (22), (56), (60) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | | #1232.
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | (61) ~ (all_54_14 = e2)
% 159.05/27.94 | | | | | | | | | | | (62) all_54_14 = e1 | all_54_14 = e0
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | BETA: splitting (62) gives:
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | (63) all_54_14 = e1
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | COMBINE_EQS: (22), (63) imply:
% 159.05/27.94 | | | | | | | | | | | | (64) all_52_11 = e1
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | SIMP: (64) implies:
% 159.05/27.94 | | | | | | | | | | | | (65) all_52_11 = e1
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | REDUCE: (2), (65) imply:
% 159.05/27.94 | | | | | | | | | | | | (66) ~ (e3 = e1)
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | SIMP: (66) implies:
% 159.05/27.94 | | | | | | | | | | | | (67) ~ (e3 = e1)
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | REDUCE: (56), (65) imply:
% 159.05/27.94 | | | | | | | | | | | | (68) ~ (e2 = e1)
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | SIMP: (68) implies:
% 159.05/27.94 | | | | | | | | | | | | (69) ~ (e2 = e1)
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | GROUND_INST: instantiating (26) with e0, e1, e3, e1,
% 159.05/27.94 | | | | | | | | | | | | simplifying with (23), (33) gives:
% 159.05/27.94 | | | | | | | | | | | | (70) e1 = e0
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | COMBINE_EQS: (4), (70) imply:
% 159.05/27.94 | | | | | | | | | | | | (71) all_58_0 = e0
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | REF_CLOSE: (3), (8), (12), (19), (26), (32), (67), (69), (71)
% 159.05/27.94 | | | | | | | | | | | | are inconsistent by sub-proof #733.
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | (72) all_54_14 = e0
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | REF_CLOSE: (22), (48), (72) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | | | #1400.
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | End of split
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | End of split
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | End of split
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | (73) all_54_2 = e1 | all_54_2 = e0
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | REF_CLOSE: (5), (24), (46), (73) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | #561.
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | End of split
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | End of split
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | End of split
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | End of split
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | End of split
% 159.05/27.94 | | | |
% 159.05/27.94 | | | Case 2:
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | (74) all_54_7 = e0
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | REF_CLOSE: (14), (18), (74) are inconsistent by sub-proof #1112.
% 159.05/27.94 | | | |
% 159.05/27.94 | | | End of split
% 159.05/27.94 | | |
% 159.05/27.94 | | Case 2:
% 159.05/27.94 | | |
% 159.05/27.94 | | | (75) all_58_12 = e0 & op(e0, e3) = e0
% 159.05/27.94 | | |
% 159.05/27.94 | | | ALPHA: (75) implies:
% 159.05/27.94 | | | (76) all_58_12 = e0
% 159.05/27.94 | | |
% 159.05/27.94 | | | REF_CLOSE: (3), (7), (76) are inconsistent by sub-proof #1463.
% 159.05/27.94 | | |
% 159.05/27.94 | | End of split
% 159.05/27.94 | |
% 159.05/27.94 | End of split
% 159.05/27.94 |
% 159.05/27.94 End of proof
% 159.05/27.94
% 159.05/27.94 Sub-proof #534 shows that the following formulas are inconsistent:
% 159.05/27.94 ----------------------------------------------------------------
% 159.05/27.94 (1) all_58_0 = e1
% 159.05/27.94 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 159.05/27.94 (3) ~ (e2 = e0)
% 159.05/27.94 (4) op(e2, e3) = e2
% 159.05/27.94 (5) ~ (e1 = e0)
% 159.05/27.94 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.94
% 159.05/27.94 Begin of proof
% 159.05/27.94 |
% 159.05/27.94 | BETA: splitting (2) gives:
% 159.05/27.94 |
% 159.05/27.94 | Case 1:
% 159.05/27.94 | |
% 159.05/27.94 | | (7) all_58_0 = e0 & op(e3, e3) = e0
% 159.05/27.94 | |
% 159.05/27.94 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #1520.
% 159.05/27.94 | |
% 159.05/27.94 | Case 2:
% 159.05/27.94 | |
% 159.05/27.94 | | (8) all_58_2 = e0 & op(e2, e3) = e0
% 159.05/27.94 | |
% 159.05/27.94 | | ALPHA: (8) implies:
% 159.05/27.94 | | (9) op(e2, e3) = e0
% 159.05/27.94 | |
% 159.05/27.94 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1156.
% 159.05/27.94 | |
% 159.05/27.94 | End of split
% 159.05/27.94 |
% 159.05/27.94 End of proof
% 159.05/27.94
% 159.05/27.94 Sub-proof #535 shows that the following formulas are inconsistent:
% 159.05/27.94 ----------------------------------------------------------------
% 159.05/27.94 (1) op(e1, e3) = e3
% 159.05/27.94 (2) op(e1, e1) = e3
% 159.05/27.94 (3) op(e1, e1) = all_32_1
% 159.05/27.94 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.05/27.94 (5) all_56_14 = e3
% 159.05/27.94 (6) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.94 (7) ~ (all_52_3 = e1)
% 159.05/27.94 (8) op(e3, e1) = e3
% 159.05/27.94 (9) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/27.94 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/27.94 (10) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.94 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.94 (11) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.94 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.94 (12) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.94 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.94 (13) all_54_13 = all_52_7
% 159.05/27.94 (14) op(e1, e1) = all_6_2
% 159.05/27.94 (15) ~ (all_52_7 = e3)
% 159.05/27.94 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.94 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.94 e1)
% 159.05/27.94 (17) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/27.94 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/27.94 (18) ~ (all_52_6 = all_52_14)
% 159.05/27.94 (19) ~ (all_52_11 = e3)
% 159.05/27.94 (20) ~ (all_52_2 = all_52_3)
% 159.05/27.94 (21) ~ (all_52_4 = all_52_6)
% 159.05/27.94 (22) op(e3, e3) = all_28_1
% 159.05/27.94 (23) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.94 (24) ~ (all_52_7 = all_52_11)
% 159.05/27.94 (25) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 159.05/27.94 (26) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.94 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.94 (27) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.94 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.94 (28) all_58_6 = e3
% 159.05/27.94 (29) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.94 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.94 (30) ~ (all_52_14 = e3)
% 159.05/27.94 (31) all_54_1 = all_52_4
% 159.05/27.94 (32) op(e3, e2) = all_52_4
% 159.05/27.94 (33) ~ (all_4_2 = e2)
% 159.05/27.94 (34) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.05/27.94 (35) op(e2, e3) = all_52_1
% 159.05/27.94 (36) ~ (all_52_13 = e3)
% 159.05/27.94 (37) all_54_2 = all_52_8
% 159.05/27.94 (38) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.94 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.94 (39) ~ (all_52_8 = all_52_9)
% 159.05/27.94 (40) ~ (e3 = e0)
% 159.05/27.94 (41) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.94 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.94 (42) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.94 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.94 (43) ~ (all_52_9 = all_52_13)
% 159.05/27.94 (44) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/27.94 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/27.94 e2)
% 159.05/27.94 (45) ~ (e2 = e0)
% 159.05/27.94 (46) ~ (all_52_9 = e3)
% 159.05/27.94 (47) ~ (all_52_2 = all_52_6)
% 159.05/27.94 (48) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.94 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.94 (49) ~ (all_52_3 = e2)
% 159.05/27.94 (50) op(e2, e0) = all_52_13
% 159.05/27.94 (51) op(e2, e3) = e2
% 159.05/27.94 (52) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.94 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/27.94 (53) ~ (e3 = e1)
% 159.05/27.94 (54) all_56_12 = e1
% 159.05/27.94 (55) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.94 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.94 (56) ~ (all_4_2 = e1)
% 159.05/27.94 (57) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.94 (58) ~ (all_52_3 = all_4_2)
% 159.05/27.94 (59) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.94 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.94 (60) op(e0, e0) = all_4_2
% 159.05/27.94 (61) all_54_8 = all_52_2
% 159.05/27.94 (62) all_54_7 = all_52_13
% 159.05/27.94 (63) ~ (all_52_2 = e3)
% 159.05/27.94 (64) op(e3, e3) = e1
% 159.05/27.94 (65) ~ (all_52_13 = e2)
% 159.05/27.94 (66) all_56_15 = all_4_2
% 159.05/27.94 (67) ~ (all_52_9 = all_52_11)
% 159.05/27.94 (68) ~ (all_52_13 = all_4_2)
% 159.05/27.94 (69) ~ (all_52_2 = e1)
% 159.05/27.94 (70) ~ (all_52_6 = all_52_7)
% 159.05/27.94 (71) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.94 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.94 (72) ~ (all_52_4 = e3)
% 159.05/27.94 (73) all_54_6 = all_52_9
% 159.05/27.94 (74) ~ (e2 = e1)
% 159.05/27.94 (75) ~ (all_52_4 = all_52_7)
% 159.05/27.94 (76) ~ (all_52_8 = all_52_11)
% 159.05/27.94 (77) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.94 (78) ~ (e1 = e0)
% 159.05/27.94 (79) ~ (all_52_2 = e2)
% 159.05/27.94 (80) all_58_4 = e3
% 159.05/27.94 (81) all_58_3 = e3
% 159.05/27.94 (82) op(e3, e1) = all_52_8
% 159.05/27.94 (83) ~ (all_6_2 = e2)
% 159.05/27.94 (84) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.94 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.94 e3)
% 159.05/27.94 (85) all_56_13 = e3
% 159.05/27.94 (86) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/27.94 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/27.94 (87) ~ (all_52_9 = e2)
% 159.05/27.94 (88) ~ (all_52_8 = e3)
% 159.05/27.94 (89) all_54_14 = all_52_11
% 159.05/27.94 (90) ~ (all_52_7 = all_4_2)
% 159.05/27.94 (91) op(e1, e3) = e1
% 159.05/27.94 (92) op(e0, e2) = all_52_7
% 159.05/27.94 (93) op(e1, e0) = all_52_14
% 159.05/27.94 (94) op(e3, e3) = all_22_1
% 159.05/27.94 (95) all_54_15 = all_4_2
% 159.05/27.94 (96) ~ (all_52_8 = e1)
% 159.05/27.94 (97) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.94 (98) ~ (all_52_6 = e3)
% 159.05/27.94 (99) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/27.94 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/27.94 (100) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.94 (101) ~ (all_52_3 = all_52_11)
% 159.05/27.94 (102) ~ (all_52_11 = all_4_2)
% 159.05/27.94 (103) all_54_11 = all_52_14
% 159.05/27.94 (104) ~ (all_52_13 = all_52_14)
% 159.05/27.94 (105) ~ (e3 = e2)
% 159.05/27.94 (106) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.05/27.94 (107) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/27.94 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.94 (108) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 159.05/27.94 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.05/27.94 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 159.05/27.94 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 159.05/27.94 e0)))
% 159.05/27.94 (109) all_54_9 = all_52_6
% 159.05/27.94 (110) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 159.05/27.94 (111) all_54_12 = all_52_3
% 159.05/27.94 (112) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.94 (113) ~ (all_52_14 = all_4_2)
% 159.05/27.94 (114) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.94 (115) ~ (all_52_3 = all_52_7)
% 159.05/27.94
% 159.05/27.94 Begin of proof
% 159.05/27.94 |
% 159.05/27.94 | BETA: splitting (99) gives:
% 159.05/27.94 |
% 159.05/27.94 | Case 1:
% 159.05/27.94 | |
% 159.05/27.94 | | (116) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.05/27.94 | | e0)
% 159.05/27.94 | |
% 159.05/27.94 | | BETA: splitting (116) gives:
% 159.05/27.94 | |
% 159.05/27.94 | | Case 1:
% 159.05/27.94 | | |
% 159.05/27.94 | | | (117) all_58_0 = e0 & op(e3, e3) = e0
% 159.05/27.94 | | |
% 159.05/27.94 | | | ALPHA: (117) implies:
% 159.05/27.94 | | | (118) all_58_0 = e0
% 159.05/27.94 | | |
% 159.05/27.94 | | | BETA: splitting (25) gives:
% 159.05/27.94 | | |
% 159.05/27.94 | | | Case 1:
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | (119) all_54_8 = e3
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | REF_CLOSE: (61), (63), (119) are inconsistent by sub-proof #1425.
% 159.05/27.94 | | | |
% 159.05/27.94 | | | Case 2:
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | (120) ~ (all_54_8 = e3)
% 159.05/27.94 | | | | (121) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | BETA: splitting (121) gives:
% 159.05/27.94 | | | |
% 159.05/27.94 | | | | Case 1:
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | (122) all_54_8 = e2
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | REF_CLOSE: (61), (79), (122) are inconsistent by sub-proof #1231.
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | Case 2:
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | (123) ~ (all_54_8 = e2)
% 159.05/27.94 | | | | | (124) all_54_8 = e1 | all_54_8 = e0
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | BETA: splitting (124) gives:
% 159.05/27.94 | | | | |
% 159.05/27.94 | | | | | Case 1:
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | (125) all_54_8 = e1
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | REF_CLOSE: (61), (69), (125) are inconsistent by sub-proof #1379.
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | Case 2:
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | (126) all_54_8 = e0
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | COMBINE_EQS: (61), (126) imply:
% 159.05/27.94 | | | | | | (127) all_52_2 = e0
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | SIMP: (127) implies:
% 159.05/27.94 | | | | | | (128) all_52_2 = e0
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | REDUCE: (20), (128) imply:
% 159.05/27.94 | | | | | | (129) ~ (all_52_3 = e0)
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | SIMP: (129) implies:
% 159.05/27.94 | | | | | | (130) ~ (all_52_3 = e0)
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | REDUCE: (79), (128) imply:
% 159.05/27.94 | | | | | | (131) ~ (e2 = e0)
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | REDUCE: (69), (128) imply:
% 159.05/27.94 | | | | | | (132) ~ (e1 = e0)
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | BETA: splitting (110) gives:
% 159.05/27.94 | | | | | |
% 159.05/27.94 | | | | | | Case 1:
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | (133) all_54_12 = e3
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | COMBINE_EQS: (111), (133) imply:
% 159.05/27.94 | | | | | | | (134) all_52_3 = e3
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | SIMP: (134) implies:
% 159.05/27.94 | | | | | | | (135) all_52_3 = e3
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | REDUCE: (115), (135) imply:
% 159.05/27.94 | | | | | | | (136) ~ (all_52_7 = e3)
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | REDUCE: (101), (135) imply:
% 159.05/27.94 | | | | | | | (137) ~ (all_52_11 = e3)
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | REDUCE: (58), (135) imply:
% 159.05/27.94 | | | | | | | (138) ~ (all_4_2 = e3)
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | SIMP: (138) implies:
% 159.05/27.94 | | | | | | | (139) ~ (all_4_2 = e3)
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | BETA: splitting (41) gives:
% 159.05/27.94 | | | | | | |
% 159.05/27.94 | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | (140) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 159.05/27.94 | | | | | | | | op(e2, e3) = e1)
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | REF_CLOSE: (51), (74), (78), (100), (118), (140) are
% 159.05/27.94 | | | | | | | | inconsistent by sub-proof #1160.
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | (141) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 159.05/27.94 | | | | | | | | op(e0, e3) = e1)
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | BETA: splitting (141) gives:
% 159.05/27.94 | | | | | | | |
% 159.05/27.94 | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | (142) all_58_6 = e1 & op(e1, e3) = e1
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | ALPHA: (142) implies:
% 159.05/27.94 | | | | | | | | | (143) all_58_6 = e1
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | REF_CLOSE: (28), (53), (143) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | #1073.
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | (144) all_58_12 = e1 & op(e0, e3) = e1
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | ALPHA: (144) implies:
% 159.05/27.94 | | | | | | | | | (145) all_58_12 = e1
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | BETA: splitting (84) gives:
% 159.05/27.94 | | | | | | | | |
% 159.05/27.94 | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | (146) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 159.05/27.94 | | | | | | | | | | e3 & op(e0, e2) = e3)
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | BETA: splitting (146) gives:
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | (147) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | REF_CLOSE: (53), (145), (147) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | | #1278.
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | (148) all_58_13 = e3 & op(e0, e2) = e3
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | REF_CLOSE: (15), (92), (100), (148) are inconsistent by
% 159.05/27.94 | | | | | | | | | | | sub-proof #1449.
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | End of split
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | (149) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 159.05/27.94 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | BETA: splitting (149) gives:
% 159.05/27.94 | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | (150) all_58_14 = e3 & op(e0, e1) = e3
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | ALPHA: (150) implies:
% 159.05/27.94 | | | | | | | | | | | (151) all_58_14 = e3
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | BETA: splitting (17) gives:
% 159.05/27.94 | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | (152) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 159.05/27.94 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | BETA: splitting (152) gives:
% 159.05/27.94 | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | (153) all_58_9 = e3 & op(e3, e0) = e3
% 159.05/27.94 | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | ALPHA: (153) implies:
% 159.05/27.94 | | | | | | | | | | | | | (154) all_58_9 = e3
% 159.05/27.94 | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | BETA: splitting (106) gives:
% 159.05/27.94 | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | (155) all_54_15 = e3
% 159.05/27.94 | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | REF_CLOSE: (95), (139), (155) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | | | | | #1543.
% 159.05/27.94 | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | (156) ~ (all_54_15 = e3)
% 159.05/27.94 | | | | | | | | | | | | | | (157) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.05/27.94 | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 159.05/27.94 | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | (158) all_54_15 = e2
% 159.05/27.94 | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | REF_CLOSE: (33), (95), (158) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | | | | | | #1542.
% 159.05/27.94 | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | (159) ~ (all_54_15 = e2)
% 159.05/27.94 | | | | | | | | | | | | | | | (160) all_54_15 = e1 | all_54_15 = e0
% 159.05/27.94 | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 159.05/27.94 | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | (161) all_54_15 = e1
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | REF_CLOSE: (56), (95), (161) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | | | | | | | #1541.
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | (162) all_54_15 = e0
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (162) imply:
% 159.05/27.94 | | | | | | | | | | | | | | | | (163) all_4_2 = e0
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | SIMP: (163) implies:
% 159.05/27.94 | | | | | | | | | | | | | | | | (164) all_4_2 = e0
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | REDUCE: (90), (164) imply:
% 159.05/27.94 | | | | | | | | | | | | | | | | (165) ~ (all_52_7 = e0)
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | REDUCE: (68), (164) imply:
% 159.05/27.94 | | | | | | | | | | | | | | | | (166) ~ (all_52_13 = e0)
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | REDUCE: (139), (164) imply:
% 159.05/27.94 | | | | | | | | | | | | | | | | (167) ~ (e3 = e0)
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 159.05/27.94 | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | (168) all_54_7 = e3
% 159.05/27.94 | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (62), (168) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | | | | | | | | #1428.
% 159.05/27.94 | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | (169) ~ (all_54_7 = e3)
% 159.05/27.94 | | | | | | | | | | | | | | | | | (170) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.94 | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 159.05/27.94 | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | (171) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 159.05/27.94 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 159.05/27.94 | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 159.05/27.94 | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | (172) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (51), (53), (100), (105),
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | (118), (145), (154), (172) are inconsistent by
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | sub-proof #565.
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | (173) all_58_10 = e2 & op(e2, e0) = e2
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | (174) all_58_10 = e2
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (40), (45), (51), (53), (59), (74), (78),
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | (81), (100), (174) are inconsistent by sub-proof
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | #906.
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.94 | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.94 | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | (175) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 159.05/27.94 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.05/27.94 | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 159.05/27.94 | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | (176) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | (177) all_58_11 = e2
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | | (178) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.94 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (179) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (180) all_58_4 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (74), (78), (81), (83), (100), (105), (151), (180)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #850.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (181) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (182) all_58_5 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | (183) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (184) all_58_6 = e1 & op(e1, e3) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (28), (40), (45), (51), (53),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (59), (74), (78), (80), (81), (83), (100), (105),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (151), (184) are inconsistent by sub-proof #827.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (185) all_58_7 = e1 & op(e1, e2) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (186) all_58_7 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | (187) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_58_1 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (190) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_58_0 = e2 & op(e3, e3) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (118), (191) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_58_1 = e2 & op(e3, e2) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (189), (192) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | #801.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (193) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (51), (53), (80), (100),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (118), (145), (194) are inconsistent by
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #564.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_58_9 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (196) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) e3 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (197) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_6 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (35), (40), (51), (53), (100), (105), (118),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (198) are inconsistent by sub-proof #1125.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (83), (100), (105), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (199) are inconsistent by sub-proof #799.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | (200) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_58_7 = e0 & op(e1, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_58_7 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (26), (27), (28), (35), (40), (41),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (45), (51), (53), (59), (74), (78), (80), (81),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (83), (100), (105), (145), (151), (182), (186),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (202) are inconsistent by sub-proof #563.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_58_13 = e0 & op(e0, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (204) op(e0, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (24), (37), (39), (43),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (46), (57), (62), (65), (67), (73), (76), (87),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (88), (89), (92), (96), (97), (100), (112), (165),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (166), (170), (204) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | #559.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | (205) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (16), (17), (26), (27),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (28), (29), (35), (36), (38), (40), (41), (42),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (50), (51), (53), (59), (71), (74),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (78), (80), (81), (83), (84), (86), (92), (99),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (100), (105), (107), (108), (118), (145), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (154), (206) are inconsistent by sub-proof #556.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (207) all_58_11 = e1 & op(e1, e0) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (177), (207) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | #1455.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | (208) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (209) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (16), (17), (26), (27),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (28), (29), (35), (36), (38), (40), (41), (42),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (44), (45), (50), (51), (53), (59), (71), (74),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (78), (80), (81), (83), (84), (86), (92), (99),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (100), (105), (107), (108), (118), (145), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (154), (209) are inconsistent by sub-proof #556.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (210) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (83), (100), (105), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (210) are inconsistent by sub-proof #803.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (211) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (212) all_58_15 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (213) op(e0, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | (214) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (215) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (216) all_58_4 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (74), (78), (81), (83), (100), (105), (151), (216)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #850.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (217) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (218) all_58_5 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | (219) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_0 = e2 & op(e3, e3) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (118), (220) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | #702.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_1 = e2 & op(e3, e2) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_1 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | (223) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (222), (224) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | #796.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_3 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (226) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (227) e3 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (227) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_58_4 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (15), (16), (27), (40), (45), (51),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (53), (59), (74), (78), (81), (83), (84), (92),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (100), (105), (108), (212), (213), (228) are
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #847.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | (229) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_7 = e0 & op(e1, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_58_7 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (232) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_6 = e1 & op(e1, e3) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (28), (40), (45), (51), (53),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (59), (74), (78), (80), (81), (83), (100), (105),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (151), (233) are inconsistent by sub-proof #827.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_7 = e1 & op(e1, e2) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_58_7 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (26), (27), (28), (35), (40), (41),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (51), (53), (59), (74), (78), (80), (81),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (100), (105), (145), (151), (218), (231),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) are inconsistent by sub-proof #563.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (236) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_8 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_58_0 = e1 & op(e3, e3) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_58_0 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (241) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) e1 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (242) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) e1 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (243) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_12 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (243) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_58_8 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (16), (17), (26), (27),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (29), (35), (36), (38), (40), (41), (42),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (50), (51), (53), (59), (74), (78),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (83), (84), (92), (99), (100), (105),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (108), (151), (218), (241), (244), (245)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #791.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (222), (246) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1219.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (83), (100), (105), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (154), (247) are inconsistent by sub-proof #557.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_58_11 = e1 & op(e1, e0) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_58_11 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (26), (35), (38), (40), (41), (45), (51),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (74), (78), (83), (99), (100), (105), (231),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) are inconsistent by sub-proof #743.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_58_13 = e0 & op(e0, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (251) op(e0, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (24), (37), (39), (43),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (46), (57), (62), (65), (67), (73), (76), (87),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (88), (89), (92), (96), (97), (100), (112), (165),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (166), (170), (251) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | #559.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | (252) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (253) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (51), (53), (80), (100),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (105), (118), (145), (253) are inconsistent by
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #564.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (254) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (51), (53), (100), (105),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (118), (145), (154), (254) are inconsistent by
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #565.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | (255) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (256) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (16), (17), (26), (27),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (28), (29), (35), (36), (38), (40), (41), (42),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (44), (45), (50), (51), (53), (59), (71), (74),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (78), (80), (81), (83), (84), (86), (92), (99),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (100), (105), (107), (108), (118), (145), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (154), (256) are inconsistent by sub-proof #556.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (257) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (83), (100), (105), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (257) are inconsistent by sub-proof #803.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | (258) all_58_10 = e3 & op(e2, e0) = e3
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | ALPHA: (258) implies:
% 159.05/27.95 | | | | | | | | | | | | | (259) op(e2, e0) = e3
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | REF_CLOSE: (36), (50), (100), (259) are inconsistent by
% 159.05/27.95 | | | | | | | | | | | | | sub-proof #1364.
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | (260) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 159.05/27.95 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 159.05/27.95 | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | BETA: splitting (260) gives:
% 159.05/27.95 | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | (261) all_58_11 = e3 & op(e1, e0) = e3
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | ALPHA: (261) implies:
% 159.05/27.95 | | | | | | | | | | | | | (262) all_58_11 = e3
% 159.05/27.95 | | | | | | | | | | | | | (263) op(e1, e0) = e3
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | BETA: splitting (106) gives:
% 159.05/27.95 | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | (264) all_54_15 = e3
% 159.05/27.95 | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | REF_CLOSE: (95), (139), (264) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | #1543.
% 159.05/27.95 | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | (265) ~ (all_54_15 = e3)
% 159.05/27.95 | | | | | | | | | | | | | | (266) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.05/27.95 | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 159.05/27.95 | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | (267) all_54_15 = e2
% 159.05/27.95 | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | REF_CLOSE: (33), (95), (267) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | #1542.
% 159.05/27.95 | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | (268) ~ (all_54_15 = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | (269) all_54_15 = e1 | all_54_15 = e0
% 159.05/27.95 | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 159.05/27.95 | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | (270) all_54_15 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | REF_CLOSE: (56), (95), (270) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | #1541.
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | (271) all_54_15 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (271) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | (272) all_4_2 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | (273) all_4_2 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | REDUCE: (90), (273) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | (274) ~ (all_52_7 = e0)
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | REDUCE: (68), (273) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | (275) ~ (all_52_13 = e0)
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | REDUCE: (139), (273) imply:
% 159.05/27.95 | | | | | | | | | | | | | | | | (276) ~ (e3 = e0)
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | (277) all_54_7 = e3
% 159.05/27.95 | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (62), (277) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | #1428.
% 159.05/27.95 | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | (278) ~ (all_54_7 = e3)
% 159.05/27.95 | | | | | | | | | | | | | | | | | (279) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | (280) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (281) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (282) all_58_9 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | (283) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (284) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (285) all_58_4 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (74), (78), (81), (83), (100), (105), (151), (285)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #850.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (286) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (287) all_58_5 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (10), (11), (12), (13), (14), (15),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (16), (17), (19), (24), (26), (27), (28), (29),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (50), (51), (52), (53),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (55), (57), (59), (62), (65), (67), (71), (73),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (74), (76), (78), (80), (81), (83), (84), (86),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (87), (88), (89), (92), (96), (97), (99), (100),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (105), (107), (108), (112), (118), (145), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (262), (263), (274), (275), (279), (282), (287)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #550.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | (288) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (289) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (12), (13), (14), (15), (16), (17),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (19), (24), (26), (27), (28), (29), (35), (36),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (45), (46), (50), (51), (52), (53), (55), (57),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (59), (62), (65), (67), (71), (73), (74), (76),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (78), (80), (81), (83), (84), (86), (87), (88),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (89), (92), (96), (97), (99), (100), (105), (107),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (108), (112), (118), (145), (151), (262), (274),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (275), (279), (282), (289) are inconsistent by
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | sub-proof #551.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (290) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (83), (100), (105), (151),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (290) are inconsistent by sub-proof #803.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (291) all_58_10 = e2 & op(e2, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (292) all_58_10 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (40), (45), (51), (53), (59), (74), (78),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (81), (100), (292) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | #906.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | (293) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 159.05/27.95 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (294) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (295) all_58_11 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (51), (53), (100), (105),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (118), (145), (262), (295) are inconsistent by
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | sub-proof #549.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (296) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (297) all_58_15 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | (298) op(e0, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | (299) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (300) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (301) all_58_4 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (74), (78), (81), (83), (100), (105), (151), (301)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #850.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (302) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | (303) all_58_5 = e1
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | (304) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (305) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | (306) all_58_1 = e0
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | (307) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_0 = e2 & op(e3, e3) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (118), (308) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_58_1 = e2 & op(e3, e2) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (306), (309) are inconsistent by sub-proof
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | #801.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | (310) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (51), (53), (80), (100),
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (105), (118), (145), (311) are inconsistent by
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #564.
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_58_9 = e2
% 159.05/27.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (10), (11), (12), (13), (14), (15),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (16), (17), (19), (24), (26), (27), (28), (29),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (50), (51), (52), (53),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (55), (57), (59), (62), (65), (67), (71), (73),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (74), (76), (78), (80), (81), (83), (84), (86),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (87), (88), (89), (92), (96), (97), (99), (100),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (105), (107), (108), (112), (118), (145), (151),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (262), (263), (274), (275), (279), (303), (313)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #550.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (314) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (15), (16), (27), (40), (45), (51),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (53), (59), (74), (78), (80), (81), (83), (84),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (92), (100), (105), (108), (297), (298), (314) are
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #548.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (315) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (14), (15), (19), (24), (26), (28),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (35), (37), (38), (39), (40), (43), (45), (46),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (51), (53), (57), (62), (65), (67), (73), (76),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (83), (87), (88), (89), (92), (96), (97), (100),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (105), (112), (118), (145), (262), (274), (275),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (279), (315) are inconsistent by sub-proof #553.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | (316) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (317) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (318) all_58_8 = e1
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (319) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (321) all_58_1 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | (322) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_58_0 = e2 & op(e3, e3) = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (118), (323) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_58_1 = e2 & op(e3, e2) = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (321), (324) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | #801.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | (325) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (51), (53), (80), (100),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (105), (118), (145), (326) are inconsistent by
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #564.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_9 = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (16), (17), (26), (27),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (28), (29), (35), (36), (38), (40), (41), (42),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (50), (51), (53), (55), (59), (71),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (83), (84), (86), (92),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (99), (100), (105), (107), (108), (118), (145),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | (151), (318), (321), (328) are inconsistent by
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #552.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (15), (16), (27), (40), (45), (51),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (53), (59), (74), (78), (80), (81), (83), (84),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (92), (100), (105), (108), (297), (298), (329) are
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #548.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (330) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (14), (15), (19), (24), (26), (28),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (35), (37), (38), (39), (40), (43), (45), (46),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (51), (53), (57), (62), (65), (67), (73), (76),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (83), (87), (88), (89), (92), (96), (97), (100),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (105), (112), (118), (145), (262), (274), (275),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (279), (330) are inconsistent by sub-proof #553.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (331) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (27), (40), (45), (51), (53), (59),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (74), (78), (80), (81), (83), (100), (105), (151),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (331) are inconsistent by sub-proof #803.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | (332) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | ALPHA: (332) implies:
% 159.05/27.96 | | | | | | | | | | | | | (333) all_58_15 = e3
% 159.05/27.96 | | | | | | | | | | | | | (334) op(e0, e0) = e3
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | BETA: splitting (44) gives:
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | (335) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 159.05/27.96 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | (336) all_58_12 = e2 & op(e0, e3) = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | (337) all_58_12 = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | REF_CLOSE: (26), (35), (40), (41), (51), (53), (74), (78),
% 159.05/27.96 | | | | | | | | | | | | | | | (100), (105), (118), (337) are inconsistent by
% 159.05/27.96 | | | | | | | | | | | | | | | sub-proof #1066.
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | (338) all_58_13 = e2 & op(e0, e2) = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | (339) all_58_13 = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | (340) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (26), (28), (35), (40), (45), (51), (53),
% 159.05/27.96 | | | | | | | | | | | | | | | | (59), (74), (78), (80), (81), (100), (105), (118),
% 159.05/27.96 | | | | | | | | | | | | | | | | (145), (340) are inconsistent by sub-proof #547.
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | (341) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 159.05/27.96 | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (40), (45), (53), (74), (78), (83),
% 159.05/27.96 | | | | | | | | | | | | | | | | (100), (108), (333), (339), (341) are inconsistent
% 159.05/27.96 | | | | | | | | | | | | | | | | by sub-proof #600.
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | (342) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 159.05/27.96 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | BETA: splitting (342) gives:
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | (343) all_58_14 = e2 & op(e0, e1) = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (51), (53), (100), (105),
% 159.05/27.96 | | | | | | | | | | | | | | | (118), (145), (151), (343) are inconsistent by
% 159.05/27.96 | | | | | | | | | | | | | | | sub-proof #554.
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | (344) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | (345) op(e0, e0) = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | REF_CLOSE: (100), (105), (334), (345) are inconsistent by
% 159.05/27.96 | | | | | | | | | | | | | | | sub-proof #1382.
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | (346) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.96 | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | ALPHA: (346) implies:
% 159.05/27.96 | | | | | | | | | | | (347) all_58_15 = e3
% 159.05/27.96 | | | | | | | | | | | (348) op(e0, e0) = e3
% 159.05/27.96 | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | BETA: splitting (106) gives:
% 159.05/27.96 | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | (349) all_54_15 = e3
% 159.05/27.96 | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | REF_CLOSE: (95), (139), (349) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | #1543.
% 159.05/27.96 | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | (350) ~ (all_54_15 = e3)
% 159.05/27.96 | | | | | | | | | | | | (351) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.05/27.96 | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | BETA: splitting (351) gives:
% 159.05/27.96 | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | (352) all_54_15 = e2
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | REF_CLOSE: (33), (95), (352) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | | #1542.
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | (353) ~ (all_54_15 = e2)
% 159.05/27.96 | | | | | | | | | | | | | (354) all_54_15 = e1 | all_54_15 = e0
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | BETA: splitting (114) gives:
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | (355) all_56_12 = e3
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | COMBINE_EQS: (54), (355) imply:
% 159.05/27.96 | | | | | | | | | | | | | | (356) e3 = e1
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | REDUCE: (53), (356) imply:
% 159.05/27.96 | | | | | | | | | | | | | | (357) $false
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | CLOSE: (357) is inconsistent.
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | (358) ~ (all_56_12 = e3)
% 159.05/27.96 | | | | | | | | | | | | | | (359) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | REDUCE: (54), (358) imply:
% 159.05/27.96 | | | | | | | | | | | | | | (360) ~ (e3 = e1)
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | BETA: splitting (359) gives:
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | (361) all_56_13 = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | COMBINE_EQS: (85), (361) imply:
% 159.05/27.96 | | | | | | | | | | | | | | | (362) e3 = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | SIMP: (362) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | (363) e3 = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | COMBINE_EQS: (28), (363) imply:
% 159.05/27.96 | | | | | | | | | | | | | | | (364) all_58_6 = e2
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | REF_CLOSE: (26), (35), (40), (51), (53), (100), (105), (118),
% 159.05/27.96 | | | | | | | | | | | | | | | (145), (364) are inconsistent by sub-proof #1125.
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | (365) ~ (all_56_13 = e2)
% 159.05/27.96 | | | | | | | | | | | | | | | (366) all_56_14 = e1 | all_56_15 = e0
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | BETA: splitting (354) gives:
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | (367) all_54_15 = e1
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | REF_CLOSE: (56), (95), (367) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | | | | | #1541.
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | (368) all_54_15 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (368) imply:
% 159.05/27.96 | | | | | | | | | | | | | | | | (369) all_4_2 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | SIMP: (369) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | (370) all_4_2 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | REDUCE: (90), (370) imply:
% 159.05/27.96 | | | | | | | | | | | | | | | | (371) ~ (all_52_7 = e0)
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | REDUCE: (68), (370) imply:
% 159.05/27.96 | | | | | | | | | | | | | | | | (372) ~ (all_52_13 = e0)
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | REDUCE: (139), (370) imply:
% 159.05/27.96 | | | | | | | | | | | | | | | | (373) ~ (e3 = e0)
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | (374) all_54_7 = e3
% 159.05/27.96 | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (62), (374) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | | | | | | #1428.
% 159.05/27.96 | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | (375) ~ (all_54_7 = e3)
% 159.05/27.96 | | | | | | | | | | | | | | | | | (376) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | BETA: splitting (376) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | (377) all_54_7 = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (65), (377) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | | | | | | | #1427.
% 159.05/27.96 | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | (378) ~ (all_54_7 = e2)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | (379) all_54_7 = e1 | all_54_7 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | (380) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (26), (28), (35), (40), (45), (51), (53),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | (59), (74), (78), (80), (81), (100), (105), (118),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | (145), (380) are inconsistent by sub-proof #547.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | (381) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (381) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | (382) all_58_8 = e2 & op(e1, e1) = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (83), (100), (382) are inconsistent by
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | sub-proof #1440.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | (383) all_58_14 = e2 & op(e0, e1) = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | (384) all_58_14 = e2
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (385) all_58_15 = e0 & op(e0, e0) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (386) all_58_15 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (387) op(e0, e0) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (386) imply:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (388) e3 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (388) imply:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (389) all_58_6 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (26), (35), (40), (51), (53), (64), (78),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (94), (100), (105), (145), (348), (387), (389) are
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #582.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (390) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | (391) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (391) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (392) all_58_12 = e0 & op(e0, e3) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (392) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (393) all_58_12 = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (12),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (13), (14), (15), (16), (18), (19), (21), (22),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (23), (24), (26), (27), (28), (29), (30), (31),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (32), (33), (34), (35), (36), (37), (38), (39),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (41), (42), (43), (46), (47), (48), (51), (53),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (55), (56), (57), (59), (60), (61), (62), (63),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (71), (72),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (73), (74), (75), (76), (77), (79), (80), (81),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (82), (83), (84), (87), (88), (89), (90), (91),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (92), (93), (94), (96), (97), (98), (100), (102),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (103), (104), (105), (107), (108), (109), (112),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (113), (121), (347), (348), (366), (393) are
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | (394) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (394) gives:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (395) all_58_13 = e0 & op(e0, e2) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (396) op(e0, e2) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (24), (37), (39), (43),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (46), (57), (62), (67), (73), (76), (87), (88),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (89), (92), (96), (97), (100), (112), (371),
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (372), (379), (396) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | #560.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | (397) all_58_14 = e0 & op(e0, e1) = e0
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (384), (397) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | | #1341.
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | | |
% 159.05/27.96 | | | | | | | | | End of split
% 159.05/27.96 | | | | | | | | |
% 159.05/27.96 | | | | | | | | End of split
% 159.05/27.96 | | | | | | | |
% 159.05/27.96 | | | | | | | End of split
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | Case 2:
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | (398) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | REF_CLOSE: (7), (49), (111), (130), (398) are inconsistent by
% 159.05/27.96 | | | | | | | sub-proof #1098.
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | End of split
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | End of split
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | End of split
% 159.05/27.96 | | | |
% 159.05/27.96 | | | End of split
% 159.05/27.96 | | |
% 159.05/27.96 | | Case 2:
% 159.05/27.96 | | |
% 159.05/27.96 | | | (399) all_58_2 = e0 & op(e2, e3) = e0
% 159.05/27.96 | | |
% 159.05/27.96 | | | ALPHA: (399) implies:
% 159.05/27.96 | | | (400) op(e2, e3) = e0
% 159.05/27.96 | | |
% 159.05/27.96 | | | REF_CLOSE: (45), (51), (100), (400) are inconsistent by sub-proof #1156.
% 159.05/27.96 | | |
% 159.05/27.96 | | End of split
% 159.05/27.96 | |
% 159.05/27.96 | Case 2:
% 159.05/27.96 | |
% 159.05/27.96 | | (401) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.05/27.96 | | e0)
% 159.05/27.96 | |
% 159.05/27.96 | | BETA: splitting (401) gives:
% 159.05/27.96 | |
% 159.05/27.96 | | Case 1:
% 159.05/27.96 | | |
% 159.05/27.96 | | | (402) all_58_6 = e0 & op(e1, e3) = e0
% 159.05/27.96 | | |
% 159.05/27.96 | | | REF_CLOSE: (28), (40), (402) are inconsistent by sub-proof #1350.
% 159.05/27.96 | | |
% 159.05/27.96 | | Case 2:
% 159.05/27.96 | | |
% 159.05/27.96 | | | (403) all_58_12 = e0 & op(e0, e3) = e0
% 159.05/27.96 | | |
% 159.05/27.96 | | | ALPHA: (403) implies:
% 159.05/27.96 | | | (404) all_58_12 = e0
% 159.05/27.96 | | |
% 159.05/27.96 | | | BETA: splitting (25) gives:
% 159.05/27.96 | | |
% 159.05/27.96 | | | Case 1:
% 159.05/27.96 | | | |
% 159.05/27.96 | | | | (405) all_54_8 = e3
% 159.05/27.96 | | | |
% 159.05/27.96 | | | | REF_CLOSE: (61), (63), (405) are inconsistent by sub-proof #1425.
% 159.05/27.96 | | | |
% 159.05/27.96 | | | Case 2:
% 159.05/27.96 | | | |
% 159.05/27.96 | | | | (406) ~ (all_54_8 = e3)
% 159.05/27.96 | | | | (407) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 159.05/27.96 | | | |
% 159.05/27.96 | | | | BETA: splitting (84) gives:
% 159.05/27.96 | | | |
% 159.05/27.96 | | | | Case 1:
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | | (408) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 159.05/27.96 | | | | | e2) = e3)
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | | BETA: splitting (408) gives:
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | | Case 1:
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | (409) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | REF_CLOSE: (40), (404), (409) are inconsistent by sub-proof #1375.
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | Case 2:
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | (410) all_58_13 = e3 & op(e0, e2) = e3
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | REF_CLOSE: (15), (92), (100), (410) are inconsistent by sub-proof
% 159.05/27.96 | | | | | | #1449.
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | End of split
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | Case 2:
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | | (411) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 159.05/27.96 | | | | | e0) = e3)
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | | BETA: splitting (411) gives:
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | | Case 1:
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | (412) all_58_14 = e3 & op(e0, e1) = e3
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | ALPHA: (412) implies:
% 159.05/27.96 | | | | | | (413) all_58_14 = e3
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | REF_CLOSE: (9), (12), (14), (15), (16), (17), (26), (27), (28),
% 159.05/27.96 | | | | | | (29), (35), (36), (38), (40), (41), (42), (44), (45),
% 159.05/27.96 | | | | | | (50), (51), (53), (55), (59), (71), (74), (78), (80),
% 159.05/27.96 | | | | | | (81), (83), (84), (92), (99), (100), (105), (107), (108),
% 159.05/27.96 | | | | | | (404), (413) are inconsistent by sub-proof #789.
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | Case 2:
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | (414) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | ALPHA: (414) implies:
% 159.05/27.96 | | | | | | (415) all_58_15 = e3
% 159.05/27.96 | | | | | | (416) op(e0, e0) = e3
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | BETA: splitting (114) gives:
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | | Case 1:
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | (417) all_56_12 = e3
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | COMBINE_EQS: (54), (417) imply:
% 159.05/27.96 | | | | | | | (418) e3 = e1
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | REDUCE: (53), (418) imply:
% 159.05/27.96 | | | | | | | (419) $false
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | CLOSE: (419) is inconsistent.
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | Case 2:
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | (420) ~ (all_56_12 = e3)
% 159.05/27.96 | | | | | | | (421) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | REDUCE: (54), (420) imply:
% 159.05/27.96 | | | | | | | (422) ~ (e3 = e1)
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | BETA: splitting (421) gives:
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | | Case 1:
% 159.05/27.96 | | | | | | | |
% 159.05/27.96 | | | | | | | | (423) all_56_13 = e2
% 159.05/27.96 | | | | | | | |
% 159.05/27.96 | | | | | | | | COMBINE_EQS: (85), (423) imply:
% 159.05/27.96 | | | | | | | | (424) e3 = e2
% 159.05/27.96 | | | | | | | |
% 159.05/27.96 | | | | | | | | REF_CLOSE: (26), (28), (35), (40), (41), (51), (53), (74), (78),
% 159.05/27.96 | | | | | | | | (100), (105), (404), (424) are inconsistent by
% 159.05/27.96 | | | | | | | | sub-proof #832.
% 159.05/27.96 | | | | | | | |
% 159.05/27.96 | | | | | | | Case 2:
% 159.05/27.96 | | | | | | | |
% 159.05/27.96 | | | | | | | | (425) ~ (all_56_13 = e2)
% 159.05/27.96 | | | | | | | | (426) all_56_14 = e1 | all_56_15 = e0
% 159.05/27.96 | | | | | | | |
% 159.05/27.96 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (12), (13),
% 159.05/27.96 | | | | | | | | (14), (15), (16), (18), (19), (21), (22), (23), (24),
% 159.05/27.96 | | | | | | | | (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 159.05/27.96 | | | | | | | | (35), (36), (37), (38), (39), (41), (42), (43), (46),
% 159.05/27.96 | | | | | | | | (47), (48), (51), (53), (55), (56), (57), (59), (60),
% 159.05/27.96 | | | | | | | | (61), (62), (63), (65), (66), (67), (68), (69), (70),
% 159.05/27.96 | | | | | | | | (71), (72), (73), (74), (75), (76), (77), (79), (80),
% 159.05/27.96 | | | | | | | | (81), (82), (83), (84), (87), (88), (89), (90), (91),
% 159.05/27.96 | | | | | | | | (92), (93), (94), (96), (97), (98), (100), (102),
% 159.05/27.96 | | | | | | | | (103), (104), (105), (107), (108), (109), (112),
% 159.05/27.96 | | | | | | | | (113), (404), (407), (415), (416), (426) are
% 159.05/27.96 | | | | | | | | inconsistent by sub-proof #536.
% 159.05/27.96 | | | | | | | |
% 159.05/27.96 | | | | | | | End of split
% 159.05/27.96 | | | | | | |
% 159.05/27.96 | | | | | | End of split
% 159.05/27.96 | | | | | |
% 159.05/27.96 | | | | | End of split
% 159.05/27.96 | | | | |
% 159.05/27.96 | | | | End of split
% 159.05/27.96 | | | |
% 159.05/27.96 | | | End of split
% 159.05/27.96 | | |
% 159.05/27.96 | | End of split
% 159.05/27.96 | |
% 159.05/27.96 | End of split
% 159.05/27.96 |
% 159.05/27.96 End of proof
% 159.05/27.96
% 159.05/27.96 Sub-proof #536 shows that the following formulas are inconsistent:
% 159.05/27.96 ----------------------------------------------------------------
% 159.05/27.96 (1) op(e1, e3) = e3
% 159.05/27.96 (2) op(e1, e1) = e3
% 159.05/27.96 (3) op(e1, e1) = all_32_1
% 159.05/27.96 (4) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.05/27.96 (5) all_56_14 = e3
% 159.05/27.96 (6) all_58_15 = e3
% 159.05/27.96 (7) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.96 (8) op(e3, e1) = e3
% 159.05/27.96 (9) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/27.96 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/27.96 (10) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.96 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.96 (11) all_54_13 = all_52_7
% 159.05/27.96 (12) op(e1, e1) = all_6_2
% 159.05/27.96 (13) ~ (all_52_7 = e3)
% 159.05/27.96 (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/27.96 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/27.96 e1)
% 159.05/27.96 (15) ~ (all_52_6 = all_52_14)
% 159.05/27.96 (16) ~ (all_52_11 = e3)
% 159.05/27.96 (17) ~ (all_52_4 = all_52_6)
% 159.05/27.96 (18) op(e3, e3) = all_28_1
% 159.05/27.96 (19) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.96 (20) ~ (all_52_7 = all_52_11)
% 159.05/27.96 (21) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.96 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.96 (22) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/27.96 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/27.96 (23) all_58_6 = e3
% 159.05/27.96 (24) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/27.96 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/27.96 (25) ~ (all_52_14 = e3)
% 159.05/27.96 (26) all_58_12 = e0
% 159.05/27.96 (27) all_54_1 = all_52_4
% 159.05/27.96 (28) op(e3, e2) = all_52_4
% 159.05/27.96 (29) ~ (all_4_2 = e2)
% 159.05/27.96 (30) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.05/27.96 (31) op(e2, e3) = all_52_1
% 159.05/27.96 (32) ~ (all_52_13 = e3)
% 159.05/27.96 (33) all_54_2 = all_52_8
% 159.05/27.96 (34) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.96 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.96 (35) ~ (all_52_8 = all_52_9)
% 159.05/27.96 (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/27.96 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/27.96 (37) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.96 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.96 (38) ~ (all_52_9 = all_52_13)
% 159.05/27.96 (39) all_56_14 = e1 | all_56_15 = e0
% 159.05/27.96 (40) ~ (all_52_9 = e3)
% 159.05/27.96 (41) ~ (all_52_2 = all_52_6)
% 159.05/27.96 (42) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.96 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.96 (43) op(e2, e3) = e2
% 159.05/27.97 (44) ~ (e3 = e1)
% 159.05/27.97 (45) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.97 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.97 (46) ~ (all_4_2 = e1)
% 159.05/27.97 (47) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.97 (48) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.97 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.97 (49) op(e0, e0) = all_4_2
% 159.05/27.97 (50) all_54_8 = all_52_2
% 159.05/27.97 (51) all_54_7 = all_52_13
% 159.05/27.97 (52) ~ (all_52_2 = e3)
% 159.05/27.97 (53) ~ (all_52_13 = e2)
% 159.05/27.97 (54) all_56_15 = all_4_2
% 159.05/27.97 (55) ~ (all_52_9 = all_52_11)
% 159.05/27.97 (56) ~ (all_52_13 = all_4_2)
% 159.05/27.97 (57) ~ (all_52_2 = e1)
% 159.05/27.97 (58) ~ (all_52_6 = all_52_7)
% 159.05/27.97 (59) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.97 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.97 (60) ~ (all_52_4 = e3)
% 159.05/27.97 (61) all_54_6 = all_52_9
% 159.05/27.97 (62) ~ (e2 = e1)
% 159.05/27.97 (63) ~ (all_52_4 = all_52_7)
% 159.05/27.97 (64) ~ (all_52_8 = all_52_11)
% 159.05/27.97 (65) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.97 (66) ~ (all_52_2 = e2)
% 159.05/27.97 (67) all_58_4 = e3
% 159.05/27.97 (68) all_58_3 = e3
% 159.05/27.97 (69) op(e3, e1) = all_52_8
% 159.05/27.97 (70) ~ (all_6_2 = e2)
% 159.05/27.97 (71) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/27.97 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/27.97 e3)
% 159.05/27.97 (72) ~ (all_52_9 = e2)
% 159.05/27.97 (73) ~ (all_52_8 = e3)
% 159.05/27.97 (74) all_54_14 = all_52_11
% 159.05/27.97 (75) ~ (all_52_7 = all_4_2)
% 159.05/27.97 (76) op(e1, e3) = e1
% 159.05/27.97 (77) op(e0, e2) = all_52_7
% 159.05/27.97 (78) op(e1, e0) = all_52_14
% 159.05/27.97 (79) op(e3, e3) = all_22_1
% 159.05/27.97 (80) ~ (all_52_8 = e1)
% 159.05/27.97 (81) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 159.05/27.97 (82) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.97 (83) ~ (all_52_6 = e3)
% 159.05/27.97 (84) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.97 (85) ~ (all_52_11 = all_4_2)
% 159.05/27.97 (86) all_54_11 = all_52_14
% 159.05/27.97 (87) ~ (all_52_13 = all_52_14)
% 159.05/27.97 (88) ~ (e3 = e2)
% 159.05/27.97 (89) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/27.97 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.97 (90) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/27.97 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/27.97 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/27.97 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/27.97 (91) all_54_9 = all_52_6
% 159.05/27.97 (92) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.97 (93) ~ (all_52_14 = all_4_2)
% 159.05/27.97 (94) op(e0, e0) = e3
% 159.05/27.97
% 159.05/27.97 Begin of proof
% 159.05/27.97 |
% 159.05/27.97 | BETA: splitting (81) gives:
% 159.05/27.97 |
% 159.05/27.97 | Case 1:
% 159.05/27.97 | |
% 159.05/27.97 | | (95) all_54_8 = e2
% 159.05/27.97 | |
% 159.05/27.97 | | REF_CLOSE: (50), (66), (95) are inconsistent by sub-proof #1231.
% 159.05/27.97 | |
% 159.05/27.97 | Case 2:
% 159.05/27.97 | |
% 159.05/27.97 | | (96) all_54_8 = e1 | all_54_8 = e0
% 159.05/27.97 | |
% 159.05/27.97 | | BETA: splitting (96) gives:
% 159.05/27.97 | |
% 159.05/27.97 | | Case 1:
% 159.05/27.97 | | |
% 159.05/27.97 | | | (97) all_54_8 = e1
% 159.05/27.97 | | |
% 159.05/27.97 | | | REF_CLOSE: (50), (57), (97) are inconsistent by sub-proof #1379.
% 159.05/27.97 | | |
% 159.05/27.97 | | Case 2:
% 159.05/27.97 | | |
% 159.05/27.97 | | | (98) all_54_8 = e0
% 159.05/27.97 | | |
% 159.05/27.97 | | | COMBINE_EQS: (50), (98) imply:
% 159.05/27.97 | | | (99) all_52_2 = e0
% 159.05/27.97 | | |
% 159.05/27.97 | | | SIMP: (99) implies:
% 159.05/27.97 | | | (100) all_52_2 = e0
% 159.05/27.97 | | |
% 159.05/27.97 | | | REDUCE: (41), (100) imply:
% 159.05/27.97 | | | (101) ~ (all_52_6 = e0)
% 159.05/27.97 | | |
% 159.05/27.97 | | | SIMP: (101) implies:
% 159.05/27.97 | | | (102) ~ (all_52_6 = e0)
% 159.05/27.97 | | |
% 159.05/27.97 | | | REDUCE: (52), (100) imply:
% 159.05/27.97 | | | (103) ~ (e3 = e0)
% 159.05/27.97 | | |
% 159.05/27.97 | | | SIMP: (103) implies:
% 159.05/27.97 | | | (104) ~ (e3 = e0)
% 159.05/27.97 | | |
% 159.05/27.97 | | | REDUCE: (57), (100) imply:
% 159.05/27.97 | | | (105) ~ (e1 = e0)
% 159.05/27.97 | | |
% 159.05/27.97 | | | SIMP: (105) implies:
% 159.05/27.97 | | | (106) ~ (e1 = e0)
% 159.05/27.97 | | |
% 159.05/27.97 | | | BETA: splitting (36) gives:
% 159.05/27.97 | | |
% 159.05/27.97 | | | Case 1:
% 159.05/27.97 | | | |
% 159.05/27.97 | | | | (107) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 159.05/27.97 | | | | = e1)
% 159.05/27.97 | | | |
% 159.05/27.97 | | | | BETA: splitting (107) gives:
% 159.05/27.97 | | | |
% 159.05/27.97 | | | | Case 1:
% 159.05/27.97 | | | | |
% 159.05/27.97 | | | | | (108) all_58_0 = e1 & op(e3, e3) = e1
% 159.05/27.97 | | | | |
% 159.05/27.97 | | | | | ALPHA: (108) implies:
% 159.05/27.97 | | | | | (109) all_58_0 = e1
% 159.05/27.97 | | | | | (110) op(e3, e3) = e1
% 159.05/27.97 | | | | |
% 159.05/27.97 | | | | | BETA: splitting (39) gives:
% 159.05/27.97 | | | | |
% 159.05/27.97 | | | | | Case 1:
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | (111) all_56_14 = e1
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | REF_CLOSE: (5), (44), (111) are inconsistent by sub-proof #585.
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | Case 2:
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | (112) all_56_15 = e0
% 159.05/27.97 | | | | | | (113) ~ (all_56_14 = e1)
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | COMBINE_EQS: (54), (112) imply:
% 159.05/27.97 | | | | | | (114) all_4_2 = e0
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | SIMP: (114) implies:
% 159.05/27.97 | | | | | | (115) all_4_2 = e0
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | REDUCE: (75), (115) imply:
% 159.05/27.97 | | | | | | (116) ~ (all_52_7 = e0)
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | REDUCE: (85), (115) imply:
% 159.05/27.97 | | | | | | (117) ~ (all_52_11 = e0)
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | REDUCE: (56), (115) imply:
% 159.05/27.97 | | | | | | (118) ~ (all_52_13 = e0)
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | REDUCE: (93), (115) imply:
% 159.05/27.97 | | | | | | (119) ~ (all_52_14 = e0)
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | REDUCE: (29), (115) imply:
% 159.05/27.97 | | | | | | (120) ~ (e2 = e0)
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | SIMP: (120) implies:
% 159.05/27.97 | | | | | | (121) ~ (e2 = e0)
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | REDUCE: (49), (115) imply:
% 159.05/27.97 | | | | | | (122) op(e0, e0) = e0
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | BETA: splitting (90) gives:
% 159.05/27.97 | | | | | |
% 159.05/27.97 | | | | | | Case 1:
% 159.05/27.97 | | | | | | |
% 159.05/27.97 | | | | | | | (123) all_58_15 = e0 & op(e0, e0) = e0
% 159.05/27.97 | | | | | | |
% 159.05/27.97 | | | | | | | ALPHA: (123) implies:
% 159.05/27.97 | | | | | | | (124) all_58_15 = e0
% 159.05/27.97 | | | | | | |
% 159.05/27.97 | | | | | | | REF_CLOSE: (6), (104), (124) are inconsistent by sub-proof #1318.
% 159.05/27.97 | | | | | | |
% 159.05/27.97 | | | | | | Case 2:
% 159.05/27.97 | | | | | | |
% 159.05/27.97 | | | | | | | (125) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 159.05/27.97 | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.05/27.97 | | | | | | | e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 159.05/27.97 | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 159.05/27.97 | | | | | | | op(e0, e1) = e0))
% 159.05/27.97 | | | | | | |
% 159.05/27.97 | | | | | | | ALPHA: (125) implies:
% 159.05/27.97 | | | | | | | (126) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 159.05/27.97 | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.97 | | | | | | |
% 159.05/27.97 | | | | | | | BETA: splitting (19) gives:
% 159.05/27.97 | | | | | | |
% 159.05/27.97 | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | |
% 159.05/27.97 | | | | | | | | (127) all_54_7 = e3
% 159.05/27.97 | | | | | | | |
% 159.05/27.97 | | | | | | | | REF_CLOSE: (32), (51), (127) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | #1428.
% 159.05/27.97 | | | | | | | |
% 159.05/27.97 | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | |
% 159.05/27.97 | | | | | | | | (128) ~ (all_54_7 = e3)
% 159.05/27.97 | | | | | | | | (129) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/27.97 | | | | | | | |
% 159.05/27.97 | | | | | | | | BETA: splitting (129) gives:
% 159.05/27.97 | | | | | | | |
% 159.05/27.97 | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | |
% 159.05/27.97 | | | | | | | | | (130) all_54_7 = e2
% 159.05/27.97 | | | | | | | | |
% 159.05/27.97 | | | | | | | | | REF_CLOSE: (51), (53), (130) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | #1427.
% 159.05/27.97 | | | | | | | | |
% 159.05/27.97 | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | |
% 159.05/27.97 | | | | | | | | | (131) ~ (all_54_7 = e2)
% 159.05/27.97 | | | | | | | | | (132) all_54_7 = e1 | all_54_7 = e0
% 159.05/27.97 | | | | | | | | |
% 159.05/27.97 | | | | | | | | | BETA: splitting (22) gives:
% 159.05/27.97 | | | | | | | | |
% 159.05/27.97 | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | (133) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 159.05/27.97 | | | | | | | | | | & op(e2, e1) = e2)
% 159.05/27.97 | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | REF_CLOSE: (10), (21), (23), (26), (31), (43), (44), (48),
% 159.05/27.97 | | | | | | | | | | (62), (67), (68), (84), (88), (104), (106), (109),
% 159.05/27.97 | | | | | | | | | | (121), (133) are inconsistent by sub-proof #813.
% 159.05/27.97 | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | (134) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2
% 159.05/27.97 | | | | | | | | | | & op(e0, e1) = e2)
% 159.05/27.97 | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | BETA: splitting (134) gives:
% 159.05/27.97 | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | (135) all_58_8 = e2 & op(e1, e1) = e2
% 159.05/27.97 | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | REF_CLOSE: (12), (70), (84), (135) are inconsistent by
% 159.05/27.97 | | | | | | | | | | | sub-proof #1440.
% 159.05/27.97 | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | (136) all_58_14 = e2 & op(e0, e1) = e2
% 159.05/27.97 | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | ALPHA: (136) implies:
% 159.05/27.97 | | | | | | | | | | | (137) all_58_14 = e2
% 159.05/27.97 | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | BETA: splitting (48) gives:
% 159.05/27.97 | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | (138) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 159.05/27.97 | | | | | | | | | | | | & op(e2, e2) = e0)
% 159.05/27.97 | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | REF_CLOSE: (43), (68), (84), (104), (121), (138) are
% 159.05/27.97 | | | | | | | | | | | | inconsistent by sub-proof #755.
% 159.05/27.97 | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | (139) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 159.05/27.97 | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 159.05/27.97 | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | BETA: splitting (139) gives:
% 159.05/27.97 | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | (140) all_58_5 = e0 & op(e2, e1) = e0
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | ALPHA: (140) implies:
% 159.05/27.97 | | | | | | | | | | | | | (141) all_58_5 = e0
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | BETA: splitting (132) gives:
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | (142) all_54_7 = e1
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | COMBINE_EQS: (51), (142) imply:
% 159.05/27.97 | | | | | | | | | | | | | | (143) all_52_13 = e1
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | SIMP: (143) implies:
% 159.05/27.97 | | | | | | | | | | | | | | (144) all_52_13 = e1
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | REDUCE: (38), (144) imply:
% 159.05/27.97 | | | | | | | | | | | | | | (145) ~ (all_52_9 = e1)
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | REDUCE: (87), (144) imply:
% 159.05/27.97 | | | | | | | | | | | | | | (146) ~ (all_52_14 = e1)
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | SIMP: (146) implies:
% 159.05/27.97 | | | | | | | | | | | | | | (147) ~ (all_52_14 = e1)
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | REDUCE: (32), (144) imply:
% 159.05/27.97 | | | | | | | | | | | | | | (148) ~ (e3 = e1)
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | REDUCE: (53), (144) imply:
% 159.05/27.97 | | | | | | | | | | | | | | (149) ~ (e2 = e1)
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | (150) all_54_6 = e3
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | COMBINE_EQS: (61), (150) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | (151) all_52_9 = e3
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | REDUCE: (40), (151) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | (152) $false
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | (153) ~ (all_54_6 = e3)
% 159.05/27.97 | | | | | | | | | | | | | | | (154) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (10), (11), (13), (15), (16),
% 159.05/27.97 | | | | | | | | | | | | | | | (17), (18), (20), (21), (23), (25), (26), (27),
% 159.05/27.97 | | | | | | | | | | | | | | | (28), (30), (31), (33), (34), (35), (37), (40),
% 159.05/27.97 | | | | | | | | | | | | | | | (42), (43), (44), (45), (47), (48), (55), (58),
% 159.05/27.97 | | | | | | | | | | | | | | | (59), (60), (61), (62), (63), (64), (65), (67),
% 159.05/27.97 | | | | | | | | | | | | | | | (68), (69), (72), (73), (74), (78), (79), (80),
% 159.05/27.97 | | | | | | | | | | | | | | | (82), (83), (84), (86), (88), (91), (92), (94),
% 159.05/27.97 | | | | | | | | | | | | | | | (102), (104), (106), (109), (110), (116), (117),
% 159.05/27.97 | | | | | | | | | | | | | | | (119), (122), (126), (137), (141), (145), (147),
% 159.05/27.97 | | | | | | | | | | | | | | | (154) are inconsistent by sub-proof #538.
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | (155) all_54_7 = e0
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | REF_CLOSE: (51), (118), (155) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | | | | | | #1112.
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | (156) all_58_10 = e0 & op(e2, e0) = e0
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | ALPHA: (156) implies:
% 159.05/27.97 | | | | | | | | | | | | | (157) all_58_10 = e0
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | BETA: splitting (45) gives:
% 159.05/27.97 | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | (158) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 159.05/27.97 | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | (159) all_58_4 = e0 & op(e3, e1) = e0
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | REF_CLOSE: (67), (104), (159) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | | | | | | | #1344.
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | (160) all_58_5 = e0 & op(e2, e1) = e0
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | (161) all_58_5 = e0
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | REF_CLOSE: (10), (43), (44), (62), (68), (84), (106), (157),
% 159.05/27.97 | | | | | | | | | | | | | | | (161) are inconsistent by sub-proof #839.
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | (162) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 159.05/27.97 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 159.05/27.97 | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | (163) all_58_8 = e0 & op(e1, e1) = e0
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | (164) all_58_8 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | (165) op(e1, e1) = e0
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 159.05/27.97 | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | (166) all_54_7 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (166) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | (167) all_52_13 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | (168) all_52_13 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | REDUCE: (38), (168) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | (169) ~ (all_52_9 = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | REDUCE: (87), (168) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | (170) ~ (all_52_14 = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | SIMP: (170) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | (171) ~ (all_52_14 = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | REDUCE: (32), (168) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | (172) ~ (e3 = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | REDUCE: (53), (168) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | (173) ~ (e2 = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | (174) all_54_6 = e3
% 159.05/27.97 | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (174) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | (175) all_52_9 = e3
% 159.05/27.97 | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | REDUCE: (40), (175) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | (176) $false
% 159.05/27.97 | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 159.05/27.97 | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | (177) ~ (all_54_6 = e3)
% 159.05/27.97 | | | | | | | | | | | | | | | | | (178) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | (179) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 159.05/27.97 | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | (180) all_58_0 = e0 & op(e3, e3) = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (109), (180) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | #1520.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | (181) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | (182) all_58_1 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | (183) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (23), (26), (31), (43), (44), (62),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | (68), (79), (84), (88), (94), (104), (106), (110),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | (122), (183) are inconsistent by sub-proof #543.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | (184) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | (185) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | (186) all_58_5 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | (187) all_54_6 = e2
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (72), (187) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | #1192.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | (188) ~ (all_54_6 = e2)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | (189) all_54_6 = e1 | all_54_6 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (190) all_54_6 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (169), (190) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | #562.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (191) all_54_6 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (191) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (192) all_52_9 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (192) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (193) all_52_9 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (193) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (194) ~ (all_52_8 = e0)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | (195) all_54_2 = e3
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (195) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | (196) all_52_8 = e3
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (196) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | (197) $false
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | (198) ~ (all_54_2 = e3)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | (199) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_54_2 = e2
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (200) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_52_8 = e2
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (201) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (202) ~ (e3 = e2)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (201) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (203) op(e3, e1) = e2
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (84) with e3, all_32_1, e1, e1,
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (2), (3) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_32_1 = e3
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (84) with e0, all_32_1, e1, e1,
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (3), (165) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_32_1 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (84) with e1, e3, e3, e1,
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1), (76) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (206) e3 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (84) with e2, e3, e1, e3,
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (8), (203) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (207) e3 = e2
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (205) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (208) e3 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (208) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (209) e3 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (207) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (210) e2 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (209) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (211) e2 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (211) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (212) e1 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (212) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_58_5 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (23), (26), (31), (43), (44), (62),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (79), (84), (88), (94), (104), (106), (110),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (214) are inconsistent by sub-proof #543.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (186), (213) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | #935.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_10 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (8), (10), (16), (18), (21), (23), (25),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (26), (31), (33), (34), (35), (37), (40), (42),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (47), (48), (55), (59), (61),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (62), (64), (65), (67), (68), (69), (72), (73),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (74), (78), (79), (80), (84), (86), (88), (92),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (94), (104), (106), (109), (110), (119), (121),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (126), (137), (169), (171), (178), (182),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (216) are inconsistent by sub-proof #539.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_54_2 = e1 | all_54_2 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (80), (194), (217) are inconsistent by
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #561.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | (218) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | (219) all_58_10 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (157), (219) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | #1279.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.97 | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | (220) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 159.05/27.97 | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | (221) all_58_4 = e0 & op(e3, e1) = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (104), (221) are inconsistent by sub-proof
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | #1344.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | (222) all_58_9 = e0 & op(e3, e0) = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | (223) all_58_9 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | (224) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (43), (44), (48), (62), (68), (84), (104),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | (106), (121), (223), (224) are inconsistent by
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | sub-proof #537.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | (225) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | (226) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | (227) all_58_11 = e2
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | (228) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (229) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (23), (26), (31), (43), (44), (67),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (88), (94), (104), (106), (110),
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (122), (229) are inconsistent by sub-proof #545.
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | (231) all_58_5 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | (232) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_9 = e1 & op(e3, e0) = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_9 = e1
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (234) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (235) e1 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (235) implies:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (236) e1 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (236) imply:
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_58_5 = e0
% 159.05/27.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (10), (11), (13), (15), (16),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (17), (18), (20), (21), (23), (25), (26), (27),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (28), (30), (31), (33), (34), (35), (37), (40),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (42), (43), (44), (45), (47), (48), (55), (58),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (59), (60), (61), (62), (63), (64), (65), (67),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (68), (69), (72), (73), (74), (78), (79), (80),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (82), (83), (84), (86), (88), (91), (92), (94),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (102), (104), (106), (109), (110), (116), (117),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (119), (122), (126), (137), (169), (171), (178),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (237) are inconsistent by sub-proof #538.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_10 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (43), (44), (48), (62), (68), (84), (104),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (106), (121), (231), (239) are inconsistent by
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #754.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | (240) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_58_11 = e1 & op(e1, e0) = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (227), (241) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | #1455.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_58_15 = e1 & op(e0, e0) = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_58_15 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (243) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (244) e3 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (244) implies:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (245) e3 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (245) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_58_6 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (26), (31), (43), (44), (79), (84),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | (88), (94), (104), (106), (110), (122), (246) are
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | (247) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (106), (137), (164), (247) are inconsistent
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #542.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | (248) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | (249) all_58_15 = e2
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | (250) op(e0, e0) = e2
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (13), (14), (21), (22), (23), (26),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | (31), (43), (44), (48), (62), (67), (68), (70),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | (71), (77), (84), (88), (90), (104), (106), (109),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | (121), (249), (250) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | | #812.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | (251) all_54_7 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | REF_CLOSE: (51), (118), (251) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | | | | | #1112.
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | (252) all_58_14 = e0 & op(e0, e1) = e0
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | REF_CLOSE: (121), (137), (252) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | | | | #1341.
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | End of split
% 159.05/27.98 | | | | | | | |
% 159.05/27.98 | | | | | | | End of split
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | End of split
% 159.05/27.98 | | | | | |
% 159.05/27.98 | | | | | End of split
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | Case 2:
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | (253) all_58_2 = e1 & op(e2, e3) = e1
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | ALPHA: (253) implies:
% 159.05/27.98 | | | | | (254) op(e2, e3) = e1
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | REF_CLOSE: (43), (62), (84), (254) are inconsistent by sub-proof
% 159.05/27.98 | | | | | #1430.
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | End of split
% 159.05/27.98 | | | |
% 159.05/27.98 | | | Case 2:
% 159.05/27.98 | | | |
% 159.05/27.98 | | | | (255) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 159.05/27.98 | | | | e3) = e1)
% 159.05/27.98 | | | |
% 159.05/27.98 | | | | BETA: splitting (255) gives:
% 159.05/27.98 | | | |
% 159.05/27.98 | | | | Case 1:
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | (256) all_58_6 = e1 & op(e1, e3) = e1
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | REF_CLOSE: (23), (44), (256) are inconsistent by sub-proof #1347.
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | Case 2:
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | (257) all_58_12 = e1 & op(e0, e3) = e1
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | REF_CLOSE: (26), (106), (257) are inconsistent by sub-proof #1422.
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | End of split
% 159.05/27.98 | | | |
% 159.05/27.98 | | | End of split
% 159.05/27.98 | | |
% 159.05/27.98 | | End of split
% 159.05/27.98 | |
% 159.05/27.98 | End of split
% 159.05/27.98 |
% 159.05/27.98 End of proof
% 159.05/27.98
% 159.05/27.98 Sub-proof #537 shows that the following formulas are inconsistent:
% 159.05/27.98 ----------------------------------------------------------------
% 159.05/27.98 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.98 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.98 (2) ~ (e3 = e0)
% 159.05/27.98 (3) ~ (e2 = e0)
% 159.05/27.98 (4) op(e2, e3) = e2
% 159.05/27.98 (5) ~ (e3 = e1)
% 159.05/27.98 (6) all_58_9 = e0
% 159.05/27.98 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.98 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.98 (8) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 159.05/27.98 (9) ~ (e2 = e1)
% 159.05/27.98 (10) ~ (e1 = e0)
% 159.05/27.98 (11) all_58_3 = e3
% 159.05/27.98 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.98
% 159.05/27.98 Begin of proof
% 159.05/27.98 |
% 159.05/27.98 | BETA: splitting (8) gives:
% 159.05/27.98 |
% 159.05/27.98 | Case 1:
% 159.05/27.98 | |
% 159.05/27.98 | | (13) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.98 | |
% 159.05/27.98 | | ALPHA: (13) implies:
% 159.05/27.98 | | (14) all_58_9 = e2
% 159.05/27.98 | |
% 159.05/27.98 | | COMBINE_EQS: (6), (14) imply:
% 159.05/27.98 | | (15) e2 = e0
% 159.05/27.98 | |
% 159.05/27.98 | | REDUCE: (3), (15) imply:
% 159.05/27.98 | | (16) $false
% 159.05/27.98 | |
% 159.05/27.98 | | CLOSE: (16) is inconsistent.
% 159.05/27.98 | |
% 159.05/27.98 | Case 2:
% 159.05/27.98 | |
% 159.05/27.98 | | (17) all_58_10 = e2 & op(e2, e0) = e2
% 159.05/27.98 | |
% 159.05/27.98 | | ALPHA: (17) implies:
% 159.05/27.98 | | (18) all_58_10 = e2
% 159.05/27.98 | |
% 159.05/27.98 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (18) are
% 159.05/27.98 | | inconsistent by sub-proof #906.
% 159.05/27.98 | |
% 159.05/27.98 | End of split
% 159.05/27.98 |
% 159.05/27.98 End of proof
% 159.05/27.98
% 159.05/27.98 Sub-proof #538 shows that the following formulas are inconsistent:
% 159.05/27.98 ----------------------------------------------------------------
% 159.05/27.98 (1) op(e1, e1) = e3
% 159.05/27.98 (2) op(e1, e1) = all_32_1
% 159.05/27.98 (3) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.05/27.98 (4) op(e3, e1) = e3
% 159.05/27.98 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.98 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.98 (6) all_54_13 = all_52_7
% 159.05/27.98 (7) ~ (all_52_7 = e3)
% 159.05/27.98 (8) ~ (all_52_6 = all_52_14)
% 159.05/27.98 (9) ~ (all_52_14 = e0)
% 159.05/27.98 (10) ~ (all_52_11 = e3)
% 159.05/27.98 (11) ~ (all_52_4 = all_52_6)
% 159.05/27.98 (12) op(e3, e3) = all_28_1
% 159.05/27.98 (13) ~ (all_52_7 = all_52_11)
% 159.05/27.98 (14) all_58_0 = e1
% 159.05/27.98 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.98 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.98 (16) all_58_6 = e3
% 159.05/27.98 (17) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.98 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.98 (18) ~ (all_52_14 = e3)
% 159.05/27.98 (19) all_58_12 = e0
% 159.05/27.98 (20) all_54_1 = all_52_4
% 159.05/27.98 (21) op(e3, e2) = all_52_4
% 159.05/27.98 (22) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.05/27.98 (23) all_58_14 = e2
% 159.05/27.98 (24) op(e2, e3) = all_52_1
% 159.05/27.98 (25) all_54_2 = all_52_8
% 159.05/27.98 (26) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.98 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.98 (27) ~ (all_52_8 = all_52_9)
% 159.05/27.98 (28) ~ (e3 = e0)
% 159.05/27.98 (29) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.98 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.98 (30) op(e0, e0) = e0
% 159.05/27.98 (31) ~ (all_52_9 = e3)
% 159.05/27.98 (32) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.98 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.98 (33) op(e2, e3) = e2
% 159.05/27.98 (34) ~ (e3 = e1)
% 159.05/27.98 (35) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.98 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.98 (36) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.98 (37) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.98 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.98 (38) ~ (all_52_7 = e0)
% 159.05/27.98 (39) op(e3, e3) = e1
% 159.05/27.98 (40) all_58_5 = e0
% 159.05/27.98 (41) ~ (all_52_9 = all_52_11)
% 159.05/27.98 (42) ~ (all_52_6 = e0)
% 159.05/27.98 (43) ~ (all_52_6 = all_52_7)
% 159.05/27.98 (44) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.98 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.98 (45) ~ (all_52_4 = e3)
% 159.05/27.98 (46) all_54_6 = all_52_9
% 159.05/27.98 (47) ~ (e2 = e1)
% 159.05/27.98 (48) ~ (all_52_4 = all_52_7)
% 159.05/27.98 (49) ~ (all_52_8 = all_52_11)
% 159.05/27.98 (50) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.98 (51) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.98 (52) ~ (e1 = e0)
% 159.05/27.98 (53) all_58_4 = e3
% 159.05/27.98 (54) all_58_3 = e3
% 159.05/27.98 (55) op(e3, e1) = all_52_8
% 159.05/27.98 (56) ~ (all_52_14 = e1)
% 159.05/27.98 (57) ~ (all_52_9 = e2)
% 159.05/27.98 (58) ~ (all_52_8 = e3)
% 159.05/27.98 (59) all_54_14 = all_52_11
% 159.05/27.98 (60) op(e1, e0) = all_52_14
% 159.05/27.98 (61) op(e3, e3) = all_22_1
% 159.05/27.98 (62) ~ (all_52_8 = e1)
% 159.05/27.98 (63) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.98 (64) ~ (all_52_6 = e3)
% 159.05/27.98 (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.98 (66) all_54_11 = all_52_14
% 159.05/27.98 (67) ~ (e3 = e2)
% 159.05/27.98 (68) ~ (all_52_9 = e1)
% 159.05/27.98 (69) ~ (all_52_11 = e0)
% 159.05/27.98 (70) all_54_9 = all_52_6
% 159.05/27.98 (71) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.98 (72) op(e0, e0) = e3
% 159.05/27.98
% 159.05/27.98 Begin of proof
% 159.05/27.98 |
% 159.05/27.98 | BETA: splitting (44) gives:
% 159.05/27.98 |
% 159.05/27.98 | Case 1:
% 159.05/27.98 | |
% 159.05/27.98 | | (73) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 159.05/27.98 | | e1)
% 159.05/27.98 | |
% 159.05/27.98 | | REF_CLOSE: (12), (15), (16), (19), (24), (28), (30), (33), (34), (39), (40),
% 159.05/27.98 | | (52), (53), (61), (65), (67), (72), (73) are inconsistent by
% 159.05/27.98 | | sub-proof #544.
% 159.05/27.98 | |
% 159.05/27.98 | Case 2:
% 159.05/27.98 | |
% 159.05/27.98 | | (74) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 159.05/27.98 | | e1)
% 159.05/27.98 | |
% 159.05/27.98 | | BETA: splitting (74) gives:
% 159.05/27.98 | |
% 159.05/27.98 | | Case 1:
% 159.05/27.98 | | |
% 159.05/27.98 | | | (75) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.98 | | |
% 159.05/27.98 | | | ALPHA: (75) implies:
% 159.05/27.98 | | | (76) all_58_8 = e1
% 159.05/27.98 | | | (77) op(e1, e1) = e1
% 159.05/27.98 | | |
% 159.05/27.98 | | | BETA: splitting (5) gives:
% 159.05/27.98 | | |
% 159.05/27.98 | | | Case 1:
% 159.05/27.98 | | | |
% 159.05/27.98 | | | | (78) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 159.05/27.98 | | | | = e1)
% 159.05/27.98 | | | |
% 159.05/27.98 | | | | REF_CLOSE: (12), (15), (16), (19), (24), (28), (30), (33), (34), (39),
% 159.05/27.98 | | | | (47), (52), (54), (61), (65), (67), (72), (78) are
% 159.05/27.98 | | | | inconsistent by sub-proof #543.
% 159.05/27.98 | | | |
% 159.05/27.98 | | | Case 2:
% 159.05/27.98 | | | |
% 159.05/27.98 | | | | (79) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 159.05/27.98 | | | | = e1)
% 159.05/27.98 | | | |
% 159.05/27.98 | | | | BETA: splitting (79) gives:
% 159.05/27.98 | | | |
% 159.05/27.98 | | | | Case 1:
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | (80) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | ALPHA: (80) implies:
% 159.05/27.98 | | | | | (81) all_58_5 = e1
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | COMBINE_EQS: (40), (81) imply:
% 159.05/27.98 | | | | | (82) e1 = e0
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | SIMP: (82) implies:
% 159.05/27.98 | | | | | (83) e1 = e0
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | COMBINE_EQS: (76), (83) imply:
% 159.05/27.98 | | | | | (84) all_58_8 = e0
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | REF_CLOSE: (12), (15), (16), (19), (23), (24), (28), (30), (33), (34),
% 159.05/27.98 | | | | | (39), (40), (44), (47), (52), (53), (61), (65), (67), (72),
% 159.05/27.98 | | | | | (84) are inconsistent by sub-proof #541.
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | Case 2:
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | (85) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | ALPHA: (85) implies:
% 159.05/27.98 | | | | | (86) all_58_10 = e1
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | BETA: splitting (29) gives:
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | | Case 1:
% 159.05/27.98 | | | | | |
% 159.05/27.98 | | | | | | (87) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 159.05/27.98 | | | | | | e2) = e2)
% 159.05/27.98 | | | | | |
% 159.05/27.98 | | | | | | BETA: splitting (87) gives:
% 159.05/27.98 | | | | | |
% 159.05/27.98 | | | | | | Case 1:
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | | (88) all_58_0 = e2 & op(e3, e3) = e2
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | | REF_CLOSE: (14), (47), (88) are inconsistent by sub-proof #802.
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | Case 2:
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | | (89) all_58_1 = e2 & op(e3, e2) = e2
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | | ALPHA: (89) implies:
% 159.05/27.98 | | | | | | | (90) all_58_1 = e2
% 159.05/27.98 | | | | | | | (91) op(e3, e2) = e2
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | | BETA: splitting (50) gives:
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | |
% 159.05/27.98 | | | | | | | | (92) all_54_11 = e3
% 159.05/27.98 | | | | | | | |
% 159.05/27.98 | | | | | | | | REF_CLOSE: (18), (66), (92) are inconsistent by sub-proof #1415.
% 159.05/27.98 | | | | | | | |
% 159.05/27.98 | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | |
% 159.05/27.98 | | | | | | | | (93) ~ (all_54_11 = e3)
% 159.05/27.98 | | | | | | | | (94) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.98 | | | | | | | |
% 159.05/27.98 | | | | | | | | BETA: splitting (94) gives:
% 159.05/27.98 | | | | | | | |
% 159.05/27.98 | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | | (95) all_54_11 = e2
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | | COMBINE_EQS: (66), (95) imply:
% 159.05/27.98 | | | | | | | | | (96) all_52_14 = e2
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | | SIMP: (96) implies:
% 159.05/27.98 | | | | | | | | | (97) all_52_14 = e2
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | | REDUCE: (8), (97) imply:
% 159.05/27.98 | | | | | | | | | (98) ~ (all_52_6 = e2)
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | | BETA: splitting (3) gives:
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | (99) all_54_9 = e3
% 159.05/27.98 | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | REF_CLOSE: (64), (70), (99) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | #1181.
% 159.05/27.98 | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | (100) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.05/27.98 | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | BETA: splitting (100) gives:
% 159.05/27.98 | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | (101) all_54_9 = e2
% 159.05/27.98 | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | REF_CLOSE: (70), (98), (101) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | #1180.
% 159.05/27.98 | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | (102) all_54_9 = e1 | all_54_9 = e0
% 159.05/27.98 | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | BETA: splitting (102) gives:
% 159.05/27.98 | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | (103) all_54_9 = e1
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | COMBINE_EQS: (70), (103) imply:
% 159.05/27.98 | | | | | | | | | | | | (104) all_52_6 = e1
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | SIMP: (104) implies:
% 159.05/27.98 | | | | | | | | | | | | (105) all_52_6 = e1
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | REDUCE: (11), (105) imply:
% 159.05/27.98 | | | | | | | | | | | | (106) ~ (all_52_4 = e1)
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | REDUCE: (43), (105) imply:
% 159.05/27.98 | | | | | | | | | | | | (107) ~ (all_52_7 = e1)
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | SIMP: (107) implies:
% 159.05/27.98 | | | | | | | | | | | | (108) ~ (all_52_7 = e1)
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | BETA: splitting (63) gives:
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | (109) all_54_13 = e3
% 159.05/27.98 | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (109) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | | #1435.
% 159.05/27.98 | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | (110) ~ (all_54_13 = e3)
% 159.05/27.98 | | | | | | | | | | | | | (111) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/27.98 | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | BETA: splitting (111) gives:
% 159.05/27.98 | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | (112) all_54_13 = e2
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | COMBINE_EQS: (6), (112) imply:
% 159.05/27.98 | | | | | | | | | | | | | | (113) all_52_7 = e2
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | SIMP: (113) implies:
% 159.05/27.98 | | | | | | | | | | | | | | (114) all_52_7 = e2
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | REDUCE: (48), (114) imply:
% 159.05/27.98 | | | | | | | | | | | | | | (115) ~ (all_52_4 = e2)
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | REDUCE: (13), (114) imply:
% 159.05/27.98 | | | | | | | | | | | | | | (116) ~ (all_52_11 = e2)
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | SIMP: (116) implies:
% 159.05/27.98 | | | | | | | | | | | | | | (117) ~ (all_52_11 = e2)
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | REDUCE: (7), (114) imply:
% 159.05/27.98 | | | | | | | | | | | | | | (118) ~ (e3 = e2)
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | (119) all_54_1 = e3
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | COMBINE_EQS: (20), (119) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | (120) all_52_4 = e3
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | REDUCE: (45), (120) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | (121) $false
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | CLOSE: (121) is inconsistent.
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | (122) ~ (all_54_1 = e3)
% 159.05/27.98 | | | | | | | | | | | | | | | (123) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | (124) all_54_14 = e3
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | REF_CLOSE: (10), (59), (124) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | | | | | #1413.
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | (125) ~ (all_54_14 = e3)
% 159.05/27.98 | | | | | | | | | | | | | | | | (126) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | (127) all_54_1 = e2
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (127) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | (128) all_52_4 = e2
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | REDUCE: (115), (128) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | (129) $false
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | (130) ~ (all_54_1 = e2)
% 159.05/27.98 | | | | | | | | | | | | | | | | | (131) all_54_1 = e1 | all_54_1 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (132) all_54_1 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (132) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (133) all_52_4 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | REDUCE: (106), (133) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (134) $false
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (135) all_54_1 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (135) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (136) all_52_4 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | REDUCE: (45), (136) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (137) ~ (e3 = e0)
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | REDUCE: (115), (136) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (138) ~ (e2 = e0)
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | SIMP: (138) implies:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (139) ~ (e2 = e0)
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | REDUCE: (21), (136) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | (140) op(e3, e2) = e0
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | (141) all_54_14 = e2
% 159.05/27.98 | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (117), (141) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | #1232.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | (142) ~ (all_54_14 = e2)
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | (143) all_54_14 = e1 | all_54_14 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (144) all_54_14 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (144) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (145) all_52_11 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | SIMP: (145) implies:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (146) all_52_11 = e1
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (146) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (147) ~ (e3 = e1)
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (146) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (148) ~ (e2 = e1)
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with e0, e2, e2, e3,
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | simplifying with (91), (140) gives:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (149) e2 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (149) imply:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (150) all_58_1 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (12), (14), (15),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (16), (17), (18), (19), (23), (24), (25), (26),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (35), (36), (37), (39), (40), (41), (44), (46),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (47), (49), (50), (51), (52), (53), (54), (55),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (65),
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (66), (67), (68), (71), (72), (86), (139), (150)
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #539.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | (151) all_54_14 = e0
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (69), (151) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | | #1400.
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | (152) all_54_13 = e1 | all_54_13 = e0
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | | REF_CLOSE: (6), (38), (108), (152) are inconsistent by
% 159.05/27.98 | | | | | | | | | | | | | | sub-proof #875.
% 159.05/27.98 | | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | (153) all_54_9 = e0
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | | REF_CLOSE: (42), (70), (153) are inconsistent by sub-proof
% 159.05/27.98 | | | | | | | | | | | | #1170.
% 159.05/27.98 | | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | | |
% 159.05/27.98 | | | | | | | | | End of split
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | Case 2:
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | | (154) all_54_11 = e1 | all_54_11 = e0
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | | REF_CLOSE: (9), (56), (66), (154) are inconsistent by
% 159.05/27.98 | | | | | | | | | sub-proof #1227.
% 159.05/27.98 | | | | | | | | |
% 159.05/27.98 | | | | | | | | End of split
% 159.05/27.98 | | | | | | | |
% 159.05/27.98 | | | | | | | End of split
% 159.05/27.98 | | | | | | |
% 159.05/27.98 | | | | | | End of split
% 159.05/27.98 | | | | | |
% 159.05/27.98 | | | | | Case 2:
% 159.05/27.98 | | | | | |
% 159.05/27.98 | | | | | | (155) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 159.05/27.98 | | | | | | e0) = e2)
% 159.05/27.98 | | | | | |
% 159.05/27.98 | | | | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (12), (14), (15), (16),
% 159.05/27.98 | | | | | | (17), (18), (19), (23), (24), (25), (26), (27), (28),
% 159.05/27.98 | | | | | | (30), (31), (32), (33), (34), (35), (36), (39), (40),
% 159.05/27.98 | | | | | | (41), (44), (46), (49), (50), (51), (52), (53), (54),
% 159.05/27.98 | | | | | | (55), (56), (57), (58), (59), (60), (61), (62), (65),
% 159.05/27.98 | | | | | | (66), (67), (68), (71), (72), (76), (77), (155) are
% 159.05/27.98 | | | | | | inconsistent by sub-proof #540.
% 159.05/27.98 | | | | | |
% 159.05/27.98 | | | | | End of split
% 159.05/27.98 | | | | |
% 159.05/27.98 | | | | End of split
% 159.05/27.98 | | | |
% 159.05/27.98 | | | End of split
% 159.05/27.98 | | |
% 159.05/27.98 | | Case 2:
% 159.05/27.98 | | |
% 159.05/27.98 | | | (156) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.98 | | |
% 159.05/27.98 | | | REF_CLOSE: (23), (47), (156) are inconsistent by sub-proof #1339.
% 159.05/27.98 | | |
% 159.05/27.98 | | End of split
% 159.05/27.98 | |
% 159.05/27.98 | End of split
% 159.05/27.98 |
% 159.05/27.98 End of proof
% 159.05/27.98
% 159.05/27.98 Sub-proof #539 shows that the following formulas are inconsistent:
% 159.05/27.98 ----------------------------------------------------------------
% 159.05/27.98 (1) op(e1, e1) = e3
% 159.05/27.98 (2) op(e1, e1) = all_32_1
% 159.05/27.98 (3) op(e3, e1) = e3
% 159.05/27.98 (4) all_58_1 = e0
% 159.05/27.98 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.98 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.98 (6) ~ (all_52_14 = e0)
% 159.05/27.98 (7) ~ (all_52_11 = e3)
% 159.05/27.98 (8) op(e3, e3) = all_28_1
% 159.05/27.98 (9) all_58_0 = e1
% 159.05/27.98 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.98 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.98 (11) all_58_6 = e3
% 159.05/27.98 (12) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.98 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.98 (13) ~ (all_52_14 = e3)
% 159.05/27.98 (14) all_58_12 = e0
% 159.05/27.98 (15) all_58_14 = e2
% 159.05/27.98 (16) op(e2, e3) = all_52_1
% 159.05/27.98 (17) all_54_2 = all_52_8
% 159.05/27.98 (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.98 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.98 (19) ~ (all_52_8 = all_52_9)
% 159.05/27.98 (20) ~ (e3 = e0)
% 159.05/27.98 (21) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/27.98 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.98 (22) op(e0, e0) = e0
% 159.05/27.98 (23) ~ (e2 = e0)
% 159.05/27.98 (24) ~ (all_52_9 = e3)
% 159.05/27.99 (25) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.99 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.99 (26) op(e2, e3) = e2
% 159.05/27.99 (27) ~ (e3 = e1)
% 159.05/27.99 (28) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.99 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.99 (29) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.99 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/27.99 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/27.99 (31) all_58_10 = e1
% 159.05/27.99 (32) op(e3, e3) = e1
% 159.05/27.99 (33) all_58_5 = e0
% 159.05/27.99 (34) ~ (all_52_9 = all_52_11)
% 159.05/27.99 (35) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.99 (36) all_54_6 = all_52_9
% 159.05/27.99 (37) ~ (e2 = e1)
% 159.05/27.99 (38) ~ (all_52_8 = all_52_11)
% 159.05/27.99 (39) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.99 (40) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.99 (41) ~ (e1 = e0)
% 159.05/27.99 (42) all_58_4 = e3
% 159.05/27.99 (43) all_58_3 = e3
% 159.05/27.99 (44) op(e3, e1) = all_52_8
% 159.05/27.99 (45) ~ (all_52_14 = e1)
% 159.05/27.99 (46) ~ (all_52_9 = e2)
% 159.05/27.99 (47) ~ (all_52_8 = e3)
% 159.05/27.99 (48) all_54_14 = all_52_11
% 159.05/27.99 (49) op(e1, e0) = all_52_14
% 159.05/27.99 (50) op(e3, e3) = all_22_1
% 159.05/27.99 (51) ~ (all_52_8 = e1)
% 159.05/27.99 (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.99 (53) all_54_11 = all_52_14
% 159.05/27.99 (54) ~ (e3 = e2)
% 159.05/27.99 (55) ~ (all_52_9 = e1)
% 159.05/27.99 (56) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.99 (57) op(e0, e0) = e3
% 159.05/27.99
% 159.05/27.99 Begin of proof
% 159.05/27.99 |
% 159.05/27.99 | BETA: splitting (35) gives:
% 159.05/27.99 |
% 159.05/27.99 | Case 1:
% 159.05/27.99 | |
% 159.05/27.99 | | (58) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 159.05/27.99 | | e1)
% 159.05/27.99 | |
% 159.05/27.99 | | BETA: splitting (58) gives:
% 159.05/27.99 | |
% 159.05/27.99 | | Case 1:
% 159.05/27.99 | | |
% 159.05/27.99 | | | (59) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/27.99 | | |
% 159.05/27.99 | | | REF_CLOSE: (8), (10), (11), (14), (16), (20), (22), (26), (27), (32),
% 159.05/27.99 | | | (41), (42), (50), (52), (54), (57), (59) are inconsistent by
% 159.05/27.99 | | | sub-proof #545.
% 159.05/27.99 | | |
% 159.05/27.99 | | Case 2:
% 159.05/27.99 | | |
% 159.05/27.99 | | | (60) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/27.99 | | |
% 159.05/27.99 | | | ALPHA: (60) implies:
% 159.05/27.99 | | | (61) all_58_5 = e1
% 159.05/27.99 | | |
% 159.05/27.99 | | | REF_CLOSE: (5), (20), (23), (26), (27), (30), (31), (37), (41), (43),
% 159.05/27.99 | | | (52), (61) are inconsistent by sub-proof #754.
% 159.05/27.99 | | |
% 159.05/27.99 | | End of split
% 159.05/27.99 | |
% 159.05/27.99 | Case 2:
% 159.05/27.99 | |
% 159.05/27.99 | | (62) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 159.05/27.99 | | e1)
% 159.05/27.99 | |
% 159.05/27.99 | | BETA: splitting (62) gives:
% 159.05/27.99 | |
% 159.05/27.99 | | Case 1:
% 159.05/27.99 | | |
% 159.05/27.99 | | | (63) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.99 | | |
% 159.05/27.99 | | | ALPHA: (63) implies:
% 159.05/27.99 | | | (64) all_58_8 = e1
% 159.05/27.99 | | | (65) op(e1, e1) = e1
% 159.05/27.99 | | |
% 159.05/27.99 | | | BETA: splitting (21) gives:
% 159.05/27.99 | | |
% 159.05/27.99 | | | Case 1:
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | (66) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 159.05/27.99 | | | | = e2)
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | BETA: splitting (66) gives:
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | Case 1:
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | (67) all_58_0 = e2 & op(e3, e3) = e2
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | REF_CLOSE: (9), (37), (67) are inconsistent by sub-proof #802.
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | Case 2:
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | (68) all_58_1 = e2 & op(e3, e2) = e2
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | REF_CLOSE: (4), (23), (68) are inconsistent by sub-proof #801.
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | End of split
% 159.05/27.99 | | | |
% 159.05/27.99 | | | Case 2:
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | (69) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 159.05/27.99 | | | | = e2)
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/27.99 | | | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (24),
% 159.05/27.99 | | | | (25), (26), (27), (28), (29), (32), (33), (34), (35), (36),
% 159.05/27.99 | | | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 159.05/27.99 | | | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 159.05/27.99 | | | | (64), (65), (69) are inconsistent by sub-proof #540.
% 159.05/27.99 | | | |
% 159.05/27.99 | | | End of split
% 159.05/27.99 | | |
% 159.05/27.99 | | Case 2:
% 159.05/27.99 | | |
% 159.05/27.99 | | | (70) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.99 | | |
% 159.05/27.99 | | | REF_CLOSE: (15), (37), (70) are inconsistent by sub-proof #1339.
% 159.05/27.99 | | |
% 159.05/27.99 | | End of split
% 159.05/27.99 | |
% 159.05/27.99 | End of split
% 159.05/27.99 |
% 159.05/27.99 End of proof
% 159.05/27.99
% 159.05/27.99 Sub-proof #540 shows that the following formulas are inconsistent:
% 159.05/27.99 ----------------------------------------------------------------
% 159.05/27.99 (1) op(e1, e1) = e3
% 159.05/27.99 (2) op(e1, e1) = all_32_1
% 159.05/27.99 (3) op(e3, e1) = e3
% 159.05/27.99 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/27.99 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/27.99 (5) ~ (all_52_14 = e0)
% 159.05/27.99 (6) ~ (all_52_11 = e3)
% 159.05/27.99 (7) op(e3, e3) = all_28_1
% 159.05/27.99 (8) all_58_0 = e1
% 159.05/27.99 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.99 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.99 (10) all_58_6 = e3
% 159.05/27.99 (11) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.05/27.99 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.99 (12) ~ (all_52_14 = e3)
% 159.05/27.99 (13) all_58_12 = e0
% 159.05/27.99 (14) all_58_14 = e2
% 159.05/27.99 (15) op(e2, e3) = all_52_1
% 159.05/27.99 (16) all_54_2 = all_52_8
% 159.05/27.99 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/27.99 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/27.99 (18) ~ (all_52_8 = all_52_9)
% 159.05/27.99 (19) ~ (e3 = e0)
% 159.05/27.99 (20) op(e0, e0) = e0
% 159.05/27.99 (21) ~ (all_52_9 = e3)
% 159.05/27.99 (22) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/27.99 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/27.99 (23) op(e2, e3) = e2
% 159.05/27.99 (24) ~ (e3 = e1)
% 159.05/27.99 (25) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/27.99 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/27.99 (26) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.99 (27) op(e3, e3) = e1
% 159.05/27.99 (28) all_58_5 = e0
% 159.05/27.99 (29) ~ (all_52_9 = all_52_11)
% 159.05/27.99 (30) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.99 (31) all_54_6 = all_52_9
% 159.05/27.99 (32) ~ (all_52_8 = all_52_11)
% 159.05/27.99 (33) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.99 (34) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/27.99 (35) ~ (e1 = e0)
% 159.05/27.99 (36) all_58_4 = e3
% 159.05/27.99 (37) all_58_3 = e3
% 159.05/27.99 (38) op(e3, e1) = all_52_8
% 159.05/27.99 (39) ~ (all_52_14 = e1)
% 159.05/27.99 (40) ~ (all_52_9 = e2)
% 159.05/27.99 (41) ~ (all_52_8 = e3)
% 159.05/27.99 (42) all_54_14 = all_52_11
% 159.05/27.99 (43) op(e1, e0) = all_52_14
% 159.05/27.99 (44) op(e3, e3) = all_22_1
% 159.05/27.99 (45) ~ (all_52_8 = e1)
% 159.05/27.99 (46) op(e1, e1) = e1
% 159.05/27.99 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.99 (48) all_54_11 = all_52_14
% 159.05/27.99 (49) ~ (e3 = e2)
% 159.05/27.99 (50) ~ (all_52_9 = e1)
% 159.05/27.99 (51) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.99 (52) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/27.99 (53) all_58_8 = e1
% 159.05/27.99 (54) op(e0, e0) = e3
% 159.05/27.99
% 159.05/27.99 Begin of proof
% 159.05/27.99 |
% 159.05/27.99 | BETA: splitting (52) gives:
% 159.05/27.99 |
% 159.05/27.99 | Case 1:
% 159.05/27.99 | |
% 159.05/27.99 | | (55) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/27.99 | |
% 159.05/27.99 | | REF_CLOSE: (8), (9), (10), (13), (15), (19), (23), (24), (36), (47), (49),
% 159.05/27.99 | | (55) are inconsistent by sub-proof #830.
% 159.05/27.99 | |
% 159.05/27.99 | Case 2:
% 159.05/27.99 | |
% 159.05/27.99 | | (56) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/27.99 | |
% 159.05/27.99 | | ALPHA: (56) implies:
% 159.05/27.99 | | (57) all_58_9 = e2
% 159.05/27.99 | |
% 159.05/27.99 | | BETA: splitting (33) gives:
% 159.05/27.99 | |
% 159.05/27.99 | | Case 1:
% 159.05/27.99 | | |
% 159.05/27.99 | | | (58) all_54_11 = e3
% 159.05/27.99 | | |
% 159.05/27.99 | | | REF_CLOSE: (12), (48), (58) are inconsistent by sub-proof #1415.
% 159.05/27.99 | | |
% 159.05/27.99 | | Case 2:
% 159.05/27.99 | | |
% 159.05/27.99 | | | (59) ~ (all_54_11 = e3)
% 159.05/27.99 | | | (60) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.05/27.99 | | |
% 159.05/27.99 | | | BETA: splitting (60) gives:
% 159.05/27.99 | | |
% 159.05/27.99 | | | Case 1:
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | (61) all_54_11 = e2
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | COMBINE_EQS: (48), (61) imply:
% 159.05/27.99 | | | | (62) all_52_14 = e2
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | SIMP: (62) implies:
% 159.05/27.99 | | | | (63) all_52_14 = e2
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | REDUCE: (12), (63) imply:
% 159.05/27.99 | | | | (64) ~ (e3 = e2)
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | REDUCE: (39), (63) imply:
% 159.05/27.99 | | | | (65) ~ (e2 = e1)
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | REDUCE: (5), (63) imply:
% 159.05/27.99 | | | | (66) ~ (e2 = e0)
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | REDUCE: (43), (63) imply:
% 159.05/27.99 | | | | (67) op(e1, e0) = e2
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | BETA: splitting (17) gives:
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | Case 1:
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | (68) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 159.05/27.99 | | | | | e2) = e2)
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | BETA: splitting (68) gives:
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | Case 1:
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | (69) all_58_6 = e2 & op(e1, e3) = e2
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | ALPHA: (69) implies:
% 159.05/27.99 | | | | | | (70) all_58_6 = e2
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | REF_CLOSE: (8), (9), (13), (15), (19), (23), (24), (47), (49), (70)
% 159.05/27.99 | | | | | | are inconsistent by sub-proof #1154.
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | Case 2:
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | (71) all_58_7 = e2 & op(e1, e2) = e2
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | ALPHA: (71) implies:
% 159.05/27.99 | | | | | | (72) all_58_7 = e2
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | BETA: splitting (22) gives:
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | Case 1:
% 159.05/27.99 | | | | | | |
% 159.05/27.99 | | | | | | | (73) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 159.05/27.99 | | | | | | | op(e1, e2) = e0)
% 159.05/27.99 | | | | | | |
% 159.05/27.99 | | | | | | | REF_CLOSE: (10), (19), (66), (72), (73) are inconsistent by
% 159.05/27.99 | | | | | | | sub-proof #1044.
% 159.05/27.99 | | | | | | |
% 159.05/27.99 | | | | | | Case 2:
% 159.05/27.99 | | | | | | |
% 159.05/27.99 | | | | | | | (74) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 159.05/27.99 | | | | | | | op(e1, e0) = e0)
% 159.05/27.99 | | | | | | |
% 159.05/27.99 | | | | | | | BETA: splitting (74) gives:
% 159.05/27.99 | | | | | | |
% 159.05/27.99 | | | | | | | Case 1:
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | | (75) all_58_8 = e0 & op(e1, e1) = e0
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | | ALPHA: (75) implies:
% 159.05/27.99 | | | | | | | | (76) all_58_8 = e0
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | | REF_CLOSE: (7), (9), (10), (13), (14), (15), (19), (20), (23),
% 159.05/27.99 | | | | | | | | (24), (27), (28), (30), (35), (36), (44), (47), (49),
% 159.05/27.99 | | | | | | | | (54), (65), (76) are inconsistent by sub-proof #541.
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | Case 2:
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | | (77) all_58_11 = e0 & op(e1, e0) = e0
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | | ALPHA: (77) implies:
% 159.05/27.99 | | | | | | | | (78) op(e1, e0) = e0
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | | BETA: splitting (34) gives:
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | | Case 1:
% 159.05/27.99 | | | | | | | | |
% 159.05/27.99 | | | | | | | | | (79) all_54_6 = e2
% 159.05/27.99 | | | | | | | | |
% 159.05/27.99 | | | | | | | | | REF_CLOSE: (31), (40), (79) are inconsistent by sub-proof
% 159.05/27.99 | | | | | | | | | #1192.
% 159.05/27.99 | | | | | | | | |
% 159.05/27.99 | | | | | | | | Case 2:
% 159.05/27.99 | | | | | | | | |
% 159.05/27.99 | | | | | | | | | (80) all_54_6 = e1 | all_54_6 = e0
% 159.05/27.99 | | | | | | | | |
% 159.05/27.99 | | | | | | | | | BETA: splitting (80) gives:
% 159.05/27.99 | | | | | | | | |
% 159.05/27.99 | | | | | | | | | Case 1:
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | (81) all_54_6 = e1
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | REF_CLOSE: (31), (50), (81) are inconsistent by sub-proof
% 159.05/27.99 | | | | | | | | | | #562.
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | Case 2:
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | (82) all_54_6 = e0
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | COMBINE_EQS: (31), (82) imply:
% 159.05/27.99 | | | | | | | | | | (83) all_52_9 = e0
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | SIMP: (83) implies:
% 159.05/27.99 | | | | | | | | | | (84) all_52_9 = e0
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | REDUCE: (18), (84) imply:
% 159.05/27.99 | | | | | | | | | | (85) ~ (all_52_8 = e0)
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | REDUCE: (29), (84) imply:
% 159.05/27.99 | | | | | | | | | | (86) ~ (all_52_11 = e0)
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | SIMP: (86) implies:
% 159.05/27.99 | | | | | | | | | | (87) ~ (all_52_11 = e0)
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | REDUCE: (21), (84) imply:
% 159.05/27.99 | | | | | | | | | | (88) ~ (e3 = e0)
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | BETA: splitting (26) gives:
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | Case 1:
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | (89) all_54_2 = e3
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | COMBINE_EQS: (16), (89) imply:
% 159.05/27.99 | | | | | | | | | | | (90) all_52_8 = e3
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | REDUCE: (41), (90) imply:
% 159.05/27.99 | | | | | | | | | | | (91) $false
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | CLOSE: (91) is inconsistent.
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | Case 2:
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | (92) ~ (all_54_2 = e3)
% 159.05/27.99 | | | | | | | | | | | (93) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | BETA: splitting (93) gives:
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | Case 1:
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | (94) all_54_2 = e2
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | COMBINE_EQS: (16), (94) imply:
% 159.05/27.99 | | | | | | | | | | | | (95) all_52_8 = e2
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | REDUCE: (32), (95) imply:
% 159.05/27.99 | | | | | | | | | | | | (96) ~ (all_52_11 = e2)
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | SIMP: (96) implies:
% 159.05/27.99 | | | | | | | | | | | | (97) ~ (all_52_11 = e2)
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | REDUCE: (38), (95) imply:
% 159.05/27.99 | | | | | | | | | | | | (98) op(e3, e1) = e2
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | BETA: splitting (51) gives:
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | Case 1:
% 159.05/27.99 | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | (99) all_54_14 = e3
% 159.05/27.99 | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | REF_CLOSE: (6), (42), (99) are inconsistent by sub-proof
% 159.05/27.99 | | | | | | | | | | | | | #1413.
% 159.05/27.99 | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | Case 2:
% 159.05/27.99 | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | (100) ~ (all_54_14 = e3)
% 159.05/27.99 | | | | | | | | | | | | | (101) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/27.99 | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | BETA: splitting (101) gives:
% 159.05/27.99 | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | Case 1:
% 159.05/27.99 | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | (102) all_54_14 = e2
% 159.05/27.99 | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | REF_CLOSE: (42), (97), (102) are inconsistent by sub-proof
% 159.05/27.99 | | | | | | | | | | | | | | #1232.
% 159.05/27.99 | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | Case 2:
% 159.05/27.99 | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | (103) ~ (all_54_14 = e2)
% 159.05/27.99 | | | | | | | | | | | | | | (104) all_54_14 = e1 | all_54_14 = e0
% 159.05/27.99 | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 159.05/27.99 | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | Case 1:
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | (105) all_54_14 = e1
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | COMBINE_EQS: (42), (105) imply:
% 159.05/27.99 | | | | | | | | | | | | | | | (106) all_52_11 = e1
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | SIMP: (106) implies:
% 159.05/27.99 | | | | | | | | | | | | | | | (107) all_52_11 = e1
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | REDUCE: (6), (107) imply:
% 159.05/27.99 | | | | | | | | | | | | | | | (108) ~ (e3 = e1)
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | REDUCE: (97), (107) imply:
% 159.05/27.99 | | | | | | | | | | | | | | | (109) ~ (e2 = e1)
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e0, e2, e0, e1,
% 159.05/27.99 | | | | | | | | | | | | | | | simplifying with (67), (78) gives:
% 159.05/27.99 | | | | | | | | | | | | | | | (110) e2 = e0
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e3, all_32_1, e1, e1,
% 159.05/27.99 | | | | | | | | | | | | | | | simplifying with (1), (2) gives:
% 159.05/27.99 | | | | | | | | | | | | | | | (111) all_32_1 = e3
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e1, all_32_1, e1, e1,
% 159.05/27.99 | | | | | | | | | | | | | | | simplifying with (2), (46) gives:
% 159.05/27.99 | | | | | | | | | | | | | | | (112) all_32_1 = e1
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e2, e3, e1, e3,
% 159.05/27.99 | | | | | | | | | | | | | | | simplifying with (3), (98) gives:
% 159.05/27.99 | | | | | | | | | | | | | | | (113) e3 = e2
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | COMBINE_EQS: (111), (112) imply:
% 159.05/27.99 | | | | | | | | | | | | | | | (114) e3 = e1
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | SIMP: (114) implies:
% 159.05/27.99 | | | | | | | | | | | | | | | (115) e3 = e1
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | COMBINE_EQS: (113), (115) imply:
% 159.05/27.99 | | | | | | | | | | | | | | | (116) e2 = e1
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | SIMP: (116) implies:
% 159.05/27.99 | | | | | | | | | | | | | | | (117) e2 = e1
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | COMBINE_EQS: (110), (117) imply:
% 159.05/27.99 | | | | | | | | | | | | | | | (118) e1 = e0
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | SIMP: (118) implies:
% 159.05/27.99 | | | | | | | | | | | | | | | (119) e1 = e0
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | COMBINE_EQS: (53), (119) imply:
% 159.05/27.99 | | | | | | | | | | | | | | | (120) all_58_8 = e0
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (13), (14), (15), (19), (20),
% 159.05/27.99 | | | | | | | | | | | | | | | (23), (24), (27), (28), (30), (35), (36), (44),
% 159.05/27.99 | | | | | | | | | | | | | | | (47), (49), (54), (65), (120) are inconsistent by
% 159.05/27.99 | | | | | | | | | | | | | | | sub-proof #541.
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | Case 2:
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | (121) all_54_14 = e0
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | | REF_CLOSE: (42), (87), (121) are inconsistent by sub-proof
% 159.05/27.99 | | | | | | | | | | | | | | | #1400.
% 159.05/27.99 | | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | | End of split
% 159.05/27.99 | | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | | End of split
% 159.05/27.99 | | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | End of split
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | Case 2:
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | (122) all_54_2 = e1 | all_54_2 = e0
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | | REF_CLOSE: (16), (45), (85), (122) are inconsistent by
% 159.05/27.99 | | | | | | | | | | | | sub-proof #561.
% 159.05/27.99 | | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | | End of split
% 159.05/27.99 | | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | | End of split
% 159.05/27.99 | | | | | | | | | |
% 159.05/27.99 | | | | | | | | | End of split
% 159.05/27.99 | | | | | | | | |
% 159.05/27.99 | | | | | | | | End of split
% 159.05/27.99 | | | | | | | |
% 159.05/27.99 | | | | | | | End of split
% 159.05/27.99 | | | | | | |
% 159.05/27.99 | | | | | | End of split
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | End of split
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | Case 2:
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | (123) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 159.05/27.99 | | | | | e0) = e2)
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | BETA: splitting (123) gives:
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | | Case 1:
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | (124) all_58_8 = e2 & op(e1, e1) = e2
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | REF_CLOSE: (14), (19), (24), (25), (30), (35), (36), (65), (66),
% 159.05/27.99 | | | | | | (124) are inconsistent by sub-proof #1338.
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | Case 2:
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | (125) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | ALPHA: (125) implies:
% 159.05/27.99 | | | | | | (126) all_58_11 = e2
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | | REF_CLOSE: (4), (11), (23), (24), (28), (35), (37), (47), (57),
% 159.05/27.99 | | | | | | (65), (66), (126) are inconsistent by sub-proof #677.
% 159.05/27.99 | | | | | |
% 159.05/27.99 | | | | | End of split
% 159.05/27.99 | | | | |
% 159.05/27.99 | | | | End of split
% 159.05/27.99 | | | |
% 159.05/27.99 | | | Case 2:
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | (127) all_54_11 = e1 | all_54_11 = e0
% 159.05/27.99 | | | |
% 159.05/27.99 | | | | REF_CLOSE: (5), (39), (48), (127) are inconsistent by sub-proof #1227.
% 159.05/27.99 | | | |
% 159.05/27.99 | | | End of split
% 159.05/27.99 | | |
% 159.05/27.99 | | End of split
% 159.05/27.99 | |
% 159.05/27.99 | End of split
% 159.05/27.99 |
% 159.05/27.99 End of proof
% 159.05/27.99
% 159.05/27.99 Sub-proof #541 shows that the following formulas are inconsistent:
% 159.05/27.99 ----------------------------------------------------------------
% 159.05/27.99 (1) op(e3, e3) = all_28_1
% 159.05/27.99 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.99 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.99 (3) all_58_6 = e3
% 159.05/27.99 (4) all_58_12 = e0
% 159.05/27.99 (5) all_58_14 = e2
% 159.05/27.99 (6) op(e2, e3) = all_52_1
% 159.05/27.99 (7) ~ (e3 = e0)
% 159.05/27.99 (8) op(e0, e0) = e0
% 159.05/27.99 (9) op(e2, e3) = e2
% 159.05/27.99 (10) ~ (e3 = e1)
% 159.05/27.99 (11) op(e3, e3) = e1
% 159.05/27.99 (12) all_58_5 = e0
% 159.05/27.99 (13) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/27.99 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.99 (14) ~ (e2 = e1)
% 159.05/27.99 (15) ~ (e1 = e0)
% 159.05/27.99 (16) all_58_4 = e3
% 159.05/27.99 (17) op(e3, e3) = all_22_1
% 159.05/27.99 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.99 (19) all_58_8 = e0
% 159.05/27.99 (20) ~ (e3 = e2)
% 159.05/27.99 (21) op(e0, e0) = e3
% 159.05/27.99
% 159.05/27.99 Begin of proof
% 159.05/27.99 |
% 159.05/27.99 | BETA: splitting (13) gives:
% 159.05/27.99 |
% 159.05/27.99 | Case 1:
% 159.05/27.99 | |
% 159.05/27.99 | | (22) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 159.05/27.99 | | e1)
% 159.05/27.99 | |
% 159.05/27.99 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (15),
% 159.05/27.99 | | (16), (17), (18), (20), (21), (22) are inconsistent by sub-proof
% 159.05/27.99 | | #544.
% 159.05/27.99 | |
% 159.05/27.99 | Case 2:
% 159.05/27.99 | |
% 159.05/27.99 | | (23) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 159.05/27.99 | | e1)
% 159.05/27.99 | |
% 159.05/27.99 | | REF_CLOSE: (5), (14), (15), (19), (23) are inconsistent by sub-proof #542.
% 159.05/27.99 | |
% 159.05/27.99 | End of split
% 159.05/27.99 |
% 159.05/27.99 End of proof
% 159.05/27.99
% 159.05/27.99 Sub-proof #542 shows that the following formulas are inconsistent:
% 159.05/27.99 ----------------------------------------------------------------
% 159.05/27.99 (1) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/27.99 (2) all_58_14 = e2
% 159.05/27.99 (3) ~ (e2 = e1)
% 159.05/27.99 (4) ~ (e1 = e0)
% 159.05/27.99 (5) all_58_8 = e0
% 159.05/27.99
% 159.05/27.99 Begin of proof
% 159.05/27.99 |
% 159.05/27.99 | BETA: splitting (1) gives:
% 159.05/27.99 |
% 159.05/27.99 | Case 1:
% 159.05/27.99 | |
% 159.05/27.99 | | (6) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/27.99 | |
% 159.05/27.99 | | ALPHA: (6) implies:
% 159.05/27.99 | | (7) all_58_8 = e1
% 159.05/27.99 | |
% 159.05/27.99 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1445.
% 159.05/27.99 | |
% 159.05/27.99 | Case 2:
% 159.05/27.99 | |
% 159.05/27.99 | | (8) all_58_14 = e1 & op(e0, e1) = e1
% 159.05/27.99 | |
% 159.05/27.99 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #1339.
% 159.05/27.99 | |
% 159.05/27.99 | End of split
% 159.05/27.99 |
% 159.05/27.99 End of proof
% 159.05/27.99
% 159.05/27.99 Sub-proof #543 shows that the following formulas are inconsistent:
% 159.05/27.99 ----------------------------------------------------------------
% 159.05/27.99 (1) op(e3, e3) = all_28_1
% 159.05/27.99 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.99 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.99 (3) all_58_6 = e3
% 159.05/27.99 (4) all_58_12 = e0
% 159.05/27.99 (5) op(e2, e3) = all_52_1
% 159.05/27.99 (6) ~ (e3 = e0)
% 159.05/27.99 (7) op(e0, e0) = e0
% 159.05/27.99 (8) op(e2, e3) = e2
% 159.05/27.99 (9) ~ (e3 = e1)
% 159.05/27.99 (10) op(e3, e3) = e1
% 159.05/27.99 (11) ~ (e2 = e1)
% 159.05/27.99 (12) ~ (e1 = e0)
% 159.05/27.99 (13) all_58_3 = e3
% 159.05/27.99 (14) op(e3, e3) = all_22_1
% 159.05/27.99 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.99 (16) ~ (e3 = e2)
% 159.05/27.99 (17) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 159.05/27.99 (18) op(e0, e0) = e3
% 159.05/27.99
% 159.05/27.99 Begin of proof
% 159.05/27.99 |
% 159.05/27.99 | BETA: splitting (17) gives:
% 159.05/27.99 |
% 159.05/27.99 | Case 1:
% 159.05/27.99 | |
% 159.05/27.99 | | (19) all_58_2 = e1 & op(e2, e3) = e1
% 159.05/27.99 | |
% 159.05/27.99 | | ALPHA: (19) implies:
% 159.05/27.99 | | (20) op(e2, e3) = e1
% 159.05/27.99 | |
% 159.05/27.99 | | REF_CLOSE: (8), (11), (15), (20) are inconsistent by sub-proof #1430.
% 159.05/27.99 | |
% 159.05/27.99 | Case 2:
% 159.05/27.99 | |
% 159.05/27.99 | | (21) all_58_3 = e1 & op(e2, e2) = e1
% 159.05/27.99 | |
% 159.05/27.99 | | ALPHA: (21) implies:
% 159.05/27.99 | | (22) all_58_3 = e1
% 159.05/27.99 | |
% 159.05/27.99 | | COMBINE_EQS: (13), (22) imply:
% 159.05/27.99 | | (23) e3 = e1
% 159.05/27.99 | |
% 159.05/27.99 | | COMBINE_EQS: (3), (23) imply:
% 159.05/27.99 | | (24) all_58_6 = e1
% 159.05/27.99 | |
% 159.05/27.99 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (14), (15),
% 159.05/27.99 | | (16), (18), (24) are inconsistent by sub-proof #546.
% 159.05/27.99 | |
% 159.05/27.99 | End of split
% 159.05/27.99 |
% 159.05/27.99 End of proof
% 159.05/27.99
% 159.05/27.99 Sub-proof #544 shows that the following formulas are inconsistent:
% 159.05/27.99 ----------------------------------------------------------------
% 159.05/27.99 (1) op(e3, e3) = all_28_1
% 159.05/27.99 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/27.99 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/27.99 (3) all_58_6 = e3
% 159.05/27.99 (4) all_58_12 = e0
% 159.05/27.99 (5) op(e2, e3) = all_52_1
% 159.05/27.99 (6) ~ (e3 = e0)
% 159.05/27.99 (7) op(e0, e0) = e0
% 159.05/27.99 (8) op(e2, e3) = e2
% 159.05/27.99 (9) ~ (e3 = e1)
% 159.05/27.99 (10) op(e3, e3) = e1
% 159.05/27.99 (11) all_58_5 = e0
% 159.05/27.99 (12) ~ (e1 = e0)
% 159.05/27.99 (13) all_58_4 = e3
% 159.05/27.99 (14) op(e3, e3) = all_22_1
% 159.05/27.99 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/27.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/27.99 (16) ~ (e3 = e2)
% 159.05/28.00 (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 159.05/28.00 (18) op(e0, e0) = e3
% 159.05/28.00
% 159.05/28.00 Begin of proof
% 159.05/28.00 |
% 159.05/28.00 | BETA: splitting (17) gives:
% 159.05/28.00 |
% 159.05/28.00 | Case 1:
% 159.05/28.00 | |
% 159.05/28.00 | | (19) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/28.00 | |
% 159.05/28.00 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 159.05/28.00 | | (14), (15), (16), (18), (19) are inconsistent by sub-proof #545.
% 159.05/28.00 | |
% 159.05/28.00 | Case 2:
% 159.05/28.00 | |
% 159.05/28.00 | | (20) all_58_5 = e1 & op(e2, e1) = e1
% 159.05/28.00 | |
% 159.05/28.00 | | ALPHA: (20) implies:
% 159.05/28.00 | | (21) all_58_5 = e1
% 159.05/28.00 | |
% 159.05/28.00 | | REF_CLOSE: (11), (12), (21) are inconsistent by sub-proof #935.
% 159.05/28.00 | |
% 159.05/28.00 | End of split
% 159.05/28.00 |
% 159.05/28.00 End of proof
% 159.05/28.00
% 159.05/28.00 Sub-proof #545 shows that the following formulas are inconsistent:
% 159.05/28.00 ----------------------------------------------------------------
% 159.05/28.00 (1) op(e3, e3) = all_28_1
% 159.05/28.00 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.00 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.00 (3) all_58_6 = e3
% 159.05/28.00 (4) all_58_12 = e0
% 159.05/28.00 (5) op(e2, e3) = all_52_1
% 159.05/28.00 (6) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/28.00 (7) ~ (e3 = e0)
% 159.05/28.00 (8) op(e0, e0) = e0
% 159.05/28.00 (9) op(e2, e3) = e2
% 159.05/28.00 (10) ~ (e3 = e1)
% 159.05/28.00 (11) op(e3, e3) = e1
% 159.05/28.00 (12) ~ (e1 = e0)
% 159.05/28.00 (13) all_58_4 = e3
% 159.05/28.00 (14) op(e3, e3) = all_22_1
% 159.05/28.00 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.00 (16) ~ (e3 = e2)
% 159.05/28.00 (17) op(e0, e0) = e3
% 159.05/28.00
% 159.05/28.00 Begin of proof
% 159.05/28.00 |
% 159.05/28.00 | ALPHA: (6) implies:
% 159.05/28.00 | (18) all_58_4 = e1
% 159.05/28.00 |
% 159.05/28.00 | COMBINE_EQS: (13), (18) imply:
% 159.05/28.00 | (19) e3 = e1
% 159.05/28.00 |
% 159.05/28.00 | COMBINE_EQS: (3), (19) imply:
% 159.05/28.00 | (20) all_58_6 = e1
% 159.05/28.00 |
% 159.05/28.00 | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (14), (15),
% 159.05/28.00 | (16), (17), (20) are inconsistent by sub-proof #546.
% 159.05/28.00 |
% 159.05/28.00 End of proof
% 159.05/28.00
% 159.05/28.00 Sub-proof #546 shows that the following formulas are inconsistent:
% 159.05/28.00 ----------------------------------------------------------------
% 159.05/28.00 (1) op(e3, e3) = all_28_1
% 159.05/28.00 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.00 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.00 (3) all_58_12 = e0
% 159.05/28.00 (4) all_58_6 = e1
% 159.05/28.00 (5) op(e2, e3) = all_52_1
% 159.05/28.00 (6) ~ (e3 = e0)
% 159.05/28.00 (7) op(e0, e0) = e0
% 159.05/28.00 (8) op(e2, e3) = e2
% 159.05/28.00 (9) ~ (e3 = e1)
% 159.05/28.00 (10) op(e3, e3) = e1
% 159.05/28.00 (11) ~ (e1 = e0)
% 159.05/28.00 (12) op(e3, e3) = all_22_1
% 159.05/28.00 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.00 (14) ~ (e3 = e2)
% 159.05/28.00 (15) op(e0, e0) = e3
% 159.05/28.00
% 159.05/28.00 Begin of proof
% 159.05/28.00 |
% 159.05/28.00 | BETA: splitting (2) gives:
% 159.05/28.00 |
% 159.05/28.00 | Case 1:
% 159.05/28.00 | |
% 159.05/28.00 | | (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 159.05/28.00 | | e3)
% 159.05/28.00 | |
% 159.05/28.00 | | REF_CLOSE: (1), (5), (7), (8), (10), (11), (12), (13), (14), (15), (16) are
% 159.05/28.00 | | inconsistent by sub-proof #583.
% 159.05/28.00 | |
% 159.05/28.00 | Case 2:
% 159.05/28.00 | |
% 159.05/28.00 | | (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 159.05/28.00 | | e3)
% 159.05/28.00 | |
% 159.05/28.00 | | REF_CLOSE: (3), (4), (6), (9), (17) are inconsistent by sub-proof #758.
% 159.05/28.00 | |
% 159.05/28.00 | End of split
% 159.05/28.00 |
% 159.05/28.00 End of proof
% 159.05/28.00
% 159.05/28.00 Sub-proof #547 shows that the following formulas are inconsistent:
% 159.05/28.00 ----------------------------------------------------------------
% 159.05/28.00 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.00 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.00 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.00 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.00 (3) all_58_6 = e3
% 159.05/28.00 (4) op(e2, e3) = all_52_1
% 159.05/28.00 (5) ~ (e3 = e0)
% 159.05/28.00 (6) ~ (e2 = e0)
% 159.05/28.00 (7) op(e2, e3) = e2
% 159.05/28.00 (8) ~ (e3 = e1)
% 159.05/28.00 (9) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 159.05/28.00 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.00 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.00 (11) ~ (e2 = e1)
% 159.05/28.00 (12) ~ (e1 = e0)
% 159.05/28.00 (13) all_58_4 = e3
% 159.05/28.00 (14) all_58_3 = e3
% 159.05/28.00 (15) all_58_0 = e0
% 159.05/28.00 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.00 (17) ~ (e3 = e2)
% 159.05/28.00 (18) all_58_12 = e1
% 159.05/28.00
% 159.05/28.00 Begin of proof
% 159.05/28.00 |
% 159.05/28.00 | BETA: splitting (9) gives:
% 159.05/28.00 |
% 159.05/28.00 | Case 1:
% 159.05/28.00 | |
% 159.05/28.00 | | (19) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/28.00 | |
% 159.05/28.00 | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (13), (15), (16), (17), (18), (19)
% 159.05/28.00 | | are inconsistent by sub-proof #564.
% 159.05/28.00 | |
% 159.05/28.00 | Case 2:
% 159.05/28.00 | |
% 159.05/28.00 | | (20) all_58_5 = e2 & op(e2, e1) = e2
% 159.05/28.00 | |
% 159.05/28.00 | | ALPHA: (20) implies:
% 159.05/28.00 | | (21) all_58_5 = e2
% 159.05/28.00 | |
% 159.05/28.00 | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (12), (14), (16), (21) are
% 159.05/28.00 | | inconsistent by sub-proof #898.
% 159.05/28.00 | |
% 159.05/28.00 | End of split
% 159.05/28.00 |
% 159.05/28.00 End of proof
% 159.05/28.00
% 159.05/28.00 Sub-proof #548 shows that the following formulas are inconsistent:
% 159.05/28.00 ----------------------------------------------------------------
% 159.05/28.00 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.00 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.00 (2) op(e1, e1) = all_6_2
% 159.05/28.00 (3) ~ (all_52_7 = e3)
% 159.05/28.00 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.05/28.00 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.00 (5) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.00 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.00 (6) ~ (e3 = e0)
% 159.05/28.00 (7) ~ (e2 = e0)
% 159.05/28.00 (8) op(e2, e3) = e2
% 159.05/28.00 (9) ~ (e3 = e1)
% 159.05/28.00 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.00 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.00 (11) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/28.00 (12) op(e0, e0) = e2
% 159.05/28.00 (13) all_58_15 = e2
% 159.05/28.00 (14) ~ (e2 = e1)
% 159.05/28.00 (15) ~ (e1 = e0)
% 159.05/28.00 (16) all_58_4 = e3
% 159.05/28.00 (17) all_58_3 = e3
% 159.05/28.00 (18) ~ (all_6_2 = e2)
% 159.05/28.00 (19) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/28.00 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.00 e3)
% 159.05/28.00 (20) op(e0, e2) = all_52_7
% 159.05/28.00 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.00 (22) ~ (e3 = e2)
% 159.05/28.00 (23) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.00 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/28.00 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/28.00 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/28.00
% 159.05/28.00 Begin of proof
% 159.05/28.00 |
% 159.05/28.00 | ALPHA: (11) implies:
% 159.05/28.00 | (24) all_58_3 = e0
% 159.05/28.00 |
% 159.05/28.00 | COMBINE_EQS: (17), (24) imply:
% 159.05/28.00 | (25) e3 = e0
% 159.05/28.00 |
% 159.05/28.00 | SIMP: (25) implies:
% 159.05/28.00 | (26) e3 = e0
% 159.05/28.00 |
% 159.05/28.00 | COMBINE_EQS: (16), (26) imply:
% 159.05/28.00 | (27) all_58_4 = e0
% 159.05/28.00 |
% 159.05/28.00 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 159.05/28.00 | (14), (15), (17), (18), (19), (20), (21), (22), (23), (27) are
% 159.05/28.00 | inconsistent by sub-proof #847.
% 159.05/28.00 |
% 159.05/28.00 End of proof
% 159.05/28.00
% 159.05/28.00 Sub-proof #549 shows that the following formulas are inconsistent:
% 159.05/28.00 ----------------------------------------------------------------
% 159.05/28.00 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.00 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.00 (2) all_58_6 = e3
% 159.05/28.00 (3) op(e2, e3) = all_52_1
% 159.05/28.00 (4) ~ (e3 = e0)
% 159.05/28.00 (5) op(e2, e3) = e2
% 159.05/28.00 (6) ~ (e3 = e1)
% 159.05/28.00 (7) all_58_11 = e2
% 159.05/28.00 (8) all_58_0 = e0
% 159.05/28.00 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.00 (10) ~ (e3 = e2)
% 159.05/28.00 (11) all_58_12 = e1
% 159.05/28.00 (12) all_58_11 = e3
% 159.05/28.00
% 159.05/28.00 Begin of proof
% 159.05/28.00 |
% 159.05/28.00 | COMBINE_EQS: (7), (12) imply:
% 159.05/28.00 | (13) e3 = e2
% 159.05/28.00 |
% 159.05/28.00 | SIMP: (13) implies:
% 159.05/28.00 | (14) e3 = e2
% 159.05/28.00 |
% 159.05/28.00 | COMBINE_EQS: (2), (14) imply:
% 159.05/28.00 | (15) all_58_6 = e2
% 159.05/28.00 |
% 159.05/28.00 | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (15) are
% 159.05/28.00 | inconsistent by sub-proof #1125.
% 159.05/28.00 |
% 159.05/28.00 End of proof
% 159.05/28.00
% 159.05/28.00 Sub-proof #550 shows that the following formulas are inconsistent:
% 159.05/28.00 ----------------------------------------------------------------
% 159.05/28.00 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/28.00 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/28.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/28.00 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.00 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/28.00 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/28.00 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.00 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.00 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.00 (6) all_58_14 = e3
% 159.05/28.00 (7) all_54_13 = all_52_7
% 159.05/28.00 (8) op(e1, e1) = all_6_2
% 159.05/28.00 (9) ~ (all_52_7 = e3)
% 159.05/28.00 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/28.00 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/28.00 e1)
% 159.05/28.00 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/28.00 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/28.00 (12) ~ (all_52_11 = e3)
% 159.05/28.00 (13) ~ (all_52_7 = all_52_11)
% 159.05/28.00 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.00 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.00 (15) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.00 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.00 (16) all_58_6 = e3
% 159.05/28.00 (17) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/28.00 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/28.00 (18) op(e2, e3) = all_52_1
% 159.05/28.00 (19) ~ (all_52_13 = e3)
% 159.05/28.00 (20) all_54_2 = all_52_8
% 159.05/28.00 (21) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/28.00 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/28.00 (22) ~ (all_52_8 = all_52_9)
% 159.05/28.00 (23) ~ (e3 = e0)
% 159.05/28.00 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/28.00 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/28.00 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/28.00 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/28.00 (26) ~ (all_52_9 = all_52_13)
% 159.05/28.00 (27) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.00 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/28.00 e2)
% 159.05/28.00 (28) ~ (e2 = e0)
% 159.05/28.00 (29) ~ (all_52_9 = e3)
% 159.05/28.00 (30) op(e2, e0) = all_52_13
% 159.05/28.00 (31) op(e2, e3) = e2
% 159.05/28.00 (32) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.00 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/28.00 (33) ~ (e3 = e1)
% 159.05/28.00 (34) all_58_5 = e1
% 159.05/28.00 (35) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/28.00 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/28.00 (36) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/28.00 (37) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.00 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.00 (38) ~ (all_52_7 = e0)
% 159.05/28.00 (39) all_54_7 = all_52_13
% 159.05/28.00 (40) ~ (all_52_13 = e2)
% 159.05/28.00 (41) ~ (all_52_9 = all_52_11)
% 159.05/28.00 (42) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/28.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/28.00 (43) all_54_6 = all_52_9
% 159.05/28.00 (44) ~ (e2 = e1)
% 159.05/28.00 (45) ~ (all_52_8 = all_52_11)
% 159.05/28.00 (46) ~ (all_52_13 = e0)
% 159.05/28.00 (47) ~ (e1 = e0)
% 159.05/28.00 (48) all_58_4 = e3
% 159.05/28.00 (49) all_58_3 = e3
% 159.05/28.00 (50) ~ (all_6_2 = e2)
% 159.05/28.00 (51) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/28.00 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.00 e3)
% 159.05/28.00 (52) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/28.00 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/28.00 (53) ~ (all_52_9 = e2)
% 159.05/28.00 (54) ~ (all_52_8 = e3)
% 159.05/28.00 (55) all_54_14 = all_52_11
% 159.05/28.00 (56) op(e1, e0) = e3
% 159.05/28.00 (57) all_58_9 = e2
% 159.05/28.00 (58) op(e0, e2) = all_52_7
% 159.05/28.00 (59) all_58_0 = e0
% 159.05/28.00 (60) ~ (all_52_8 = e1)
% 159.05/28.00 (61) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/28.00 (62) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/28.00 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/28.00 (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.00 (64) ~ (e3 = e2)
% 159.05/28.00 (65) all_58_12 = e1
% 159.05/28.00 (66) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/28.00 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.00 (67) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.00 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/28.00 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/28.00 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/28.00 (68) all_58_11 = e3
% 159.05/28.00 (69) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/28.00 (70) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/28.00
% 159.05/28.00 Begin of proof
% 159.05/28.00 |
% 159.05/28.00 | BETA: splitting (4) gives:
% 159.05/28.00 |
% 159.05/28.00 | Case 1:
% 159.05/28.00 | |
% 159.05/28.00 | | (71) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 159.05/28.00 | | e1)
% 159.05/28.00 | |
% 159.05/28.00 | | BETA: splitting (71) gives:
% 159.05/28.00 | |
% 159.05/28.00 | | Case 1:
% 159.05/28.00 | | |
% 159.05/28.00 | | | (72) all_58_9 = e1 & op(e3, e0) = e1
% 159.05/28.00 | | |
% 159.05/28.00 | | | ALPHA: (72) implies:
% 159.05/28.00 | | | (73) all_58_9 = e1
% 159.05/28.00 | | |
% 159.05/28.00 | | | REF_CLOSE: (44), (57), (73) are inconsistent by sub-proof #1324.
% 159.05/28.00 | | |
% 159.05/28.00 | | Case 2:
% 159.05/28.00 | | |
% 159.05/28.00 | | | (74) all_58_10 = e1 & op(e2, e0) = e1
% 159.05/28.00 | | |
% 159.05/28.00 | | | ALPHA: (74) implies:
% 159.05/28.00 | | | (75) all_58_10 = e1
% 159.05/28.00 | | |
% 159.05/28.00 | | | REF_CLOSE: (5), (23), (28), (31), (33), (34), (37), (44), (47), (49),
% 159.05/28.00 | | | (63), (75) are inconsistent by sub-proof #754.
% 159.05/28.00 | | |
% 159.05/28.00 | | End of split
% 159.05/28.00 | |
% 159.05/28.00 | Case 2:
% 159.05/28.00 | |
% 159.05/28.00 | | (76) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/28.00 | | e1)
% 159.05/28.00 | |
% 159.05/28.00 | | BETA: splitting (76) gives:
% 159.05/28.00 | |
% 159.05/28.00 | | Case 1:
% 159.05/28.00 | | |
% 159.05/28.00 | | | (77) all_58_11 = e1 & op(e1, e0) = e1
% 159.05/28.00 | | |
% 159.05/28.00 | | | ALPHA: (77) implies:
% 159.05/28.00 | | | (78) op(e1, e0) = e1
% 159.05/28.00 | | |
% 159.05/28.00 | | | REF_CLOSE: (33), (56), (63), (78) are inconsistent by sub-proof #1275.
% 159.05/28.00 | | |
% 159.05/28.00 | | Case 2:
% 159.05/28.00 | | |
% 159.05/28.00 | | | (79) all_58_15 = e1 & op(e0, e0) = e1
% 159.05/28.00 | | |
% 159.05/28.00 | | | ALPHA: (79) implies:
% 159.05/28.00 | | | (80) op(e0, e0) = e1
% 159.05/28.00 | | |
% 159.05/28.00 | | | BETA: splitting (2) gives:
% 159.05/28.00 | | |
% 159.05/28.00 | | | Case 1:
% 159.05/28.00 | | | |
% 159.05/28.00 | | | | (81) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 159.05/28.00 | | | | = e1)
% 159.05/28.00 | | | |
% 159.05/28.00 | | | | BETA: splitting (81) gives:
% 159.05/28.00 | | | |
% 159.05/28.00 | | | | Case 1:
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | (82) all_58_6 = e1 & op(e1, e3) = e1
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | REF_CLOSE: (5), (6), (8), (15), (16), (23), (28), (31), (33), (37),
% 159.05/28.00 | | | | | (44), (47), (48), (49), (50), (63), (64), (82) are
% 159.05/28.00 | | | | | inconsistent by sub-proof #827.
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | Case 2:
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | (83) all_58_7 = e1 & op(e1, e2) = e1
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | ALPHA: (83) implies:
% 159.05/28.00 | | | | | (84) all_58_7 = e1
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | BETA: splitting (32) gives:
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | Case 1:
% 159.05/28.00 | | | | | |
% 159.05/28.00 | | | | | | (85) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 159.05/28.00 | | | | | | e2) = e0)
% 159.05/28.00 | | | | | |
% 159.05/28.00 | | | | | | BETA: splitting (85) gives:
% 159.05/28.00 | | | | | |
% 159.05/28.00 | | | | | | Case 1:
% 159.05/28.00 | | | | | | |
% 159.05/28.00 | | | | | | | (86) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/28.00 | | | | | | |
% 159.05/28.00 | | | | | | | ALPHA: (86) implies:
% 159.05/28.00 | | | | | | | (87) all_58_1 = e0
% 159.05/28.00 | | | | | | |
% 159.05/28.00 | | | | | | | BETA: splitting (27) gives:
% 159.05/28.00 | | | | | | |
% 159.05/28.00 | | | | | | | Case 1:
% 159.05/28.00 | | | | | | | |
% 159.05/28.00 | | | | | | | | (88) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 159.05/28.00 | | | | | | | | op(e0, e2) = e2)
% 159.05/28.00 | | | | | | | |
% 159.05/28.00 | | | | | | | | BETA: splitting (88) gives:
% 159.05/28.00 | | | | | | | |
% 159.05/28.00 | | | | | | | | Case 1:
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | (89) all_58_12 = e2 & op(e0, e3) = e2
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | ALPHA: (89) implies:
% 159.05/28.00 | | | | | | | | | (90) all_58_12 = e2
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | REF_CLOSE: (14), (18), (23), (24), (31), (33), (44), (47),
% 159.05/28.00 | | | | | | | | | (59), (63), (64), (90) are inconsistent by
% 159.05/28.00 | | | | | | | | | sub-proof #1066.
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | Case 2:
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | (91) all_58_13 = e2 & op(e0, e2) = e2
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | ALPHA: (91) implies:
% 159.05/28.00 | | | | | | | | | (92) all_58_13 = e2
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | BETA: splitting (52) gives:
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | Case 1:
% 159.05/28.00 | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | (93) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 &
% 159.05/28.00 | | | | | | | | | | op(e3, e2) = e1)
% 159.05/28.00 | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | BETA: splitting (93) gives:
% 159.05/28.00 | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | Case 1:
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | (94) all_58_0 = e1 & op(e3, e3) = e1
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | ALPHA: (94) implies:
% 159.05/28.00 | | | | | | | | | | | (95) all_58_0 = e1
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | COMBINE_EQS: (59), (95) imply:
% 159.05/28.00 | | | | | | | | | | | (96) e1 = e0
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | SIMP: (96) implies:
% 159.05/28.00 | | | | | | | | | | | (97) e1 = e0
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | COMBINE_EQS: (84), (97) imply:
% 159.05/28.00 | | | | | | | | | | | (98) all_58_7 = e0
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | REF_CLOSE: (3), (33), (44), (47), (49), (87), (92), (98) are
% 159.05/28.00 | | | | | | | | | | | inconsistent by sub-proof #752.
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | Case 2:
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | (99) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | ALPHA: (99) implies:
% 159.05/28.00 | | | | | | | | | | | (100) all_58_1 = e1
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | COMBINE_EQS: (87), (100) imply:
% 159.05/28.00 | | | | | | | | | | | (101) e1 = e0
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | SIMP: (101) implies:
% 159.05/28.00 | | | | | | | | | | | (102) e1 = e0
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | COMBINE_EQS: (84), (102) imply:
% 159.05/28.00 | | | | | | | | | | | (103) all_58_7 = e0
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | | REF_CLOSE: (3), (33), (44), (47), (49), (87), (92), (103) are
% 159.05/28.00 | | | | | | | | | | | inconsistent by sub-proof #752.
% 159.05/28.00 | | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | End of split
% 159.05/28.00 | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | Case 2:
% 159.05/28.00 | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | (104) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 159.05/28.00 | | | | | | | | | | & op(e3, e0) = e1)
% 159.05/28.00 | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | | REF_CLOSE: (5), (6), (8), (15), (23), (28), (31), (33), (37),
% 159.05/28.00 | | | | | | | | | | (44), (47), (49), (50), (57), (63), (64), (104)
% 159.05/28.00 | | | | | | | | | | are inconsistent by sub-proof #555.
% 159.05/28.00 | | | | | | | | | |
% 159.05/28.00 | | | | | | | | | End of split
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | End of split
% 159.05/28.00 | | | | | | | |
% 159.05/28.00 | | | | | | | Case 2:
% 159.05/28.00 | | | | | | | |
% 159.05/28.00 | | | | | | | | (105) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 159.05/28.00 | | | | | | | | op(e0, e0) = e2)
% 159.05/28.00 | | | | | | | |
% 159.05/28.00 | | | | | | | | BETA: splitting (105) gives:
% 159.05/28.00 | | | | | | | |
% 159.05/28.00 | | | | | | | | Case 1:
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | (106) all_58_14 = e2 & op(e0, e1) = e2
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | REF_CLOSE: (6), (14), (16), (18), (23), (31), (33), (59),
% 159.05/28.00 | | | | | | | | | (63), (64), (65), (106) are inconsistent by
% 159.05/28.00 | | | | | | | | | sub-proof #554.
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | Case 2:
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | (107) all_58_15 = e2 & op(e0, e0) = e2
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | ALPHA: (107) implies:
% 159.05/28.00 | | | | | | | | | (108) op(e0, e0) = e2
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | | REF_CLOSE: (44), (63), (80), (108) are inconsistent by
% 159.05/28.00 | | | | | | | | | sub-proof #1386.
% 159.05/28.00 | | | | | | | | |
% 159.05/28.00 | | | | | | | | End of split
% 159.05/28.00 | | | | | | | |
% 159.05/28.00 | | | | | | | End of split
% 159.05/28.00 | | | | | | |
% 159.05/28.00 | | | | | | Case 2:
% 159.05/28.00 | | | | | | |
% 159.05/28.00 | | | | | | | (109) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/28.00 | | | | | | |
% 159.05/28.00 | | | | | | | REF_CLOSE: (5), (6), (8), (15), (23), (28), (31), (33), (37),
% 159.05/28.00 | | | | | | | (44), (47), (48), (49), (50), (63), (64), (109) are
% 159.05/28.00 | | | | | | | inconsistent by sub-proof #799.
% 159.05/28.00 | | | | | | |
% 159.05/28.00 | | | | | | End of split
% 159.05/28.00 | | | | | |
% 159.05/28.00 | | | | | Case 2:
% 159.05/28.00 | | | | | |
% 159.05/28.00 | | | | | | (110) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 159.05/28.00 | | | | | | op(e0, e2) = e0)
% 159.05/28.00 | | | | | |
% 159.05/28.00 | | | | | | REF_CLOSE: (1), (7), (8), (9), (12), (13), (14), (16), (18), (20),
% 159.05/28.00 | | | | | | (21), (22), (23), (26), (28), (29), (31), (33), (36),
% 159.05/28.00 | | | | | | (38), (39), (40), (41), (43), (45), (46), (50), (53),
% 159.05/28.00 | | | | | | (54), (55), (58), (59), (60), (61), (63), (64), (65),
% 159.05/28.00 | | | | | | (68), (69), (70), (110) are inconsistent by sub-proof
% 159.05/28.00 | | | | | | #553.
% 159.05/28.00 | | | | | |
% 159.05/28.00 | | | | | End of split
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | End of split
% 159.05/28.00 | | | |
% 159.05/28.00 | | | Case 2:
% 159.05/28.00 | | | |
% 159.05/28.00 | | | | (111) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 159.05/28.00 | | | | e0) = e1)
% 159.05/28.00 | | | |
% 159.05/28.00 | | | | BETA: splitting (111) gives:
% 159.05/28.00 | | | |
% 159.05/28.00 | | | | Case 1:
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | (112) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.05/28.00 | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.05/28.00 | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 159.05/28.00 | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 159.05/28.00 | | | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 159.05/28.00 | | | | | (55), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 159.05/28.00 | | | | | (66), (67), (68), (69), (70), (112) are inconsistent by
% 159.05/28.00 | | | | | sub-proof #551.
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | Case 2:
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | (113) all_58_11 = e1 & op(e1, e0) = e1
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | ALPHA: (113) implies:
% 159.05/28.00 | | | | | (114) op(e1, e0) = e1
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | | REF_CLOSE: (33), (56), (63), (114) are inconsistent by sub-proof
% 159.05/28.00 | | | | | #1275.
% 159.05/28.00 | | | | |
% 159.05/28.00 | | | | End of split
% 159.05/28.00 | | | |
% 159.05/28.00 | | | End of split
% 159.05/28.00 | | |
% 159.05/28.00 | | End of split
% 159.05/28.00 | |
% 159.05/28.00 | End of split
% 159.05/28.00 |
% 159.05/28.00 End of proof
% 159.05/28.00
% 159.05/28.00 Sub-proof #551 shows that the following formulas are inconsistent:
% 159.05/28.00 ----------------------------------------------------------------
% 159.05/28.01 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/28.01 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/28.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/28.01 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.01 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.01 (4) all_58_14 = e3
% 159.05/28.01 (5) all_54_13 = all_52_7
% 159.05/28.01 (6) op(e1, e1) = all_6_2
% 159.05/28.01 (7) ~ (all_52_7 = e3)
% 159.05/28.01 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.05/28.01 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.01 (9) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/28.01 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/28.01 (10) ~ (all_52_11 = e3)
% 159.05/28.01 (11) ~ (all_52_7 = all_52_11)
% 159.05/28.01 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.01 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.01 (13) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.01 (14) all_58_6 = e3
% 159.05/28.01 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/28.01 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/28.01 (16) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/28.01 (17) op(e2, e3) = all_52_1
% 159.05/28.01 (18) ~ (all_52_13 = e3)
% 159.05/28.01 (19) all_54_2 = all_52_8
% 159.05/28.01 (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/28.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/28.01 (21) ~ (all_52_8 = all_52_9)
% 159.05/28.01 (22) ~ (e3 = e0)
% 159.05/28.01 (23) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/28.01 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/28.01 (24) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/28.01 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/28.01 (25) ~ (all_52_9 = all_52_13)
% 159.05/28.01 (26) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.01 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/28.01 e2)
% 159.05/28.01 (27) ~ (e2 = e0)
% 159.05/28.01 (28) ~ (all_52_9 = e3)
% 159.05/28.01 (29) op(e2, e0) = all_52_13
% 159.05/28.01 (30) op(e2, e3) = e2
% 159.05/28.01 (31) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.01 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/28.01 (32) ~ (e3 = e1)
% 159.05/28.01 (33) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/28.01 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/28.01 (34) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/28.01 (35) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.01 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.01 (36) ~ (all_52_7 = e0)
% 159.05/28.01 (37) all_54_7 = all_52_13
% 159.05/28.01 (38) ~ (all_52_13 = e2)
% 159.05/28.01 (39) ~ (all_52_9 = all_52_11)
% 159.05/28.01 (40) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/28.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/28.01 (41) all_54_6 = all_52_9
% 159.05/28.01 (42) ~ (e2 = e1)
% 159.05/28.01 (43) ~ (all_52_8 = all_52_11)
% 159.05/28.01 (44) ~ (all_52_13 = e0)
% 159.05/28.01 (45) ~ (e1 = e0)
% 159.05/28.01 (46) all_58_4 = e3
% 159.05/28.01 (47) all_58_3 = e3
% 159.05/28.01 (48) ~ (all_6_2 = e2)
% 159.05/28.01 (49) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/28.01 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.01 e3)
% 159.05/28.01 (50) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/28.01 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/28.01 (51) ~ (all_52_9 = e2)
% 159.05/28.01 (52) ~ (all_52_8 = e3)
% 159.05/28.01 (53) all_54_14 = all_52_11
% 159.05/28.01 (54) all_58_9 = e2
% 159.05/28.01 (55) op(e0, e2) = all_52_7
% 159.05/28.01 (56) all_58_0 = e0
% 159.05/28.01 (57) ~ (all_52_8 = e1)
% 159.05/28.01 (58) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/28.01 (59) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/28.01 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/28.01 (60) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.01 (61) ~ (e3 = e2)
% 159.05/28.01 (62) all_58_12 = e1
% 159.05/28.01 (63) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/28.01 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.01 (64) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.01 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/28.01 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/28.01 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/28.01 (65) all_58_11 = e3
% 159.05/28.01 (66) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/28.01 (67) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/28.01
% 159.05/28.01 Begin of proof
% 159.05/28.01 |
% 159.05/28.01 | ALPHA: (16) implies:
% 159.05/28.01 | (68) all_58_8 = e1
% 159.05/28.01 |
% 159.05/28.01 | BETA: splitting (31) gives:
% 159.05/28.01 |
% 159.05/28.01 | Case 1:
% 159.05/28.01 | |
% 159.05/28.01 | | (69) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 159.05/28.01 | | e0)
% 159.05/28.01 | |
% 159.05/28.01 | | BETA: splitting (69) gives:
% 159.05/28.01 | |
% 159.05/28.01 | | Case 1:
% 159.05/28.01 | | |
% 159.05/28.01 | | | (70) all_58_1 = e0 & op(e3, e2) = e0
% 159.05/28.01 | | |
% 159.05/28.01 | | | ALPHA: (70) implies:
% 159.05/28.01 | | | (71) all_58_1 = e0
% 159.05/28.01 | | |
% 159.05/28.01 | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (12), (13), (14), (15),
% 159.05/28.01 | | | (17), (18), (20), (22), (23), (24), (26), (27), (29), (30),
% 159.05/28.01 | | | (32), (33), (35), (40), (42), (45), (46), (47), (48), (49),
% 159.05/28.01 | | | (50), (54), (55), (56), (59), (60), (61), (62), (63), (64),
% 159.05/28.01 | | | (68), (71) are inconsistent by sub-proof #552.
% 159.05/28.01 | | |
% 159.05/28.01 | | Case 2:
% 159.05/28.01 | | |
% 159.05/28.01 | | | (72) all_58_3 = e0 & op(e2, e2) = e0
% 159.05/28.01 | | |
% 159.05/28.01 | | | REF_CLOSE: (3), (4), (6), (13), (22), (27), (30), (32), (35), (42), (45),
% 159.05/28.01 | | | (46), (47), (48), (60), (61), (72) are inconsistent by
% 159.05/28.01 | | | sub-proof #799.
% 159.05/28.01 | | |
% 159.05/28.01 | | End of split
% 159.05/28.01 | |
% 159.05/28.01 | Case 2:
% 159.05/28.01 | |
% 159.05/28.01 | | (73) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.05/28.01 | | e0)
% 159.05/28.01 | |
% 159.05/28.01 | | REF_CLOSE: (1), (5), (6), (7), (10), (11), (12), (14), (17), (19), (20),
% 159.05/28.01 | | (21), (22), (25), (27), (28), (30), (32), (34), (36), (37), (38),
% 159.05/28.01 | | (39), (41), (43), (44), (48), (51), (52), (53), (55), (56), (57),
% 159.05/28.01 | | (58), (60), (61), (62), (65), (66), (67), (73) are inconsistent
% 159.05/28.01 | | by sub-proof #553.
% 159.05/28.01 | |
% 159.05/28.01 | End of split
% 159.05/28.01 |
% 159.05/28.01 End of proof
% 159.05/28.01
% 159.05/28.01 Sub-proof #552 shows that the following formulas are inconsistent:
% 159.05/28.01 ----------------------------------------------------------------
% 159.05/28.01 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/28.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/28.01 (2) all_58_1 = e0
% 159.05/28.01 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.01 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.01 (4) all_58_14 = e3
% 159.05/28.01 (5) op(e1, e1) = all_6_2
% 159.05/28.01 (6) ~ (all_52_7 = e3)
% 159.05/28.01 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.05/28.01 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.01 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/28.01 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/28.01 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.01 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.01 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.01 (11) all_58_6 = e3
% 159.05/28.01 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/28.01 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/28.01 (13) op(e2, e3) = all_52_1
% 159.05/28.01 (14) ~ (all_52_13 = e3)
% 159.05/28.01 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/28.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/28.01 (16) ~ (e3 = e0)
% 159.05/28.01 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/28.01 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/28.01 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/28.01 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/28.01 (19) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.01 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/28.01 e2)
% 159.05/28.01 (20) ~ (e2 = e0)
% 159.05/28.01 (21) op(e2, e0) = all_52_13
% 159.05/28.01 (22) op(e2, e3) = e2
% 159.05/28.01 (23) ~ (e3 = e1)
% 159.05/28.01 (24) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/28.01 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/28.01 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.01 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.01 (26) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/28.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/28.01 (27) ~ (e2 = e1)
% 159.05/28.01 (28) ~ (e1 = e0)
% 159.05/28.01 (29) all_58_4 = e3
% 159.05/28.01 (30) all_58_3 = e3
% 159.05/28.01 (31) ~ (all_6_2 = e2)
% 159.05/28.01 (32) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/28.01 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.01 e3)
% 159.05/28.01 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/28.01 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/28.01 (34) all_58_9 = e2
% 159.05/28.01 (35) op(e0, e2) = all_52_7
% 159.05/28.01 (36) all_58_0 = e0
% 159.05/28.01 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/28.01 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/28.01 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.01 (39) ~ (e3 = e2)
% 159.05/28.01 (40) all_58_12 = e1
% 159.05/28.01 (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/28.01 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.01 (42) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.01 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/28.01 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/28.01 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/28.01 (43) all_58_8 = e1
% 159.05/28.01
% 159.05/28.01 Begin of proof
% 159.05/28.01 |
% 159.05/28.01 | BETA: splitting (33) gives:
% 159.05/28.01 |
% 159.05/28.01 | Case 1:
% 159.05/28.01 | |
% 159.05/28.01 | | (44) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 159.05/28.01 | | e1)
% 159.05/28.01 | |
% 159.05/28.01 | | BETA: splitting (44) gives:
% 159.05/28.01 | |
% 159.05/28.01 | | Case 1:
% 159.05/28.01 | | |
% 159.05/28.01 | | | (45) all_58_0 = e1 & op(e3, e3) = e1
% 159.05/28.01 | | |
% 159.05/28.01 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.05/28.01 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.05/28.01 | | | (25), (26), (27), (28), (29), (30), (31), (32), (35), (36),
% 159.05/28.01 | | | (37), (38), (39), (40), (41), (42), (43), (45) are inconsistent
% 159.05/28.01 | | | by sub-proof #558.
% 159.05/28.01 | | |
% 159.05/28.01 | | Case 2:
% 159.05/28.01 | | |
% 159.05/28.01 | | | (46) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/28.01 | | |
% 159.05/28.01 | | | ALPHA: (46) implies:
% 159.05/28.01 | | | (47) all_58_1 = e1
% 159.05/28.01 | | |
% 159.05/28.01 | | | COMBINE_EQS: (2), (47) imply:
% 159.05/28.01 | | | (48) e1 = e0
% 159.05/28.01 | | |
% 159.05/28.01 | | | SIMP: (48) implies:
% 159.05/28.01 | | | (49) e1 = e0
% 159.05/28.01 | | |
% 159.05/28.01 | | | COMBINE_EQS: (40), (49) imply:
% 159.05/28.01 | | | (50) all_58_12 = e0
% 159.05/28.01 | | |
% 159.05/28.01 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.05/28.01 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.05/28.01 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (35),
% 159.05/28.01 | | | (37), (38), (39), (41), (42), (50) are inconsistent by
% 159.05/28.01 | | | sub-proof #789.
% 159.05/28.01 | | |
% 159.05/28.01 | | End of split
% 159.05/28.01 | |
% 159.05/28.01 | Case 2:
% 159.05/28.01 | |
% 159.05/28.01 | | (51) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 159.05/28.01 | | e1)
% 159.05/28.01 | |
% 159.05/28.01 | | REF_CLOSE: (3), (4), (5), (10), (16), (20), (22), (23), (25), (27), (28),
% 159.05/28.01 | | (30), (31), (34), (38), (39), (51) are inconsistent by sub-proof
% 159.05/28.01 | | #555.
% 159.05/28.01 | |
% 159.05/28.01 | End of split
% 159.05/28.01 |
% 159.05/28.01 End of proof
% 159.05/28.01
% 159.05/28.01 Sub-proof #553 shows that the following formulas are inconsistent:
% 159.05/28.01 ----------------------------------------------------------------
% 159.05/28.01 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/28.01 (2) all_54_13 = all_52_7
% 159.05/28.01 (3) op(e1, e1) = all_6_2
% 159.05/28.01 (4) ~ (all_52_7 = e3)
% 159.05/28.01 (5) ~ (all_52_11 = e3)
% 159.05/28.01 (6) ~ (all_52_7 = all_52_11)
% 159.05/28.01 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.01 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.01 (8) all_58_6 = e3
% 159.05/28.01 (9) op(e2, e3) = all_52_1
% 159.05/28.01 (10) all_54_2 = all_52_8
% 159.05/28.01 (11) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/28.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/28.01 (12) ~ (all_52_8 = all_52_9)
% 159.05/28.01 (13) ~ (e3 = e0)
% 159.05/28.01 (14) ~ (all_52_9 = all_52_13)
% 159.05/28.01 (15) ~ (e2 = e0)
% 159.05/28.01 (16) ~ (all_52_9 = e3)
% 159.05/28.01 (17) op(e2, e3) = e2
% 159.05/28.01 (18) ~ (e3 = e1)
% 159.05/28.01 (19) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/28.01 (20) ~ (all_52_7 = e0)
% 159.05/28.01 (21) all_54_7 = all_52_13
% 159.05/28.01 (22) ~ (all_52_13 = e2)
% 159.05/28.01 (23) ~ (all_52_9 = all_52_11)
% 159.05/28.01 (24) all_54_6 = all_52_9
% 159.05/28.01 (25) ~ (all_52_8 = all_52_11)
% 159.05/28.01 (26) ~ (all_52_13 = e0)
% 159.05/28.01 (27) ~ (all_6_2 = e2)
% 159.05/28.01 (28) ~ (all_52_9 = e2)
% 159.05/28.01 (29) ~ (all_52_8 = e3)
% 159.05/28.01 (30) all_54_14 = all_52_11
% 159.05/28.01 (31) op(e0, e2) = all_52_7
% 159.05/28.01 (32) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/28.01 (33) all_58_0 = e0
% 159.05/28.01 (34) ~ (all_52_8 = e1)
% 159.05/28.01 (35) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/28.01 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.01 (37) ~ (e3 = e2)
% 159.05/28.01 (38) all_58_12 = e1
% 159.05/28.01 (39) all_58_11 = e3
% 159.05/28.01 (40) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/28.01 (41) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/28.01
% 159.05/28.01 Begin of proof
% 159.05/28.01 |
% 159.05/28.01 | BETA: splitting (32) gives:
% 159.05/28.01 |
% 159.05/28.01 | Case 1:
% 159.05/28.01 | |
% 159.05/28.01 | | (42) all_58_7 = e0 & op(e1, e2) = e0
% 159.05/28.01 | |
% 159.05/28.01 | | ALPHA: (42) implies:
% 159.05/28.01 | | (43) all_58_7 = e0
% 159.05/28.01 | |
% 159.05/28.01 | | BETA: splitting (11) gives:
% 159.05/28.01 | |
% 159.05/28.01 | | Case 1:
% 159.05/28.01 | | |
% 159.05/28.01 | | | (44) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 159.05/28.01 | | | e2)
% 159.05/28.01 | | |
% 159.05/28.01 | | | BETA: splitting (44) gives:
% 159.05/28.01 | | |
% 159.05/28.01 | | | Case 1:
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | (45) all_58_6 = e2 & op(e1, e3) = e2
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | ALPHA: (45) implies:
% 159.05/28.01 | | | | (46) all_58_6 = e2
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | REF_CLOSE: (7), (9), (13), (17), (18), (33), (36), (37), (38), (46) are
% 159.05/28.01 | | | | inconsistent by sub-proof #1125.
% 159.05/28.01 | | | |
% 159.05/28.01 | | | Case 2:
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | (47) all_58_7 = e2 & op(e1, e2) = e2
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | REF_CLOSE: (15), (43), (47) are inconsistent by sub-proof #746.
% 159.05/28.01 | | | |
% 159.05/28.01 | | | End of split
% 159.05/28.01 | | |
% 159.05/28.01 | | Case 2:
% 159.05/28.01 | | |
% 159.05/28.01 | | | (48) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 159.05/28.01 | | | e2)
% 159.05/28.01 | | |
% 159.05/28.01 | | | BETA: splitting (48) gives:
% 159.05/28.01 | | |
% 159.05/28.01 | | | Case 1:
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | (49) all_58_8 = e2 & op(e1, e1) = e2
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | REF_CLOSE: (3), (27), (36), (49) are inconsistent by sub-proof #1440.
% 159.05/28.01 | | | |
% 159.05/28.01 | | | Case 2:
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | (50) all_58_11 = e2 & op(e1, e0) = e2
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | ALPHA: (50) implies:
% 159.05/28.01 | | | | (51) all_58_11 = e2
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | COMBINE_EQS: (39), (51) imply:
% 159.05/28.01 | | | | (52) e3 = e2
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | COMBINE_EQS: (8), (52) imply:
% 159.05/28.01 | | | | (53) all_58_6 = e2
% 159.05/28.01 | | | |
% 159.05/28.01 | | | | REF_CLOSE: (7), (9), (13), (17), (18), (33), (36), (37), (38), (53) are
% 159.05/28.01 | | | | inconsistent by sub-proof #1125.
% 159.05/28.01 | | | |
% 159.05/28.01 | | | End of split
% 159.05/28.01 | | |
% 159.05/28.01 | | End of split
% 159.05/28.01 | |
% 159.05/28.01 | Case 2:
% 159.05/28.01 | |
% 159.05/28.01 | | (54) all_58_13 = e0 & op(e0, e2) = e0
% 159.05/28.01 | |
% 159.05/28.01 | | ALPHA: (54) implies:
% 159.05/28.01 | | (55) op(e0, e2) = e0
% 159.05/28.01 | |
% 159.05/28.01 | | REF_CLOSE: (1), (2), (4), (5), (6), (10), (12), (14), (16), (19), (20),
% 159.05/28.01 | | (21), (22), (23), (24), (25), (26), (28), (29), (30), (31), (34),
% 159.05/28.01 | | (35), (36), (40), (41), (55) are inconsistent by sub-proof #559.
% 159.05/28.01 | |
% 159.05/28.01 | End of split
% 159.05/28.01 |
% 159.05/28.01 End of proof
% 159.05/28.01
% 159.05/28.01 Sub-proof #554 shows that the following formulas are inconsistent:
% 159.05/28.01 ----------------------------------------------------------------
% 159.05/28.01 (1) all_58_14 = e3
% 159.05/28.01 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.01 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.01 (3) all_58_6 = e3
% 159.05/28.01 (4) op(e2, e3) = all_52_1
% 159.05/28.01 (5) ~ (e3 = e0)
% 159.05/28.01 (6) op(e2, e3) = e2
% 159.05/28.01 (7) ~ (e3 = e1)
% 159.05/28.01 (8) all_58_14 = e2 & op(e0, e1) = e2
% 159.05/28.01 (9) all_58_0 = e0
% 159.05/28.01 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.01 (11) ~ (e3 = e2)
% 159.05/28.01 (12) all_58_12 = e1
% 159.05/28.01
% 159.05/28.01 Begin of proof
% 159.05/28.01 |
% 159.05/28.01 | ALPHA: (8) implies:
% 159.05/28.01 | (13) all_58_14 = e2
% 159.05/28.01 |
% 159.05/28.01 | COMBINE_EQS: (1), (13) imply:
% 159.05/28.01 | (14) e3 = e2
% 159.05/28.01 |
% 159.05/28.01 | COMBINE_EQS: (3), (14) imply:
% 159.05/28.01 | (15) all_58_6 = e2
% 159.05/28.01 |
% 159.05/28.01 | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (12), (15) are
% 159.05/28.01 | inconsistent by sub-proof #1125.
% 159.05/28.01 |
% 159.05/28.01 End of proof
% 159.05/28.01
% 159.05/28.01 Sub-proof #555 shows that the following formulas are inconsistent:
% 159.05/28.01 ----------------------------------------------------------------
% 159.05/28.01 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.01 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.01 (2) all_58_14 = e3
% 159.05/28.01 (3) op(e1, e1) = all_6_2
% 159.05/28.01 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.01 (5) ~ (e3 = e0)
% 159.05/28.01 (6) ~ (e2 = e0)
% 159.05/28.01 (7) op(e2, e3) = e2
% 159.05/28.01 (8) ~ (e3 = e1)
% 159.05/28.01 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.01 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.01 (10) ~ (e2 = e1)
% 159.05/28.01 (11) ~ (e1 = e0)
% 159.05/28.01 (12) all_58_3 = e3
% 159.05/28.01 (13) ~ (all_6_2 = e2)
% 159.05/28.01 (14) all_58_9 = e2
% 159.05/28.01 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.01 (16) ~ (e3 = e2)
% 159.05/28.01 (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/28.01
% 159.05/28.01 Begin of proof
% 159.05/28.01 |
% 159.05/28.01 | BETA: splitting (17) gives:
% 159.05/28.01 |
% 159.05/28.01 | Case 1:
% 159.05/28.01 | |
% 159.05/28.01 | | (18) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/28.01 | |
% 159.05/28.01 | | ALPHA: (18) implies:
% 159.05/28.01 | | (19) all_58_4 = e1
% 159.05/28.01 | |
% 159.05/28.01 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.01 | | (13), (15), (16), (19) are inconsistent by sub-proof #850.
% 159.05/28.01 | |
% 159.05/28.01 | Case 2:
% 159.05/28.01 | |
% 159.05/28.01 | | (20) all_58_9 = e1 & op(e3, e0) = e1
% 159.05/28.01 | |
% 159.05/28.01 | | REF_CLOSE: (10), (14), (20) are inconsistent by sub-proof #1325.
% 159.05/28.01 | |
% 159.05/28.01 | End of split
% 159.05/28.01 |
% 159.05/28.01 End of proof
% 159.05/28.01
% 159.05/28.01 Sub-proof #556 shows that the following formulas are inconsistent:
% 159.05/28.01 ----------------------------------------------------------------
% 159.05/28.01 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/28.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/28.01 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.01 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.01 (3) all_58_14 = e3
% 159.05/28.01 (4) op(e1, e1) = all_6_2
% 159.05/28.01 (5) ~ (all_52_7 = e3)
% 159.05/28.01 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.05/28.01 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.01 (7) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/28.01 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/28.01 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.01 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.01 (9) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.01 (10) all_58_6 = e3
% 159.05/28.01 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/28.01 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/28.01 (12) all_58_8 = e1 & op(e1, e1) = e1
% 159.05/28.01 (13) op(e2, e3) = all_52_1
% 159.05/28.01 (14) ~ (all_52_13 = e3)
% 159.05/28.01 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/28.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/28.01 (16) ~ (e3 = e0)
% 159.05/28.01 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/28.01 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/28.01 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/28.01 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/28.01 (19) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.01 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/28.01 e2)
% 159.05/28.02 (20) ~ (e2 = e0)
% 159.05/28.02 (21) all_58_9 = e3
% 159.05/28.02 (22) op(e2, e0) = all_52_13
% 159.05/28.02 (23) op(e2, e3) = e2
% 159.05/28.02 (24) ~ (e3 = e1)
% 159.05/28.02 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.02 (26) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/28.02 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/28.02 (27) ~ (e2 = e1)
% 159.05/28.02 (28) ~ (e1 = e0)
% 159.05/28.02 (29) all_58_4 = e3
% 159.05/28.02 (30) all_58_3 = e3
% 159.05/28.02 (31) ~ (all_6_2 = e2)
% 159.05/28.02 (32) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/28.02 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.02 e3)
% 159.05/28.02 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/28.02 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/28.02 (34) op(e0, e2) = all_52_7
% 159.05/28.02 (35) all_58_0 = e0
% 159.05/28.02 (36) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/28.02 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/28.02 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.02 (38) ~ (e3 = e2)
% 159.05/28.02 (39) all_58_12 = e1
% 159.05/28.02 (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/28.02 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.02 (41) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.02 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/28.02 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/28.02 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | ALPHA: (12) implies:
% 159.05/28.02 | (42) all_58_8 = e1
% 159.05/28.02 |
% 159.05/28.02 | BETA: splitting (18) gives:
% 159.05/28.02 |
% 159.05/28.02 | Case 1:
% 159.05/28.02 | |
% 159.05/28.02 | | (43) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 159.05/28.02 | | e2)
% 159.05/28.02 | |
% 159.05/28.02 | | BETA: splitting (43) gives:
% 159.05/28.02 | |
% 159.05/28.02 | | Case 1:
% 159.05/28.02 | | |
% 159.05/28.02 | | | (44) all_58_0 = e2 & op(e3, e3) = e2
% 159.05/28.02 | | |
% 159.05/28.02 | | | REF_CLOSE: (20), (35), (44) are inconsistent by sub-proof #702.
% 159.05/28.02 | | |
% 159.05/28.02 | | Case 2:
% 159.05/28.02 | | |
% 159.05/28.02 | | | (45) all_58_1 = e2 & op(e3, e2) = e2
% 159.05/28.02 | | |
% 159.05/28.02 | | | ALPHA: (45) implies:
% 159.05/28.02 | | | (46) all_58_1 = e2
% 159.05/28.02 | | |
% 159.05/28.02 | | | BETA: splitting (33) gives:
% 159.05/28.02 | | |
% 159.05/28.02 | | | Case 1:
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | (47) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 159.05/28.02 | | | | = e1)
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | BETA: splitting (47) gives:
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | Case 1:
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | (48) all_58_0 = e1 & op(e3, e3) = e1
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.05/28.02 | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 159.05/28.02 | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 159.05/28.02 | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (48) are
% 159.05/28.02 | | | | | inconsistent by sub-proof #558.
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | Case 2:
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | (49) all_58_1 = e1 & op(e3, e2) = e1
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | REF_CLOSE: (27), (46), (49) are inconsistent by sub-proof #1219.
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | End of split
% 159.05/28.02 | | | |
% 159.05/28.02 | | | Case 2:
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | (50) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 159.05/28.02 | | | | = e1)
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | REF_CLOSE: (2), (3), (4), (9), (16), (20), (21), (23), (24), (25), (27),
% 159.05/28.02 | | | | (28), (29), (30), (31), (37), (38), (50) are inconsistent by
% 159.05/28.02 | | | | sub-proof #557.
% 159.05/28.02 | | | |
% 159.05/28.02 | | | End of split
% 159.05/28.02 | | |
% 159.05/28.02 | | End of split
% 159.05/28.02 | |
% 159.05/28.02 | Case 2:
% 159.05/28.02 | |
% 159.05/28.02 | | (51) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 159.05/28.02 | | e2)
% 159.05/28.02 | |
% 159.05/28.02 | | BETA: splitting (51) gives:
% 159.05/28.02 | |
% 159.05/28.02 | | Case 1:
% 159.05/28.02 | | |
% 159.05/28.02 | | | (52) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/28.02 | | |
% 159.05/28.02 | | | REF_CLOSE: (8), (10), (13), (16), (23), (24), (29), (35), (37), (38),
% 159.05/28.02 | | | (39), (52) are inconsistent by sub-proof #564.
% 159.05/28.02 | | |
% 159.05/28.02 | | Case 2:
% 159.05/28.02 | | |
% 159.05/28.02 | | | (53) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/28.02 | | |
% 159.05/28.02 | | | REF_CLOSE: (8), (10), (13), (16), (21), (23), (24), (35), (37), (38),
% 159.05/28.02 | | | (39), (53) are inconsistent by sub-proof #565.
% 159.05/28.02 | | |
% 159.05/28.02 | | End of split
% 159.05/28.02 | |
% 159.05/28.02 | End of split
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #557 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.02 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.02 (2) all_58_14 = e3
% 159.05/28.02 (3) op(e1, e1) = all_6_2
% 159.05/28.02 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.02 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.02 (5) ~ (e3 = e0)
% 159.05/28.02 (6) ~ (e2 = e0)
% 159.05/28.02 (7) all_58_9 = e3
% 159.05/28.02 (8) op(e2, e3) = e2
% 159.05/28.02 (9) ~ (e3 = e1)
% 159.05/28.02 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.02 (11) ~ (e2 = e1)
% 159.05/28.02 (12) ~ (e1 = e0)
% 159.05/28.02 (13) all_58_4 = e3
% 159.05/28.02 (14) all_58_3 = e3
% 159.05/28.02 (15) ~ (all_6_2 = e2)
% 159.05/28.02 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.02 (17) ~ (e3 = e2)
% 159.05/28.02 (18) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | BETA: splitting (18) gives:
% 159.05/28.02 |
% 159.05/28.02 | Case 1:
% 159.05/28.02 | |
% 159.05/28.02 | | (19) all_58_4 = e1 & op(e3, e1) = e1
% 159.05/28.02 | |
% 159.05/28.02 | | ALPHA: (19) implies:
% 159.05/28.02 | | (20) all_58_4 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 159.05/28.02 | | (15), (16), (17), (20) are inconsistent by sub-proof #850.
% 159.05/28.02 | |
% 159.05/28.02 | Case 2:
% 159.05/28.02 | |
% 159.05/28.02 | | (21) all_58_9 = e1 & op(e3, e0) = e1
% 159.05/28.02 | |
% 159.05/28.02 | | ALPHA: (21) implies:
% 159.05/28.02 | | (22) all_58_9 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | COMBINE_EQS: (7), (22) imply:
% 159.05/28.02 | | (23) e3 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | COMBINE_EQS: (13), (23) imply:
% 159.05/28.02 | | (24) all_58_4 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 159.05/28.02 | | (15), (16), (17), (24) are inconsistent by sub-proof #850.
% 159.05/28.02 | |
% 159.05/28.02 | End of split
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #558 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/28.02 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/28.02 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.02 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.02 (3) all_58_14 = e3
% 159.05/28.02 (4) op(e1, e1) = all_6_2
% 159.05/28.02 (5) ~ (all_52_7 = e3)
% 159.05/28.02 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.05/28.02 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.02 (7) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/28.02 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/28.02 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.02 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.02 (9) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.02 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.02 (10) all_58_6 = e3
% 159.05/28.02 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/28.02 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/28.02 (12) op(e2, e3) = all_52_1
% 159.05/28.02 (13) ~ (all_52_13 = e3)
% 159.05/28.02 (14) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/28.02 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/28.02 (15) ~ (e3 = e0)
% 159.05/28.02 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/28.02 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/28.02 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/28.02 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/28.02 (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.02 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/28.02 e2)
% 159.05/28.02 (19) ~ (e2 = e0)
% 159.05/28.02 (20) op(e2, e0) = all_52_13
% 159.05/28.02 (21) all_58_0 = e1 & op(e3, e3) = e1
% 159.05/28.02 (22) op(e2, e3) = e2
% 159.05/28.02 (23) ~ (e3 = e1)
% 159.05/28.02 (24) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.02 (25) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/28.02 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/28.02 (26) ~ (e2 = e1)
% 159.05/28.02 (27) ~ (e1 = e0)
% 159.05/28.02 (28) all_58_4 = e3
% 159.05/28.02 (29) all_58_3 = e3
% 159.05/28.02 (30) ~ (all_6_2 = e2)
% 159.05/28.02 (31) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/28.02 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.02 e3)
% 159.05/28.02 (32) op(e0, e2) = all_52_7
% 159.05/28.02 (33) all_58_0 = e0
% 159.05/28.02 (34) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/28.02 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/28.02 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.02 (36) ~ (e3 = e2)
% 159.05/28.02 (37) all_58_12 = e1
% 159.05/28.02 (38) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/28.02 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.02 (39) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.02 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/28.02 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/28.02 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/28.02 (40) all_58_8 = e1
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | ALPHA: (21) implies:
% 159.05/28.02 | (41) all_58_0 = e1
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (33), (41) imply:
% 159.05/28.02 | (42) e1 = e0
% 159.05/28.02 |
% 159.05/28.02 | SIMP: (42) implies:
% 159.05/28.02 | (43) e1 = e0
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (37), (43) imply:
% 159.05/28.02 | (44) all_58_12 = e0
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (40), (43) imply:
% 159.05/28.02 | (45) all_58_8 = e0
% 159.05/28.02 |
% 159.05/28.02 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.02 | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 159.05/28.02 | (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 159.05/28.02 | (38), (39), (41), (44), (45) are inconsistent by sub-proof #790.
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #559 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/28.02 (2) all_54_13 = all_52_7
% 159.05/28.02 (3) ~ (all_52_7 = e3)
% 159.05/28.02 (4) ~ (all_52_11 = e3)
% 159.05/28.02 (5) ~ (all_52_7 = all_52_11)
% 159.05/28.02 (6) all_54_2 = all_52_8
% 159.05/28.02 (7) ~ (all_52_8 = all_52_9)
% 159.05/28.02 (8) ~ (all_52_9 = all_52_13)
% 159.05/28.02 (9) ~ (all_52_9 = e3)
% 159.05/28.02 (10) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/28.02 (11) ~ (all_52_7 = e0)
% 159.05/28.02 (12) all_54_7 = all_52_13
% 159.05/28.02 (13) ~ (all_52_13 = e2)
% 159.05/28.02 (14) ~ (all_52_9 = all_52_11)
% 159.05/28.02 (15) all_54_6 = all_52_9
% 159.05/28.02 (16) op(e0, e2) = e0
% 159.05/28.02 (17) ~ (all_52_8 = all_52_11)
% 159.05/28.02 (18) ~ (all_52_13 = e0)
% 159.05/28.02 (19) ~ (all_52_9 = e2)
% 159.05/28.02 (20) ~ (all_52_8 = e3)
% 159.05/28.02 (21) all_54_14 = all_52_11
% 159.05/28.02 (22) op(e0, e2) = all_52_7
% 159.05/28.02 (23) ~ (all_52_8 = e1)
% 159.05/28.02 (24) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/28.02 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.02 (26) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.05/28.02 (27) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | BETA: splitting (26) gives:
% 159.05/28.02 |
% 159.05/28.02 | Case 1:
% 159.05/28.02 | |
% 159.05/28.02 | | (28) all_54_7 = e2
% 159.05/28.02 | |
% 159.05/28.02 | | REF_CLOSE: (12), (13), (28) are inconsistent by sub-proof #1427.
% 159.05/28.02 | |
% 159.05/28.02 | Case 2:
% 159.05/28.02 | |
% 159.05/28.02 | | (29) all_54_7 = e1 | all_54_7 = e0
% 159.05/28.02 | |
% 159.05/28.02 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.02 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 159.05/28.02 | | (25), (27), (29) are inconsistent by sub-proof #560.
% 159.05/28.02 | |
% 159.05/28.02 | End of split
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #560 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/28.02 (2) all_54_13 = all_52_7
% 159.05/28.02 (3) ~ (all_52_7 = e3)
% 159.05/28.02 (4) ~ (all_52_11 = e3)
% 159.05/28.02 (5) ~ (all_52_7 = all_52_11)
% 159.05/28.02 (6) all_54_2 = all_52_8
% 159.05/28.02 (7) ~ (all_52_8 = all_52_9)
% 159.05/28.02 (8) ~ (all_52_9 = all_52_13)
% 159.05/28.02 (9) ~ (all_52_9 = e3)
% 159.05/28.02 (10) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/28.02 (11) ~ (all_52_7 = e0)
% 159.05/28.02 (12) all_54_7 = all_52_13
% 159.05/28.02 (13) ~ (all_52_9 = all_52_11)
% 159.05/28.02 (14) all_54_6 = all_52_9
% 159.05/28.02 (15) op(e0, e2) = e0
% 159.05/28.02 (16) ~ (all_52_8 = all_52_11)
% 159.05/28.02 (17) ~ (all_52_13 = e0)
% 159.05/28.02 (18) ~ (all_52_9 = e2)
% 159.05/28.02 (19) ~ (all_52_8 = e3)
% 159.05/28.02 (20) all_54_14 = all_52_11
% 159.05/28.02 (21) op(e0, e2) = all_52_7
% 159.05/28.02 (22) ~ (all_52_8 = e1)
% 159.05/28.02 (23) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 159.05/28.02 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.02 (25) all_54_7 = e1 | all_54_7 = e0
% 159.05/28.02 (26) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | BETA: splitting (25) gives:
% 159.05/28.02 |
% 159.05/28.02 | Case 1:
% 159.05/28.02 | |
% 159.05/28.02 | | (27) all_54_7 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | COMBINE_EQS: (12), (27) imply:
% 159.05/28.02 | | (28) all_52_13 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | SIMP: (28) implies:
% 159.05/28.02 | | (29) all_52_13 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | REDUCE: (8), (29) imply:
% 159.05/28.02 | | (30) ~ (all_52_9 = e1)
% 159.05/28.02 | |
% 159.05/28.02 | | BETA: splitting (1) gives:
% 159.05/28.02 | |
% 159.05/28.02 | | Case 1:
% 159.05/28.02 | | |
% 159.05/28.02 | | | (31) all_54_6 = e3
% 159.05/28.02 | | |
% 159.05/28.02 | | | REF_CLOSE: (9), (14), (31) are inconsistent by sub-proof #1193.
% 159.05/28.02 | | |
% 159.05/28.02 | | Case 2:
% 159.05/28.02 | | |
% 159.05/28.02 | | | (32) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 159.05/28.02 | | |
% 159.05/28.02 | | | BETA: splitting (32) gives:
% 159.05/28.02 | | |
% 159.05/28.02 | | | Case 1:
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | (33) all_54_6 = e2
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | REF_CLOSE: (14), (18), (33) are inconsistent by sub-proof #1192.
% 159.05/28.02 | | | |
% 159.05/28.02 | | | Case 2:
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | (34) all_54_6 = e1 | all_54_6 = e0
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | BETA: splitting (34) gives:
% 159.05/28.02 | | | |
% 159.05/28.02 | | | | Case 1:
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | (35) all_54_6 = e1
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | REF_CLOSE: (14), (30), (35) are inconsistent by sub-proof #562.
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | Case 2:
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | (36) all_54_6 = e0
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | COMBINE_EQS: (14), (36) imply:
% 159.05/28.02 | | | | | (37) all_52_9 = e0
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | SIMP: (37) implies:
% 159.05/28.02 | | | | | (38) all_52_9 = e0
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | REDUCE: (7), (38) imply:
% 159.05/28.02 | | | | | (39) ~ (all_52_8 = e0)
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | REDUCE: (13), (38) imply:
% 159.05/28.02 | | | | | (40) ~ (all_52_11 = e0)
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | SIMP: (40) implies:
% 159.05/28.02 | | | | | (41) ~ (all_52_11 = e0)
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | BETA: splitting (10) gives:
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | | Case 1:
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | | (42) all_54_2 = e3
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | | COMBINE_EQS: (6), (42) imply:
% 159.05/28.02 | | | | | | (43) all_52_8 = e3
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | | REDUCE: (19), (43) imply:
% 159.05/28.02 | | | | | | (44) $false
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | | CLOSE: (44) is inconsistent.
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | Case 2:
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | | (45) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | | BETA: splitting (45) gives:
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | | Case 1:
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | | (46) all_54_2 = e2
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | | COMBINE_EQS: (6), (46) imply:
% 159.05/28.02 | | | | | | | (47) all_52_8 = e2
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | | REDUCE: (16), (47) imply:
% 159.05/28.02 | | | | | | | (48) ~ (all_52_11 = e2)
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | | SIMP: (48) implies:
% 159.05/28.02 | | | | | | | (49) ~ (all_52_11 = e2)
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | | BETA: splitting (26) gives:
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | | Case 1:
% 159.05/28.02 | | | | | | | |
% 159.05/28.02 | | | | | | | | (50) all_54_14 = e3
% 159.05/28.02 | | | | | | | |
% 159.05/28.02 | | | | | | | | REF_CLOSE: (4), (20), (50) are inconsistent by sub-proof #1413.
% 159.05/28.02 | | | | | | | |
% 159.05/28.02 | | | | | | | Case 2:
% 159.05/28.02 | | | | | | | |
% 159.05/28.02 | | | | | | | | (51) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 159.05/28.02 | | | | | | | |
% 159.05/28.02 | | | | | | | | REF_CLOSE: (2), (3), (5), (11), (15), (20), (21), (23), (24),
% 159.05/28.02 | | | | | | | | (41), (49), (51) are inconsistent by sub-proof #873.
% 159.05/28.02 | | | | | | | |
% 159.05/28.02 | | | | | | | End of split
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | Case 2:
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | | (52) all_54_2 = e1 | all_54_2 = e0
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | | REF_CLOSE: (6), (22), (39), (52) are inconsistent by sub-proof
% 159.05/28.02 | | | | | | | #561.
% 159.05/28.02 | | | | | | |
% 159.05/28.02 | | | | | | End of split
% 159.05/28.02 | | | | | |
% 159.05/28.02 | | | | | End of split
% 159.05/28.02 | | | | |
% 159.05/28.02 | | | | End of split
% 159.05/28.02 | | | |
% 159.05/28.02 | | | End of split
% 159.05/28.02 | | |
% 159.05/28.02 | | End of split
% 159.05/28.02 | |
% 159.05/28.02 | Case 2:
% 159.05/28.02 | |
% 159.05/28.02 | | (53) all_54_7 = e0
% 159.05/28.02 | |
% 159.05/28.02 | | REF_CLOSE: (12), (17), (53) are inconsistent by sub-proof #1112.
% 159.05/28.02 | |
% 159.05/28.02 | End of split
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #561 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) all_54_2 = e1 | all_54_2 = e0
% 159.05/28.02 (2) all_54_2 = all_52_8
% 159.05/28.02 (3) ~ (all_52_8 = e1)
% 159.05/28.02 (4) ~ (all_52_8 = e0)
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | BETA: splitting (1) gives:
% 159.05/28.02 |
% 159.05/28.02 | Case 1:
% 159.05/28.02 | |
% 159.05/28.02 | | (5) all_54_2 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | COMBINE_EQS: (2), (5) imply:
% 159.05/28.02 | | (6) all_52_8 = e1
% 159.05/28.02 | |
% 159.05/28.02 | | REDUCE: (3), (6) imply:
% 159.05/28.02 | | (7) $false
% 159.05/28.02 | |
% 159.05/28.02 | | CLOSE: (7) is inconsistent.
% 159.05/28.02 | |
% 159.05/28.02 | Case 2:
% 159.05/28.02 | |
% 159.05/28.02 | | (8) all_54_2 = e0
% 159.05/28.02 | |
% 159.05/28.02 | | COMBINE_EQS: (2), (8) imply:
% 159.05/28.02 | | (9) all_52_8 = e0
% 159.05/28.02 | |
% 159.05/28.02 | | REDUCE: (4), (9) imply:
% 159.05/28.02 | | (10) $false
% 159.05/28.02 | |
% 159.05/28.02 | | CLOSE: (10) is inconsistent.
% 159.05/28.02 | |
% 159.05/28.02 | End of split
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #562 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) all_54_6 = all_52_9
% 159.05/28.02 (2) all_54_6 = e1
% 159.05/28.02 (3) ~ (all_52_9 = e1)
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (1), (2) imply:
% 159.05/28.02 | (4) all_52_9 = e1
% 159.05/28.02 |
% 159.05/28.02 | SIMP: (4) implies:
% 159.05/28.02 | (5) all_52_9 = e1
% 159.05/28.02 |
% 159.05/28.02 | REDUCE: (3), (5) imply:
% 159.05/28.02 | (6) $false
% 159.05/28.02 |
% 159.05/28.02 | CLOSE: (6) is inconsistent.
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #563 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.02 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.02 (2) all_58_14 = e3
% 159.05/28.02 (3) op(e1, e1) = all_6_2
% 159.05/28.02 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.02 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.02 (5) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.02 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.02 (6) all_58_6 = e3
% 159.05/28.02 (7) all_58_7 = e0
% 159.05/28.02 (8) op(e2, e3) = all_52_1
% 159.05/28.02 (9) ~ (e3 = e0)
% 159.05/28.02 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/28.02 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/28.02 (11) ~ (e2 = e0)
% 159.05/28.02 (12) op(e2, e3) = e2
% 159.05/28.02 (13) ~ (e3 = e1)
% 159.05/28.02 (14) all_58_5 = e1
% 159.05/28.02 (15) all_58_7 = e1
% 159.05/28.02 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.02 (17) ~ (e2 = e1)
% 159.05/28.02 (18) ~ (e1 = e0)
% 159.05/28.02 (19) all_58_4 = e3
% 159.05/28.02 (20) all_58_3 = e3
% 159.05/28.02 (21) ~ (all_6_2 = e2)
% 159.05/28.02 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.02 (23) ~ (e3 = e2)
% 159.05/28.02 (24) all_58_12 = e1
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (7), (15) imply:
% 159.05/28.02 | (25) e1 = e0
% 159.05/28.02 |
% 159.05/28.02 | SIMP: (25) implies:
% 159.05/28.02 | (26) e1 = e0
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (24), (26) imply:
% 159.05/28.02 | (27) all_58_12 = e0
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (14), (26) imply:
% 159.05/28.02 | (28) all_58_5 = e0
% 159.05/28.02 |
% 159.05/28.02 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 159.05/28.02 | (16), (17), (18), (19), (20), (21), (22), (23), (27), (28) are
% 159.05/28.02 | inconsistent by sub-proof #826.
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #564 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.02 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.02 (2) all_58_6 = e3
% 159.05/28.02 (3) op(e2, e3) = all_52_1
% 159.05/28.02 (4) ~ (e3 = e0)
% 159.05/28.02 (5) all_58_4 = e2 & op(e3, e1) = e2
% 159.05/28.02 (6) op(e2, e3) = e2
% 159.05/28.02 (7) ~ (e3 = e1)
% 159.05/28.02 (8) all_58_4 = e3
% 159.05/28.02 (9) all_58_0 = e0
% 159.05/28.02 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.02 (11) ~ (e3 = e2)
% 159.05/28.02 (12) all_58_12 = e1
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | ALPHA: (5) implies:
% 159.05/28.02 | (13) all_58_4 = e2
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (8), (13) imply:
% 159.05/28.02 | (14) e3 = e2
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (2), (14) imply:
% 159.05/28.02 | (15) all_58_6 = e2
% 159.05/28.02 |
% 159.05/28.02 | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (15) are
% 159.05/28.02 | inconsistent by sub-proof #1125.
% 159.05/28.02 |
% 159.05/28.02 End of proof
% 159.05/28.02
% 159.05/28.02 Sub-proof #565 shows that the following formulas are inconsistent:
% 159.05/28.02 ----------------------------------------------------------------
% 159.05/28.02 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.02 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.02 (2) all_58_6 = e3
% 159.05/28.02 (3) all_58_9 = e2 & op(e3, e0) = e2
% 159.05/28.02 (4) op(e2, e3) = all_52_1
% 159.05/28.02 (5) ~ (e3 = e0)
% 159.05/28.02 (6) all_58_9 = e3
% 159.05/28.02 (7) op(e2, e3) = e2
% 159.05/28.02 (8) ~ (e3 = e1)
% 159.05/28.02 (9) all_58_0 = e0
% 159.05/28.02 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.02 (11) ~ (e3 = e2)
% 159.05/28.02 (12) all_58_12 = e1
% 159.05/28.02
% 159.05/28.02 Begin of proof
% 159.05/28.02 |
% 159.05/28.02 | ALPHA: (3) implies:
% 159.05/28.02 | (13) all_58_9 = e2
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (6), (13) imply:
% 159.05/28.02 | (14) e3 = e2
% 159.05/28.02 |
% 159.05/28.02 | SIMP: (14) implies:
% 159.05/28.02 | (15) e3 = e2
% 159.05/28.02 |
% 159.05/28.02 | COMBINE_EQS: (2), (15) imply:
% 159.05/28.02 | (16) all_58_6 = e2
% 159.05/28.02 |
% 159.05/28.03 | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (12), (16) are
% 159.05/28.03 | inconsistent by sub-proof #1125.
% 159.05/28.03 |
% 159.05/28.03 End of proof
% 159.05/28.03
% 159.05/28.03 Sub-proof #566 shows that the following formulas are inconsistent:
% 159.05/28.03 ----------------------------------------------------------------
% 159.05/28.03 (1) op(e1, e1) = e3
% 159.05/28.03 (2) all_56_14 = e3
% 159.05/28.03 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/28.03 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/28.03 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.03 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/28.03 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/28.03 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.03 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.03 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.03 (7) op(e3, e3) = all_10_2
% 159.05/28.03 (8) ~ (all_10_2 = e1)
% 159.05/28.03 (9) op(e1, e1) = all_6_2
% 159.05/28.03 (10) ~ (all_52_7 = e3)
% 159.05/28.03 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/28.03 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.05/28.03 e1)
% 159.05/28.03 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/28.03 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/28.03 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.05/28.03 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.05/28.03 (14) all_56_12 = all_10_2
% 159.05/28.03 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.03 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.03 (16) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.03 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.03 (17) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/28.03 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/28.03 (18) op(e3, e2) = all_52_4
% 159.05/28.03 (19) ~ (all_4_2 = e2)
% 159.05/28.03 (20) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/28.03 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/28.03 (21) all_54_0 = all_10_2
% 159.05/28.03 (22) op(e2, e1) = all_52_9
% 159.05/28.03 (23) op(e2, e3) = all_52_1
% 159.05/28.03 (24) ~ (all_52_13 = e3)
% 159.05/28.03 (25) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/28.03 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/28.03 (26) ~ (all_10_2 = e0)
% 159.05/28.03 (27) ~ (e3 = e0)
% 159.05/28.03 (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/28.03 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/28.03 (29) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/28.03 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/28.03 (30) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.03 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/28.03 e2)
% 159.05/28.03 (31) ~ (e2 = e0)
% 159.05/28.03 (32) ~ (all_52_9 = e3)
% 159.05/28.03 (33) ~ (all_52_2 = all_52_6)
% 159.05/28.03 (34) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/28.03 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/28.03 (35) op(e1, e3) = all_52_2
% 159.05/28.03 (36) op(e2, e0) = all_52_13
% 159.05/28.03 (37) op(e2, e3) = e2
% 159.05/28.03 (38) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.03 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/28.03 (39) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.05/28.03 (40) ~ (e3 = e1)
% 159.05/28.03 (41) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/28.03 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/28.03 (42) op(e1, e2) = all_52_6
% 159.05/28.03 (43) ( ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 159.05/28.03 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e0) & op(e3,
% 159.05/28.03 e3) = all_28_1 & $i(all_28_1))
% 159.05/28.03 (44) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 159.05/28.03 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.05/28.03 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 159.05/28.03 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.05/28.03 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.05/28.03 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.05/28.03 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 159.05/28.03 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 159.05/28.03 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 159.05/28.03 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.05/28.03 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.05/28.03 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 159.05/28.03 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.05/28.03 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.05/28.03 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 159.05/28.03 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 159.05/28.03 = e0)
% 159.05/28.03 (45) ~ (all_4_2 = e1)
% 159.05/28.03 (46) ~ (all_52_4 = all_10_2)
% 159.05/28.03 (47) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.03 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.03 (48) op(e0, e0) = all_4_2
% 159.05/28.03 (49) all_56_15 = all_4_2
% 159.05/28.03 (50) op(e0, e1) = all_52_11
% 159.05/28.03 (51) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 159.05/28.03 (52) all_56_6 = e1
% 159.05/28.03 (53) ~ (all_52_13 = all_4_2)
% 159.05/28.03 (54) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/28.03 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/28.03 (55) ~ (all_52_4 = e3)
% 159.05/28.03 (56) ~ (all_10_2 = e2)
% 159.05/28.03 (57) ~ (e2 = e1)
% 159.05/28.03 (58) ~ (e1 = e0)
% 159.05/28.03 (59) ~ (all_52_2 = e2)
% 159.05/28.03 (60) all_58_3 = e3
% 159.05/28.03 (61) ~ (all_6_2 = e2)
% 159.05/28.03 (62) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/28.03 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.03 e3)
% 159.05/28.03 (63) all_56_13 = e3
% 159.05/28.03 (64) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/28.03 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/28.03 (65) ~ (all_52_9 = e2)
% 159.05/28.03 (66) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.05/28.03 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.03 (67) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.05/28.03 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.05/28.03 e3) = all_22_1 & $i(all_22_1))
% 159.05/28.03 (68) ~ (all_52_7 = all_4_2)
% 159.05/28.03 (69) op(e1, e3) = e1
% 159.05/28.03 (70) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/28.03 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/28.03 (71) op(e0, e2) = all_52_7
% 159.05/28.03 (72) op(e1, e0) = all_52_14
% 159.05/28.03 (73) ~ (all_52_6 = e3)
% 159.05/28.03 (74) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/28.03 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/28.03 (75) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.03 (76) ~ (e3 = e2)
% 159.05/28.03 (77) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/28.03 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.03 (78) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.03 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/28.03 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/28.03 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/28.03 (79) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/28.03
% 159.05/28.03 Begin of proof
% 159.05/28.03 |
% 159.05/28.03 | BETA: splitting (43) gives:
% 159.05/28.03 |
% 159.05/28.03 | Case 1:
% 159.05/28.03 | |
% 159.05/28.03 | | (80) ~ (all_28_0 = e2) & op(all_28_1, e1) = all_28_0 & op(e3, e3) =
% 159.05/28.03 | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 159.05/28.03 | |
% 159.05/28.03 | | ALPHA: (80) implies:
% 159.05/28.03 | | (81) op(e3, e3) = all_28_1
% 159.05/28.03 | |
% 159.05/28.03 | | BETA: splitting (13) gives:
% 159.05/28.03 | |
% 159.05/28.03 | | Case 1:
% 159.05/28.03 | | |
% 159.05/28.03 | | | (82) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 159.05/28.03 | | | e3)
% 159.05/28.03 | | |
% 159.05/28.03 | | | BETA: splitting (82) gives:
% 159.05/28.03 | | |
% 159.05/28.03 | | | Case 1:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | (83) all_58_4 = e3 & op(e3, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | ALPHA: (83) implies:
% 159.05/28.03 | | | | (84) all_58_4 = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.03 | | | | (15), (16), (17), (18), (20), (21), (23), (24), (25), (26),
% 159.05/28.03 | | | | (27), (28), (29), (30), (31), (34), (35), (36), (37), (38),
% 159.05/28.03 | | | | (39), (40), (41), (42), (46), (47), (50), (54), (55), (56),
% 159.05/28.03 | | | | (57), (58), (60), (61), (62), (64), (66), (67), (69), (70),
% 159.05/28.03 | | | | (71), (73), (74), (75), (76), (77), (78), (81), (84) are
% 159.05/28.03 | | | | inconsistent by sub-proof #616.
% 159.05/28.03 | | | |
% 159.05/28.03 | | | Case 2:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | (85) all_58_5 = e3 & op(e2, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | ALPHA: (85) implies:
% 159.05/28.03 | | | | (86) op(e2, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | REF_CLOSE: (22), (32), (75), (86) are inconsistent by sub-proof #1196.
% 159.05/28.03 | | | |
% 159.05/28.03 | | | End of split
% 159.05/28.03 | | |
% 159.05/28.03 | | Case 2:
% 159.05/28.03 | | |
% 159.05/28.03 | | | (87) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 159.05/28.03 | | | e3)
% 159.05/28.03 | | |
% 159.05/28.03 | | | BETA: splitting (87) gives:
% 159.05/28.03 | | |
% 159.05/28.03 | | | Case 1:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | (88) all_58_8 = e3 & op(e1, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | ALPHA: (88) implies:
% 159.05/28.03 | | | | (89) all_58_8 = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | BETA: splitting (39) gives:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | Case 1:
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | (90) all_54_0 = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | COMBINE_EQS: (21), (90) imply:
% 159.05/28.03 | | | | | (91) all_10_2 = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | SIMP: (91) implies:
% 159.05/28.03 | | | | | (92) all_10_2 = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | COMBINE_EQS: (14), (92) imply:
% 159.05/28.03 | | | | | (93) all_56_12 = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | BETA: splitting (67) gives:
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | Case 1:
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | (94) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3,
% 159.05/28.03 | | | | | | e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | ALPHA: (94) implies:
% 159.05/28.03 | | | | | | (95) op(e3, e3) = all_22_1
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.03 | | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.05/28.03 | | | | | | (25), (26), (27), (28), (29), (30), (31), (33), (34),
% 159.05/28.03 | | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (44),
% 159.05/28.03 | | | | | | (45), (47), (48), (49), (50), (51), (52), (53), (54),
% 159.05/28.03 | | | | | | (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 159.05/28.03 | | | | | | (64), (65), (66), (68), (69), (70), (71), (72), (73),
% 159.05/28.03 | | | | | | (74), (75), (76), (77), (78), (79), (81), (89), (93),
% 159.05/28.03 | | | | | | (95) are inconsistent by sub-proof #568.
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | Case 2:
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | (96) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | ALPHA: (96) implies:
% 159.05/28.03 | | | | | | (97) op(e3, e3) = all_22_1
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.03 | | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.05/28.03 | | | | | | (25), (26), (27), (28), (29), (30), (31), (33), (34),
% 159.05/28.03 | | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (44),
% 159.05/28.03 | | | | | | (45), (47), (48), (49), (50), (51), (52), (53), (54),
% 159.05/28.03 | | | | | | (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 159.05/28.03 | | | | | | (64), (65), (66), (68), (69), (70), (71), (72), (73),
% 159.05/28.03 | | | | | | (74), (75), (76), (77), (78), (79), (81), (89), (93),
% 159.05/28.03 | | | | | | (97) are inconsistent by sub-proof #568.
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | End of split
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | Case 2:
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | (98) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | REF_CLOSE: (8), (21), (26), (56), (98) are inconsistent by sub-proof
% 159.05/28.03 | | | | | #1307.
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | End of split
% 159.05/28.03 | | | |
% 159.05/28.03 | | | Case 2:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | (99) all_58_14 = e3 & op(e0, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | ALPHA: (99) implies:
% 159.05/28.03 | | | | (100) all_58_14 = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.03 | | | | (15), (16), (17), (18), (20), (21), (23), (24), (25), (26),
% 159.05/28.03 | | | | (27), (28), (29), (30), (31), (34), (35), (36), (37), (38),
% 159.05/28.03 | | | | (39), (40), (41), (42), (46), (47), (54), (55), (56), (57),
% 159.05/28.03 | | | | (58), (60), (61), (62), (64), (66), (67), (69), (70), (71),
% 159.05/28.03 | | | | (73), (74), (75), (76), (77), (78), (81), (100) are
% 159.05/28.03 | | | | inconsistent by sub-proof #622.
% 159.05/28.03 | | | |
% 159.05/28.03 | | | End of split
% 159.05/28.03 | | |
% 159.05/28.03 | | End of split
% 159.05/28.03 | |
% 159.05/28.03 | Case 2:
% 159.05/28.03 | |
% 159.05/28.03 | | (101) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1)
% 159.05/28.03 | |
% 159.05/28.03 | | ALPHA: (101) implies:
% 159.05/28.03 | | (102) ~ (all_28_1 = e0)
% 159.05/28.03 | | (103) op(e3, e3) = all_28_1
% 159.05/28.03 | |
% 159.05/28.03 | | BETA: splitting (13) gives:
% 159.05/28.03 | |
% 159.05/28.03 | | Case 1:
% 159.05/28.03 | | |
% 159.05/28.03 | | | (104) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 159.05/28.03 | | | e3)
% 159.05/28.03 | | |
% 159.05/28.03 | | | BETA: splitting (104) gives:
% 159.05/28.03 | | |
% 159.05/28.03 | | | Case 1:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | (105) all_58_4 = e3 & op(e3, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | ALPHA: (105) implies:
% 159.05/28.03 | | | | (106) all_58_4 = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.03 | | | | (15), (16), (17), (18), (20), (21), (23), (24), (25), (26),
% 159.05/28.03 | | | | (27), (28), (29), (30), (31), (34), (35), (36), (37), (38),
% 159.05/28.03 | | | | (39), (40), (41), (42), (46), (47), (50), (54), (55), (56),
% 159.05/28.03 | | | | (57), (58), (60), (61), (62), (64), (66), (67), (69), (70),
% 159.05/28.03 | | | | (71), (73), (74), (75), (76), (77), (78), (103), (106) are
% 159.05/28.03 | | | | inconsistent by sub-proof #616.
% 159.05/28.03 | | | |
% 159.05/28.03 | | | Case 2:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | (107) all_58_5 = e3 & op(e2, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | ALPHA: (107) implies:
% 159.05/28.03 | | | | (108) op(e2, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | REF_CLOSE: (22), (32), (75), (108) are inconsistent by sub-proof #1196.
% 159.05/28.03 | | | |
% 159.05/28.03 | | | End of split
% 159.05/28.03 | | |
% 159.05/28.03 | | Case 2:
% 159.05/28.03 | | |
% 159.05/28.03 | | | (109) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 159.05/28.03 | | | = e3)
% 159.05/28.03 | | |
% 159.05/28.03 | | | BETA: splitting (109) gives:
% 159.05/28.03 | | |
% 159.05/28.03 | | | Case 1:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | (110) all_58_8 = e3 & op(e1, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | ALPHA: (110) implies:
% 159.05/28.03 | | | | (111) all_58_8 = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | BETA: splitting (39) gives:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | Case 1:
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | (112) all_54_0 = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | COMBINE_EQS: (21), (112) imply:
% 159.05/28.03 | | | | | (113) all_10_2 = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | SIMP: (113) implies:
% 159.05/28.03 | | | | | (114) all_10_2 = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | COMBINE_EQS: (14), (114) imply:
% 159.05/28.03 | | | | | (115) all_56_12 = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | REDUCE: (7), (114) imply:
% 159.05/28.03 | | | | | (116) op(e3, e3) = e3
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | BETA: splitting (67) gives:
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | Case 1:
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | (117) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3,
% 159.05/28.03 | | | | | | e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | ALPHA: (117) implies:
% 159.05/28.03 | | | | | | (118) op(e3, e3) = all_22_1
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (12), (15),
% 159.05/28.03 | | | | | | (16), (17), (18), (19), (20), (22), (23), (25), (27),
% 159.05/28.03 | | | | | | (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 159.05/28.03 | | | | | | (38), (40), (41), (42), (44), (45), (47), (48), (49),
% 159.05/28.03 | | | | | | (50), (51), (52), (53), (54), (55), (57), (58), (59),
% 159.05/28.03 | | | | | | (60), (61), (62), (63), (64), (65), (66), (68), (69),
% 159.05/28.03 | | | | | | (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 159.05/28.03 | | | | | | (79), (102), (103), (111), (115), (116), (118) are
% 159.05/28.03 | | | | | | inconsistent by sub-proof #567.
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | Case 2:
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | (119) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | ALPHA: (119) implies:
% 159.05/28.03 | | | | | | (120) op(e3, e3) = all_22_1
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (12), (15),
% 159.05/28.03 | | | | | | (16), (17), (18), (19), (20), (22), (23), (25), (27),
% 159.05/28.03 | | | | | | (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 159.05/28.03 | | | | | | (38), (40), (41), (42), (44), (45), (47), (48), (49),
% 159.05/28.03 | | | | | | (50), (51), (52), (53), (54), (55), (57), (58), (59),
% 159.05/28.03 | | | | | | (60), (61), (62), (63), (64), (65), (66), (68), (69),
% 159.05/28.03 | | | | | | (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 159.05/28.03 | | | | | | (79), (102), (103), (111), (115), (116), (120) are
% 159.05/28.03 | | | | | | inconsistent by sub-proof #567.
% 159.05/28.03 | | | | | |
% 159.05/28.03 | | | | | End of split
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | Case 2:
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | (121) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | | REF_CLOSE: (8), (21), (26), (56), (121) are inconsistent by sub-proof
% 159.05/28.03 | | | | | #1307.
% 159.05/28.03 | | | | |
% 159.05/28.03 | | | | End of split
% 159.05/28.03 | | | |
% 159.05/28.03 | | | Case 2:
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | (122) all_58_14 = e3 & op(e0, e1) = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | ALPHA: (122) implies:
% 159.05/28.03 | | | | (123) all_58_14 = e3
% 159.05/28.03 | | | |
% 159.05/28.03 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.05/28.03 | | | | (15), (16), (17), (18), (20), (21), (23), (24), (25), (26),
% 159.05/28.03 | | | | (27), (28), (29), (30), (31), (34), (35), (36), (37), (38),
% 159.05/28.03 | | | | (39), (40), (41), (42), (46), (47), (54), (55), (56), (57),
% 159.05/28.03 | | | | (58), (60), (61), (62), (64), (66), (67), (69), (70), (71),
% 159.05/28.03 | | | | (73), (74), (75), (76), (77), (78), (103), (123) are
% 159.05/28.03 | | | | inconsistent by sub-proof #622.
% 159.05/28.03 | | | |
% 159.05/28.03 | | | End of split
% 159.05/28.03 | | |
% 159.05/28.03 | | End of split
% 159.05/28.03 | |
% 159.05/28.03 | End of split
% 159.05/28.03 |
% 159.05/28.03 End of proof
% 159.05/28.03
% 159.05/28.03 Sub-proof #567 shows that the following formulas are inconsistent:
% 159.05/28.03 ----------------------------------------------------------------
% 159.05/28.03 (1) all_56_14 = e3
% 159.05/28.03 (2) ~ (all_28_1 = e0)
% 159.05/28.03 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.05/28.03 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.05/28.03 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.03 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.05/28.03 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.05/28.03 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.03 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.05/28.03 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.05/28.03 (7) op(e1, e1) = all_6_2
% 159.05/28.03 (8) ~ (all_52_7 = e3)
% 159.05/28.03 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.05/28.03 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.05/28.03 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.05/28.03 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.05/28.03 (11) op(e3, e3) = all_28_1
% 159.05/28.03 (12) all_58_8 = e3
% 159.05/28.03 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.05/28.03 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.05/28.03 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.05/28.03 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.05/28.03 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.05/28.03 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.05/28.03 (16) op(e3, e2) = all_52_4
% 159.05/28.03 (17) ~ (all_4_2 = e2)
% 159.05/28.03 (18) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.05/28.03 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.05/28.03 (19) op(e2, e1) = all_52_9
% 159.05/28.03 (20) op(e2, e3) = all_52_1
% 159.05/28.03 (21) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.05/28.03 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.05/28.03 (22) ~ (e3 = e0)
% 159.05/28.03 (23) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.05/28.03 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.05/28.03 (24) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.05/28.03 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.05/28.03 (25) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.03 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.05/28.03 e2)
% 159.05/28.03 (26) ~ (e2 = e0)
% 159.05/28.03 (27) ~ (all_52_2 = all_52_6)
% 159.05/28.03 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.05/28.03 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.05/28.03 (29) op(e1, e3) = all_52_2
% 159.05/28.03 (30) op(e2, e0) = all_52_13
% 159.05/28.03 (31) op(e2, e3) = e2
% 159.05/28.03 (32) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.03 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.05/28.03 (33) ~ (e3 = e1)
% 159.05/28.03 (34) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.05/28.03 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.05/28.03 (35) op(e1, e2) = all_52_6
% 159.05/28.04 (36) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 159.05/28.04 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.05/28.04 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 159.05/28.04 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.05/28.04 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.05/28.04 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.05/28.04 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 159.05/28.04 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 159.05/28.04 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 159.05/28.04 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.05/28.04 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.05/28.04 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 159.05/28.04 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.05/28.04 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.05/28.04 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 159.05/28.04 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 159.05/28.04 = e0)
% 159.05/28.04 (37) ~ (all_4_2 = e1)
% 159.05/28.04 (38) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.05/28.04 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.05/28.04 (39) op(e0, e0) = all_4_2
% 159.05/28.04 (40) all_56_12 = e3
% 159.05/28.04 (41) all_56_15 = all_4_2
% 159.05/28.04 (42) op(e0, e1) = all_52_11
% 159.05/28.04 (43) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 159.05/28.04 (44) all_56_6 = e1
% 159.05/28.04 (45) ~ (all_52_13 = all_4_2)
% 159.05/28.04 (46) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.05/28.04 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.05/28.04 (47) ~ (all_52_4 = e3)
% 159.05/28.04 (48) ~ (e2 = e1)
% 159.05/28.04 (49) op(e3, e3) = e3
% 159.05/28.04 (50) ~ (e1 = e0)
% 159.05/28.04 (51) ~ (all_52_2 = e2)
% 159.05/28.04 (52) all_58_3 = e3
% 159.05/28.04 (53) ~ (all_6_2 = e2)
% 159.05/28.04 (54) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.05/28.04 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.04 e3)
% 159.05/28.04 (55) all_56_13 = e3
% 159.05/28.04 (56) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.05/28.04 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.05/28.04 (57) ~ (all_52_9 = e2)
% 159.05/28.04 (58) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.05/28.04 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.05/28.04 (59) ~ (all_52_7 = all_4_2)
% 159.05/28.04 (60) op(e1, e3) = e1
% 159.05/28.04 (61) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.05/28.04 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.05/28.04 (62) op(e0, e2) = all_52_7
% 159.05/28.04 (63) op(e1, e0) = all_52_14
% 159.05/28.04 (64) op(e3, e3) = all_22_1
% 159.05/28.04 (65) ~ (all_52_6 = e3)
% 159.05/28.04 (66) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.05/28.04 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.05/28.04 (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.05/28.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.05/28.04 (68) ~ (e3 = e2)
% 159.05/28.04 (69) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.05/28.04 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.04 (70) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.05/28.04 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.05/28.04 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.05/28.04 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.05/28.04 (71) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.05/28.04
% 159.05/28.04 Begin of proof
% 159.05/28.04 |
% 159.05/28.04 | BETA: splitting (54) gives:
% 159.05/28.04 |
% 159.05/28.04 | Case 1:
% 159.05/28.04 | |
% 159.05/28.04 | | (72) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 159.05/28.04 | | e3)
% 159.05/28.04 | |
% 159.05/28.04 | | BETA: splitting (72) gives:
% 159.05/28.04 | |
% 159.05/28.04 | | Case 1:
% 159.05/28.04 | | |
% 159.05/28.04 | | | (73) all_58_12 = e3 & op(e0, e3) = e3
% 159.05/28.04 | | |
% 159.05/28.04 | | | ALPHA: (73) implies:
% 159.05/28.04 | | | (74) all_58_12 = e3
% 159.05/28.04 | | |
% 159.05/28.04 | | | REF_CLOSE: (11), (22), (23), (26), (29), (31), (33), (48), (49), (50),
% 159.05/28.04 | | | (60), (64), (66), (67), (73), (74) are inconsistent by
% 159.05/28.04 | | | sub-proof #664.
% 159.05/28.04 | | |
% 159.05/28.04 | | Case 2:
% 159.05/28.04 | | |
% 159.05/28.04 | | | (75) all_58_13 = e3 & op(e0, e2) = e3
% 159.05/28.04 | | |
% 159.05/28.04 | | | REF_CLOSE: (8), (62), (67), (75) are inconsistent by sub-proof #1449.
% 159.05/28.04 | | |
% 159.05/28.04 | | End of split
% 159.05/28.04 | |
% 159.05/28.04 | Case 2:
% 159.05/28.04 | |
% 159.05/28.04 | | (76) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.05/28.04 | | e3)
% 159.05/28.04 | |
% 159.05/28.04 | | BETA: splitting (76) gives:
% 159.05/28.04 | |
% 159.05/28.04 | | Case 1:
% 159.05/28.04 | | |
% 159.05/28.04 | | | (77) all_58_14 = e3 & op(e0, e1) = e3
% 159.05/28.04 | | |
% 159.05/28.04 | | | ALPHA: (77) implies:
% 159.05/28.04 | | | (78) all_58_14 = e3
% 159.05/28.04 | | |
% 159.05/28.04 | | | REF_CLOSE: (6), (7), (12), (14), (22), (26), (31), (33), (34), (38), (46),
% 159.05/28.04 | | | (48), (50), (52), (53), (67), (68), (78) are inconsistent by
% 159.05/28.04 | | | sub-proof #780.
% 159.05/28.04 | | |
% 159.05/28.04 | | Case 2:
% 159.05/28.04 | | |
% 159.05/28.04 | | | (79) all_58_15 = e3 & op(e0, e0) = e3
% 159.05/28.04 | | |
% 159.05/28.04 | | | ALPHA: (79) implies:
% 159.05/28.04 | | | (80) all_58_15 = e3
% 159.05/28.04 | | | (81) op(e0, e0) = e3
% 159.05/28.04 | | |
% 159.05/28.04 | | | BETA: splitting (13) gives:
% 159.05/28.04 | | |
% 159.05/28.04 | | | Case 1:
% 159.05/28.04 | | | |
% 159.05/28.04 | | | | (82) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 159.05/28.04 | | | | = e3)
% 159.05/28.04 | | | |
% 159.05/28.04 | | | | BETA: splitting (82) gives:
% 159.05/28.04 | | | |
% 159.05/28.04 | | | | Case 1:
% 159.05/28.04 | | | | |
% 159.05/28.04 | | | | | (83) all_58_0 = e3 & op(e3, e3) = e3
% 159.05/28.04 | | | | |
% 159.05/28.04 | | | | | ALPHA: (83) implies:
% 159.05/28.04 | | | | | (84) all_58_0 = e3
% 159.05/28.04 | | | | |
% 159.05/28.04 | | | | | GROUND_INST: instantiating (67) with all_4_2, e3, e0, e0, simplifying
% 159.05/28.04 | | | | | with (39), (81) gives:
% 159.05/28.04 | | | | | (85) all_4_2 = e3
% 159.05/28.04 | | | | |
% 159.05/28.04 | | | | | GROUND_INST: instantiating (67) with all_52_2, e1, e3, e1, simplifying
% 159.05/28.04 | | | | | with (29), (60) gives:
% 159.05/28.04 | | | | | (86) all_52_2 = e1
% 159.05/28.04 | | | | |
% 159.05/28.04 | | | | | GROUND_INST: instantiating (67) with all_22_1, all_28_1, e3, e3,
% 159.05/28.04 | | | | | simplifying with (11), (64) gives:
% 159.05/28.04 | | | | | (87) all_28_1 = all_22_1
% 159.05/28.04 | | | | |
% 159.32/28.04 | | | | | GROUND_INST: instantiating (67) with e3, all_28_1, e3, e3, simplifying
% 159.32/28.04 | | | | | with (11), (49) gives:
% 159.32/28.04 | | | | | (88) all_28_1 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | COMBINE_EQS: (87), (88) imply:
% 159.32/28.04 | | | | | (89) all_22_1 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | COMBINE_EQS: (41), (85) imply:
% 159.32/28.04 | | | | | (90) all_56_15 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REDUCE: (27), (86) imply:
% 159.32/28.04 | | | | | (91) ~ (all_52_6 = e1)
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | SIMP: (91) implies:
% 159.32/28.04 | | | | | (92) ~ (all_52_6 = e1)
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REDUCE: (51), (86) imply:
% 159.32/28.04 | | | | | (93) ~ (e2 = e1)
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REDUCE: (45), (85) imply:
% 159.32/28.04 | | | | | (94) ~ (all_52_13 = e3)
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 159.32/28.04 | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.32/28.04 | | | | | (24), (25), (26), (28), (29), (30), (31), (32), (34), (35),
% 159.32/28.04 | | | | | (36), (37), (38), (39), (40), (42), (43), (44), (46), (47),
% 159.32/28.04 | | | | | (48), (50), (52), (53), (54), (55), (56), (57), (58), (61),
% 159.32/28.04 | | | | | (62), (63), (65), (66), (67), (69), (70), (80), (84), (85),
% 159.32/28.04 | | | | | (86), (90), (92), (94) are inconsistent by sub-proof #594.
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | Case 2:
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | (95) all_58_2 = e3 & op(e2, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | ALPHA: (95) implies:
% 159.32/28.04 | | | | | (96) op(e2, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REF_CLOSE: (20), (31), (67), (68), (96) are inconsistent by sub-proof
% 159.32/28.04 | | | | | #1159.
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | End of split
% 159.32/28.04 | | | |
% 159.32/28.04 | | | Case 2:
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | (97) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 159.32/28.04 | | | | = e3)
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | BETA: splitting (97) gives:
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | Case 1:
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | (98) all_58_6 = e3 & op(e1, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | ALPHA: (98) implies:
% 159.32/28.04 | | | | | (99) all_58_6 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REF_CLOSE: (5), (6), (7), (12), (13), (14), (15), (16), (20), (22),
% 159.32/28.04 | | | | | (23), (26), (31), (33), (34), (38), (46), (47), (48), (50),
% 159.32/28.04 | | | | | (52), (53), (61), (66), (67), (68), (70), (80), (81), (99)
% 159.32/28.04 | | | | | are inconsistent by sub-proof #588.
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | Case 2:
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | (100) all_58_12 = e3 & op(e0, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | ALPHA: (100) implies:
% 159.32/28.04 | | | | | (101) all_58_12 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (11), (12), (13), (14), (15),
% 159.32/28.04 | | | | | (16), (17), (20), (21), (22), (23), (26), (28), (31), (33),
% 159.32/28.04 | | | | | (34), (37), (38), (39), (40), (41), (46), (47), (48), (50),
% 159.32/28.04 | | | | | (52), (53), (54), (55), (61), (62), (64), (66), (67), (68),
% 159.32/28.04 | | | | | (70), (71), (80), (81), (101) are inconsistent by sub-proof
% 159.32/28.04 | | | | | #569.
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | End of split
% 159.32/28.04 | | | |
% 159.32/28.04 | | | End of split
% 159.32/28.04 | | |
% 159.32/28.04 | | End of split
% 159.32/28.04 | |
% 159.32/28.04 | End of split
% 159.32/28.04 |
% 159.32/28.04 End of proof
% 159.32/28.04
% 159.32/28.04 Sub-proof #568 shows that the following formulas are inconsistent:
% 159.32/28.04 ----------------------------------------------------------------
% 159.32/28.04 (1) all_56_14 = e3
% 159.32/28.04 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.04 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.04 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.04 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.32/28.04 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.04 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.04 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.04 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.04 (6) op(e3, e3) = all_10_2
% 159.32/28.04 (7) ~ (all_10_2 = e1)
% 159.32/28.04 (8) op(e1, e1) = all_6_2
% 159.32/28.04 (9) ~ (all_52_7 = e3)
% 159.32/28.04 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.32/28.04 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.32/28.04 e1)
% 159.32/28.04 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.32/28.04 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.32/28.04 (12) op(e3, e3) = all_28_1
% 159.32/28.04 (13) all_58_8 = e3
% 159.32/28.04 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.04 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.04 (15) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.04 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.04 (16) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.04 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.04 (17) op(e3, e2) = all_52_4
% 159.32/28.04 (18) ~ (all_4_2 = e2)
% 159.32/28.04 (19) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.32/28.04 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.32/28.04 (20) all_54_0 = all_10_2
% 159.32/28.04 (21) op(e2, e1) = all_52_9
% 159.32/28.04 (22) op(e2, e3) = all_52_1
% 159.32/28.04 (23) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.32/28.04 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.32/28.04 (24) ~ (all_10_2 = e0)
% 159.32/28.04 (25) ~ (e3 = e0)
% 159.32/28.04 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.04 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.04 (27) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.32/28.04 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.32/28.04 (28) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.32/28.04 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.32/28.04 e2)
% 159.32/28.04 (29) ~ (e2 = e0)
% 159.32/28.04 (30) ~ (all_52_2 = all_52_6)
% 159.32/28.04 (31) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.04 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.04 (32) op(e1, e3) = all_52_2
% 159.32/28.04 (33) op(e2, e0) = all_52_13
% 159.32/28.04 (34) op(e2, e3) = e2
% 159.32/28.04 (35) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.04 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.32/28.04 (36) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.32/28.04 (37) ~ (e3 = e1)
% 159.32/28.04 (38) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.04 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.04 (39) op(e1, e2) = all_52_6
% 159.32/28.04 (40) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 159.32/28.04 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.32/28.04 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 159.32/28.04 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.32/28.04 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.32/28.04 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.32/28.04 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 159.32/28.04 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 159.32/28.04 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 159.32/28.04 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.32/28.04 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.32/28.04 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 159.32/28.04 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.32/28.04 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.32/28.04 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 159.32/28.04 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 159.32/28.04 = e0)
% 159.32/28.04 (41) ~ (all_4_2 = e1)
% 159.32/28.04 (42) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.04 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.04 (43) op(e0, e0) = all_4_2
% 159.32/28.04 (44) all_56_12 = e3
% 159.32/28.04 (45) all_56_15 = all_4_2
% 159.32/28.04 (46) op(e0, e1) = all_52_11
% 159.32/28.04 (47) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 159.32/28.04 (48) all_56_6 = e1
% 159.32/28.04 (49) ~ (all_52_13 = all_4_2)
% 159.32/28.04 (50) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.04 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.04 (51) ~ (all_52_4 = e3)
% 159.32/28.04 (52) ~ (all_10_2 = e2)
% 159.32/28.04 (53) ~ (e2 = e1)
% 159.32/28.04 (54) ~ (e1 = e0)
% 159.32/28.04 (55) ~ (all_52_2 = e2)
% 159.32/28.04 (56) all_58_3 = e3
% 159.32/28.04 (57) ~ (all_6_2 = e2)
% 159.32/28.04 (58) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.32/28.04 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.32/28.04 e3)
% 159.32/28.04 (59) all_56_13 = e3
% 159.32/28.04 (60) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.32/28.04 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.32/28.04 (61) ~ (all_52_9 = e2)
% 159.32/28.04 (62) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.32/28.04 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.32/28.04 (63) ~ (all_52_7 = all_4_2)
% 159.32/28.04 (64) op(e1, e3) = e1
% 159.32/28.04 (65) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.32/28.04 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.32/28.04 (66) op(e0, e2) = all_52_7
% 159.32/28.04 (67) op(e1, e0) = all_52_14
% 159.32/28.04 (68) op(e3, e3) = all_22_1
% 159.32/28.04 (69) ~ (all_52_6 = e3)
% 159.32/28.04 (70) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.32/28.04 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.32/28.04 (71) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.04 (72) ~ (e3 = e2)
% 159.32/28.04 (73) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.32/28.04 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.04 (74) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.04 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.04 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.04 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.04 (75) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.32/28.04
% 159.32/28.04 Begin of proof
% 159.32/28.04 |
% 159.32/28.04 | BETA: splitting (58) gives:
% 159.32/28.04 |
% 159.32/28.04 | Case 1:
% 159.32/28.04 | |
% 159.32/28.04 | | (76) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 159.32/28.04 | | e3)
% 159.32/28.04 | |
% 159.32/28.04 | | BETA: splitting (76) gives:
% 159.32/28.04 | |
% 159.32/28.04 | | Case 1:
% 159.32/28.04 | | |
% 159.32/28.04 | | | (77) all_58_12 = e3 & op(e0, e3) = e3
% 159.32/28.04 | | |
% 159.32/28.04 | | | ALPHA: (77) implies:
% 159.32/28.04 | | | (78) all_58_12 = e3
% 159.32/28.04 | | |
% 159.32/28.04 | | | REF_CLOSE: (6), (7), (12), (20), (24), (26), (29), (32), (34), (36), (52),
% 159.32/28.04 | | | (53), (54), (64), (68), (70), (71), (77), (78) are inconsistent
% 159.32/28.04 | | | by sub-proof #663.
% 159.32/28.04 | | |
% 159.32/28.04 | | Case 2:
% 159.32/28.04 | | |
% 159.32/28.04 | | | (79) all_58_13 = e3 & op(e0, e2) = e3
% 159.32/28.04 | | |
% 159.32/28.04 | | | REF_CLOSE: (9), (66), (71), (79) are inconsistent by sub-proof #1449.
% 159.32/28.04 | | |
% 159.32/28.04 | | End of split
% 159.32/28.04 | |
% 159.32/28.04 | Case 2:
% 159.32/28.04 | |
% 159.32/28.04 | | (80) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.32/28.04 | | e3)
% 159.32/28.04 | |
% 159.32/28.04 | | BETA: splitting (80) gives:
% 159.32/28.04 | |
% 159.32/28.04 | | Case 1:
% 159.32/28.04 | | |
% 159.32/28.04 | | | (81) all_58_14 = e3 & op(e0, e1) = e3
% 159.32/28.04 | | |
% 159.32/28.04 | | | ALPHA: (81) implies:
% 159.32/28.04 | | | (82) all_58_14 = e3
% 159.32/28.04 | | |
% 159.32/28.04 | | | REF_CLOSE: (5), (8), (13), (15), (25), (29), (34), (37), (38), (42), (50),
% 159.32/28.04 | | | (53), (54), (56), (57), (71), (72), (82) are inconsistent by
% 159.32/28.04 | | | sub-proof #780.
% 159.32/28.04 | | |
% 159.32/28.04 | | Case 2:
% 159.32/28.04 | | |
% 159.32/28.04 | | | (83) all_58_15 = e3 & op(e0, e0) = e3
% 159.32/28.04 | | |
% 159.32/28.04 | | | ALPHA: (83) implies:
% 159.32/28.04 | | | (84) all_58_15 = e3
% 159.32/28.04 | | | (85) op(e0, e0) = e3
% 159.32/28.04 | | |
% 159.32/28.04 | | | BETA: splitting (14) gives:
% 159.32/28.04 | | |
% 159.32/28.04 | | | Case 1:
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | (86) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 159.32/28.04 | | | | = e3)
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | BETA: splitting (86) gives:
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | Case 1:
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | (87) all_58_0 = e3 & op(e3, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | ALPHA: (87) implies:
% 159.32/28.04 | | | | | (88) all_58_0 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | GROUND_INST: instantiating (71) with all_4_2, e3, e0, e0, simplifying
% 159.32/28.04 | | | | | with (43), (85) gives:
% 159.32/28.04 | | | | | (89) all_4_2 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | GROUND_INST: instantiating (71) with all_52_2, e1, e3, e1, simplifying
% 159.32/28.04 | | | | | with (32), (64) gives:
% 159.32/28.04 | | | | | (90) all_52_2 = e1
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | COMBINE_EQS: (45), (89) imply:
% 159.32/28.04 | | | | | (91) all_56_15 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REDUCE: (30), (90) imply:
% 159.32/28.04 | | | | | (92) ~ (all_52_6 = e1)
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | SIMP: (92) implies:
% 159.32/28.04 | | | | | (93) ~ (all_52_6 = e1)
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REDUCE: (55), (90) imply:
% 159.32/28.04 | | | | | (94) ~ (e2 = e1)
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REDUCE: (49), (89) imply:
% 159.32/28.04 | | | | | (95) ~ (all_52_13 = e3)
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (13), (14),
% 159.32/28.04 | | | | | (15), (16), (17), (18), (19), (21), (22), (23), (25), (26),
% 159.32/28.04 | | | | | (27), (28), (29), (31), (32), (33), (34), (35), (38), (39),
% 159.32/28.04 | | | | | (40), (41), (42), (43), (44), (46), (47), (48), (50), (51),
% 159.32/28.04 | | | | | (53), (54), (56), (57), (58), (59), (60), (61), (62), (65),
% 159.32/28.04 | | | | | (66), (67), (69), (70), (71), (73), (74), (84), (88), (89),
% 159.32/28.04 | | | | | (90), (91), (93), (95) are inconsistent by sub-proof #594.
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | Case 2:
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | (96) all_58_2 = e3 & op(e2, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | ALPHA: (96) implies:
% 159.32/28.04 | | | | | (97) op(e2, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REF_CLOSE: (22), (34), (71), (72), (97) are inconsistent by sub-proof
% 159.32/28.04 | | | | | #1159.
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | End of split
% 159.32/28.04 | | | |
% 159.32/28.04 | | | Case 2:
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | (98) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 159.32/28.04 | | | | = e3)
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | BETA: splitting (98) gives:
% 159.32/28.04 | | | |
% 159.32/28.04 | | | | Case 1:
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | (99) all_58_6 = e3 & op(e1, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | ALPHA: (99) implies:
% 159.32/28.04 | | | | | (100) all_58_6 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REF_CLOSE: (4), (5), (8), (13), (14), (15), (16), (17), (22), (25),
% 159.32/28.04 | | | | | (26), (29), (34), (37), (38), (42), (50), (51), (53), (54),
% 159.32/28.04 | | | | | (56), (57), (65), (70), (71), (72), (74), (84), (85), (100)
% 159.32/28.04 | | | | | are inconsistent by sub-proof #588.
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | Case 2:
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | (101) all_58_12 = e3 & op(e0, e3) = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | ALPHA: (101) implies:
% 159.32/28.04 | | | | | (102) all_58_12 = e3
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (12), (13), (14), (15), (16),
% 159.32/28.04 | | | | | (17), (18), (22), (23), (25), (26), (29), (31), (34), (37),
% 159.32/28.04 | | | | | (38), (41), (42), (43), (44), (45), (50), (51), (53), (54),
% 159.32/28.04 | | | | | (56), (57), (58), (59), (65), (66), (68), (70), (71), (72),
% 159.32/28.04 | | | | | (74), (75), (84), (85), (102) are inconsistent by sub-proof
% 159.32/28.04 | | | | | #569.
% 159.32/28.04 | | | | |
% 159.32/28.04 | | | | End of split
% 159.32/28.04 | | | |
% 159.32/28.04 | | | End of split
% 159.32/28.04 | | |
% 159.32/28.04 | | End of split
% 159.32/28.04 | |
% 159.32/28.04 | End of split
% 159.32/28.04 |
% 159.32/28.04 End of proof
% 159.32/28.04
% 159.32/28.04 Sub-proof #569 shows that the following formulas are inconsistent:
% 159.32/28.04 ----------------------------------------------------------------
% 159.32/28.04 (1) all_56_14 = e3
% 159.32/28.04 (2) all_58_15 = e3
% 159.32/28.04 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.04 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.04 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.04 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.04 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.04 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.04 (6) op(e1, e1) = all_6_2
% 159.32/28.04 (7) ~ (all_52_7 = e3)
% 159.32/28.04 (8) all_58_12 = e3
% 159.32/28.04 (9) op(e3, e3) = all_28_1
% 159.32/28.04 (10) all_58_8 = e3
% 159.32/28.04 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.04 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.04 (12) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.04 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.05 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.05 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.05 (14) op(e3, e2) = all_52_4
% 159.32/28.05 (15) ~ (all_4_2 = e2)
% 159.32/28.05 (16) op(e2, e3) = all_52_1
% 159.32/28.05 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.32/28.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.32/28.05 (18) ~ (e3 = e0)
% 159.32/28.05 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.05 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.05 (20) ~ (e2 = e0)
% 159.32/28.05 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.05 (22) op(e2, e3) = e2
% 159.32/28.05 (23) ~ (e3 = e1)
% 159.32/28.05 (24) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.05 (25) ~ (all_4_2 = e1)
% 159.32/28.05 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.05 (27) op(e0, e0) = all_4_2
% 159.32/28.05 (28) all_56_12 = e3
% 159.32/28.05 (29) all_56_15 = all_4_2
% 159.32/28.05 (30) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.05 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.05 (31) ~ (all_52_4 = e3)
% 159.32/28.05 (32) ~ (e2 = e1)
% 159.32/28.05 (33) ~ (e1 = e0)
% 159.32/28.05 (34) all_58_3 = e3
% 159.32/28.05 (35) ~ (all_6_2 = e2)
% 159.32/28.05 (36) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.32/28.05 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.32/28.05 e3)
% 159.32/28.05 (37) all_56_13 = e3
% 159.32/28.05 (38) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.32/28.05 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.32/28.05 (39) op(e0, e2) = all_52_7
% 159.32/28.05 (40) op(e3, e3) = all_22_1
% 159.32/28.05 (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.32/28.05 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.32/28.05 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.05 (43) ~ (e3 = e2)
% 159.32/28.05 (44) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.05 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.05 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.05 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.05 (45) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.32/28.05 (46) op(e0, e0) = e3
% 159.32/28.05
% 159.32/28.05 Begin of proof
% 159.32/28.05 |
% 159.32/28.05 | BETA: splitting (41) gives:
% 159.32/28.05 |
% 159.32/28.05 | Case 1:
% 159.32/28.05 | |
% 159.32/28.05 | | (47) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.32/28.05 | | e0)
% 159.32/28.05 | |
% 159.32/28.05 | | BETA: splitting (47) gives:
% 159.32/28.05 | |
% 159.32/28.05 | | Case 1:
% 159.32/28.05 | | |
% 159.32/28.05 | | | (48) all_58_0 = e0 & op(e3, e3) = e0
% 159.32/28.05 | | |
% 159.32/28.05 | | | ALPHA: (48) implies:
% 159.32/28.05 | | | (49) all_58_0 = e0
% 159.32/28.05 | | |
% 159.32/28.05 | | | BETA: splitting (38) gives:
% 159.32/28.05 | | |
% 159.32/28.05 | | | Case 1:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | (50) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 159.32/28.05 | | | | = e3)
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | REF_CLOSE: (14), (18), (31), (42), (49), (50) are inconsistent by
% 159.32/28.05 | | | | sub-proof #645.
% 159.32/28.05 | | | |
% 159.32/28.05 | | | Case 2:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | (51) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 159.32/28.05 | | | | = e3)
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | BETA: splitting (51) gives:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | Case 1:
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | (52) all_58_4 = e3 & op(e3, e1) = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | ALPHA: (52) implies:
% 159.32/28.05 | | | | | (53) all_58_4 = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | REF_CLOSE: (5), (6), (8), (10), (11), (12), (16), (18), (19), (20),
% 159.32/28.05 | | | | | (22), (23), (24), (26), (30), (32), (33), (34), (35), (42),
% 159.32/28.05 | | | | | (43), (49), (53) are inconsistent by sub-proof #586.
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | Case 2:
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | (54) all_58_9 = e3 & op(e3, e0) = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | ALPHA: (54) implies:
% 159.32/28.05 | | | | | (55) all_58_9 = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | REF_CLOSE: (2), (4), (5), (13), (18), (20), (22), (23), (26), (32),
% 159.32/28.05 | | | | | (33), (34), (42), (43), (44), (46), (55) are inconsistent
% 159.32/28.05 | | | | | by sub-proof #589.
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | End of split
% 159.32/28.05 | | | |
% 159.32/28.05 | | | End of split
% 159.32/28.05 | | |
% 159.32/28.05 | | Case 2:
% 159.32/28.05 | | |
% 159.32/28.05 | | | (56) all_58_2 = e0 & op(e2, e3) = e0
% 159.32/28.05 | | |
% 159.32/28.05 | | | ALPHA: (56) implies:
% 159.32/28.05 | | | (57) op(e2, e3) = e0
% 159.32/28.05 | | |
% 159.32/28.05 | | | REF_CLOSE: (20), (22), (42), (57) are inconsistent by sub-proof #1156.
% 159.32/28.05 | | |
% 159.32/28.05 | | End of split
% 159.32/28.05 | |
% 159.32/28.05 | Case 2:
% 159.32/28.05 | |
% 159.32/28.05 | | (58) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.32/28.05 | | e0)
% 159.32/28.05 | |
% 159.32/28.05 | | BETA: splitting (58) gives:
% 159.32/28.05 | |
% 159.32/28.05 | | Case 1:
% 159.32/28.05 | | |
% 159.32/28.05 | | | (59) all_58_6 = e0 & op(e1, e3) = e0
% 159.32/28.05 | | |
% 159.32/28.05 | | | ALPHA: (59) implies:
% 159.32/28.05 | | | (60) all_58_6 = e0
% 159.32/28.05 | | |
% 159.32/28.05 | | | BETA: splitting (38) gives:
% 159.32/28.05 | | |
% 159.32/28.05 | | | Case 1:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | (61) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 159.32/28.05 | | | | = e3)
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | BETA: splitting (61) gives:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | Case 1:
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | (62) all_58_0 = e3 & op(e3, e3) = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | ALPHA: (62) implies:
% 159.32/28.05 | | | | | (63) all_58_0 = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | BETA: splitting (19) gives:
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | Case 1:
% 159.32/28.05 | | | | | |
% 159.32/28.05 | | | | | | (64) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 159.32/28.05 | | | | | | e3) = e1)
% 159.32/28.05 | | | | | |
% 159.32/28.05 | | | | | | BETA: splitting (64) gives:
% 159.32/28.05 | | | | | |
% 159.32/28.05 | | | | | | Case 1:
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | (65) all_58_0 = e1 & op(e3, e3) = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | ALPHA: (65) implies:
% 159.32/28.05 | | | | | | | (66) all_58_0 = e1
% 159.32/28.05 | | | | | | | (67) op(e3, e3) = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | COMBINE_EQS: (63), (66) imply:
% 159.32/28.05 | | | | | | | (68) e3 = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | COMBINE_EQS: (28), (68) imply:
% 159.32/28.05 | | | | | | | (69) all_56_12 = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | COMBINE_EQS: (8), (68) imply:
% 159.32/28.05 | | | | | | | (70) all_58_12 = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 159.32/28.05 | | | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 159.32/28.05 | | | | | | | (22), (23), (24), (25), (26), (27), (29), (30), (31),
% 159.32/28.05 | | | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 159.32/28.05 | | | | | | | (41), (42), (43), (44), (45), (67), (69), (70) are
% 159.32/28.05 | | | | | | | inconsistent by sub-proof #571.
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | Case 2:
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | (71) all_58_2 = e1 & op(e2, e3) = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | ALPHA: (71) implies:
% 159.32/28.05 | | | | | | | (72) op(e2, e3) = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | REF_CLOSE: (22), (32), (42), (72) are inconsistent by sub-proof
% 159.32/28.05 | | | | | | | #1430.
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | End of split
% 159.32/28.05 | | | | | |
% 159.32/28.05 | | | | | Case 2:
% 159.32/28.05 | | | | | |
% 159.32/28.05 | | | | | | (73) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 159.32/28.05 | | | | | | e3) = e1)
% 159.32/28.05 | | | | | |
% 159.32/28.05 | | | | | | BETA: splitting (73) gives:
% 159.32/28.05 | | | | | |
% 159.32/28.05 | | | | | | Case 1:
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | (74) all_58_6 = e1 & op(e1, e3) = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | ALPHA: (74) implies:
% 159.32/28.05 | | | | | | | (75) all_58_6 = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | REF_CLOSE: (33), (60), (75) are inconsistent by sub-proof #735.
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | Case 2:
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | (76) all_58_12 = e1 & op(e0, e3) = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | ALPHA: (76) implies:
% 159.32/28.05 | | | | | | | (77) all_58_12 = e1
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | | REF_CLOSE: (8), (23), (77) are inconsistent by sub-proof #1516.
% 159.32/28.05 | | | | | | |
% 159.32/28.05 | | | | | | End of split
% 159.32/28.05 | | | | | |
% 159.32/28.05 | | | | | End of split
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | Case 2:
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | (78) all_58_1 = e3 & op(e3, e2) = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | ALPHA: (78) implies:
% 159.32/28.05 | | | | | (79) op(e3, e2) = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | REF_CLOSE: (14), (31), (42), (79) are inconsistent by sub-proof #1540.
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | End of split
% 159.32/28.05 | | | |
% 159.32/28.05 | | | Case 2:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | (80) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 159.32/28.05 | | | | = e3)
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | BETA: splitting (80) gives:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | Case 1:
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | (81) all_58_4 = e3 & op(e3, e1) = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | ALPHA: (81) implies:
% 159.32/28.05 | | | | | (82) all_58_4 = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | REF_CLOSE: (5), (6), (8), (10), (11), (12), (16), (18), (19), (20),
% 159.32/28.05 | | | | | (22), (23), (24), (26), (30), (32), (33), (34), (35), (42),
% 159.32/28.05 | | | | | (43), (60), (82) are inconsistent by sub-proof #570.
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | Case 2:
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | (83) all_58_9 = e3 & op(e3, e0) = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | ALPHA: (83) implies:
% 159.32/28.05 | | | | | (84) all_58_9 = e3
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | REF_CLOSE: (2), (4), (5), (13), (18), (20), (22), (23), (26), (32),
% 159.32/28.05 | | | | | (33), (34), (42), (43), (44), (46), (84) are inconsistent
% 159.32/28.05 | | | | | by sub-proof #589.
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | End of split
% 159.32/28.05 | | | |
% 159.32/28.05 | | | End of split
% 159.32/28.05 | | |
% 159.32/28.05 | | Case 2:
% 159.32/28.05 | | |
% 159.32/28.05 | | | (85) all_58_12 = e0 & op(e0, e3) = e0
% 159.32/28.05 | | |
% 159.32/28.05 | | | REF_CLOSE: (8), (18), (85) are inconsistent by sub-proof #1505.
% 159.32/28.05 | | |
% 159.32/28.05 | | End of split
% 159.32/28.05 | |
% 159.32/28.05 | End of split
% 159.32/28.05 |
% 159.32/28.05 End of proof
% 159.32/28.05
% 159.32/28.05 Sub-proof #570 shows that the following formulas are inconsistent:
% 159.32/28.05 ----------------------------------------------------------------
% 159.32/28.05 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.05 (2) op(e1, e1) = all_6_2
% 159.32/28.05 (3) all_58_12 = e3
% 159.32/28.05 (4) all_58_8 = e3
% 159.32/28.05 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.05 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.05 (6) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.05 (7) op(e2, e3) = all_52_1
% 159.32/28.05 (8) ~ (e3 = e0)
% 159.32/28.05 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.05 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.05 (10) ~ (e2 = e0)
% 159.32/28.05 (11) all_58_6 = e0
% 159.32/28.05 (12) op(e2, e3) = e2
% 159.32/28.05 (13) ~ (e3 = e1)
% 159.32/28.05 (14) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.05 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.05 (16) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.05 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.05 (17) ~ (e2 = e1)
% 159.32/28.05 (18) ~ (e1 = e0)
% 159.32/28.05 (19) all_58_4 = e3
% 159.32/28.05 (20) all_58_3 = e3
% 159.32/28.05 (21) ~ (all_6_2 = e2)
% 159.32/28.05 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.05 (23) ~ (e3 = e2)
% 159.32/28.05
% 159.32/28.05 Begin of proof
% 159.32/28.05 |
% 159.32/28.05 | BETA: splitting (6) gives:
% 159.32/28.05 |
% 159.32/28.05 | Case 1:
% 159.32/28.05 | |
% 159.32/28.05 | | (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 159.32/28.05 | | e2)
% 159.32/28.05 | |
% 159.32/28.05 | | BETA: splitting (24) gives:
% 159.32/28.05 | |
% 159.32/28.05 | | Case 1:
% 159.32/28.05 | | |
% 159.32/28.05 | | | (25) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.05 | | |
% 159.32/28.05 | | | ALPHA: (25) implies:
% 159.32/28.05 | | | (26) all_58_4 = e2
% 159.32/28.05 | | |
% 159.32/28.05 | | | COMBINE_EQS: (19), (26) imply:
% 159.32/28.05 | | | (27) e3 = e2
% 159.32/28.05 | | |
% 159.32/28.05 | | | REF_CLOSE: (3), (5), (7), (8), (9), (11), (12), (13), (17), (18), (22),
% 159.32/28.05 | | | (23), (27) are inconsistent by sub-proof #772.
% 159.32/28.05 | | |
% 159.32/28.05 | | Case 2:
% 159.32/28.05 | | |
% 159.32/28.05 | | | (28) all_58_5 = e2 & op(e2, e1) = e2
% 159.32/28.05 | | |
% 159.32/28.05 | | | ALPHA: (28) implies:
% 159.32/28.05 | | | (29) all_58_5 = e2
% 159.32/28.05 | | |
% 159.32/28.05 | | | REF_CLOSE: (1), (8), (10), (12), (13), (15), (17), (18), (20), (22), (29)
% 159.32/28.05 | | | are inconsistent by sub-proof #898.
% 159.32/28.05 | | |
% 159.32/28.05 | | End of split
% 159.32/28.05 | |
% 159.32/28.05 | Case 2:
% 159.32/28.05 | |
% 159.32/28.05 | | (30) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 159.32/28.05 | | e2)
% 159.32/28.05 | |
% 159.32/28.05 | | REF_CLOSE: (2), (4), (8), (10), (13), (14), (16), (17), (18), (19), (21),
% 159.32/28.05 | | (22), (30) are inconsistent by sub-proof #592.
% 159.32/28.05 | |
% 159.32/28.05 | End of split
% 159.32/28.05 |
% 159.32/28.05 End of proof
% 159.32/28.05
% 159.32/28.05 Sub-proof #571 shows that the following formulas are inconsistent:
% 159.32/28.05 ----------------------------------------------------------------
% 159.32/28.05 (1) all_56_14 = e3
% 159.32/28.05 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.05 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.05 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.05 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.05 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.05 (5) op(e1, e1) = all_6_2
% 159.32/28.05 (6) ~ (all_52_7 = e3)
% 159.32/28.05 (7) op(e3, e3) = all_28_1
% 159.32/28.05 (8) all_58_8 = e3
% 159.32/28.05 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.05 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.05 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.05 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.05 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.05 (12) op(e3, e2) = all_52_4
% 159.32/28.05 (13) ~ (all_4_2 = e2)
% 159.32/28.05 (14) op(e2, e3) = all_52_1
% 159.32/28.05 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.32/28.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.32/28.05 (16) ~ (e3 = e0)
% 159.32/28.05 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.05 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.05 (18) ~ (e2 = e0)
% 159.32/28.05 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.05 (20) op(e2, e3) = e2
% 159.32/28.05 (21) ~ (e3 = e1)
% 159.32/28.05 (22) all_56_12 = e1
% 159.32/28.05 (23) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.05 (24) ~ (all_4_2 = e1)
% 159.32/28.05 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.05 (26) op(e0, e0) = all_4_2
% 159.32/28.05 (27) op(e3, e3) = e1
% 159.32/28.05 (28) all_56_15 = all_4_2
% 159.32/28.05 (29) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.05 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.05 (30) ~ (all_52_4 = e3)
% 159.32/28.05 (31) ~ (e2 = e1)
% 159.32/28.05 (32) ~ (e1 = e0)
% 159.32/28.05 (33) all_58_3 = e3
% 159.32/28.05 (34) ~ (all_6_2 = e2)
% 159.32/28.05 (35) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.32/28.05 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.32/28.05 e3)
% 159.32/28.05 (36) all_56_13 = e3
% 159.32/28.05 (37) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.32/28.05 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.32/28.05 (38) op(e0, e2) = all_52_7
% 159.32/28.05 (39) op(e3, e3) = all_22_1
% 159.32/28.05 (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.32/28.05 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.32/28.05 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.05 (42) ~ (e3 = e2)
% 159.32/28.05 (43) all_58_12 = e1
% 159.32/28.05 (44) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.05 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.05 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.05 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.05 (45) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.32/28.05
% 159.32/28.05 Begin of proof
% 159.32/28.05 |
% 159.32/28.05 | BETA: splitting (45) gives:
% 159.32/28.05 |
% 159.32/28.05 | Case 1:
% 159.32/28.05 | |
% 159.32/28.05 | | (46) all_56_12 = e3
% 159.32/28.05 | |
% 159.32/28.05 | | REF_CLOSE: (21), (22), (46) are inconsistent by sub-proof #1191.
% 159.32/28.05 | |
% 159.32/28.05 | Case 2:
% 159.32/28.05 | |
% 159.32/28.05 | | (47) ~ (all_56_12 = e3)
% 159.32/28.05 | | (48) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.32/28.05 | |
% 159.32/28.05 | | REDUCE: (22), (47) imply:
% 159.32/28.05 | | (49) ~ (e3 = e1)
% 159.32/28.05 | |
% 159.32/28.05 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.32/28.05 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 159.32/28.05 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 159.32/28.05 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (48) are
% 159.32/28.05 | | inconsistent by sub-proof #572.
% 159.32/28.05 | |
% 159.32/28.05 | End of split
% 159.32/28.05 |
% 159.32/28.05 End of proof
% 159.32/28.05
% 159.32/28.05 Sub-proof #572 shows that the following formulas are inconsistent:
% 159.32/28.05 ----------------------------------------------------------------
% 159.32/28.05 (1) all_56_14 = e3
% 159.32/28.05 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.05 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.05 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.05 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.05 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.05 (5) op(e1, e1) = all_6_2
% 159.32/28.05 (6) ~ (all_52_7 = e3)
% 159.32/28.05 (7) op(e3, e3) = all_28_1
% 159.32/28.05 (8) all_58_8 = e3
% 159.32/28.05 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.05 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.05 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.05 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.05 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.05 (12) op(e3, e2) = all_52_4
% 159.32/28.05 (13) ~ (all_4_2 = e2)
% 159.32/28.05 (14) op(e2, e3) = all_52_1
% 159.32/28.05 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.32/28.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.32/28.05 (16) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.32/28.05 (17) ~ (e3 = e0)
% 159.32/28.05 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.05 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.05 (19) ~ (e2 = e0)
% 159.32/28.05 (20) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.05 (21) op(e2, e3) = e2
% 159.32/28.05 (22) ~ (e3 = e1)
% 159.32/28.05 (23) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.05 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.05 (24) ~ (all_4_2 = e1)
% 159.32/28.05 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.05 (26) op(e0, e0) = all_4_2
% 159.32/28.05 (27) op(e3, e3) = e1
% 159.32/28.05 (28) all_56_15 = all_4_2
% 159.32/28.05 (29) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.05 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.05 (30) ~ (all_52_4 = e3)
% 159.32/28.05 (31) ~ (e2 = e1)
% 159.32/28.05 (32) ~ (e1 = e0)
% 159.32/28.05 (33) all_58_3 = e3
% 159.32/28.05 (34) ~ (all_6_2 = e2)
% 159.32/28.05 (35) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.32/28.05 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.32/28.05 e3)
% 159.32/28.05 (36) all_56_13 = e3
% 159.32/28.05 (37) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.32/28.05 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.32/28.05 (38) op(e0, e2) = all_52_7
% 159.32/28.05 (39) op(e3, e3) = all_22_1
% 159.32/28.05 (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.32/28.05 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.32/28.05 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.05 (42) ~ (e3 = e2)
% 159.32/28.05 (43) all_58_12 = e1
% 159.32/28.05 (44) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.05 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.05 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.05 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.05
% 159.32/28.05 Begin of proof
% 159.32/28.05 |
% 159.32/28.05 | BETA: splitting (35) gives:
% 159.32/28.05 |
% 159.32/28.05 | Case 1:
% 159.32/28.05 | |
% 159.32/28.05 | | (45) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 159.32/28.05 | | e3)
% 159.32/28.05 | |
% 159.32/28.05 | | REF_CLOSE: (6), (22), (38), (41), (43), (45) are inconsistent by sub-proof
% 159.32/28.05 | | #996.
% 159.32/28.05 | |
% 159.32/28.05 | Case 2:
% 159.32/28.05 | |
% 159.32/28.05 | | (46) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.32/28.05 | | e3)
% 159.32/28.05 | |
% 159.32/28.05 | | BETA: splitting (46) gives:
% 159.32/28.05 | |
% 159.32/28.05 | | Case 1:
% 159.32/28.05 | | |
% 159.32/28.05 | | | (47) all_58_14 = e3 & op(e0, e1) = e3
% 159.32/28.05 | | |
% 159.32/28.05 | | | ALPHA: (47) implies:
% 159.32/28.05 | | | (48) all_58_14 = e3
% 159.32/28.05 | | |
% 159.32/28.05 | | | REF_CLOSE: (4), (5), (8), (10), (17), (19), (21), (22), (23), (25), (29),
% 159.32/28.05 | | | (31), (32), (33), (34), (41), (42), (48) are inconsistent by
% 159.32/28.05 | | | sub-proof #780.
% 159.32/28.05 | | |
% 159.32/28.05 | | Case 2:
% 159.32/28.05 | | |
% 159.32/28.05 | | | (49) all_58_15 = e3 & op(e0, e0) = e3
% 159.32/28.05 | | |
% 159.32/28.05 | | | ALPHA: (49) implies:
% 159.32/28.05 | | | (50) all_58_15 = e3
% 159.32/28.05 | | | (51) op(e0, e0) = e3
% 159.32/28.05 | | |
% 159.32/28.05 | | | BETA: splitting (40) gives:
% 159.32/28.05 | | |
% 159.32/28.05 | | | Case 1:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | (52) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 159.32/28.05 | | | | = e0)
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | BETA: splitting (52) gives:
% 159.32/28.05 | | | |
% 159.32/28.05 | | | | Case 1:
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | (53) all_58_0 = e0 & op(e3, e3) = e0
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | ALPHA: (53) implies:
% 159.32/28.05 | | | | | (54) all_58_0 = e0
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 159.32/28.05 | | | | | (13), (14), (15), (16), (17), (18), (20), (21), (22), (24),
% 159.32/28.05 | | | | | (25), (26), (27), (28), (29), (30), (31), (33), (34), (36),
% 159.32/28.05 | | | | | (37), (39), (41), (42), (43), (44), (50), (51), (54) are
% 159.32/28.05 | | | | | inconsistent by sub-proof #574.
% 159.32/28.05 | | | | |
% 159.32/28.05 | | | | Case 2:
% 159.32/28.05 | | | | |
% 159.32/28.06 | | | | | (55) all_58_2 = e0 & op(e2, e3) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | ALPHA: (55) implies:
% 159.32/28.06 | | | | | (56) op(e2, e3) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | REF_CLOSE: (19), (21), (41), (56) are inconsistent by sub-proof #1156.
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | End of split
% 159.32/28.06 | | | |
% 159.32/28.06 | | | Case 2:
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | (57) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 159.32/28.06 | | | | = e0)
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | BETA: splitting (57) gives:
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | Case 1:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | (58) all_58_6 = e0 & op(e1, e3) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | ALPHA: (58) implies:
% 159.32/28.06 | | | | | (59) all_58_6 = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | BETA: splitting (16) gives:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | Case 1:
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | (60) all_56_13 = e2
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | REF_CLOSE: (36), (42), (60) are inconsistent by sub-proof #674.
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | Case 2:
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | (61) ~ (all_56_13 = e2)
% 159.32/28.06 | | | | | | (62) all_56_14 = e1 | all_56_15 = e0
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | REF_CLOSE: (1), (7), (9), (14), (17), (21), (22), (24), (26), (27),
% 159.32/28.06 | | | | | | (28), (39), (41), (42), (43), (51), (59), (62) are
% 159.32/28.06 | | | | | | inconsistent by sub-proof #573.
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | End of split
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | Case 2:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | (63) all_58_12 = e0 & op(e0, e3) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | REF_CLOSE: (32), (43), (63) are inconsistent by sub-proof #1260.
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | End of split
% 159.32/28.06 | | | |
% 159.32/28.06 | | | End of split
% 159.32/28.06 | | |
% 159.32/28.06 | | End of split
% 159.32/28.06 | |
% 159.32/28.06 | End of split
% 159.32/28.06 |
% 159.32/28.06 End of proof
% 159.32/28.06
% 159.32/28.06 Sub-proof #573 shows that the following formulas are inconsistent:
% 159.32/28.06 ----------------------------------------------------------------
% 159.32/28.06 (1) all_56_14 = e3
% 159.32/28.06 (2) op(e3, e3) = all_28_1
% 159.32/28.06 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.06 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.06 (4) op(e2, e3) = all_52_1
% 159.32/28.06 (5) ~ (e3 = e0)
% 159.32/28.06 (6) all_56_14 = e1 | all_56_15 = e0
% 159.32/28.06 (7) all_58_6 = e0
% 159.32/28.06 (8) op(e2, e3) = e2
% 159.32/28.06 (9) ~ (e3 = e1)
% 159.32/28.06 (10) ~ (all_4_2 = e1)
% 159.32/28.06 (11) op(e0, e0) = all_4_2
% 159.32/28.06 (12) op(e3, e3) = e1
% 159.32/28.06 (13) all_56_15 = all_4_2
% 159.32/28.06 (14) op(e3, e3) = all_22_1
% 159.32/28.06 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.06 (16) ~ (e3 = e2)
% 159.32/28.06 (17) all_58_12 = e1
% 159.32/28.06 (18) op(e0, e0) = e3
% 159.32/28.06
% 159.32/28.06 Begin of proof
% 159.32/28.06 |
% 159.32/28.06 | BETA: splitting (6) gives:
% 159.32/28.06 |
% 159.32/28.06 | Case 1:
% 159.32/28.06 | |
% 159.32/28.06 | | (19) all_56_14 = e1
% 159.32/28.06 | |
% 159.32/28.06 | | REF_CLOSE: (1), (9), (19) are inconsistent by sub-proof #585.
% 159.32/28.06 | |
% 159.32/28.06 | Case 2:
% 159.32/28.06 | |
% 159.32/28.06 | | (20) all_56_15 = e0
% 159.32/28.06 | | (21) ~ (all_56_14 = e1)
% 159.32/28.06 | |
% 159.32/28.06 | | COMBINE_EQS: (13), (20) imply:
% 159.32/28.06 | | (22) all_4_2 = e0
% 159.32/28.06 | |
% 159.32/28.06 | | SIMP: (22) implies:
% 159.32/28.06 | | (23) all_4_2 = e0
% 159.32/28.06 | |
% 159.32/28.06 | | REDUCE: (10), (23) imply:
% 159.32/28.06 | | (24) ~ (e1 = e0)
% 159.32/28.06 | |
% 159.32/28.06 | | SIMP: (24) implies:
% 159.32/28.06 | | (25) ~ (e1 = e0)
% 159.32/28.06 | |
% 159.32/28.06 | | REDUCE: (11), (23) imply:
% 159.32/28.06 | | (26) op(e0, e0) = e0
% 159.32/28.06 | |
% 159.32/28.06 | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (12), (14), (15), (16), (17),
% 159.32/28.06 | | (18), (25), (26) are inconsistent by sub-proof #582.
% 159.32/28.06 | |
% 159.32/28.06 | End of split
% 159.32/28.06 |
% 159.32/28.06 End of proof
% 159.32/28.06
% 159.32/28.06 Sub-proof #574 shows that the following formulas are inconsistent:
% 159.32/28.06 ----------------------------------------------------------------
% 159.32/28.06 (1) all_56_14 = e3
% 159.32/28.06 (2) all_58_15 = e3
% 159.32/28.06 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.06 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.06 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.06 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.06 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.06 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.06 (6) op(e1, e1) = all_6_2
% 159.32/28.06 (7) op(e3, e3) = all_28_1
% 159.32/28.06 (8) all_58_8 = e3
% 159.32/28.06 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.06 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.06 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.06 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.06 (11) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.06 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.06 (12) op(e3, e2) = all_52_4
% 159.32/28.06 (13) ~ (all_4_2 = e2)
% 159.32/28.06 (14) op(e2, e3) = all_52_1
% 159.32/28.06 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.32/28.06 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.32/28.06 (16) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.32/28.06 (17) ~ (e3 = e0)
% 159.32/28.06 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.06 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.06 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.06 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.06 (20) op(e2, e3) = e2
% 159.32/28.06 (21) ~ (e3 = e1)
% 159.32/28.06 (22) ~ (all_4_2 = e1)
% 159.32/28.06 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.06 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.06 (24) op(e0, e0) = all_4_2
% 159.32/28.06 (25) op(e3, e3) = e1
% 159.32/28.06 (26) all_56_15 = all_4_2
% 159.32/28.06 (27) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.06 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.06 (28) ~ (all_52_4 = e3)
% 159.32/28.06 (29) ~ (e2 = e1)
% 159.32/28.06 (30) all_58_3 = e3
% 159.32/28.06 (31) ~ (all_6_2 = e2)
% 159.32/28.06 (32) all_56_13 = e3
% 159.32/28.06 (33) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.32/28.06 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.32/28.06 (34) op(e3, e3) = all_22_1
% 159.32/28.06 (35) all_58_0 = e0
% 159.32/28.06 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.06 (37) ~ (e3 = e2)
% 159.32/28.06 (38) all_58_12 = e1
% 159.32/28.06 (39) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.06 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.06 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.06 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.06 (40) op(e0, e0) = e3
% 159.32/28.06
% 159.32/28.06 Begin of proof
% 159.32/28.06 |
% 159.32/28.06 | BETA: splitting (16) gives:
% 159.32/28.06 |
% 159.32/28.06 | Case 1:
% 159.32/28.06 | |
% 159.32/28.06 | | (41) all_56_13 = e2
% 159.32/28.06 | |
% 159.32/28.06 | | REF_CLOSE: (32), (37), (41) are inconsistent by sub-proof #674.
% 159.32/28.06 | |
% 159.32/28.06 | Case 2:
% 159.32/28.06 | |
% 159.32/28.06 | | (42) ~ (all_56_13 = e2)
% 159.32/28.06 | | (43) all_56_14 = e1 | all_56_15 = e0
% 159.32/28.06 | |
% 159.32/28.06 | | BETA: splitting (43) gives:
% 159.32/28.06 | |
% 159.32/28.06 | | Case 1:
% 159.32/28.06 | | |
% 159.32/28.06 | | | (44) all_56_14 = e1
% 159.32/28.06 | | |
% 159.32/28.06 | | | REF_CLOSE: (1), (21), (44) are inconsistent by sub-proof #585.
% 159.32/28.06 | | |
% 159.32/28.06 | | Case 2:
% 159.32/28.06 | | |
% 159.32/28.06 | | | (45) all_56_15 = e0
% 159.32/28.06 | | | (46) ~ (all_56_14 = e1)
% 159.32/28.06 | | |
% 159.32/28.06 | | | COMBINE_EQS: (26), (45) imply:
% 159.32/28.06 | | | (47) all_4_2 = e0
% 159.32/28.06 | | |
% 159.32/28.06 | | | SIMP: (47) implies:
% 159.32/28.06 | | | (48) all_4_2 = e0
% 159.32/28.06 | | |
% 159.32/28.06 | | | REDUCE: (13), (48) imply:
% 159.32/28.06 | | | (49) ~ (e2 = e0)
% 159.32/28.06 | | |
% 159.32/28.06 | | | SIMP: (49) implies:
% 159.32/28.06 | | | (50) ~ (e2 = e0)
% 159.32/28.06 | | |
% 159.32/28.06 | | | REDUCE: (22), (48) imply:
% 159.32/28.06 | | | (51) ~ (e1 = e0)
% 159.32/28.06 | | |
% 159.32/28.06 | | | SIMP: (51) implies:
% 159.32/28.06 | | | (52) ~ (e1 = e0)
% 159.32/28.06 | | |
% 159.32/28.06 | | | REDUCE: (24), (48) imply:
% 159.32/28.06 | | | (53) op(e0, e0) = e0
% 159.32/28.06 | | |
% 159.32/28.06 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 159.32/28.06 | | | (15), (17), (18), (19), (20), (21), (23), (25), (27), (28),
% 159.32/28.06 | | | (29), (30), (31), (33), (34), (35), (36), (37), (38), (39),
% 159.32/28.06 | | | (40), (50), (52), (53) are inconsistent by sub-proof #575.
% 159.32/28.06 | | |
% 159.32/28.06 | | End of split
% 159.32/28.06 | |
% 159.32/28.06 | End of split
% 159.32/28.06 |
% 159.32/28.06 End of proof
% 159.32/28.06
% 159.32/28.06 Sub-proof #575 shows that the following formulas are inconsistent:
% 159.32/28.06 ----------------------------------------------------------------
% 159.32/28.06 (1) all_58_15 = e3
% 159.32/28.06 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.06 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.06 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.06 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.06 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.06 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.06 (5) op(e1, e1) = all_6_2
% 159.32/28.06 (6) op(e3, e3) = all_28_1
% 159.32/28.06 (7) all_58_8 = e3
% 159.32/28.06 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.06 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.06 (9) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.06 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.06 (10) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.06 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.06 (11) op(e3, e2) = all_52_4
% 159.32/28.06 (12) op(e2, e3) = all_52_1
% 159.32/28.06 (13) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.32/28.06 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.32/28.06 (14) ~ (e3 = e0)
% 159.32/28.06 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.06 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.06 (16) op(e0, e0) = e0
% 159.32/28.06 (17) ~ (e2 = e0)
% 159.32/28.06 (18) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.06 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.06 (19) op(e2, e3) = e2
% 159.32/28.06 (20) ~ (e3 = e1)
% 159.32/28.06 (21) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.06 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.06 (22) op(e3, e3) = e1
% 159.32/28.06 (23) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.06 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.06 (24) ~ (all_52_4 = e3)
% 159.32/28.06 (25) ~ (e2 = e1)
% 159.32/28.06 (26) ~ (e1 = e0)
% 159.32/28.06 (27) all_58_3 = e3
% 159.32/28.06 (28) ~ (all_6_2 = e2)
% 159.32/28.06 (29) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.32/28.06 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.32/28.06 (30) op(e3, e3) = all_22_1
% 159.32/28.06 (31) all_58_0 = e0
% 159.32/28.06 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.06 (33) ~ (e3 = e2)
% 159.32/28.06 (34) all_58_12 = e1
% 159.32/28.06 (35) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.06 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.06 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.06 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.06 (36) op(e0, e0) = e3
% 159.32/28.06
% 159.32/28.06 Begin of proof
% 159.32/28.06 |
% 159.32/28.06 | BETA: splitting (8) gives:
% 159.32/28.06 |
% 159.32/28.06 | Case 1:
% 159.32/28.06 | |
% 159.32/28.06 | | (37) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 159.32/28.06 | | e3)
% 159.32/28.06 | |
% 159.32/28.06 | | REF_CLOSE: (6), (12), (16), (19), (22), (26), (30), (32), (33), (36), (37)
% 159.32/28.06 | | are inconsistent by sub-proof #583.
% 159.32/28.06 | |
% 159.32/28.06 | Case 2:
% 159.32/28.06 | |
% 159.32/28.06 | | (38) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 159.32/28.06 | | e3)
% 159.32/28.06 | |
% 159.32/28.06 | | BETA: splitting (38) gives:
% 159.32/28.06 | |
% 159.32/28.06 | | Case 1:
% 159.32/28.06 | | |
% 159.32/28.06 | | | (39) all_58_6 = e3 & op(e1, e3) = e3
% 159.32/28.06 | | |
% 159.32/28.06 | | | ALPHA: (39) implies:
% 159.32/28.06 | | | (40) all_58_6 = e3
% 159.32/28.06 | | |
% 159.32/28.06 | | | BETA: splitting (21) gives:
% 159.32/28.06 | | |
% 159.32/28.06 | | | Case 1:
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | (41) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 159.32/28.06 | | | | = e0)
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | BETA: splitting (41) gives:
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | Case 1:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | (42) all_58_2 = e0 & op(e2, e3) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | ALPHA: (42) implies:
% 159.32/28.06 | | | | | (43) op(e2, e3) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | REF_CLOSE: (17), (19), (32), (43) are inconsistent by sub-proof #1156.
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | Case 2:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | (44) all_58_3 = e0 & op(e2, e2) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | ALPHA: (44) implies:
% 159.32/28.06 | | | | | (45) all_58_3 = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | COMBINE_EQS: (27), (45) imply:
% 159.32/28.06 | | | | | (46) e3 = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | SIMP: (46) implies:
% 159.32/28.06 | | | | | (47) e3 = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | COMBINE_EQS: (40), (47) imply:
% 159.32/28.06 | | | | | (48) all_58_6 = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | REF_CLOSE: (6), (8), (12), (14), (16), (19), (20), (22), (26), (30),
% 159.32/28.06 | | | | | (32), (33), (34), (36), (48) are inconsistent by sub-proof
% 159.32/28.06 | | | | | #582.
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | End of split
% 159.32/28.06 | | | |
% 159.32/28.06 | | | Case 2:
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | (49) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 159.32/28.06 | | | | = e0)
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | BETA: splitting (49) gives:
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | Case 1:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | (50) all_58_5 = e0 & op(e2, e1) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | ALPHA: (50) implies:
% 159.32/28.06 | | | | | (51) all_58_5 = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | BETA: splitting (4) gives:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | Case 1:
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | (52) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 159.32/28.06 | | | | | | e2) = e1)
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | REF_CLOSE: (19), (20), (25), (27), (32), (52) are inconsistent by
% 159.32/28.06 | | | | | | sub-proof #840.
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | Case 2:
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | (53) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2,
% 159.32/28.06 | | | | | | e0) = e1)
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | BETA: splitting (53) gives:
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | Case 1:
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | (54) all_58_5 = e1 & op(e2, e1) = e1
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | ALPHA: (54) implies:
% 159.32/28.06 | | | | | | | (55) all_58_5 = e1
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | REF_CLOSE: (26), (51), (55) are inconsistent by sub-proof #935.
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | Case 2:
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | (56) all_58_10 = e1 & op(e2, e0) = e1
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | ALPHA: (56) implies:
% 159.32/28.06 | | | | | | | (57) all_58_10 = e1
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | BETA: splitting (29) gives:
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | Case 1:
% 159.32/28.06 | | | | | | | |
% 159.32/28.06 | | | | | | | | (58) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 159.32/28.06 | | | | | | | | op(e3, e2) = e3)
% 159.32/28.06 | | | | | | | |
% 159.32/28.06 | | | | | | | | REF_CLOSE: (6), (11), (16), (22), (24), (26), (30), (32), (36),
% 159.32/28.06 | | | | | | | | (58) are inconsistent by sub-proof #581.
% 159.32/28.06 | | | | | | | |
% 159.32/28.06 | | | | | | | Case 2:
% 159.32/28.06 | | | | | | | |
% 159.32/28.06 | | | | | | | | (59) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 159.32/28.06 | | | | | | | | op(e3, e0) = e3)
% 159.32/28.06 | | | | | | | |
% 159.32/28.06 | | | | | | | | BETA: splitting (59) gives:
% 159.32/28.06 | | | | | | | |
% 159.32/28.06 | | | | | | | | Case 1:
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | | (60) all_58_4 = e3 & op(e3, e1) = e3
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | | ALPHA: (60) implies:
% 159.32/28.06 | | | | | | | | | (61) all_58_4 = e3
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | | BETA: splitting (9) gives:
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | | Case 1:
% 159.32/28.06 | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | (62) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 159.32/28.06 | | | | | | | | | | op(e2, e1) = e2)
% 159.32/28.06 | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | BETA: splitting (62) gives:
% 159.32/28.06 | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | Case 1:
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | (63) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | REF_CLOSE: (8), (12), (14), (15), (19), (20), (25), (26),
% 159.32/28.06 | | | | | | | | | | | (31), (32), (33), (40), (61), (63) are
% 159.32/28.06 | | | | | | | | | | | inconsistent by sub-proof #593.
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | Case 2:
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | (64) all_58_5 = e2 & op(e2, e1) = e2
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | ALPHA: (64) implies:
% 159.32/28.06 | | | | | | | | | | | (65) all_58_5 = e2
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | REF_CLOSE: (14), (17), (19), (21), (26), (27), (32), (57),
% 159.32/28.06 | | | | | | | | | | | (65) are inconsistent by sub-proof #899.
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | End of split
% 159.32/28.06 | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | Case 2:
% 159.32/28.06 | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | (66) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2
% 159.32/28.06 | | | | | | | | | | & op(e0, e1) = e2)
% 159.32/28.06 | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | BETA: splitting (66) gives:
% 159.32/28.06 | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | Case 1:
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | (67) all_58_8 = e2 & op(e1, e1) = e2
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | REF_CLOSE: (5), (28), (32), (67) are inconsistent by
% 159.32/28.06 | | | | | | | | | | | sub-proof #1440.
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | Case 2:
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | (68) all_58_14 = e2 & op(e0, e1) = e2
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | ALPHA: (68) implies:
% 159.32/28.06 | | | | | | | | | | | (69) all_58_14 = e2
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | BETA: splitting (23) gives:
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | Case 1:
% 159.32/28.06 | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | (70) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 159.32/28.06 | | | | | | | | | | | | & op(e2, e1) = e1)
% 159.32/28.06 | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | BETA: splitting (70) gives:
% 159.32/28.06 | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | Case 1:
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | (71) all_58_4 = e1 & op(e3, e1) = e1
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | REF_CLOSE: (20), (61), (71) are inconsistent by sub-proof
% 159.32/28.06 | | | | | | | | | | | | | #1345.
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | Case 2:
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | (72) all_58_5 = e1 & op(e2, e1) = e1
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | ALPHA: (72) implies:
% 159.32/28.06 | | | | | | | | | | | | | (73) all_58_5 = e1
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | COMBINE_EQS: (51), (73) imply:
% 159.32/28.06 | | | | | | | | | | | | | (74) e1 = e0
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | COMBINE_EQS: (57), (74) imply:
% 159.32/28.06 | | | | | | | | | | | | | (75) all_58_10 = e0
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12),
% 159.32/28.06 | | | | | | | | | | | | | (13), (14), (15), (16), (17), (18), (19), (20),
% 159.32/28.06 | | | | | | | | | | | | | (21), (22), (25), (26), (27), (28), (30), (31),
% 159.32/28.06 | | | | | | | | | | | | | (32), (33), (34), (36), (40), (73), (75) are
% 159.32/28.06 | | | | | | | | | | | | | inconsistent by sub-proof #576.
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | End of split
% 159.32/28.06 | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | Case 2:
% 159.32/28.06 | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | (76) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 159.32/28.06 | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 159.32/28.06 | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | BETA: splitting (76) gives:
% 159.32/28.06 | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | Case 1:
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | (77) all_58_8 = e1 & op(e1, e1) = e1
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | REF_CLOSE: (7), (20), (77) are inconsistent by sub-proof
% 159.32/28.06 | | | | | | | | | | | | | #959.
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | Case 2:
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | (78) all_58_14 = e1 & op(e0, e1) = e1
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | | REF_CLOSE: (25), (69), (78) are inconsistent by sub-proof
% 159.32/28.06 | | | | | | | | | | | | | #1339.
% 159.32/28.06 | | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | | End of split
% 159.32/28.06 | | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | | End of split
% 159.32/28.06 | | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | | End of split
% 159.32/28.06 | | | | | | | | | |
% 159.32/28.06 | | | | | | | | | End of split
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | Case 2:
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | | (79) all_58_9 = e3 & op(e3, e0) = e3
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | | ALPHA: (79) implies:
% 159.32/28.06 | | | | | | | | | (80) all_58_9 = e3
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | | REF_CLOSE: (1), (3), (4), (8), (10), (12), (14), (15), (17),
% 159.32/28.06 | | | | | | | | | (19), (20), (21), (25), (26), (27), (31), (32),
% 159.32/28.06 | | | | | | | | | (33), (35), (36), (40), (80) are inconsistent by
% 159.32/28.06 | | | | | | | | | sub-proof #590.
% 159.32/28.06 | | | | | | | | |
% 159.32/28.06 | | | | | | | | End of split
% 159.32/28.06 | | | | | | | |
% 159.32/28.06 | | | | | | | End of split
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | End of split
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | End of split
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | Case 2:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | (81) all_58_10 = e0 & op(e2, e0) = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | ALPHA: (81) implies:
% 159.32/28.06 | | | | | (82) all_58_10 = e0
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | BETA: splitting (4) gives:
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | | Case 1:
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | (83) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 159.32/28.06 | | | | | | e2) = e1)
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | REF_CLOSE: (19), (20), (25), (27), (32), (83) are inconsistent by
% 159.32/28.06 | | | | | | sub-proof #840.
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | Case 2:
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | (84) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2,
% 159.32/28.06 | | | | | | e0) = e1)
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | BETA: splitting (84) gives:
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | | Case 1:
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | (85) all_58_5 = e1 & op(e2, e1) = e1
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | ALPHA: (85) implies:
% 159.32/28.06 | | | | | | | (86) all_58_5 = e1
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), (13),
% 159.32/28.06 | | | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 159.32/28.06 | | | | | | | (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 159.32/28.06 | | | | | | | (36), (40), (82), (86) are inconsistent by sub-proof
% 159.32/28.06 | | | | | | | #576.
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | Case 2:
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | (87) all_58_10 = e1 & op(e2, e0) = e1
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | | REF_CLOSE: (26), (82), (87) are inconsistent by sub-proof #1373.
% 159.32/28.06 | | | | | | |
% 159.32/28.06 | | | | | | End of split
% 159.32/28.06 | | | | | |
% 159.32/28.06 | | | | | End of split
% 159.32/28.06 | | | | |
% 159.32/28.06 | | | | End of split
% 159.32/28.06 | | | |
% 159.32/28.06 | | | End of split
% 159.32/28.06 | | |
% 159.32/28.06 | | Case 2:
% 159.32/28.06 | | |
% 159.32/28.06 | | | (88) all_58_12 = e3 & op(e0, e3) = e3
% 159.32/28.06 | | |
% 159.32/28.06 | | | REF_CLOSE: (20), (34), (88) are inconsistent by sub-proof #1278.
% 159.32/28.06 | | |
% 159.32/28.06 | | End of split
% 159.32/28.06 | |
% 159.32/28.06 | End of split
% 159.32/28.06 |
% 159.32/28.06 End of proof
% 159.32/28.06
% 159.32/28.06 Sub-proof #576 shows that the following formulas are inconsistent:
% 159.32/28.06 ----------------------------------------------------------------
% 159.32/28.06 (1) all_58_15 = e3
% 159.32/28.06 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.06 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.06 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.06 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.06 (4) op(e1, e1) = all_6_2
% 159.32/28.06 (5) op(e3, e3) = all_28_1
% 159.32/28.06 (6) all_58_8 = e3
% 159.32/28.06 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.06 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.06 (8) all_58_6 = e3
% 159.32/28.06 (9) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.06 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.06 (10) op(e2, e3) = all_52_1
% 159.32/28.06 (11) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.32/28.06 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.32/28.06 (12) ~ (e3 = e0)
% 159.32/28.06 (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.06 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.06 (14) op(e0, e0) = e0
% 159.32/28.06 (15) ~ (e2 = e0)
% 159.32/28.06 (16) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.06 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.06 (17) op(e2, e3) = e2
% 159.32/28.06 (18) ~ (e3 = e1)
% 159.32/28.06 (19) all_58_5 = e1
% 159.32/28.06 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.06 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.06 (21) op(e3, e3) = e1
% 159.32/28.06 (22) ~ (e2 = e1)
% 159.32/28.06 (23) ~ (e1 = e0)
% 159.32/28.06 (24) all_58_3 = e3
% 159.32/28.06 (25) ~ (all_6_2 = e2)
% 159.32/28.06 (26) all_58_10 = e0
% 159.32/28.06 (27) op(e3, e3) = all_22_1
% 159.32/28.06 (28) all_58_0 = e0
% 159.32/28.06 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.06 (30) ~ (e3 = e2)
% 159.32/28.06 (31) all_58_12 = e1
% 159.32/28.06 (32) op(e0, e0) = e3
% 159.32/28.06
% 159.32/28.06 Begin of proof
% 159.32/28.06 |
% 159.32/28.06 | BETA: splitting (3) gives:
% 159.32/28.06 |
% 159.32/28.06 | Case 1:
% 159.32/28.06 | |
% 159.32/28.06 | | (33) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 159.32/28.06 | | e1)
% 159.32/28.06 | |
% 159.32/28.06 | | BETA: splitting (33) gives:
% 159.32/28.06 | |
% 159.32/28.06 | | Case 1:
% 159.32/28.06 | | |
% 159.32/28.06 | | | (34) all_58_9 = e1 & op(e3, e0) = e1
% 159.32/28.06 | | |
% 159.32/28.06 | | | ALPHA: (34) implies:
% 159.32/28.06 | | | (35) all_58_9 = e1
% 159.32/28.06 | | |
% 159.32/28.06 | | | BETA: splitting (9) gives:
% 159.32/28.06 | | |
% 159.32/28.06 | | | Case 1:
% 159.32/28.06 | | | |
% 159.32/28.06 | | | | (36) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 159.32/28.06 | | | | = e2)
% 159.32/28.06 | | | |
% 159.32/28.07 | | | | REF_CLOSE: (12), (15), (17), (19), (20), (22), (23), (24), (29), (35),
% 159.32/28.07 | | | | (36) are inconsistent by sub-proof #580.
% 159.32/28.07 | | | |
% 159.32/28.07 | | | Case 2:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | (37) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 159.32/28.07 | | | | e0) = e2)
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | BETA: splitting (37) gives:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | Case 1:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (38) all_58_11 = e2 & op(e1, e0) = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (10), (12), (14), (15), (16),
% 159.32/28.07 | | | | | (17), (18), (21), (22), (23), (27), (29), (30), (31), (32),
% 159.32/28.07 | | | | | (38) are inconsistent by sub-proof #578.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | Case 2:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (39) all_58_15 = e2 & op(e0, e0) = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | ALPHA: (39) implies:
% 159.32/28.07 | | | | | (40) op(e0, e0) = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (29), (30), (32), (40) are inconsistent by sub-proof #1382.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | End of split
% 159.32/28.07 | | | |
% 159.32/28.07 | | | End of split
% 159.32/28.07 | | |
% 159.32/28.07 | | Case 2:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (41) all_58_10 = e1 & op(e2, e0) = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | ALPHA: (41) implies:
% 159.32/28.07 | | | (42) all_58_10 = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (23), (26), (42) are inconsistent by sub-proof #1279.
% 159.32/28.07 | | |
% 159.32/28.07 | | End of split
% 159.32/28.07 | |
% 159.32/28.07 | Case 2:
% 159.32/28.07 | |
% 159.32/28.07 | | (43) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.32/28.07 | | e1)
% 159.32/28.07 | |
% 159.32/28.07 | | BETA: splitting (43) gives:
% 159.32/28.07 | |
% 159.32/28.07 | | Case 1:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (44) all_58_11 = e1 & op(e1, e0) = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | ALPHA: (44) implies:
% 159.32/28.07 | | | (45) all_58_11 = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | BETA: splitting (11) gives:
% 159.32/28.07 | | |
% 159.32/28.07 | | | Case 1:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | (46) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 159.32/28.07 | | | | = e2)
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | BETA: splitting (46) gives:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | Case 1:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (47) all_58_6 = e2 & op(e1, e3) = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | ALPHA: (47) implies:
% 159.32/28.07 | | | | | (48) all_58_6 = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (7), (10), (12), (13), (17), (18), (22), (23), (28), (29),
% 159.32/28.07 | | | | | (30), (48) are inconsistent by sub-proof #1157.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | Case 2:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (49) all_58_7 = e2 & op(e1, e2) = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | ALPHA: (49) implies:
% 159.32/28.07 | | | | | (50) all_58_7 = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | BETA: splitting (16) gives:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | Case 1:
% 159.32/28.07 | | | | | |
% 159.32/28.07 | | | | | | (51) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 159.32/28.07 | | | | | | e2) = e0)
% 159.32/28.07 | | | | | |
% 159.32/28.07 | | | | | | BETA: splitting (51) gives:
% 159.32/28.07 | | | | | |
% 159.32/28.07 | | | | | | Case 1:
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | (52) all_58_6 = e0 & op(e1, e3) = e0
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | ALPHA: (52) implies:
% 159.32/28.07 | | | | | | | (53) all_58_6 = e0
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | REF_CLOSE: (5), (7), (10), (12), (14), (17), (18), (21), (23),
% 159.32/28.07 | | | | | | | (27), (29), (30), (31), (32), (53) are inconsistent by
% 159.32/28.07 | | | | | | | sub-proof #582.
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | Case 2:
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | (54) all_58_7 = e0 & op(e1, e2) = e0
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | REF_CLOSE: (15), (50), (54) are inconsistent by sub-proof #1468.
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | End of split
% 159.32/28.07 | | | | | |
% 159.32/28.07 | | | | | Case 2:
% 159.32/28.07 | | | | | |
% 159.32/28.07 | | | | | | (55) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1,
% 159.32/28.07 | | | | | | e0) = e0)
% 159.32/28.07 | | | | | |
% 159.32/28.07 | | | | | | BETA: splitting (55) gives:
% 159.32/28.07 | | | | | |
% 159.32/28.07 | | | | | | Case 1:
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | (56) all_58_8 = e0 & op(e1, e1) = e0
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (12), (14), (17), (18), (21),
% 159.32/28.07 | | | | | | | (23), (27), (29), (30), (31), (32), (56) are
% 159.32/28.07 | | | | | | | inconsistent by sub-proof #579.
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | Case 2:
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | (57) all_58_11 = e0 & op(e1, e0) = e0
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | | REF_CLOSE: (23), (45), (57) are inconsistent by sub-proof #577.
% 159.32/28.07 | | | | | | |
% 159.32/28.07 | | | | | | End of split
% 159.32/28.07 | | | | | |
% 159.32/28.07 | | | | | End of split
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | End of split
% 159.32/28.07 | | | |
% 159.32/28.07 | | | Case 2:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | (58) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 159.32/28.07 | | | | = e2)
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | BETA: splitting (58) gives:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | Case 1:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (59) all_58_8 = e2 & op(e1, e1) = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (4), (25), (29), (59) are inconsistent by sub-proof #1440.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | Case 2:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (60) all_58_11 = e2 & op(e1, e0) = e2
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (10), (12), (14), (15), (16),
% 159.32/28.07 | | | | | (17), (18), (21), (22), (23), (27), (29), (30), (31), (32),
% 159.32/28.07 | | | | | (60) are inconsistent by sub-proof #578.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | End of split
% 159.32/28.07 | | | |
% 159.32/28.07 | | | End of split
% 159.32/28.07 | | |
% 159.32/28.07 | | Case 2:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (61) all_58_15 = e1 & op(e0, e0) = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (1), (18), (61) are inconsistent by sub-proof #1010.
% 159.32/28.07 | | |
% 159.32/28.07 | | End of split
% 159.32/28.07 | |
% 159.32/28.07 | End of split
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #577 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) all_58_11 = e0 & op(e1, e0) = e0
% 159.32/28.07 (2) all_58_11 = e1
% 159.32/28.07 (3) ~ (e1 = e0)
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | ALPHA: (1) implies:
% 159.32/28.07 | (4) all_58_11 = e0
% 159.32/28.07 |
% 159.32/28.07 | COMBINE_EQS: (2), (4) imply:
% 159.32/28.07 | (5) e1 = e0
% 159.32/28.07 |
% 159.32/28.07 | REDUCE: (3), (5) imply:
% 159.32/28.07 | (6) $false
% 159.32/28.07 |
% 159.32/28.07 | CLOSE: (6) is inconsistent.
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #578 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.07 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.07 (2) op(e3, e3) = all_28_1
% 159.32/28.07 (3) all_58_8 = e3
% 159.32/28.07 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.07 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.07 (5) all_58_6 = e3
% 159.32/28.07 (6) op(e2, e3) = all_52_1
% 159.32/28.07 (7) ~ (e3 = e0)
% 159.32/28.07 (8) op(e0, e0) = e0
% 159.32/28.07 (9) ~ (e2 = e0)
% 159.32/28.07 (10) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.07 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.07 (11) op(e2, e3) = e2
% 159.32/28.07 (12) ~ (e3 = e1)
% 159.32/28.07 (13) op(e3, e3) = e1
% 159.32/28.07 (14) ~ (e2 = e1)
% 159.32/28.07 (15) ~ (e1 = e0)
% 159.32/28.07 (16) op(e3, e3) = all_22_1
% 159.32/28.07 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07 (18) ~ (e3 = e2)
% 159.32/28.07 (19) all_58_11 = e2 & op(e1, e0) = e2
% 159.32/28.07 (20) all_58_12 = e1
% 159.32/28.07 (21) op(e0, e0) = e3
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | ALPHA: (19) implies:
% 159.32/28.07 | (22) all_58_11 = e2
% 159.32/28.07 |
% 159.32/28.07 | BETA: splitting (1) gives:
% 159.32/28.07 |
% 159.32/28.07 | Case 1:
% 159.32/28.07 | |
% 159.32/28.07 | | (23) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 159.32/28.07 | | e1)
% 159.32/28.07 | |
% 159.32/28.07 | | BETA: splitting (23) gives:
% 159.32/28.07 | |
% 159.32/28.07 | | Case 1:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (24) all_58_6 = e1 & op(e1, e3) = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | ALPHA: (24) implies:
% 159.32/28.07 | | | (25) all_58_6 = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (5), (12), (25) are inconsistent by sub-proof #1073.
% 159.32/28.07 | | |
% 159.32/28.07 | | Case 2:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (26) all_58_7 = e1 & op(e1, e2) = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | ALPHA: (26) implies:
% 159.32/28.07 | | | (27) all_58_7 = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | BETA: splitting (10) gives:
% 159.32/28.07 | | |
% 159.32/28.07 | | | Case 1:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 159.32/28.07 | | | | = e0)
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | BETA: splitting (28) gives:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | Case 1:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (29) all_58_6 = e0 & op(e1, e3) = e0
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | ALPHA: (29) implies:
% 159.32/28.07 | | | | | (30) all_58_6 = e0
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (11), (12), (13), (15), (16),
% 159.32/28.07 | | | | | (17), (18), (20), (21), (30) are inconsistent by sub-proof
% 159.32/28.07 | | | | | #582.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | Case 2:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (31) all_58_7 = e0 & op(e1, e2) = e0
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | ALPHA: (31) implies:
% 159.32/28.07 | | | | | (32) all_58_7 = e0
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (15), (27), (32) are inconsistent by sub-proof #1072.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | End of split
% 159.32/28.07 | | | |
% 159.32/28.07 | | | Case 2:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | (33) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.07 | | | | = e0)
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | BETA: splitting (33) gives:
% 159.32/28.07 | | | |
% 159.32/28.07 | | | | Case 1:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (34) all_58_8 = e0 & op(e1, e1) = e0
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (15),
% 159.32/28.07 | | | | | (16), (17), (18), (20), (21), (34) are inconsistent by
% 159.32/28.07 | | | | | sub-proof #579.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | Case 2:
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | (35) all_58_11 = e0 & op(e1, e0) = e0
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | | REF_CLOSE: (9), (22), (35) are inconsistent by sub-proof #1470.
% 159.32/28.07 | | | | |
% 159.32/28.07 | | | | End of split
% 159.32/28.07 | | | |
% 159.32/28.07 | | | End of split
% 159.32/28.07 | | |
% 159.32/28.07 | | End of split
% 159.32/28.07 | |
% 159.32/28.07 | Case 2:
% 159.32/28.07 | |
% 159.32/28.07 | | (36) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 159.32/28.07 | | e1)
% 159.32/28.07 | |
% 159.32/28.07 | | BETA: splitting (36) gives:
% 159.32/28.07 | |
% 159.32/28.07 | | Case 1:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (37) all_58_8 = e1 & op(e1, e1) = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | ALPHA: (37) implies:
% 159.32/28.07 | | | (38) all_58_8 = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (3), (12), (38) are inconsistent by sub-proof #950.
% 159.32/28.07 | | |
% 159.32/28.07 | | Case 2:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (39) all_58_11 = e1 & op(e1, e0) = e1
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (14), (22), (39) are inconsistent by sub-proof #1455.
% 159.32/28.07 | | |
% 159.32/28.07 | | End of split
% 159.32/28.07 | |
% 159.32/28.07 | End of split
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #579 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) op(e3, e3) = all_28_1
% 159.32/28.07 (2) all_58_8 = e3
% 159.32/28.07 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.07 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.07 (4) all_58_6 = e3
% 159.32/28.07 (5) op(e2, e3) = all_52_1
% 159.32/28.07 (6) ~ (e3 = e0)
% 159.32/28.07 (7) op(e0, e0) = e0
% 159.32/28.07 (8) all_58_8 = e0 & op(e1, e1) = e0
% 159.32/28.07 (9) op(e2, e3) = e2
% 159.32/28.07 (10) ~ (e3 = e1)
% 159.32/28.07 (11) op(e3, e3) = e1
% 159.32/28.07 (12) ~ (e1 = e0)
% 159.32/28.07 (13) op(e3, e3) = all_22_1
% 159.32/28.07 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07 (15) ~ (e3 = e2)
% 159.32/28.07 (16) all_58_12 = e1
% 159.32/28.07 (17) op(e0, e0) = e3
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | ALPHA: (8) implies:
% 159.32/28.07 | (18) all_58_8 = e0
% 159.32/28.07 |
% 159.32/28.07 | COMBINE_EQS: (2), (18) imply:
% 159.32/28.07 | (19) e3 = e0
% 159.32/28.07 |
% 159.32/28.07 | COMBINE_EQS: (4), (19) imply:
% 159.32/28.07 | (20) all_58_6 = e0
% 159.32/28.07 |
% 159.32/28.07 | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 159.32/28.07 | (16), (17), (20) are inconsistent by sub-proof #582.
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #580 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) ~ (e3 = e0)
% 159.32/28.07 (2) ~ (e2 = e0)
% 159.32/28.07 (3) op(e2, e3) = e2
% 159.32/28.07 (4) all_58_5 = e1
% 159.32/28.07 (5) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.07 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 159.32/28.07 (7) ~ (e2 = e1)
% 159.32/28.07 (8) ~ (e1 = e0)
% 159.32/28.07 (9) all_58_3 = e3
% 159.32/28.07 (10) all_58_9 = e1
% 159.32/28.07 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | BETA: splitting (6) gives:
% 159.32/28.07 |
% 159.32/28.07 | Case 1:
% 159.32/28.07 | |
% 159.32/28.07 | | (12) all_58_9 = e2 & op(e3, e0) = e2
% 159.32/28.07 | |
% 159.32/28.07 | | ALPHA: (12) implies:
% 159.32/28.07 | | (13) all_58_9 = e2
% 159.32/28.07 | |
% 159.32/28.07 | | REF_CLOSE: (7), (10), (13) are inconsistent by sub-proof #1324.
% 159.32/28.07 | |
% 159.32/28.07 | Case 2:
% 159.32/28.07 | |
% 159.32/28.07 | | (14) all_58_10 = e2 & op(e2, e0) = e2
% 159.32/28.07 | |
% 159.32/28.07 | | ALPHA: (14) implies:
% 159.32/28.07 | | (15) all_58_10 = e2
% 159.32/28.07 | |
% 159.32/28.07 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (15) are inconsistent by
% 159.32/28.07 | | sub-proof #907.
% 159.32/28.07 | |
% 159.32/28.07 | End of split
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #581 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 159.32/28.07 (2) op(e3, e3) = all_28_1
% 159.32/28.07 (3) op(e3, e2) = all_52_4
% 159.32/28.07 (4) op(e0, e0) = e0
% 159.32/28.07 (5) op(e3, e3) = e1
% 159.32/28.07 (6) ~ (all_52_4 = e3)
% 159.32/28.07 (7) ~ (e1 = e0)
% 159.32/28.07 (8) op(e3, e3) = all_22_1
% 159.32/28.07 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07 (10) op(e0, e0) = e3
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | BETA: splitting (1) gives:
% 159.32/28.07 |
% 159.32/28.07 | Case 1:
% 159.32/28.07 | |
% 159.32/28.07 | | (11) all_58_0 = e3 & op(e3, e3) = e3
% 159.32/28.07 | |
% 159.32/28.07 | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11) are inconsistent by
% 159.32/28.07 | | sub-proof #584.
% 159.32/28.07 | |
% 159.32/28.07 | Case 2:
% 159.32/28.07 | |
% 159.32/28.07 | | (12) all_58_1 = e3 & op(e3, e2) = e3
% 159.32/28.07 | |
% 159.32/28.07 | | ALPHA: (12) implies:
% 159.32/28.07 | | (13) op(e3, e2) = e3
% 159.32/28.07 | |
% 159.32/28.07 | | REF_CLOSE: (3), (6), (9), (13) are inconsistent by sub-proof #1540.
% 159.32/28.07 | |
% 159.32/28.07 | End of split
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #582 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) op(e3, e3) = all_28_1
% 159.32/28.07 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.07 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.07 (3) op(e2, e3) = all_52_1
% 159.32/28.07 (4) ~ (e3 = e0)
% 159.32/28.07 (5) op(e0, e0) = e0
% 159.32/28.07 (6) all_58_6 = e0
% 159.32/28.07 (7) op(e2, e3) = e2
% 159.32/28.07 (8) ~ (e3 = e1)
% 159.32/28.07 (9) op(e3, e3) = e1
% 159.32/28.07 (10) ~ (e1 = e0)
% 159.32/28.07 (11) op(e3, e3) = all_22_1
% 159.32/28.07 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07 (13) ~ (e3 = e2)
% 159.32/28.07 (14) all_58_12 = e1
% 159.32/28.07 (15) op(e0, e0) = e3
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | BETA: splitting (2) gives:
% 159.32/28.07 |
% 159.32/28.07 | Case 1:
% 159.32/28.07 | |
% 159.32/28.07 | | (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 159.32/28.07 | | e3)
% 159.32/28.07 | |
% 159.32/28.07 | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (13), (15), (16) are
% 159.32/28.07 | | inconsistent by sub-proof #583.
% 159.32/28.07 | |
% 159.32/28.07 | Case 2:
% 159.32/28.07 | |
% 159.32/28.07 | | (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 159.32/28.07 | | e3)
% 159.32/28.07 | |
% 159.32/28.07 | | BETA: splitting (17) gives:
% 159.32/28.07 | |
% 159.32/28.07 | | Case 1:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (18) all_58_6 = e3 & op(e1, e3) = e3
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (4), (6), (18) are inconsistent by sub-proof #749.
% 159.32/28.07 | | |
% 159.32/28.07 | | Case 2:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (19) all_58_12 = e3 & op(e0, e3) = e3
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (8), (14), (19) are inconsistent by sub-proof #1278.
% 159.32/28.07 | | |
% 159.32/28.07 | | End of split
% 159.32/28.07 | |
% 159.32/28.07 | End of split
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #583 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) op(e3, e3) = all_28_1
% 159.32/28.07 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 159.32/28.07 (3) op(e2, e3) = all_52_1
% 159.32/28.07 (4) op(e0, e0) = e0
% 159.32/28.07 (5) op(e2, e3) = e2
% 159.32/28.07 (6) op(e3, e3) = e1
% 159.32/28.07 (7) ~ (e1 = e0)
% 159.32/28.07 (8) op(e3, e3) = all_22_1
% 159.32/28.07 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07 (10) ~ (e3 = e2)
% 159.32/28.07 (11) op(e0, e0) = e3
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | BETA: splitting (2) gives:
% 159.32/28.07 |
% 159.32/28.07 | Case 1:
% 159.32/28.07 | |
% 159.32/28.07 | | (12) all_58_0 = e3 & op(e3, e3) = e3
% 159.32/28.07 | |
% 159.32/28.07 | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (11), (12) are inconsistent by
% 159.32/28.07 | | sub-proof #584.
% 159.32/28.07 | |
% 159.32/28.07 | Case 2:
% 159.32/28.07 | |
% 159.32/28.07 | | (13) all_58_2 = e3 & op(e2, e3) = e3
% 159.32/28.07 | |
% 159.32/28.07 | | ALPHA: (13) implies:
% 159.32/28.07 | | (14) op(e2, e3) = e3
% 159.32/28.07 | |
% 159.32/28.07 | | REF_CLOSE: (3), (5), (9), (10), (14) are inconsistent by sub-proof #1159.
% 159.32/28.07 | |
% 159.32/28.07 | End of split
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #584 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) op(e3, e3) = all_28_1
% 159.32/28.07 (2) op(e0, e0) = e0
% 159.32/28.07 (3) all_58_0 = e3 & op(e3, e3) = e3
% 159.32/28.07 (4) op(e3, e3) = e1
% 159.32/28.07 (5) ~ (e1 = e0)
% 159.32/28.07 (6) op(e3, e3) = all_22_1
% 159.32/28.07 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07 (8) op(e0, e0) = e3
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | ALPHA: (3) implies:
% 159.32/28.07 | (9) op(e3, e3) = e3
% 159.32/28.07 |
% 159.32/28.07 | GROUND_INST: instantiating (7) with e0, e3, e0, e0, simplifying with (2), (8)
% 159.32/28.07 | gives:
% 159.32/28.07 | (10) e3 = e0
% 159.32/28.07 |
% 159.32/28.07 | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10) are inconsistent by sub-proof
% 159.32/28.07 | #659.
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #585 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) all_56_14 = e3
% 159.32/28.07 (2) all_56_14 = e1
% 159.32/28.07 (3) ~ (e3 = e1)
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | COMBINE_EQS: (1), (2) imply:
% 159.32/28.07 | (4) e3 = e1
% 159.32/28.07 |
% 159.32/28.07 | SIMP: (4) implies:
% 159.32/28.07 | (5) e3 = e1
% 159.32/28.07 |
% 159.32/28.07 | REDUCE: (3), (5) imply:
% 159.32/28.07 | (6) $false
% 159.32/28.07 |
% 159.32/28.07 | CLOSE: (6) is inconsistent.
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #586 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.07 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.07 (2) op(e1, e1) = all_6_2
% 159.32/28.07 (3) all_58_12 = e3
% 159.32/28.07 (4) all_58_8 = e3
% 159.32/28.07 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.07 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.07 (6) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.07 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.07 (7) op(e2, e3) = all_52_1
% 159.32/28.07 (8) ~ (e3 = e0)
% 159.32/28.07 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.07 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.07 (10) ~ (e2 = e0)
% 159.32/28.07 (11) op(e2, e3) = e2
% 159.32/28.07 (12) ~ (e3 = e1)
% 159.32/28.07 (13) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.07 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.07 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.07 (15) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.07 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.07 (16) ~ (e2 = e1)
% 159.32/28.07 (17) ~ (e1 = e0)
% 159.32/28.07 (18) all_58_4 = e3
% 159.32/28.07 (19) all_58_3 = e3
% 159.32/28.07 (20) ~ (all_6_2 = e2)
% 159.32/28.07 (21) all_58_0 = e0
% 159.32/28.07 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07 (23) ~ (e3 = e2)
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | BETA: splitting (6) gives:
% 159.32/28.07 |
% 159.32/28.07 | Case 1:
% 159.32/28.07 | |
% 159.32/28.07 | | (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 159.32/28.07 | | e2)
% 159.32/28.07 | |
% 159.32/28.07 | | BETA: splitting (24) gives:
% 159.32/28.07 | |
% 159.32/28.07 | | Case 1:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (25) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (3), (5), (7), (8), (9), (11), (12), (16), (17), (18), (21),
% 159.32/28.07 | | | (22), (23), (25) are inconsistent by sub-proof #587.
% 159.32/28.07 | | |
% 159.32/28.07 | | Case 2:
% 159.32/28.07 | | |
% 159.32/28.07 | | | (26) all_58_5 = e2 & op(e2, e1) = e2
% 159.32/28.07 | | |
% 159.32/28.07 | | | ALPHA: (26) implies:
% 159.32/28.07 | | | (27) all_58_5 = e2
% 159.32/28.07 | | |
% 159.32/28.07 | | | REF_CLOSE: (1), (8), (10), (11), (12), (14), (16), (17), (19), (22), (27)
% 159.32/28.07 | | | are inconsistent by sub-proof #898.
% 159.32/28.07 | | |
% 159.32/28.07 | | End of split
% 159.32/28.07 | |
% 159.32/28.07 | Case 2:
% 159.32/28.07 | |
% 159.32/28.07 | | (28) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 159.32/28.07 | | e2)
% 159.32/28.07 | |
% 159.32/28.07 | | REF_CLOSE: (2), (4), (8), (10), (12), (13), (15), (16), (17), (18), (20),
% 159.32/28.07 | | (22), (28) are inconsistent by sub-proof #592.
% 159.32/28.07 | |
% 159.32/28.07 | End of split
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #587 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) all_58_12 = e3
% 159.32/28.07 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.07 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.07 (3) op(e2, e3) = all_52_1
% 159.32/28.07 (4) ~ (e3 = e0)
% 159.32/28.07 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.07 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.07 (6) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.07 (7) op(e2, e3) = e2
% 159.32/28.07 (8) ~ (e3 = e1)
% 159.32/28.07 (9) ~ (e2 = e1)
% 159.32/28.07 (10) ~ (e1 = e0)
% 159.32/28.07 (11) all_58_4 = e3
% 159.32/28.07 (12) all_58_0 = e0
% 159.32/28.07 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.07 (14) ~ (e3 = e2)
% 159.32/28.07
% 159.32/28.07 Begin of proof
% 159.32/28.07 |
% 159.32/28.07 | ALPHA: (6) implies:
% 159.32/28.07 | (15) all_58_4 = e2
% 159.32/28.07 |
% 159.32/28.07 | COMBINE_EQS: (11), (15) imply:
% 159.32/28.07 | (16) e3 = e2
% 159.32/28.07 |
% 159.32/28.07 | COMBINE_EQS: (1), (16) imply:
% 159.32/28.07 | (17) all_58_12 = e2
% 159.32/28.07 |
% 159.32/28.07 | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (17) are
% 159.32/28.07 | inconsistent by sub-proof #1066.
% 159.32/28.07 |
% 159.32/28.07 End of proof
% 159.32/28.07
% 159.32/28.07 Sub-proof #588 shows that the following formulas are inconsistent:
% 159.32/28.07 ----------------------------------------------------------------
% 159.32/28.07 (1) all_58_15 = e3
% 159.32/28.07 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.07 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.07 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.07 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.07 (4) op(e1, e1) = all_6_2
% 159.32/28.07 (5) all_58_8 = e3
% 159.32/28.07 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.07 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.07 (7) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.07 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.07 (8) all_58_6 = e3
% 159.32/28.07 (9) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.07 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.07 (10) op(e3, e2) = all_52_4
% 159.32/28.07 (11) op(e2, e3) = all_52_1
% 159.32/28.07 (12) ~ (e3 = e0)
% 159.32/28.07 (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.07 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.07 (14) ~ (e2 = e0)
% 159.32/28.07 (15) op(e2, e3) = e2
% 159.32/28.07 (16) ~ (e3 = e1)
% 159.32/28.07 (17) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.07 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.07 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.08 (19) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.08 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.08 (20) ~ (all_52_4 = e3)
% 159.32/28.08 (21) ~ (e2 = e1)
% 159.32/28.08 (22) ~ (e1 = e0)
% 159.32/28.08 (23) all_58_3 = e3
% 159.32/28.08 (24) ~ (all_6_2 = e2)
% 159.32/28.08 (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.32/28.08 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.32/28.08 (26) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.32/28.08 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.32/28.08 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.08 (28) ~ (e3 = e2)
% 159.32/28.08 (29) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.08 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.08 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.08 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.08 (30) op(e0, e0) = e3
% 159.32/28.08
% 159.32/28.08 Begin of proof
% 159.32/28.08 |
% 159.32/28.08 | BETA: splitting (26) gives:
% 159.32/28.08 |
% 159.32/28.08 | Case 1:
% 159.32/28.08 | |
% 159.32/28.08 | | (31) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.32/28.08 | | e0)
% 159.32/28.08 | |
% 159.32/28.08 | | BETA: splitting (31) gives:
% 159.32/28.08 | |
% 159.32/28.08 | | Case 1:
% 159.32/28.08 | | |
% 159.32/28.08 | | | (32) all_58_0 = e0 & op(e3, e3) = e0
% 159.32/28.08 | | |
% 159.32/28.08 | | | ALPHA: (32) implies:
% 159.32/28.08 | | | (33) all_58_0 = e0
% 159.32/28.08 | | |
% 159.32/28.08 | | | BETA: splitting (25) gives:
% 159.32/28.08 | | |
% 159.32/28.08 | | | Case 1:
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | (34) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 159.32/28.08 | | | | = e3)
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | REF_CLOSE: (10), (12), (20), (27), (33), (34) are inconsistent by
% 159.32/28.08 | | | | sub-proof #645.
% 159.32/28.08 | | | |
% 159.32/28.08 | | | Case 2:
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | (35) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 159.32/28.08 | | | | = e3)
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | BETA: splitting (35) gives:
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | Case 1:
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | (36) all_58_4 = e3 & op(e3, e1) = e3
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | ALPHA: (36) implies:
% 159.32/28.08 | | | | | (37) all_58_4 = e3
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | BETA: splitting (7) gives:
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | Case 1:
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | (38) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 159.32/28.08 | | | | | | e1) = e2)
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | BETA: splitting (38) gives:
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | Case 1:
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | (39) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | REF_CLOSE: (6), (8), (11), (12), (13), (15), (16), (21), (22),
% 159.32/28.08 | | | | | | | (27), (28), (33), (37), (39) are inconsistent by
% 159.32/28.08 | | | | | | | sub-proof #593.
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | Case 2:
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | (40) all_58_5 = e2 & op(e2, e1) = e2
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | ALPHA: (40) implies:
% 159.32/28.08 | | | | | | | (41) all_58_5 = e2
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | REF_CLOSE: (3), (12), (14), (15), (16), (18), (21), (22), (23),
% 159.32/28.08 | | | | | | | (27), (41) are inconsistent by sub-proof #898.
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | End of split
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | Case 2:
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | (42) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 159.32/28.08 | | | | | | e1) = e2)
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | REF_CLOSE: (4), (5), (12), (14), (16), (17), (19), (21), (22), (24),
% 159.32/28.08 | | | | | | (27), (37), (42) are inconsistent by sub-proof #592.
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | End of split
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | Case 2:
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | (43) all_58_9 = e3 & op(e3, e0) = e3
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | ALPHA: (43) implies:
% 159.32/28.08 | | | | | (44) all_58_9 = e3
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (11), (12), (13), (14), (15),
% 159.32/28.08 | | | | | (16), (18), (21), (22), (23), (27), (28), (29), (30), (33),
% 159.32/28.08 | | | | | (44) are inconsistent by sub-proof #590.
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | End of split
% 159.32/28.08 | | | |
% 159.32/28.08 | | | End of split
% 159.32/28.08 | | |
% 159.32/28.08 | | Case 2:
% 159.32/28.08 | | |
% 159.32/28.08 | | | (45) all_58_2 = e0 & op(e2, e3) = e0
% 159.32/28.08 | | |
% 159.32/28.08 | | | ALPHA: (45) implies:
% 159.32/28.08 | | | (46) op(e2, e3) = e0
% 159.32/28.08 | | |
% 159.32/28.08 | | | REF_CLOSE: (14), (15), (27), (46) are inconsistent by sub-proof #1156.
% 159.32/28.08 | | |
% 159.32/28.08 | | End of split
% 159.32/28.08 | |
% 159.32/28.08 | Case 2:
% 159.32/28.08 | |
% 159.32/28.08 | | (47) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.32/28.08 | | e0)
% 159.32/28.08 | |
% 159.32/28.08 | | BETA: splitting (47) gives:
% 159.32/28.08 | |
% 159.32/28.08 | | Case 1:
% 159.32/28.08 | | |
% 159.32/28.08 | | | (48) all_58_6 = e0 & op(e1, e3) = e0
% 159.32/28.08 | | |
% 159.32/28.08 | | | ALPHA: (48) implies:
% 159.32/28.08 | | | (49) all_58_6 = e0
% 159.32/28.08 | | |
% 159.32/28.08 | | | REF_CLOSE: (8), (12), (49) are inconsistent by sub-proof #1321.
% 159.32/28.08 | | |
% 159.32/28.08 | | Case 2:
% 159.32/28.08 | | |
% 159.32/28.08 | | | (50) all_58_12 = e0 & op(e0, e3) = e0
% 159.32/28.08 | | |
% 159.32/28.08 | | | ALPHA: (50) implies:
% 159.32/28.08 | | | (51) all_58_12 = e0
% 159.32/28.08 | | |
% 159.32/28.08 | | | BETA: splitting (25) gives:
% 159.32/28.08 | | |
% 159.32/28.08 | | | Case 1:
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | (52) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 159.32/28.08 | | | | = e3)
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | REF_CLOSE: (8), (10), (13), (15), (16), (20), (21), (22), (27), (51),
% 159.32/28.08 | | | | (52) are inconsistent by sub-proof #808.
% 159.32/28.08 | | | |
% 159.32/28.08 | | | Case 2:
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | (53) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 159.32/28.08 | | | | = e3)
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | BETA: splitting (53) gives:
% 159.32/28.08 | | | |
% 159.32/28.08 | | | | Case 1:
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | (54) all_58_4 = e3 & op(e3, e1) = e3
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | ALPHA: (54) implies:
% 159.32/28.08 | | | | | (55) all_58_4 = e3
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | BETA: splitting (7) gives:
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | Case 1:
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | (56) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 159.32/28.08 | | | | | | e1) = e2)
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | BETA: splitting (56) gives:
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | Case 1:
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | (57) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | ALPHA: (57) implies:
% 159.32/28.08 | | | | | | | (58) all_58_4 = e2
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | COMBINE_EQS: (55), (58) imply:
% 159.32/28.08 | | | | | | | (59) e3 = e2
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | REF_CLOSE: (6), (8), (11), (12), (13), (15), (16), (21), (22),
% 159.32/28.08 | | | | | | | (27), (28), (51), (59) are inconsistent by sub-proof
% 159.32/28.08 | | | | | | | #832.
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | Case 2:
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | (60) all_58_5 = e2 & op(e2, e1) = e2
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | ALPHA: (60) implies:
% 159.32/28.08 | | | | | | | (61) all_58_5 = e2
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | | REF_CLOSE: (3), (12), (14), (15), (16), (18), (21), (22), (23),
% 159.32/28.08 | | | | | | | (27), (61) are inconsistent by sub-proof #898.
% 159.32/28.08 | | | | | | |
% 159.32/28.08 | | | | | | End of split
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | Case 2:
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | (62) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 159.32/28.08 | | | | | | e1) = e2)
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | | REF_CLOSE: (4), (5), (12), (14), (16), (17), (19), (21), (22), (24),
% 159.32/28.08 | | | | | | (27), (55), (62) are inconsistent by sub-proof #592.
% 159.32/28.08 | | | | | |
% 159.32/28.08 | | | | | End of split
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | Case 2:
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | (63) all_58_9 = e3 & op(e3, e0) = e3
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | ALPHA: (63) implies:
% 159.32/28.08 | | | | | (64) all_58_9 = e3
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | | REF_CLOSE: (1), (2), (3), (9), (12), (14), (15), (16), (18), (21),
% 159.32/28.08 | | | | | (22), (23), (27), (28), (29), (30), (64) are inconsistent
% 159.32/28.08 | | | | | by sub-proof #589.
% 159.32/28.08 | | | | |
% 159.32/28.08 | | | | End of split
% 159.32/28.08 | | | |
% 159.32/28.08 | | | End of split
% 159.32/28.08 | | |
% 159.32/28.08 | | End of split
% 159.32/28.08 | |
% 159.32/28.08 | End of split
% 159.32/28.08 |
% 159.32/28.08 End of proof
% 159.32/28.08
% 159.32/28.08 Sub-proof #589 shows that the following formulas are inconsistent:
% 159.32/28.08 ----------------------------------------------------------------
% 159.32/28.08 (1) all_58_15 = e3
% 159.32/28.08 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.08 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.08 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.08 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.08 (4) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.08 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.08 (5) ~ (e3 = e0)
% 159.32/28.08 (6) ~ (e2 = e0)
% 159.32/28.08 (7) all_58_9 = e3
% 159.32/28.08 (8) op(e2, e3) = e2
% 159.32/28.08 (9) ~ (e3 = e1)
% 159.32/28.08 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.08 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.08 (11) ~ (e2 = e1)
% 159.32/28.08 (12) ~ (e1 = e0)
% 159.32/28.08 (13) all_58_3 = e3
% 159.32/28.08 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.08 (15) ~ (e3 = e2)
% 159.32/28.08 (16) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.08 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.08 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.08 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.08 (17) op(e0, e0) = e3
% 159.32/28.08
% 159.32/28.08 Begin of proof
% 159.32/28.08 |
% 159.32/28.08 | BETA: splitting (4) gives:
% 159.32/28.08 |
% 159.32/28.08 | Case 1:
% 159.32/28.08 | |
% 159.32/28.08 | | (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 159.32/28.08 | | e2)
% 159.32/28.08 | |
% 159.32/28.08 | | BETA: splitting (18) gives:
% 159.32/28.08 | |
% 159.32/28.08 | | Case 1:
% 159.32/28.08 | | |
% 159.32/28.08 | | | (19) all_58_9 = e2 & op(e3, e0) = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | ALPHA: (19) implies:
% 159.32/28.08 | | | (20) all_58_9 = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | REF_CLOSE: (7), (15), (20) are inconsistent by sub-proof #1245.
% 159.32/28.08 | | |
% 159.32/28.08 | | Case 2:
% 159.32/28.08 | | |
% 159.32/28.08 | | | (21) all_58_10 = e2 & op(e2, e0) = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | ALPHA: (21) implies:
% 159.32/28.08 | | | (22) all_58_10 = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | REF_CLOSE: (3), (5), (6), (8), (9), (10), (11), (12), (13), (14), (22) are
% 159.32/28.08 | | | inconsistent by sub-proof #906.
% 159.32/28.08 | | |
% 159.32/28.08 | | End of split
% 159.32/28.08 | |
% 159.32/28.08 | Case 2:
% 159.32/28.08 | |
% 159.32/28.08 | | (23) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.32/28.08 | | e2)
% 159.32/28.08 | |
% 159.32/28.08 | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (11), (12), (14), (15), (16), (17),
% 159.32/28.08 | | (23) are inconsistent by sub-proof #591.
% 159.32/28.08 | |
% 159.32/28.08 | End of split
% 159.32/28.08 |
% 159.32/28.08 End of proof
% 159.32/28.08
% 159.32/28.08 Sub-proof #590 shows that the following formulas are inconsistent:
% 159.32/28.08 ----------------------------------------------------------------
% 159.32/28.08 (1) all_58_15 = e3
% 159.32/28.08 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.08 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.08 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.08 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.08 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.08 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.08 (5) all_58_6 = e3
% 159.32/28.08 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.08 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.08 (7) op(e2, e3) = all_52_1
% 159.32/28.08 (8) ~ (e3 = e0)
% 159.32/28.08 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.08 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.08 (10) ~ (e2 = e0)
% 159.32/28.08 (11) all_58_9 = e3
% 159.32/28.08 (12) op(e2, e3) = e2
% 159.32/28.08 (13) ~ (e3 = e1)
% 159.32/28.08 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.08 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.08 (15) ~ (e2 = e1)
% 159.32/28.08 (16) ~ (e1 = e0)
% 159.32/28.08 (17) all_58_3 = e3
% 159.32/28.08 (18) all_58_0 = e0
% 159.32/28.08 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.08 (20) ~ (e3 = e2)
% 159.32/28.08 (21) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.08 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.08 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.08 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.08 (22) op(e0, e0) = e3
% 159.32/28.08
% 159.32/28.08 Begin of proof
% 159.32/28.08 |
% 159.32/28.08 | BETA: splitting (6) gives:
% 159.32/28.08 |
% 159.32/28.08 | Case 1:
% 159.32/28.08 | |
% 159.32/28.08 | | (23) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 159.32/28.08 | | e2)
% 159.32/28.08 | |
% 159.32/28.08 | | BETA: splitting (23) gives:
% 159.32/28.08 | |
% 159.32/28.08 | | Case 1:
% 159.32/28.08 | | |
% 159.32/28.08 | | | (24) all_58_9 = e2 & op(e3, e0) = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | ALPHA: (24) implies:
% 159.32/28.08 | | | (25) all_58_9 = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | COMBINE_EQS: (11), (25) imply:
% 159.32/28.08 | | | (26) e3 = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | COMBINE_EQS: (5), (26) imply:
% 159.32/28.08 | | | (27) all_58_6 = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | REF_CLOSE: (4), (7), (8), (9), (12), (13), (15), (16), (18), (19), (20),
% 159.32/28.08 | | | (27) are inconsistent by sub-proof #1157.
% 159.32/28.08 | | |
% 159.32/28.08 | | Case 2:
% 159.32/28.08 | | |
% 159.32/28.08 | | | (28) all_58_10 = e2 & op(e2, e0) = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | ALPHA: (28) implies:
% 159.32/28.08 | | | (29) all_58_10 = e2
% 159.32/28.08 | | |
% 159.32/28.08 | | | REF_CLOSE: (3), (8), (10), (12), (13), (14), (15), (16), (17), (19), (29)
% 159.32/28.08 | | | are inconsistent by sub-proof #906.
% 159.32/28.08 | | |
% 159.32/28.08 | | End of split
% 159.32/28.08 | |
% 159.32/28.08 | Case 2:
% 159.32/28.08 | |
% 159.32/28.08 | | (30) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.32/28.08 | | e2)
% 159.32/28.08 | |
% 159.32/28.08 | | REF_CLOSE: (1), (2), (8), (10), (11), (13), (15), (16), (19), (20), (21),
% 159.32/28.08 | | (22), (30) are inconsistent by sub-proof #591.
% 159.32/28.08 | |
% 159.32/28.08 | End of split
% 159.32/28.08 |
% 159.32/28.08 End of proof
% 159.32/28.08
% 159.32/28.08 Sub-proof #591 shows that the following formulas are inconsistent:
% 159.32/28.08 ----------------------------------------------------------------
% 159.32/28.08 (1) all_58_15 = e3
% 159.32/28.08 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.08 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.08 (3) ~ (e3 = e0)
% 159.32/28.08 (4) ~ (e2 = e0)
% 159.32/28.08 (5) all_58_9 = e3
% 159.32/28.08 (6) ~ (e3 = e1)
% 159.32/28.08 (7) ~ (e2 = e1)
% 159.32/28.08 (8) ~ (e1 = e0)
% 159.32/28.08 (9) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.08 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.08 (11) ~ (e3 = e2)
% 159.32/28.08 (12) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.08 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.08 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.08 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.08 (13) op(e0, e0) = e3
% 159.32/28.08
% 159.32/28.08 Begin of proof
% 159.32/28.08 |
% 159.32/28.08 | BETA: splitting (9) gives:
% 159.32/28.08 |
% 159.32/28.08 | Case 1:
% 159.32/28.08 | |
% 159.32/28.08 | | (14) all_58_11 = e2 & op(e1, e0) = e2
% 159.32/28.08 | |
% 159.32/28.08 | | ALPHA: (14) implies:
% 159.32/28.08 | | (15) all_58_11 = e2
% 159.32/28.08 | |
% 159.32/28.08 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (12), (15) are
% 159.32/28.08 | | inconsistent by sub-proof #1316.
% 159.32/28.08 | |
% 159.32/28.08 | Case 2:
% 159.32/28.08 | |
% 159.32/28.08 | | (16) all_58_15 = e2 & op(e0, e0) = e2
% 159.32/28.08 | |
% 159.32/28.08 | | ALPHA: (16) implies:
% 159.32/28.08 | | (17) op(e0, e0) = e2
% 159.32/28.08 | |
% 159.32/28.08 | | REF_CLOSE: (10), (11), (13), (17) are inconsistent by sub-proof #1382.
% 159.32/28.08 | |
% 159.32/28.08 | End of split
% 159.32/28.08 |
% 159.32/28.08 End of proof
% 159.32/28.08
% 159.32/28.08 Sub-proof #592 shows that the following formulas are inconsistent:
% 159.32/28.08 ----------------------------------------------------------------
% 159.32/28.08 (1) op(e1, e1) = all_6_2
% 159.32/28.08 (2) all_58_8 = e3
% 159.32/28.08 (3) ~ (e3 = e0)
% 159.32/28.08 (4) ~ (e2 = e0)
% 159.32/28.08 (5) ~ (e3 = e1)
% 159.32/28.08 (6) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.08 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.08 (7) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.08 (8) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.08 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.08 (9) ~ (e2 = e1)
% 159.32/28.08 (10) ~ (e1 = e0)
% 159.32/28.08 (11) all_58_4 = e3
% 159.32/28.08 (12) ~ (all_6_2 = e2)
% 159.32/28.08 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.08
% 159.32/28.08 Begin of proof
% 159.32/28.08 |
% 159.32/28.08 | BETA: splitting (7) gives:
% 159.32/28.08 |
% 159.32/28.08 | Case 1:
% 159.32/28.08 | |
% 159.32/28.08 | | (14) all_58_8 = e2 & op(e1, e1) = e2
% 159.32/28.08 | |
% 159.32/28.08 | | REF_CLOSE: (1), (12), (13), (14) are inconsistent by sub-proof #1440.
% 159.32/28.08 | |
% 159.32/28.08 | Case 2:
% 159.32/28.08 | |
% 159.32/28.08 | | (15) all_58_14 = e2 & op(e0, e1) = e2
% 159.32/28.08 | |
% 159.32/28.08 | | ALPHA: (15) implies:
% 159.32/28.08 | | (16) all_58_14 = e2
% 159.32/28.08 | |
% 159.32/28.08 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (16) are
% 159.32/28.08 | | inconsistent by sub-proof #739.
% 159.32/28.08 | |
% 159.32/28.08 | End of split
% 159.32/28.08 |
% 159.32/28.08 End of proof
% 159.32/28.08
% 159.32/28.08 Sub-proof #593 shows that the following formulas are inconsistent:
% 159.32/28.08 ----------------------------------------------------------------
% 159.32/28.08 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.08 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.08 (2) all_58_6 = e3
% 159.32/28.08 (3) op(e2, e3) = all_52_1
% 159.32/28.08 (4) ~ (e3 = e0)
% 159.32/28.08 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.08 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.08 (6) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.08 (7) op(e2, e3) = e2
% 159.32/28.08 (8) ~ (e3 = e1)
% 159.32/28.08 (9) ~ (e2 = e1)
% 159.32/28.08 (10) ~ (e1 = e0)
% 159.32/28.08 (11) all_58_4 = e3
% 159.32/28.08 (12) all_58_0 = e0
% 159.32/28.08 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.08 (14) ~ (e3 = e2)
% 159.32/28.08
% 159.32/28.08 Begin of proof
% 159.32/28.08 |
% 159.32/28.08 | ALPHA: (6) implies:
% 159.32/28.08 | (15) all_58_4 = e2
% 159.32/28.08 |
% 159.32/28.08 | COMBINE_EQS: (11), (15) imply:
% 159.32/28.08 | (16) e3 = e2
% 159.32/28.08 |
% 159.32/28.08 | COMBINE_EQS: (2), (16) imply:
% 159.32/28.08 | (17) all_58_6 = e2
% 159.32/28.08 |
% 159.32/28.08 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (17) are
% 159.32/28.08 | inconsistent by sub-proof #1157.
% 159.32/28.08 |
% 159.32/28.08 End of proof
% 159.32/28.08
% 159.32/28.08 Sub-proof #594 shows that the following formulas are inconsistent:
% 159.32/28.08 ----------------------------------------------------------------
% 159.32/28.08 (1) all_56_14 = e3
% 159.32/28.08 (2) all_58_15 = e3
% 159.32/28.08 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.32/28.08 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.32/28.08 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.08 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.32/28.08 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.32/28.08 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.08 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.32/28.08 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.32/28.08 (7) op(e1, e1) = all_6_2
% 159.32/28.08 (8) ~ (all_52_7 = e3)
% 159.32/28.08 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.32/28.08 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.32/28.08 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.32/28.08 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.32/28.08 (11) all_58_8 = e3
% 159.32/28.08 (12) all_4_2 = e3
% 159.32/28.08 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.32/28.08 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.32/28.08 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.32/28.08 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.32/28.08 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.32/28.08 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.32/28.08 (16) op(e3, e2) = all_52_4
% 159.32/28.08 (17) ~ (all_4_2 = e2)
% 159.32/28.08 (18) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.32/28.08 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.32/28.08 (19) op(e2, e1) = all_52_9
% 159.32/28.08 (20) op(e2, e3) = all_52_1
% 159.32/28.08 (21) ~ (all_52_13 = e3)
% 159.32/28.08 (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.32/28.08 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.32/28.08 (23) ~ (e3 = e0)
% 159.32/28.08 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.32/28.08 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.32/28.08 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.32/28.08 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.32/28.08 (26) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.32/28.08 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.32/28.08 e2)
% 159.32/28.08 (27) ~ (e2 = e0)
% 159.32/28.08 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.32/28.08 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.32/28.08 (29) op(e1, e3) = all_52_2
% 159.32/28.08 (30) op(e2, e0) = all_52_13
% 159.32/28.08 (31) op(e2, e3) = e2
% 159.32/28.08 (32) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.08 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.32/28.08 (33) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.32/28.08 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.08 (34) op(e1, e2) = all_52_6
% 159.32/28.08 (35) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 159.32/28.08 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.32/28.08 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 159.32/28.08 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.32/28.08 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.32/28.08 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.32/28.08 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 159.32/28.08 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 159.32/28.08 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 159.32/28.08 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.32/28.08 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.32/28.08 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 159.32/28.08 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.32/28.08 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.32/28.08 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 159.32/28.08 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 159.32/28.08 = e0)
% 159.32/28.08 (36) ~ (all_4_2 = e1)
% 159.32/28.08 (37) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.32/28.08 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.32/28.08 (38) op(e0, e0) = all_4_2
% 159.32/28.08 (39) all_56_12 = e3
% 159.32/28.08 (40) op(e0, e1) = all_52_11
% 159.32/28.08 (41) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 159.32/28.08 (42) all_56_6 = e1
% 159.32/28.08 (43) all_52_2 = e1
% 159.32/28.08 (44) all_58_0 = e3
% 159.32/28.08 (45) ~ (all_52_6 = e1)
% 159.32/28.08 (46) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.32/28.08 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.32/28.08 (47) ~ (all_52_4 = e3)
% 159.32/28.08 (48) ~ (e2 = e1)
% 159.32/28.08 (49) ~ (e1 = e0)
% 159.32/28.08 (50) all_58_3 = e3
% 159.32/28.08 (51) ~ (all_6_2 = e2)
% 159.32/28.08 (52) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.32/28.08 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.32/28.08 e3)
% 159.32/28.08 (53) all_56_13 = e3
% 159.32/28.08 (54) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.32/28.08 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.32/28.08 (55) ~ (all_52_9 = e2)
% 159.32/28.09 (56) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.32/28.09 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.32/28.09 (57) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.32/28.09 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.32/28.09 (58) op(e0, e2) = all_52_7
% 159.32/28.09 (59) op(e1, e0) = all_52_14
% 159.32/28.09 (60) ~ (all_52_6 = e3)
% 159.32/28.09 (61) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.32/28.09 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.32/28.09 (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.32/28.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.32/28.09 (63) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.32/28.09 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.09 (64) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.32/28.09 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.32/28.09 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.09 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.32/28.09 (65) all_56_15 = e3
% 159.32/28.09
% 159.32/28.09 Begin of proof
% 159.32/28.09 |
% 159.32/28.09 | REDUCE: (12), (17) imply:
% 159.32/28.09 | (66) ~ (e3 = e2)
% 159.32/28.09 |
% 159.32/28.09 | REDUCE: (12), (36) imply:
% 159.32/28.09 | (67) ~ (e3 = e1)
% 159.32/28.09 |
% 159.32/28.09 | REDUCE: (29), (43) imply:
% 159.32/28.09 | (68) op(e1, e3) = e1
% 159.32/28.09 |
% 159.32/28.09 | REDUCE: (12), (38) imply:
% 159.32/28.09 | (69) op(e0, e0) = e3
% 159.32/28.09 |
% 159.32/28.09 | BETA: splitting (41) gives:
% 159.32/28.09 |
% 159.32/28.09 | Case 1:
% 159.32/28.09 | |
% 159.32/28.09 | | (70) ~ (all_56_15 = e3)
% 159.32/28.09 | |
% 159.32/28.09 | | REDUCE: (65), (70) imply:
% 159.32/28.09 | | (71) $false
% 159.32/28.09 | |
% 159.32/28.09 | | CLOSE: (71) is inconsistent.
% 159.32/28.09 | |
% 159.32/28.09 | Case 2:
% 159.32/28.09 | |
% 159.32/28.09 | | (72) all_56_9 = e0 & op(e0, e3) = e0
% 159.32/28.09 | |
% 159.32/28.09 | | ALPHA: (72) implies:
% 159.32/28.09 | | (73) all_56_9 = e0
% 159.32/28.09 | |
% 159.32/28.09 | | BETA: splitting (61) gives:
% 159.32/28.09 | |
% 159.32/28.09 | | Case 1:
% 159.32/28.09 | | |
% 159.32/28.09 | | | (74) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.32/28.09 | | | e0)
% 159.32/28.09 | | |
% 159.32/28.09 | | | REF_CLOSE: (23), (27), (31), (44), (62), (74) are inconsistent by
% 159.32/28.09 | | | sub-proof #615.
% 159.32/28.09 | | |
% 159.32/28.09 | | Case 2:
% 159.32/28.09 | | |
% 159.32/28.09 | | | (75) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.32/28.09 | | | e0)
% 159.32/28.09 | | |
% 159.32/28.09 | | | BETA: splitting (75) gives:
% 159.32/28.09 | | |
% 159.32/28.09 | | | Case 1:
% 159.32/28.09 | | | |
% 159.32/28.09 | | | | (76) all_58_6 = e0 & op(e1, e3) = e0
% 159.32/28.09 | | | |
% 159.32/28.09 | | | | ALPHA: (76) implies:
% 159.32/28.09 | | | | (77) all_58_6 = e0
% 159.32/28.09 | | | | (78) op(e1, e3) = e0
% 159.32/28.09 | | | |
% 159.32/28.09 | | | | BETA: splitting (4) gives:
% 159.32/28.09 | | | |
% 159.32/28.09 | | | | Case 1:
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | (79) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 159.32/28.09 | | | | | e2) = e1)
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | BETA: splitting (79) gives:
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | Case 1:
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | (80) all_58_1 = e1 & op(e3, e2) = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | ALPHA: (80) implies:
% 159.32/28.09 | | | | | | (81) all_58_1 = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | BETA: splitting (64) gives:
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | Case 1:
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | (82) all_58_15 = e0 & op(e0, e0) = e0
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | ALPHA: (82) implies:
% 159.32/28.09 | | | | | | | (83) all_58_15 = e0
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | REF_CLOSE: (2), (23), (83) are inconsistent by sub-proof #1318.
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | Case 2:
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | (84) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 159.32/28.09 | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0))
% 159.32/28.09 | | | | | | | & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.09 | | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | ALPHA: (84) implies:
% 159.32/28.09 | | | | | | | (85) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.09 | | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | BETA: splitting (32) gives:
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | (86) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 159.32/28.09 | | | | | | | | op(e2, e2) = e0)
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | BETA: splitting (86) gives:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | (87) all_58_1 = e0 & op(e3, e2) = e0
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | REF_CLOSE: (49), (81), (87) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | #1327.
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | (88) all_58_3 = e0 & op(e2, e2) = e0
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | REF_CLOSE: (23), (50), (88) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | #910.
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | End of split
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | (89) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 159.32/28.09 | | | | | | | | op(e0, e2) = e0)
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | BETA: splitting (89) gives:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | (90) all_58_7 = e0 & op(e1, e2) = e0
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | ALPHA: (90) implies:
% 159.32/28.09 | | | | | | | | | (91) all_58_7 = e0
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | BETA: splitting (56) gives:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | (92) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 159.32/28.09 | | | | | | | | | | op(e2, e2) = e2)
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | BETA: splitting (92) gives:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | (93) all_58_1 = e2 & op(e3, e2) = e2
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | REF_CLOSE: (48), (81), (93) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | #1213.
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | (94) all_58_3 = e2 & op(e2, e2) = e2
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | REF_CLOSE: (50), (66), (94) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | #719.
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | (95) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2
% 159.32/28.09 | | | | | | | | | | & op(e0, e2) = e2)
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | BETA: splitting (95) gives:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | (96) all_58_7 = e2 & op(e1, e2) = e2
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | ALPHA: (96) implies:
% 159.32/28.09 | | | | | | | | | | | (97) all_58_7 = e2
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | REF_CLOSE: (27), (91), (97) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | #1086.
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | (98) all_58_13 = e2 & op(e0, e2) = e2
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | ALPHA: (98) implies:
% 159.32/28.09 | | | | | | | | | | | (99) all_58_13 = e2
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | BETA: splitting (3) gives:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | (100) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 159.32/28.09 | | | | | | | | | | | | & op(e1, e2) = e1)
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | BETA: splitting (100) gives:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (101) all_58_6 = e1 & op(e1, e3) = e1
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (101) implies:
% 159.32/28.09 | | | | | | | | | | | | | (102) all_58_6 = e1
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | COMBINE_EQS: (77), (102) imply:
% 159.32/28.09 | | | | | | | | | | | | | (103) e1 = e0
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | SIMP: (103) implies:
% 159.32/28.09 | | | | | | | | | | | | | (104) e1 = e0
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | COMBINE_EQS: (81), (104) imply:
% 159.32/28.09 | | | | | | | | | | | | | (105) all_58_1 = e0
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (50), (67), (91), (99), (105) are
% 159.32/28.09 | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (106) all_58_7 = e1 & op(e1, e2) = e1
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (106) implies:
% 159.32/28.09 | | | | | | | | | | | | | (107) op(e1, e2) = e1
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (34), (45), (62), (107) are inconsistent by
% 159.32/28.09 | | | | | | | | | | | | | sub-proof #1166.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | (108) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 159.32/28.09 | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | BETA: splitting (108) gives:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (109) all_58_8 = e1 & op(e1, e1) = e1
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (109) implies:
% 159.32/28.09 | | | | | | | | | | | | | (110) all_58_8 = e1
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (11), (67), (110) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | | | #950.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (111) all_58_11 = e1 & op(e1, e0) = e1
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (111) implies:
% 159.32/28.09 | | | | | | | | | | | | | (112) all_58_11 = e1
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (7), (13), (20), (22), (23), (24), (27), (31),
% 159.32/28.09 | | | | | | | | | | | | | (48), (49), (51), (61), (62), (66), (67), (91),
% 159.32/28.09 | | | | | | | | | | | | | (112) are inconsistent by sub-proof #743.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | (113) all_58_13 = e0 & op(e0, e2) = e0
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | ALPHA: (113) implies:
% 159.32/28.09 | | | | | | | | | (114) all_58_13 = e0
% 159.32/28.09 | | | | | | | | | (115) op(e0, e2) = e0
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | BETA: splitting (24) gives:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | (116) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 159.32/28.09 | | | | | | | | | | & op(e2, e3) = e1)
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | REF_CLOSE: (31), (44), (48), (62), (67), (116) are
% 159.32/28.09 | | | | | | | | | | inconsistent by sub-proof #809.
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | (117) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 159.32/28.09 | | | | | | | | | | & op(e0, e3) = e1)
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | BETA: splitting (117) gives:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | (118) all_58_6 = e1 & op(e1, e3) = e1
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | ALPHA: (118) implies:
% 159.32/28.09 | | | | | | | | | | | (119) all_58_6 = e1
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | REF_CLOSE: (49), (77), (119) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | #735.
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | (120) all_58_12 = e1 & op(e0, e3) = e1
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | ALPHA: (120) implies:
% 159.32/28.09 | | | | | | | | | | | (121) all_58_12 = e1
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | BETA: splitting (26) gives:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | (122) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 159.32/28.09 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | BETA: splitting (122) gives:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (123) all_58_12 = e2 & op(e0, e3) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (123) implies:
% 159.32/28.09 | | | | | | | | | | | | | (124) all_58_12 = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (13), (20), (23), (24), (31), (48), (49), (62),
% 159.32/28.09 | | | | | | | | | | | | | (66), (67), (77), (124) are inconsistent by
% 159.32/28.09 | | | | | | | | | | | | | sub-proof #1063.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (125) all_58_13 = e2 & op(e0, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (125) implies:
% 159.32/28.09 | | | | | | | | | | | | | (126) op(e0, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (27), (58), (62), (115), (126) are inconsistent by
% 159.32/28.09 | | | | | | | | | | | | | sub-proof #1040.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | (127) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 159.32/28.09 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | BETA: splitting (127) gives:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (128) all_58_14 = e2 & op(e0, e1) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (128) implies:
% 159.32/28.09 | | | | | | | | | | | | | (129) all_58_14 = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | BETA: splitting (56) gives:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | (130) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.32/28.09 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.32/28.09 | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 159.32/28.09 | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | (131) all_58_1 = e2 & op(e3, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | (132) all_58_1 = e2
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | COMBINE_EQS: (81), (132) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | (133) e2 = e1
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | REF_CLOSE: (13), (20), (23), (24), (26), (27), (31), (48),
% 159.32/28.09 | | | | | | | | | | | | | | | (49), (58), (62), (66), (67), (69), (77), (85),
% 159.32/28.09 | | | | | | | | | | | | | | | (121), (129), (133) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | | | | | #612.
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | (134) all_58_3 = e2 & op(e2, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | REF_CLOSE: (50), (66), (134) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | | | | | #719.
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | (135) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.32/28.09 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.32/28.09 | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 159.32/28.09 | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | (136) all_58_7 = e2 & op(e1, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | (137) all_58_7 = e2
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | (138) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 159.32/28.09 | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | (139) all_58_6 = e1 & op(e1, e3) = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (50), (67), (77), (81), (114),
% 159.32/28.09 | | | | | | | | | | | | | | | | | (137), (139) are inconsistent by sub-proof #611.
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | (140) all_58_7 = e1 & op(e1, e2) = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | (141) op(e1, e2) = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (45), (62), (141) are inconsistent by
% 159.32/28.09 | | | | | | | | | | | | | | | | | sub-proof #1166.
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | (142) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 159.32/28.09 | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 159.32/28.09 | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | (143) all_58_8 = e1 & op(e1, e1) = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | (144) all_58_8 = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (67), (144) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | | | | | | | #950.
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | (145) all_58_11 = e1 & op(e1, e0) = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | (146) all_58_11 = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | (147) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 159.32/28.09 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 159.32/28.09 | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (148) all_58_9 = e2 & op(e3, e0) = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (149) all_58_9 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | (150) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23), (44), (48), (49), (50), (67), (114),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | (137), (150) are inconsistent by sub-proof #856.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | (151) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | (152) all_58_4 = e0 & op(e3, e1) = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | (153) all_58_4 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | (154) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (155) all_58_0 = e2 & op(e3, e3) = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (156) all_58_0 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (156) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (157) e3 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (157) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (158) $false
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (159) all_58_1 = e2 & op(e3, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (160) all_58_1 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (160) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (161) e2 = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (20), (23), (24), (26), (27), (31), (48),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (49), (58), (62), (66), (67), (69), (77), (85),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (121), (129), (161) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | #612.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | (162) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (163) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (164) all_58_4 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (164) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (165) e2 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (165) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (166) e2 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (166) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (167) all_58_7 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (20), (22), (23), (24), (27), (31),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (48), (49), (51), (61), (62), (66), (67), (146),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (167) are inconsistent by sub-proof #743.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with e1, e0, e3, e1,
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (68), (78) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (168) e1 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (168) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | (169) all_58_1 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (50), (67), (114), (137), (169)
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #857.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | (170) all_58_9 = e0 & op(e3, e0) = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | (171) all_58_9 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (171) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | (172) e2 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (172) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | (173) all_58_7 = e0
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (20), (22), (23), (24), (27), (31),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | (48), (49), (51), (61), (62), (66), (67), (146),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | | (173) are inconsistent by sub-proof #743.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (174) all_58_10 = e2 & op(e2, e0) = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (175) all_58_10 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (27), (31), (37), (48), (49), (50),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (62), (67), (175) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | #906.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | (176) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 159.32/28.09 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.32/28.09 | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 159.32/28.09 | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (177) all_58_11 = e2 & op(e1, e0) = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (178) all_58_11 = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (146), (178) imply:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (179) e2 = e1
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (20), (23), (24), (26), (27), (31), (48),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (49), (58), (62), (66), (67), (69), (77), (85),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (121), (129), (179) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | #612.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (180) all_58_15 = e2 & op(e0, e0) = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (181) op(e0, e0) = e2
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (9), (10), (13), (15), (16),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (18), (20), (21), (23), (24), (25), (27), (28),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (30), (31), (32), (34), (37), (46), (47), (48),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (49), (50), (52), (54), (56), (57), (58), (60),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (61), (62), (63), (64), (66), (67), (115), (129),
% 159.32/28.09 | | | | | | | | | | | | | | | | | | | (137), (181) are inconsistent by sub-proof #604.
% 159.32/28.09 | | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | (182) all_58_13 = e2 & op(e0, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 159.32/28.09 | | | | | | | | | | | | | | | (183) all_58_13 = e2
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (27), (48), (49), (67), (85), (129),
% 159.32/28.09 | | | | | | | | | | | | | | | (183) are inconsistent by sub-proof #1205.
% 159.32/28.09 | | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (184) all_58_15 = e2 & op(e0, e0) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (184) implies:
% 159.32/28.09 | | | | | | | | | | | | | (185) op(e0, e0) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (62), (66), (69), (185) are inconsistent by
% 159.32/28.09 | | | | | | | | | | | | | sub-proof #1382.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | End of split
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | End of split
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | End of split
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | Case 2:
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | (186) all_58_3 = e1 & op(e2, e2) = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | ALPHA: (186) implies:
% 159.32/28.09 | | | | | | (187) all_58_3 = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | REF_CLOSE: (50), (67), (187) are inconsistent by sub-proof #841.
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | End of split
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | Case 2:
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | (188) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 159.32/28.09 | | | | | e2) = e1)
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | BETA: splitting (188) gives:
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | Case 1:
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | (189) all_58_7 = e1 & op(e1, e2) = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | ALPHA: (189) implies:
% 159.32/28.09 | | | | | | (190) op(e1, e2) = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | REF_CLOSE: (34), (45), (62), (190) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | #1166.
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | Case 2:
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | (191) all_58_13 = e1 & op(e0, e2) = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | ALPHA: (191) implies:
% 159.32/28.09 | | | | | | (192) all_58_13 = e1
% 159.32/28.09 | | | | | | (193) op(e0, e2) = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | BETA: splitting (64) gives:
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | Case 1:
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | (194) all_58_15 = e0 & op(e0, e0) = e0
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | ALPHA: (194) implies:
% 159.32/28.09 | | | | | | | (195) all_58_15 = e0
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | REF_CLOSE: (2), (23), (195) are inconsistent by sub-proof #1318.
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | Case 2:
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | (196) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 159.32/28.09 | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.32/28.09 | | | | | | | e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 159.32/28.09 | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 159.32/28.09 | | | | | | | op(e0, e1) = e0))
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | ALPHA: (196) implies:
% 159.32/28.09 | | | | | | | (197) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.32/28.09 | | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | BETA: splitting (24) gives:
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | (198) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 159.32/28.09 | | | | | | | | op(e2, e3) = e1)
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | REF_CLOSE: (31), (44), (48), (62), (67), (198) are inconsistent
% 159.32/28.09 | | | | | | | | by sub-proof #809.
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | (199) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 159.32/28.09 | | | | | | | | op(e0, e3) = e1)
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | BETA: splitting (199) gives:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | (200) all_58_6 = e1 & op(e1, e3) = e1
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | ALPHA: (200) implies:
% 159.32/28.09 | | | | | | | | | (201) all_58_6 = e1
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | REF_CLOSE: (49), (77), (201) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | | #735.
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | (202) all_58_12 = e1 & op(e0, e3) = e1
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | ALPHA: (202) implies:
% 159.32/28.09 | | | | | | | | | (203) all_58_12 = e1
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | BETA: splitting (197) gives:
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | (204) all_58_12 = e0 & op(e0, e3) = e0
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | ALPHA: (204) implies:
% 159.32/28.09 | | | | | | | | | | (205) all_58_12 = e0
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | REF_CLOSE: (2), (9), (13), (19), (20), (23), (24), (26),
% 159.32/28.09 | | | | | | | | | | (27), (31), (34), (35), (39), (40), (42), (45),
% 159.32/28.09 | | | | | | | | | | (48), (49), (53), (55), (58), (61), (62), (66),
% 159.32/28.09 | | | | | | | | | | (67), (69), (73), (191), (193), (205) are
% 159.32/28.09 | | | | | | | | | | inconsistent by sub-proof #603.
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | (206) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 159.32/28.09 | | | | | | | | | | e0 & op(e0, e1) = e0)
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | BETA: splitting (206) gives:
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | (207) all_58_13 = e0 & op(e0, e2) = e0
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | ALPHA: (207) implies:
% 159.32/28.09 | | | | | | | | | | | (208) all_58_13 = e0
% 159.32/28.09 | | | | | | | | | | | (209) op(e0, e2) = e0
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | COMBINE_EQS: (192), (208) imply:
% 159.32/28.09 | | | | | | | | | | | (210) e1 = e0
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | SIMP: (210) implies:
% 159.32/28.09 | | | | | | | | | | | (211) e1 = e0
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | COMBINE_EQS: (203), (211) imply:
% 159.32/28.09 | | | | | | | | | | | (212) all_58_12 = e0
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | REF_CLOSE: (2), (9), (13), (20), (23), (24), (26), (27),
% 159.32/28.09 | | | | | | | | | | | (31), (48), (49), (58), (61), (62), (66), (67),
% 159.32/28.09 | | | | | | | | | | | (69), (208), (209), (212) are inconsistent by
% 159.32/28.09 | | | | | | | | | | | sub-proof #621.
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | (213) all_58_14 = e0 & op(e0, e1) = e0
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | ALPHA: (213) implies:
% 159.32/28.09 | | | | | | | | | | | (214) op(e0, e1) = e0
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | BETA: splitting (26) gives:
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | (215) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 159.32/28.09 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | BETA: splitting (215) gives:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (216) all_58_12 = e2 & op(e0, e3) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (216) implies:
% 159.32/28.09 | | | | | | | | | | | | | (217) all_58_12 = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (13), (20), (23), (24), (31), (48), (49), (62),
% 159.32/28.09 | | | | | | | | | | | | | (66), (67), (77), (217) are inconsistent by
% 159.32/28.09 | | | | | | | | | | | | | sub-proof #1063.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | (218) all_58_13 = e2 & op(e0, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | ALPHA: (218) implies:
% 159.32/28.09 | | | | | | | | | | | | | (219) op(e0, e2) = e2
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | | REF_CLOSE: (48), (58), (62), (193), (219) are inconsistent by
% 159.32/28.09 | | | | | | | | | | | | | sub-proof #1319.
% 159.32/28.09 | | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | (220) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 159.32/28.09 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | | REF_CLOSE: (27), (40), (62), (66), (69), (214), (220) are
% 159.32/28.09 | | | | | | | | | | | | inconsistent by sub-proof #1371.
% 159.32/28.09 | | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | | |
% 159.32/28.09 | | | | | | | | | End of split
% 159.32/28.09 | | | | | | | | |
% 159.32/28.09 | | | | | | | | End of split
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | End of split
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | End of split
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | End of split
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | End of split
% 159.32/28.09 | | | |
% 159.32/28.09 | | | Case 2:
% 159.32/28.09 | | | |
% 159.32/28.09 | | | | (221) all_58_12 = e0 & op(e0, e3) = e0
% 159.32/28.09 | | | |
% 159.32/28.09 | | | | ALPHA: (221) implies:
% 159.32/28.09 | | | | (222) all_58_12 = e0
% 159.32/28.09 | | | |
% 159.32/28.09 | | | | BETA: splitting (4) gives:
% 159.32/28.09 | | | |
% 159.32/28.09 | | | | Case 1:
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | (223) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 159.32/28.09 | | | | | e2) = e1)
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | BETA: splitting (223) gives:
% 159.32/28.09 | | | | |
% 159.32/28.09 | | | | | Case 1:
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | (224) all_58_1 = e1 & op(e3, e2) = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | ALPHA: (224) implies:
% 159.32/28.09 | | | | | | (225) all_58_1 = e1
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | BETA: splitting (32) gives:
% 159.32/28.09 | | | | | |
% 159.32/28.09 | | | | | | Case 1:
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | (226) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 159.32/28.09 | | | | | | | op(e2, e2) = e0)
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | BETA: splitting (226) gives:
% 159.32/28.09 | | | | | | |
% 159.32/28.09 | | | | | | | Case 1:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | (227) all_58_1 = e0 & op(e3, e2) = e0
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | REF_CLOSE: (49), (225), (227) are inconsistent by sub-proof
% 159.32/28.09 | | | | | | | | #1327.
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | Case 2:
% 159.32/28.09 | | | | | | | |
% 159.32/28.09 | | | | | | | | (228) all_58_3 = e0 & op(e2, e2) = e0
% 159.32/28.09 | | | | | | | |
% 159.32/28.10 | | | | | | | | REF_CLOSE: (23), (50), (228) are inconsistent by sub-proof #910.
% 159.32/28.10 | | | | | | | |
% 159.32/28.10 | | | | | | | End of split
% 159.32/28.10 | | | | | | |
% 159.32/28.10 | | | | | | Case 2:
% 159.32/28.10 | | | | | | |
% 159.32/28.10 | | | | | | | (229) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 159.32/28.10 | | | | | | | op(e0, e2) = e0)
% 159.32/28.10 | | | | | | |
% 159.32/28.10 | | | | | | | BETA: splitting (229) gives:
% 159.32/28.10 | | | | | | |
% 159.32/28.10 | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | |
% 159.32/28.10 | | | | | | | | (230) all_58_7 = e0 & op(e1, e2) = e0
% 159.32/28.10 | | | | | | | |
% 159.32/28.10 | | | | | | | | ALPHA: (230) implies:
% 159.32/28.10 | | | | | | | | (231) all_58_7 = e0
% 159.32/28.10 | | | | | | | |
% 159.32/28.10 | | | | | | | | BETA: splitting (22) gives:
% 159.32/28.10 | | | | | | | |
% 159.32/28.10 | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | |
% 159.32/28.10 | | | | | | | | | (232) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 159.32/28.10 | | | | | | | | | op(e1, e2) = e2)
% 159.32/28.10 | | | | | | | | |
% 159.32/28.10 | | | | | | | | | BETA: splitting (232) gives:
% 159.32/28.10 | | | | | | | | |
% 159.32/28.10 | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | (233) all_58_6 = e2 & op(e1, e3) = e2
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | ALPHA: (233) implies:
% 159.32/28.10 | | | | | | | | | | (234) all_58_6 = e2
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | REF_CLOSE: (13), (20), (23), (24), (31), (48), (49), (62),
% 159.32/28.10 | | | | | | | | | | (66), (67), (222), (234) are inconsistent by
% 159.32/28.10 | | | | | | | | | | sub-proof #1153.
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | (235) all_58_7 = e2 & op(e1, e2) = e2
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | REF_CLOSE: (27), (231), (235) are inconsistent by sub-proof
% 159.32/28.10 | | | | | | | | | | #746.
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | |
% 159.32/28.10 | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | |
% 159.32/28.10 | | | | | | | | | (236) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 159.32/28.10 | | | | | | | | | op(e1, e0) = e2)
% 159.32/28.10 | | | | | | | | |
% 159.32/28.10 | | | | | | | | | BETA: splitting (236) gives:
% 159.32/28.10 | | | | | | | | |
% 159.32/28.10 | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | (237) all_58_8 = e2 & op(e1, e1) = e2
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | REF_CLOSE: (7), (51), (62), (237) are inconsistent by
% 159.32/28.10 | | | | | | | | | | sub-proof #1440.
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | (238) all_58_11 = e2 & op(e1, e0) = e2
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | ALPHA: (238) implies:
% 159.32/28.10 | | | | | | | | | | (239) all_58_11 = e2
% 159.32/28.10 | | | | | | | | | | (240) op(e1, e0) = e2
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | BETA: splitting (35) gives:
% 159.32/28.10 | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | (241) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 159.32/28.10 | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 159.32/28.10 | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 159.32/28.10 | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 159.32/28.10 | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.32/28.10 | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 159.32/28.10 | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 159.32/28.10 | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.32/28.10 | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | BETA: splitting (241) gives:
% 159.32/28.10 | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | (242) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 159.32/28.10 | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 159.32/28.10 | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 159.32/28.10 | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 159.32/28.10 | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | BETA: splitting (242) gives:
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | (243) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 159.32/28.10 | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | ALPHA: (243) implies:
% 159.32/28.10 | | | | | | | | | | | | | (244) op(e2, e3) = e3
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | REF_CLOSE: (20), (31), (62), (66), (244) are inconsistent by
% 159.32/28.10 | | | | | | | | | | | | | sub-proof #1159.
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | (245) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 159.32/28.10 | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 159.32/28.10 | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | BETA: splitting (245) gives:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | (246) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | ALPHA: (246) implies:
% 159.32/28.10 | | | | | | | | | | | | | | (247) ~ (all_56_12 = e3)
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | REDUCE: (39), (247) imply:
% 159.32/28.10 | | | | | | | | | | | | | | (248) $false
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | (249) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 159.32/28.10 | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | ALPHA: (249) implies:
% 159.32/28.10 | | | | | | | | | | | | | | (250) all_56_6 = e3
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | COMBINE_EQS: (42), (250) imply:
% 159.32/28.10 | | | | | | | | | | | | | | (251) e3 = e1
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | REDUCE: (67), (251) imply:
% 159.32/28.10 | | | | | | | | | | | | | | (252) $false
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | CLOSE: (252) is inconsistent.
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | (253) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 159.32/28.10 | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 159.32/28.10 | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | BETA: splitting (253) gives:
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | (254) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | ALPHA: (254) implies:
% 159.32/28.10 | | | | | | | | | | | | | (255) ~ (all_56_12 = e3)
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | REDUCE: (39), (255) imply:
% 159.32/28.10 | | | | | | | | | | | | | (256) $false
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | (257) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 159.32/28.10 | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | BETA: splitting (257) gives:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | (258) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | ALPHA: (258) implies:
% 159.32/28.10 | | | | | | | | | | | | | | (259) all_56_9 = e3
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | COMBINE_EQS: (73), (259) imply:
% 159.32/28.10 | | | | | | | | | | | | | | (260) e3 = e0
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | REDUCE: (23), (260) imply:
% 159.32/28.10 | | | | | | | | | | | | | | (261) $false
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | CLOSE: (261) is inconsistent.
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | (262) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 159.32/28.10 | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | ALPHA: (262) implies:
% 159.32/28.10 | | | | | | | | | | | | | | (263) ~ (all_56_12 = e3)
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | REDUCE: (39), (263) imply:
% 159.32/28.10 | | | | | | | | | | | | | | (264) $false
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | CLOSE: (264) is inconsistent.
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | (265) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 159.32/28.10 | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 159.32/28.10 | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.32/28.10 | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 159.32/28.10 | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 159.32/28.10 | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 159.32/28.10 | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 159.32/28.10 | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 159.32/28.10 | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 159.32/28.10 | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.32/28.10 | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | BETA: splitting (265) gives:
% 159.32/28.10 | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | (266) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 159.32/28.10 | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 159.32/28.10 | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.32/28.10 | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 159.32/28.10 | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | BETA: splitting (266) gives:
% 159.32/28.10 | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | (267) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 159.32/28.10 | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | ALPHA: (267) implies:
% 159.32/28.10 | | | | | | | | | | | | | (268) ~ (all_56_14 = e1)
% 159.32/28.10 | | | | | | | | | | | | | (269) op(e2, e1) = e2
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | BETA: splitting (56) gives:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | (270) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.32/28.10 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (13), (18), (20), (22), (23),
% 159.32/28.10 | | | | | | | | | | | | | | (24), (27), (28), (31), (34), (48), (49), (50),
% 159.32/28.10 | | | | | | | | | | | | | | (51), (60), (61), (62), (66), (67), (225), (231),
% 159.32/28.10 | | | | | | | | | | | | | | (239), (270) are inconsistent by sub-proof #602.
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | (271) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.32/28.10 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | (272) all_58_7 = e2 & op(e1, e2) = e2
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | (273) all_58_7 = e2
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (273) are inconsistent by sub-proof
% 159.32/28.10 | | | | | | | | | | | | | | | #1086.
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | (274) all_58_13 = e2 & op(e0, e2) = e2
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | (275) all_58_13 = e2
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | (276) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 159.32/28.10 | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (13), (20), (22), (23), (24), (27),
% 159.32/28.10 | | | | | | | | | | | | | | | | (31), (48), (49), (50), (51), (61), (62), (66),
% 159.32/28.10 | | | | | | | | | | | | | | | | (67), (222), (225), (231), (239), (275), (276) are
% 159.32/28.10 | | | | | | | | | | | | | | | | inconsistent by sub-proof #601.
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | (277) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 159.32/28.10 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | (278) all_58_14 = e1 & op(e0, e1) = e1
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (279) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (280) all_58_4 = e2 & op(e3, e1) = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | (281) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (282) all_58_4 = e0 & op(e3, e1) = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (283) all_58_4 = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (14), (23), (27), (31), (37),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (48), (49), (50), (51), (62), (64), (67), (275),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (283) are inconsistent by sub-proof #599.
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (284) all_58_5 = e0 & op(e2, e1) = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (285) op(e2, e1) = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (286) all_58_4 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_52_9, e0, e1, e2,
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (285) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (287) all_52_9 = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_52_9, e2, e1, e2,
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (269) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (288) all_52_9 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (288) imply:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (289) e2 = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (289) imply:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (290) all_58_4 = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (14), (23), (27), (31), (37),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (48), (49), (50), (51), (62), (64), (67), (275),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (290) are inconsistent by sub-proof #599.
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | (291) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (292) all_58_8 = e0 & op(e1, e1) = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (292) are inconsistent by sub-proof
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | #598.
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (293) all_58_14 = e0 & op(e0, e1) = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (294) op(e0, e1) = e0
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (23), (40), (48), (49), (50), (62),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | (64), (67), (225), (231), (275), (278), (294) are
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #597.
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (295) all_58_5 = e2 & op(e2, e1) = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (296) all_58_5 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (27), (31), (37), (48), (49), (50),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (62), (67), (296) are inconsistent by sub-proof
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | #898.
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (297) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 159.32/28.10 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (298) all_58_8 = e2 & op(e1, e1) = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (299) all_58_8 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (23), (27), (28), (34), (48), (49),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (60), (62), (66), (67), (239), (299) are
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1068.
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (300) all_58_14 = e2 & op(e0, e1) = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (301) all_58_14 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (23), (27), (48), (49), (64), (67),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (275), (301) are inconsistent by sub-proof #1204.
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | (302) all_58_15 = e1 & op(e0, e0) = e1
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (302) are inconsistent by sub-proof
% 159.32/28.10 | | | | | | | | | | | | | | | | | #1010.
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | (303) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.32/28.10 | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 159.32/28.10 | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | BETA: splitting (303) gives:
% 159.32/28.10 | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | (304) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.32/28.10 | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | ALPHA: (304) implies:
% 159.32/28.10 | | | | | | | | | | | | | | (305) ~ (all_56_13 = e2)
% 159.32/28.10 | | | | | | | | | | | | | | (306) op(e2, e1) = e1
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | (307) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (13), (18), (20), (22), (23),
% 159.32/28.10 | | | | | | | | | | | | | | | (24), (27), (28), (31), (34), (48), (49), (50),
% 159.32/28.10 | | | | | | | | | | | | | | | (51), (60), (61), (62), (66), (67), (225), (231),
% 159.32/28.10 | | | | | | | | | | | | | | | (239), (307) are inconsistent by sub-proof #602.
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | (308) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.32/28.10 | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | (309) all_58_7 = e2 & op(e1, e2) = e2
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | (310) all_58_7 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (310) are inconsistent by sub-proof
% 159.32/28.10 | | | | | | | | | | | | | | | | #1086.
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | (311) all_58_13 = e2 & op(e0, e2) = e2
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | (312) all_58_13 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | (313) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 159.32/28.10 | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (13), (20), (22), (23), (24), (27),
% 159.32/28.10 | | | | | | | | | | | | | | | | | (31), (48), (49), (50), (51), (61), (62), (66),
% 159.32/28.10 | | | | | | | | | | | | | | | | | (67), (222), (225), (231), (239), (312), (313) are
% 159.32/28.10 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #601.
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | (314) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 159.32/28.10 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (315) all_58_14 = e1 & op(e0, e1) = e1
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (316) all_58_14 = e1
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (11), (14), (19), (23),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (27), (31), (33), (37), (48), (49), (50), (51),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (62), (64), (67), (225), (231), (306), (311),
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (312), (316) are inconsistent by sub-proof #596.
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (317) all_58_15 = e1 & op(e0, e0) = e1
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (317) are inconsistent by sub-proof
% 159.32/28.10 | | | | | | | | | | | | | | | | | | #1010.
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | End of split
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | (318) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 159.32/28.10 | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | ALPHA: (318) implies:
% 159.32/28.10 | | | | | | | | | | | | | | (319) ~ (all_56_15 = e0)
% 159.32/28.10 | | | | | | | | | | | | | | (320) op(e2, e0) = e2
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 159.32/28.10 | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | (321) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (13), (18), (20), (22), (23),
% 159.32/28.10 | | | | | | | | | | | | | | | (24), (27), (28), (31), (34), (48), (49), (50),
% 159.32/28.10 | | | | | | | | | | | | | | | (51), (60), (61), (62), (66), (67), (225), (231),
% 159.32/28.10 | | | | | | | | | | | | | | | (239), (321) are inconsistent by sub-proof #602.
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | (322) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.32/28.10 | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 159.32/28.10 | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | (323) all_58_7 = e2 & op(e1, e2) = e2
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | (324) all_58_7 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (324) are inconsistent by sub-proof
% 159.32/28.10 | | | | | | | | | | | | | | | | #1086.
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | (325) all_58_13 = e2 & op(e0, e2) = e2
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | (326) all_58_13 = e2
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | (327) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 159.32/28.10 | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (13), (20), (22), (23), (24), (27),
% 159.32/28.10 | | | | | | | | | | | | | | | | | (31), (48), (49), (50), (51), (61), (62), (66),
% 159.32/28.10 | | | | | | | | | | | | | | | | | (67), (222), (225), (231), (239), (326), (327) are
% 159.32/28.10 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #601.
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | (328) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 159.32/28.10 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (329) all_58_14 = e1 & op(e0, e1) = e1
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | (330) all_58_14 = e1
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 159.32/28.10 | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | Case 1:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | (331) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (48), (50), (62), (67), (331) are
% 159.32/28.10 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.32/28.10 | | | | | | | | | | | | | | | | | | Case 2:
% 159.32/28.10 | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | (332) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.49/28.10 | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (333) all_58_5 = e1 & op(e2, e1) = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (334) op(e2, e1) = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (11), (14), (19), (23),
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (27), (31), (33), (37), (48), (49), (50), (51),
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (62), (64), (67), (225), (231), (325), (326),
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (330), (334) are inconsistent by sub-proof #596.
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (335) all_58_10 = e1 & op(e2, e0) = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (336) op(e2, e0) = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_52_13, e1, e0, e2,
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | simplifying with (30), (336) gives:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (337) all_52_13 = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_52_13, e2, e0, e2,
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | simplifying with (30), (320) gives:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (338) all_52_13 = e2
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (337), (338) imply:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (339) e2 = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | SIMP: (339) implies:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (340) e2 = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (340) imply:
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (341) all_58_11 = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (20), (22), (23), (24), (27), (31),
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (48), (49), (51), (61), (62), (66), (67), (231),
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | | (341) are inconsistent by sub-proof #743.
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.10 | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | (342) all_58_15 = e1 & op(e0, e0) = e1
% 159.49/28.10 | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (342) are inconsistent by sub-proof
% 159.49/28.10 | | | | | | | | | | | | | | | | | | #1010.
% 159.49/28.10 | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | Case 2:
% 159.49/28.10 | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | (343) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 159.49/28.10 | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 159.49/28.10 | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 159.49/28.10 | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 159.49/28.10 | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 159.49/28.10 | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.49/28.10 | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | BETA: splitting (343) gives:
% 159.49/28.10 | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | (344) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 159.49/28.10 | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | ALPHA: (344) implies:
% 159.49/28.10 | | | | | | | | | | | | | (345) ~ (all_56_13 = e2)
% 159.49/28.10 | | | | | | | | | | | | | (346) op(e0, e2) = e0
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | BETA: splitting (56) gives:
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | (347) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.49/28.10 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (13), (18), (20), (22), (23),
% 159.49/28.10 | | | | | | | | | | | | | | (24), (27), (28), (31), (34), (48), (49), (50),
% 159.49/28.10 | | | | | | | | | | | | | | (51), (60), (61), (62), (66), (67), (225), (231),
% 159.49/28.10 | | | | | | | | | | | | | | (239), (347) are inconsistent by sub-proof #602.
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | Case 2:
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | (348) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.49/28.10 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | (349) all_58_7 = e2 & op(e1, e2) = e2
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | ALPHA: (349) implies:
% 159.49/28.10 | | | | | | | | | | | | | | | (350) all_58_7 = e2
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (350) are inconsistent by sub-proof
% 159.49/28.10 | | | | | | | | | | | | | | | #1086.
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | Case 2:
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | (351) all_58_13 = e2 & op(e0, e2) = e2
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | ALPHA: (351) implies:
% 159.49/28.10 | | | | | | | | | | | | | | | (352) op(e0, e2) = e2
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | REF_CLOSE: (27), (58), (62), (346), (352) are inconsistent by
% 159.49/28.10 | | | | | | | | | | | | | | | sub-proof #1040.
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | End of split
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | Case 2:
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | (353) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 159.49/28.10 | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 159.49/28.10 | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 159.49/28.10 | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | BETA: splitting (353) gives:
% 159.49/28.10 | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | (354) all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 159.49/28.10 | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | ALPHA: (354) implies:
% 159.49/28.10 | | | | | | | | | | | | | | (355) ~ (all_56_15 = e0)
% 159.49/28.10 | | | | | | | | | | | | | | (356) op(e1, e0) = e1
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 159.49/28.10 | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | (357) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.49/28.10 | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (13), (18), (20), (22), (23),
% 159.49/28.10 | | | | | | | | | | | | | | | (24), (27), (28), (31), (34), (48), (49), (50),
% 159.49/28.10 | | | | | | | | | | | | | | | (51), (60), (61), (62), (66), (67), (225), (231),
% 159.49/28.10 | | | | | | | | | | | | | | | (239), (357) are inconsistent by sub-proof #602.
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | Case 2:
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | (358) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.49/28.10 | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | BETA: splitting (358) gives:
% 159.49/28.10 | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | (359) all_58_7 = e2 & op(e1, e2) = e2
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | ALPHA: (359) implies:
% 159.49/28.10 | | | | | | | | | | | | | | | | (360) all_58_7 = e2
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (360) are inconsistent by sub-proof
% 159.49/28.10 | | | | | | | | | | | | | | | | #1086.
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | Case 2:
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | (361) all_58_13 = e2 & op(e0, e2) = e2
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 159.49/28.10 | | | | | | | | | | | | | | | | (362) all_58_13 = e2
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 159.49/28.10 | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | (363) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 159.49/28.10 | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 159.49/28.10 | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | BETA: splitting (363) gives:
% 159.49/28.10 | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.10 | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | (364) all_58_0 = e0 & op(e3, e3) = e0
% 159.49/28.10 | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (44), (364) are inconsistent by sub-proof
% 159.49/28.10 | | | | | | | | | | | | | | | | | | #859.
% 159.49/28.10 | | | | | | | | | | | | | | | | | |
% 159.49/28.10 | | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (365) all_58_1 = e0 & op(e3, e2) = e0
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | ALPHA: (365) implies:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (366) all_58_1 = e0
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (50), (67), (231), (362), (366)
% 159.49/28.11 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #752.
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | (367) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 159.49/28.11 | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | BETA: splitting (367) gives:
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (368) all_58_4 = e0 & op(e3, e1) = e0
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (369) all_58_4 = e0
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (14), (23), (27), (31), (37),
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (48), (49), (50), (51), (62), (64), (67), (362),
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (369) are inconsistent by sub-proof #599.
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (370) all_58_9 = e0 & op(e3, e0) = e0
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (371) all_58_9 = e0
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | (372) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.49/28.11 | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (373) all_58_9 = e1 & op(e3, e0) = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (50), (67), (225), (231), (362),
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (371), (373) are inconsistent by sub-proof #595.
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_52_14, e1, e0, e1,
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | simplifying with (59), (356) gives:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (374) all_52_14 = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with all_52_14, e2, e0, e1,
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | simplifying with (59), (240) gives:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (375) all_52_14 = e2
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (375) imply:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (376) e2 = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (376) imply:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (377) all_58_11 = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (20), (22), (23), (24), (27), (31),
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (48), (49), (51), (61), (62), (66), (67), (231),
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (377) are inconsistent by sub-proof #743.
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | (378) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.49/28.11 | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (379) all_58_11 = e1 & op(e1, e0) = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (379) implies:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (380) all_58_11 = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (20), (22), (23), (24), (27), (31),
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (48), (49), (51), (61), (62), (66), (67), (231),
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (380) are inconsistent by sub-proof #743.
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | (381) all_58_15 = e1 & op(e0, e0) = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (381) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | | #1010.
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | (382) all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 159.49/28.11 | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 159.49/28.11 | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | ALPHA: (382) implies:
% 159.49/28.11 | | | | | | | | | | | | | | (383) ~ (all_56_14 = e1)
% 159.49/28.11 | | | | | | | | | | | | | | (384) op(e0, e1) = e0
% 159.49/28.11 | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 159.49/28.11 | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | (385) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.49/28.11 | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.49/28.11 | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (13), (18), (20), (22), (23),
% 159.49/28.11 | | | | | | | | | | | | | | | (24), (27), (28), (31), (34), (48), (49), (50),
% 159.49/28.11 | | | | | | | | | | | | | | | (51), (60), (61), (62), (66), (67), (225), (231),
% 159.49/28.11 | | | | | | | | | | | | | | | (239), (385) are inconsistent by sub-proof #602.
% 159.49/28.11 | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | (386) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.49/28.11 | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.49/28.11 | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | BETA: splitting (386) gives:
% 159.49/28.11 | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | (387) all_58_7 = e2 & op(e1, e2) = e2
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | ALPHA: (387) implies:
% 159.49/28.11 | | | | | | | | | | | | | | | | (388) all_58_7 = e2
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (388) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | | | | | | | | | #1086.
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | (389) all_58_13 = e2 & op(e0, e2) = e2
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | ALPHA: (389) implies:
% 159.49/28.11 | | | | | | | | | | | | | | | | (390) all_58_13 = e2
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | (391) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 159.49/28.11 | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (13), (20), (22), (23), (24), (27),
% 159.49/28.11 | | | | | | | | | | | | | | | | | (31), (48), (49), (50), (51), (61), (62), (66),
% 159.49/28.11 | | | | | | | | | | | | | | | | | (67), (222), (225), (231), (239), (390), (391) are
% 159.49/28.11 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #601.
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | (392) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 159.49/28.11 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | BETA: splitting (392) gives:
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (393) all_58_14 = e1 & op(e0, e1) = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (23), (40), (48), (49), (50), (62),
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (64), (67), (225), (231), (384), (390), (393) are
% 159.49/28.11 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #597.
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | (394) all_58_15 = e1 & op(e0, e0) = e1
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (394) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | | | | | | | | | | | #1010.
% 159.49/28.11 | | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | |
% 159.49/28.11 | | | | | | | | End of split
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | (395) all_58_13 = e0 & op(e0, e2) = e0
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | ALPHA: (395) implies:
% 159.49/28.11 | | | | | | | | (396) all_58_13 = e0
% 159.49/28.11 | | | | | | | | (397) op(e0, e2) = e0
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | REF_CLOSE: (2), (9), (13), (20), (23), (24), (26), (27), (31),
% 159.49/28.11 | | | | | | | | (48), (49), (58), (61), (62), (66), (67), (69),
% 159.49/28.11 | | | | | | | | (222), (396), (397) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | #621.
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | End of split
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | End of split
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | Case 2:
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | (398) all_58_3 = e1 & op(e2, e2) = e1
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | ALPHA: (398) implies:
% 159.49/28.11 | | | | | | (399) all_58_3 = e1
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | REF_CLOSE: (50), (67), (399) are inconsistent by sub-proof #841.
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | End of split
% 159.49/28.11 | | | | |
% 159.49/28.11 | | | | Case 2:
% 159.49/28.11 | | | | |
% 159.49/28.11 | | | | | (400) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 159.49/28.11 | | | | | e2) = e1)
% 159.49/28.11 | | | | |
% 159.49/28.11 | | | | | BETA: splitting (400) gives:
% 159.49/28.11 | | | | |
% 159.49/28.11 | | | | | Case 1:
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | (401) all_58_7 = e1 & op(e1, e2) = e1
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | ALPHA: (401) implies:
% 159.49/28.11 | | | | | | (402) all_58_7 = e1
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | BETA: splitting (22) gives:
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | Case 1:
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | | (403) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 159.49/28.11 | | | | | | | op(e1, e2) = e2)
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | | BETA: splitting (403) gives:
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | (404) all_58_6 = e2 & op(e1, e3) = e2
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | ALPHA: (404) implies:
% 159.49/28.11 | | | | | | | | (405) all_58_6 = e2
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | REF_CLOSE: (13), (20), (23), (24), (31), (48), (49), (62), (66),
% 159.49/28.11 | | | | | | | | (67), (222), (405) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | #1153.
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | (406) all_58_7 = e2 & op(e1, e2) = e2
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | ALPHA: (406) implies:
% 159.49/28.11 | | | | | | | | (407) all_58_7 = e2
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | REF_CLOSE: (48), (402), (407) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | #721.
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | End of split
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | Case 2:
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | | (408) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 159.49/28.11 | | | | | | | op(e1, e0) = e2)
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | | BETA: splitting (408) gives:
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | (409) all_58_8 = e2 & op(e1, e1) = e2
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | REF_CLOSE: (7), (51), (62), (409) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | #1440.
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | (410) all_58_11 = e2 & op(e1, e0) = e2
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | ALPHA: (410) implies:
% 159.49/28.11 | | | | | | | | (411) all_58_11 = e2
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | BETA: splitting (24) gives:
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | |
% 159.49/28.11 | | | | | | | | | (412) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 159.49/28.11 | | | | | | | | | op(e2, e3) = e1)
% 159.49/28.11 | | | | | | | | |
% 159.49/28.11 | | | | | | | | | REF_CLOSE: (31), (44), (48), (62), (67), (412) are
% 159.49/28.11 | | | | | | | | | inconsistent by sub-proof #809.
% 159.49/28.11 | | | | | | | | |
% 159.49/28.11 | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | |
% 159.49/28.11 | | | | | | | | | (413) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 159.49/28.11 | | | | | | | | | op(e0, e3) = e1)
% 159.49/28.11 | | | | | | | | |
% 159.49/28.11 | | | | | | | | | BETA: splitting (413) gives:
% 159.49/28.11 | | | | | | | | |
% 159.49/28.11 | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | (414) all_58_6 = e1 & op(e1, e3) = e1
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | ALPHA: (414) implies:
% 159.49/28.11 | | | | | | | | | | (415) all_58_6 = e1
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | BETA: splitting (28) gives:
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | (416) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 159.49/28.11 | | | | | | | | | | | & op(e1, e2) = e0)
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | BETA: splitting (416) gives:
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | (417) all_58_6 = e0 & op(e1, e3) = e0
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | REF_CLOSE: (49), (415), (417) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | | | | | #1360.
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | (418) all_58_7 = e0 & op(e1, e2) = e0
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | REF_CLOSE: (49), (402), (418) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | | | | | #992.
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | (419) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 159.49/28.11 | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | BETA: splitting (419) gives:
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | Case 1:
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | (420) all_58_8 = e0 & op(e1, e1) = e0
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | ALPHA: (420) implies:
% 159.49/28.11 | | | | | | | | | | | | (421) all_58_8 = e0
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | REF_CLOSE: (11), (23), (421) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | | | | | #781.
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | (422) all_58_11 = e0 & op(e1, e0) = e0
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | ALPHA: (422) implies:
% 159.49/28.11 | | | | | | | | | | | | (423) all_58_11 = e0
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | | REF_CLOSE: (27), (411), (423) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | | | | | #1458.
% 159.49/28.11 | | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | Case 2:
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | (424) all_58_12 = e1 & op(e0, e3) = e1
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | | REF_CLOSE: (49), (222), (424) are inconsistent by sub-proof
% 159.49/28.11 | | | | | | | | | | #1422.
% 159.49/28.11 | | | | | | | | | |
% 159.49/28.11 | | | | | | | | | End of split
% 159.49/28.11 | | | | | | | | |
% 159.49/28.11 | | | | | | | | End of split
% 159.49/28.11 | | | | | | | |
% 159.49/28.11 | | | | | | | End of split
% 159.49/28.11 | | | | | | |
% 159.49/28.11 | | | | | | End of split
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | Case 2:
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | (425) all_58_13 = e1 & op(e0, e2) = e1
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | ALPHA: (425) implies:
% 159.49/28.11 | | | | | | (426) op(e0, e2) = e1
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | | REF_CLOSE: (2), (9), (13), (19), (20), (23), (24), (26), (27), (31),
% 159.49/28.11 | | | | | | (34), (35), (39), (40), (42), (45), (48), (49), (53),
% 159.49/28.11 | | | | | | (55), (58), (61), (62), (66), (67), (69), (73), (222),
% 159.49/28.11 | | | | | | (425), (426) are inconsistent by sub-proof #603.
% 159.49/28.11 | | | | | |
% 159.49/28.11 | | | | | End of split
% 159.49/28.11 | | | | |
% 159.49/28.11 | | | | End of split
% 159.49/28.11 | | | |
% 159.49/28.11 | | | End of split
% 159.49/28.11 | | |
% 159.49/28.11 | | End of split
% 159.49/28.11 | |
% 159.49/28.11 | End of split
% 159.49/28.11 |
% 159.49/28.11 End of proof
% 159.49/28.11
% 159.49/28.11 Sub-proof #595 shows that the following formulas are inconsistent:
% 159.49/28.11 ----------------------------------------------------------------
% 159.49/28.11 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.49/28.11 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.49/28.11 (2) all_58_7 = e0
% 159.49/28.11 (3) all_58_9 = e1 & op(e3, e0) = e1
% 159.49/28.11 (4) ~ (e3 = e1)
% 159.49/28.11 (5) all_58_1 = e1
% 159.49/28.11 (6) all_58_9 = e0
% 159.49/28.11 (7) ~ (e2 = e1)
% 159.49/28.11 (8) ~ (e1 = e0)
% 159.49/28.11 (9) all_58_3 = e3
% 159.49/28.11 (10) all_58_13 = e2
% 159.49/28.11
% 159.49/28.11 Begin of proof
% 159.49/28.11 |
% 159.49/28.11 | ALPHA: (3) implies:
% 159.49/28.11 | (11) all_58_9 = e1
% 159.49/28.11 |
% 159.49/28.11 | COMBINE_EQS: (6), (11) imply:
% 159.49/28.11 | (12) e1 = e0
% 159.49/28.11 |
% 159.49/28.11 | SIMP: (12) implies:
% 159.49/28.11 | (13) e1 = e0
% 159.49/28.11 |
% 159.49/28.11 | COMBINE_EQS: (5), (13) imply:
% 159.49/28.11 | (14) all_58_1 = e0
% 159.49/28.11 |
% 159.49/28.11 | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (14) are inconsistent by
% 159.49/28.11 | sub-proof #752.
% 159.49/28.11 |
% 159.49/28.11 End of proof
% 159.49/28.11
% 159.49/28.11 Sub-proof #596 shows that the following formulas are inconsistent:
% 159.49/28.11 ----------------------------------------------------------------
% 159.49/28.11 (1) all_58_15 = e3
% 159.49/28.11 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.49/28.11 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.49/28.11 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.49/28.11 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.49/28.11 (4) op(e1, e1) = all_6_2
% 159.49/28.11 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.49/28.11 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.49/28.11 (6) all_58_8 = e3
% 159.49/28.11 (7) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.49/28.11 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.49/28.11 (8) all_58_7 = e0
% 159.49/28.11 (9) op(e2, e1) = all_52_9
% 159.49/28.11 (10) all_58_14 = e1
% 159.49/28.11 (11) ~ (e3 = e0)
% 159.49/28.11 (12) ~ (e2 = e0)
% 159.49/28.11 (13) op(e2, e3) = e2
% 159.49/28.11 (14) ~ (e3 = e1)
% 159.49/28.11 (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.49/28.11 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.49/28.11 (16) all_58_1 = e1
% 159.49/28.11 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.49/28.11 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.49/28.11 (18) op(e2, e1) = e1
% 159.49/28.11 (19) all_58_13 = e2 & op(e0, e2) = e2
% 159.49/28.11 (20) ~ (e2 = e1)
% 159.49/28.11 (21) ~ (e1 = e0)
% 159.49/28.11 (22) all_58_3 = e3
% 159.49/28.11 (23) ~ (all_6_2 = e2)
% 159.49/28.11 (24) all_58_13 = e2
% 159.49/28.11 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.49/28.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.49/28.11 (26) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.49/28.11 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.49/28.11 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.49/28.11 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.49/28.11
% 159.49/28.11 Begin of proof
% 159.49/28.11 |
% 159.49/28.11 | BETA: splitting (15) gives:
% 159.49/28.11 |
% 159.49/28.11 | Case 1:
% 159.49/28.11 | |
% 159.49/28.11 | | (27) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 159.49/28.11 | | e0)
% 159.49/28.11 | |
% 159.49/28.11 | | BETA: splitting (27) gives:
% 159.49/28.11 | |
% 159.49/28.11 | | Case 1:
% 159.49/28.11 | | |
% 159.49/28.11 | | | (28) all_58_4 = e0 & op(e3, e1) = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | ALPHA: (28) implies:
% 159.49/28.11 | | | (29) all_58_4 = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | REF_CLOSE: (1), (3), (4), (5), (7), (11), (12), (13), (14), (17), (20),
% 159.49/28.11 | | | (21), (22), (23), (24), (25), (26), (29) are inconsistent by
% 159.49/28.11 | | | sub-proof #599.
% 159.49/28.11 | | |
% 159.49/28.11 | | Case 2:
% 159.49/28.11 | | |
% 159.49/28.11 | | | (30) all_58_5 = e0 & op(e2, e1) = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | ALPHA: (30) implies:
% 159.49/28.11 | | | (31) op(e2, e1) = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | GROUND_INST: instantiating (25) with all_52_9, e0, e1, e2, simplifying
% 159.49/28.11 | | | with (9), (31) gives:
% 159.49/28.11 | | | (32) all_52_9 = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | GROUND_INST: instantiating (25) with all_52_9, e1, e1, e2, simplifying
% 159.49/28.11 | | | with (9), (18) gives:
% 159.49/28.11 | | | (33) all_52_9 = e1
% 159.49/28.11 | | |
% 159.49/28.11 | | | COMBINE_EQS: (32), (33) imply:
% 159.49/28.11 | | | (34) e1 = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | COMBINE_EQS: (16), (34) imply:
% 159.49/28.11 | | | (35) all_58_1 = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | REF_CLOSE: (2), (8), (14), (20), (21), (22), (24), (35) are inconsistent
% 159.49/28.11 | | | by sub-proof #752.
% 159.49/28.11 | | |
% 159.49/28.11 | | End of split
% 159.49/28.11 | |
% 159.49/28.11 | Case 2:
% 159.49/28.11 | |
% 159.49/28.11 | | (36) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 159.49/28.11 | | e0)
% 159.49/28.11 | |
% 159.49/28.11 | | BETA: splitting (36) gives:
% 159.49/28.11 | |
% 159.49/28.11 | | Case 1:
% 159.49/28.11 | | |
% 159.49/28.11 | | | (37) all_58_8 = e0 & op(e1, e1) = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | REF_CLOSE: (6), (11), (37) are inconsistent by sub-proof #598.
% 159.49/28.11 | | |
% 159.49/28.11 | | Case 2:
% 159.49/28.11 | | |
% 159.49/28.11 | | | (38) all_58_14 = e0 & op(e0, e1) = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | ALPHA: (38) implies:
% 159.49/28.11 | | | (39) all_58_14 = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | COMBINE_EQS: (10), (39) imply:
% 159.49/28.11 | | | (40) e1 = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | COMBINE_EQS: (16), (40) imply:
% 159.49/28.11 | | | (41) all_58_1 = e0
% 159.49/28.11 | | |
% 159.49/28.11 | | | REF_CLOSE: (2), (8), (14), (20), (21), (22), (24), (41) are inconsistent
% 159.49/28.11 | | | by sub-proof #752.
% 159.49/28.11 | | |
% 159.49/28.11 | | End of split
% 159.49/28.11 | |
% 159.49/28.11 | End of split
% 159.49/28.11 |
% 159.49/28.11 End of proof
% 159.49/28.11
% 159.49/28.11 Sub-proof #597 shows that the following formulas are inconsistent:
% 159.49/28.11 ----------------------------------------------------------------
% 159.49/28.11 (1) all_58_15 = e3
% 159.49/28.11 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.49/28.11 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.49/28.11 (3) all_58_14 = e1 & op(e0, e1) = e1
% 159.49/28.11 (4) all_58_7 = e0
% 159.49/28.11 (5) ~ (e3 = e0)
% 159.49/28.11 (6) ~ (e3 = e1)
% 159.49/28.11 (7) all_58_1 = e1
% 159.49/28.11 (8) op(e0, e1) = all_52_11
% 159.49/28.11 (9) ~ (e2 = e1)
% 159.49/28.11 (10) ~ (e1 = e0)
% 159.49/28.11 (11) op(e0, e1) = e0
% 159.49/28.11 (12) all_58_3 = e3
% 159.49/28.11 (13) all_58_13 = e2
% 159.49/28.11 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.49/28.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.49/28.11 (15) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.49/28.11 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.49/28.11 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.49/28.11 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.49/28.11
% 159.49/28.11 Begin of proof
% 159.49/28.11 |
% 159.49/28.11 | BETA: splitting (15) gives:
% 159.49/28.11 |
% 159.49/28.11 | Case 1:
% 159.49/28.11 | |
% 159.49/28.11 | | (16) all_58_15 = e0 & op(e0, e0) = e0
% 159.49/28.11 | |
% 159.49/28.11 | | REF_CLOSE: (1), (5), (16) are inconsistent by sub-proof #1013.
% 159.49/28.11 | |
% 159.49/28.11 | Case 2:
% 159.49/28.11 | |
% 159.49/28.11 | |
% 159.49/28.11 | | ALPHA: (3) implies:
% 159.49/28.11 | | (17) op(e0, e1) = e1
% 159.49/28.11 | |
% 159.49/28.11 | | GROUND_INST: instantiating (14) with all_52_11, e0, e1, e0, simplifying with
% 159.49/28.11 | | (8), (11) gives:
% 159.49/28.11 | | (18) all_52_11 = e0
% 159.49/28.11 | |
% 159.49/28.11 | | GROUND_INST: instantiating (14) with all_52_11, e1, e1, e0, simplifying with
% 159.49/28.11 | | (8), (17) gives:
% 159.49/28.11 | | (19) all_52_11 = e1
% 159.49/28.11 | |
% 159.49/28.11 | | COMBINE_EQS: (18), (19) imply:
% 159.49/28.11 | | (20) e1 = e0
% 159.49/28.11 | |
% 159.49/28.11 | | SIMP: (20) implies:
% 159.49/28.11 | | (21) e1 = e0
% 159.49/28.11 | |
% 159.49/28.11 | | COMBINE_EQS: (7), (21) imply:
% 159.49/28.11 | | (22) all_58_1 = e0
% 159.49/28.11 | |
% 159.49/28.11 | | REF_CLOSE: (2), (4), (6), (9), (10), (12), (13), (22) are inconsistent by
% 159.49/28.11 | | sub-proof #752.
% 159.49/28.11 | |
% 159.49/28.11 | End of split
% 159.49/28.11 |
% 159.49/28.11 End of proof
% 159.49/28.11
% 159.49/28.11 Sub-proof #598 shows that the following formulas are inconsistent:
% 159.49/28.11 ----------------------------------------------------------------
% 159.49/28.11 (1) all_58_8 = e0 & op(e1, e1) = e0
% 159.49/28.11 (2) all_58_8 = e3
% 159.49/28.11 (3) ~ (e3 = e0)
% 159.49/28.11
% 159.49/28.11 Begin of proof
% 159.49/28.11 |
% 159.49/28.11 | ALPHA: (1) implies:
% 159.49/28.11 | (4) all_58_8 = e0
% 159.49/28.11 |
% 159.49/28.11 | COMBINE_EQS: (2), (4) imply:
% 159.49/28.11 | (5) e3 = e0
% 159.49/28.11 |
% 159.49/28.11 | REDUCE: (3), (5) imply:
% 159.49/28.11 | (6) $false
% 159.49/28.11 |
% 159.49/28.11 | CLOSE: (6) is inconsistent.
% 159.49/28.11 |
% 159.49/28.11 End of proof
% 159.49/28.11
% 159.49/28.11 Sub-proof #599 shows that the following formulas are inconsistent:
% 159.49/28.11 ----------------------------------------------------------------
% 159.49/28.11 (1) all_58_15 = e3
% 159.49/28.11 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.49/28.11 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.49/28.11 (3) op(e1, e1) = all_6_2
% 159.49/28.11 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.49/28.11 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.49/28.11 (5) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.49/28.11 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.49/28.11 (6) ~ (e3 = e0)
% 159.49/28.11 (7) ~ (e2 = e0)
% 159.49/28.11 (8) op(e2, e3) = e2
% 159.49/28.11 (9) ~ (e3 = e1)
% 159.49/28.11 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.49/28.11 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.49/28.11 (11) ~ (e2 = e1)
% 159.49/28.11 (12) ~ (e1 = e0)
% 159.49/28.11 (13) all_58_3 = e3
% 159.49/28.11 (14) all_58_4 = e0
% 159.49/28.11 (15) ~ (all_6_2 = e2)
% 159.49/28.11 (16) all_58_13 = e2
% 159.49/28.11 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.49/28.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.49/28.11 (18) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.49/28.11 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.49/28.11 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.49/28.11 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.49/28.11
% 159.49/28.11 Begin of proof
% 159.49/28.11 |
% 159.49/28.11 | BETA: splitting (5) gives:
% 159.49/28.11 |
% 159.49/28.11 | Case 1:
% 159.49/28.11 | |
% 159.49/28.11 | | (19) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 159.49/28.11 | | e2)
% 159.49/28.11 | |
% 159.49/28.11 | | REF_CLOSE: (2), (6), (7), (8), (9), (10), (11), (12), (13), (14), (17), (19)
% 159.49/28.11 | | are inconsistent by sub-proof #855.
% 159.49/28.11 | |
% 159.49/28.11 | Case 2:
% 159.49/28.11 | |
% 159.49/28.11 | | (20) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 159.49/28.11 | | e2)
% 159.49/28.11 | |
% 159.49/28.11 | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (12), (15), (16), (17), (18),
% 159.49/28.11 | | (20) are inconsistent by sub-proof #600.
% 159.49/28.11 | |
% 159.49/28.11 | End of split
% 159.49/28.11 |
% 159.49/28.11 End of proof
% 159.49/28.11
% 159.49/28.11 Sub-proof #600 shows that the following formulas are inconsistent:
% 159.49/28.11 ----------------------------------------------------------------
% 159.49/28.11 (1) all_58_15 = e3
% 159.49/28.11 (2) op(e1, e1) = all_6_2
% 159.49/28.11 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.49/28.11 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.49/28.11 (4) ~ (e3 = e0)
% 159.49/28.11 (5) ~ (e2 = e0)
% 159.49/28.11 (6) ~ (e3 = e1)
% 159.49/28.11 (7) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.49/28.11 (8) ~ (e2 = e1)
% 159.49/28.11 (9) ~ (e1 = e0)
% 159.49/28.11 (10) ~ (all_6_2 = e2)
% 159.49/28.11 (11) all_58_13 = e2
% 159.49/28.11 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.49/28.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.49/28.11 (13) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.49/28.11 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.49/28.11 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.49/28.11 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.49/28.11
% 159.49/28.11 Begin of proof
% 159.49/28.11 |
% 159.49/28.11 | BETA: splitting (7) gives:
% 159.49/28.11 |
% 159.49/28.11 | Case 1:
% 159.49/28.11 | |
% 159.49/28.11 | | (14) all_58_8 = e2 & op(e1, e1) = e2
% 159.49/28.11 | |
% 159.49/28.11 | | REF_CLOSE: (2), (10), (12), (14) are inconsistent by sub-proof #1440.
% 159.49/28.11 | |
% 159.49/28.11 | Case 2:
% 159.49/28.11 | |
% 159.49/28.11 | | (15) all_58_14 = e2 & op(e0, e1) = e2
% 159.49/28.11 | |
% 159.49/28.11 | | ALPHA: (15) implies:
% 159.49/28.11 | | (16) all_58_14 = e2
% 159.49/28.11 | |
% 159.49/28.11 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11), (13), (16) are
% 159.49/28.11 | | inconsistent by sub-proof #1204.
% 159.49/28.11 | |
% 159.49/28.11 | End of split
% 159.49/28.11 |
% 159.49/28.11 End of proof
% 159.49/28.11
% 159.49/28.11 Sub-proof #601 shows that the following formulas are inconsistent:
% 159.49/28.11 ----------------------------------------------------------------
% 159.49/28.11 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.49/28.11 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.49/28.11 (2) op(e1, e1) = all_6_2
% 159.49/28.11 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.49/28.11 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.49/28.11 (4) all_58_12 = e0
% 159.49/28.11 (5) all_58_7 = e0
% 159.49/28.11 (6) op(e2, e3) = all_52_1
% 159.49/28.11 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.49/28.11 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.49/28.11 (8) ~ (e3 = e0)
% 159.49/28.11 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.49/28.11 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.49/28.12 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.49/28.12 (11) ~ (e2 = e0)
% 159.49/28.12 (12) op(e2, e3) = e2
% 159.49/28.12 (13) ~ (e3 = e1)
% 159.49/28.12 (14) all_58_1 = e1
% 159.49/28.12 (15) all_58_11 = e2
% 159.49/28.12 (16) ~ (e2 = e1)
% 159.49/28.12 (17) ~ (e1 = e0)
% 159.49/28.12 (18) all_58_3 = e3
% 159.49/28.12 (19) ~ (all_6_2 = e2)
% 159.49/28.12 (20) all_58_13 = e2
% 159.49/28.12 (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.49/28.12 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.49/28.12 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.49/28.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.49/28.12 (23) ~ (e3 = e2)
% 159.49/28.12
% 159.49/28.12 Begin of proof
% 159.49/28.12 |
% 159.49/28.12 | BETA: splitting (10) gives:
% 159.49/28.12 |
% 159.49/28.12 | Case 1:
% 159.49/28.12 | |
% 159.49/28.12 | | (24) all_58_12 = e1 & op(e0, e3) = e1
% 159.49/28.12 | |
% 159.49/28.12 | | ALPHA: (24) implies:
% 159.49/28.12 | | (25) all_58_12 = e1
% 159.49/28.12 | |
% 159.49/28.12 | | COMBINE_EQS: (4), (25) imply:
% 159.49/28.12 | | (26) e1 = e0
% 159.49/28.12 | |
% 159.49/28.12 | | SIMP: (26) implies:
% 159.49/28.12 | | (27) e1 = e0
% 159.49/28.12 | |
% 159.49/28.12 | | COMBINE_EQS: (14), (27) imply:
% 159.49/28.12 | | (28) all_58_1 = e0
% 159.49/28.12 | |
% 159.49/28.12 | | REF_CLOSE: (1), (5), (13), (16), (17), (18), (20), (28) are inconsistent by
% 159.49/28.12 | | sub-proof #752.
% 159.49/28.12 | |
% 159.49/28.12 | Case 2:
% 159.49/28.12 | |
% 159.49/28.12 | | (29) all_58_13 = e1 & op(e0, e2) = e1
% 159.49/28.12 | |
% 159.49/28.12 | | ALPHA: (29) implies:
% 159.49/28.12 | | (30) all_58_13 = e1
% 159.49/28.12 | |
% 159.49/28.12 | | COMBINE_EQS: (20), (30) imply:
% 159.49/28.12 | | (31) e2 = e1
% 159.49/28.12 | |
% 159.49/28.12 | | COMBINE_EQS: (15), (31) imply:
% 159.49/28.12 | | (32) all_58_11 = e1
% 159.49/28.12 | |
% 159.49/28.12 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (16), (17),
% 159.49/28.12 | | (19), (21), (22), (23), (32) are inconsistent by sub-proof #743.
% 159.49/28.12 | |
% 159.49/28.12 | End of split
% 159.49/28.12 |
% 159.49/28.12 End of proof
% 159.49/28.12
% 159.49/28.12 Sub-proof #602 shows that the following formulas are inconsistent:
% 159.49/28.12 ----------------------------------------------------------------
% 159.49/28.12 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.49/28.12 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.49/28.12 (2) op(e1, e1) = all_6_2
% 159.49/28.12 (3) all_58_8 = e3
% 159.49/28.12 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.49/28.12 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.49/28.12 (5) all_58_7 = e0
% 159.49/28.12 (6) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.49/28.12 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.49/28.12 (7) op(e2, e3) = all_52_1
% 159.49/28.12 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.49/28.12 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.49/28.12 (9) ~ (e3 = e0)
% 159.49/28.12 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.49/28.12 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.49/28.12 (11) ~ (e2 = e0)
% 159.49/28.12 (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.49/28.12 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.49/28.12 (13) op(e2, e3) = e2
% 159.49/28.12 (14) ~ (e3 = e1)
% 159.49/28.12 (15) op(e1, e2) = all_52_6
% 159.49/28.12 (16) all_58_1 = e1
% 159.49/28.12 (17) all_58_11 = e2
% 159.49/28.12 (18) ~ (e2 = e1)
% 159.49/28.12 (19) ~ (e1 = e0)
% 159.49/28.12 (20) all_58_3 = e3
% 159.49/28.12 (21) ~ (all_6_2 = e2)
% 159.49/28.12 (22) ~ (all_52_6 = e3)
% 159.49/28.12 (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.49/28.12 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.49/28.12 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.49/28.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.49/28.12 (25) ~ (e3 = e2)
% 159.49/28.12 (26) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 159.49/28.12
% 159.49/28.12 Begin of proof
% 159.49/28.12 |
% 159.49/28.12 | BETA: splitting (26) gives:
% 159.49/28.12 |
% 159.49/28.12 | Case 1:
% 159.49/28.12 | |
% 159.49/28.12 | | (27) all_58_1 = e2 & op(e3, e2) = e2
% 159.49/28.12 | |
% 159.49/28.12 | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (13), (14), (16), (17),
% 159.49/28.12 | | (18), (19), (21), (23), (24), (25), (27) are inconsistent by
% 159.49/28.12 | | sub-proof #742.
% 159.49/28.12 | |
% 159.49/28.12 | Case 2:
% 159.49/28.12 | |
% 159.49/28.12 | | (28) all_58_3 = e2 & op(e2, e2) = e2
% 159.49/28.12 | |
% 159.49/28.12 | | ALPHA: (28) implies:
% 159.49/28.12 | | (29) all_58_3 = e2
% 159.49/28.12 | |
% 159.49/28.12 | | COMBINE_EQS: (20), (29) imply:
% 159.49/28.12 | | (30) e3 = e2
% 159.49/28.12 | |
% 159.49/28.12 | | COMBINE_EQS: (3), (30) imply:
% 159.49/28.12 | | (31) all_58_8 = e2
% 159.49/28.12 | |
% 159.49/28.12 | | REF_CLOSE: (1), (6), (9), (11), (12), (14), (15), (17), (18), (19), (22),
% 159.49/28.12 | | (24), (25), (31) are inconsistent by sub-proof #1068.
% 159.49/28.12 | |
% 159.49/28.12 | End of split
% 159.49/28.12 |
% 159.49/28.12 End of proof
% 159.49/28.12
% 159.49/28.12 Sub-proof #603 shows that the following formulas are inconsistent:
% 159.49/28.12 ----------------------------------------------------------------
% 159.49/28.12 (1) all_58_15 = e3
% 159.49/28.12 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.49/28.12 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.49/28.12 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.49/28.12 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.49/28.12 (4) all_58_12 = e0
% 159.49/28.12 (5) op(e2, e1) = all_52_9
% 159.49/28.12 (6) op(e2, e3) = all_52_1
% 159.49/28.12 (7) ~ (e3 = e0)
% 159.49/28.12 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.49/28.12 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.49/28.12 (9) op(e0, e2) = e1
% 159.49/28.12 (10) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.49/28.12 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.49/28.12 e2)
% 159.49/28.12 (11) ~ (e2 = e0)
% 159.49/28.12 (12) all_58_13 = e1 & op(e0, e2) = e1
% 159.49/28.12 (13) op(e2, e3) = e2
% 159.49/28.12 (14) ~ (e3 = e1)
% 159.49/28.12 (15) op(e1, e2) = all_52_6
% 159.49/28.12 (16) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 159.49/28.12 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.49/28.12 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 159.49/28.12 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.49/28.12 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.49/28.12 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.49/28.12 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 159.49/28.12 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 159.49/28.12 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 159.49/28.12 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.49/28.12 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.49/28.12 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 159.49/28.12 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.49/28.12 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.49/28.12 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 159.49/28.12 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 159.49/28.12 = e0)
% 159.49/28.12 (17) all_56_12 = e3
% 159.49/28.12 (18) op(e0, e1) = all_52_11
% 159.49/28.12 (19) all_56_6 = e1
% 159.49/28.12 (20) ~ (all_52_6 = e1)
% 159.49/28.12 (21) ~ (e2 = e1)
% 159.49/28.12 (22) ~ (e1 = e0)
% 159.49/28.12 (23) all_56_13 = e3
% 159.49/28.12 (24) ~ (all_52_9 = e2)
% 159.49/28.12 (25) op(e0, e2) = all_52_7
% 159.49/28.12 (26) all_56_9 = e0
% 159.49/28.12 (27) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.49/28.12 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.49/28.12 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.49/28.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.49/28.12 (29) ~ (e3 = e2)
% 159.49/28.12 (30) op(e0, e0) = e3
% 159.49/28.12
% 159.49/28.12 Begin of proof
% 159.49/28.12 |
% 159.49/28.12 | BETA: splitting (10) gives:
% 159.49/28.12 |
% 159.49/28.12 | Case 1:
% 159.49/28.12 | |
% 159.49/28.12 | | (31) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 159.49/28.12 | | e2)
% 159.49/28.12 | |
% 159.49/28.12 | | REF_CLOSE: (3), (6), (7), (8), (9), (11), (13), (14), (21), (22), (25),
% 159.49/28.12 | | (27), (28), (29), (31) are inconsistent by sub-proof #902.
% 159.49/28.12 | |
% 159.49/28.12 | Case 2:
% 159.49/28.12 | |
% 159.49/28.12 | | (32) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.49/28.12 | | e2)
% 159.49/28.12 | |
% 159.49/28.12 | | BETA: splitting (32) gives:
% 159.49/28.12 | |
% 159.49/28.12 | | Case 1:
% 159.49/28.12 | | |
% 159.49/28.12 | | | (33) all_58_14 = e2 & op(e0, e1) = e2
% 159.49/28.12 | | |
% 159.49/28.12 | | | ALPHA: (33) implies:
% 159.49/28.12 | | | (34) op(e0, e1) = e2
% 159.49/28.12 | | |
% 159.49/28.12 | | | BETA: splitting (16) gives:
% 159.49/28.12 | | |
% 159.49/28.12 | | | Case 1:
% 159.49/28.12 | | | |
% 159.49/28.12 | | | | (35) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3,
% 159.49/28.12 | | | | e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2
% 159.49/28.12 | | | | & ~ (all_56_12 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 159.49/28.12 | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3,
% 159.49/28.12 | | | | e1) = e3 & op(e1, e3) = e3) | (all_56_1 = e1 & all_56_6 = e1
% 159.49/28.12 | | | | & ~ (all_56_12 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 159.49/28.12 | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3,
% 159.49/28.12 | | | | e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0
% 159.49/28.12 | | | | & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.49/28.12 | | | |
% 159.49/28.12 | | | | BETA: splitting (35) gives:
% 159.49/28.12 | | | |
% 159.49/28.12 | | | | Case 1:
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | (36) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3,
% 159.49/28.12 | | | | | e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 =
% 159.49/28.12 | | | | | e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 159.49/28.12 | | | | | e2) | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) &
% 159.49/28.12 | | | | | op(e3, e1) = e3 & op(e1, e3) = e3)
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | BETA: splitting (36) gives:
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | Case 1:
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | (37) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3,
% 159.49/28.12 | | | | | | e2) = e3 & op(e2, e3) = e3
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | ALPHA: (37) implies:
% 159.49/28.12 | | | | | | (38) op(e2, e3) = e3
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | REF_CLOSE: (6), (13), (28), (29), (38) are inconsistent by sub-proof
% 159.49/28.12 | | | | | | #1159.
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | Case 2:
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | (39) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) &
% 159.49/28.12 | | | | | | op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 &
% 159.49/28.12 | | | | | | all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 &
% 159.49/28.12 | | | | | | op(e1, e3) = e3)
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | BETA: splitting (39) gives:
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | Case 1:
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | (40) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) &
% 159.49/28.12 | | | | | | | op(e3, e2) = e2 & op(e2, e3) = e2
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | ALPHA: (40) implies:
% 159.49/28.12 | | | | | | | (41) ~ (all_56_12 = e3)
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | REDUCE: (17), (41) imply:
% 159.49/28.12 | | | | | | | (42) $false
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | CLOSE: (42) is inconsistent.
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | Case 2:
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | (43) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) &
% 159.49/28.12 | | | | | | | op(e3, e1) = e3 & op(e1, e3) = e3
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | REF_CLOSE: (14), (19), (43) are inconsistent by sub-proof #961.
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | End of split
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | End of split
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | Case 2:
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | (44) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3,
% 159.49/28.12 | | | | | e1) = e1 & op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 =
% 159.49/28.12 | | | | | e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 159.49/28.12 | | | | | e3) | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) &
% 159.49/28.12 | | | | | op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | BETA: splitting (44) gives:
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | Case 1:
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | (45) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3,
% 159.49/28.12 | | | | | | e1) = e1 & op(e1, e3) = e1
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | ALPHA: (45) implies:
% 159.49/28.12 | | | | | | (46) ~ (all_56_12 = e3)
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | REDUCE: (17), (46) imply:
% 159.49/28.12 | | | | | | (47) $false
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | CLOSE: (47) is inconsistent.
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | Case 2:
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | (48) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) &
% 159.49/28.12 | | | | | | op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 &
% 159.49/28.12 | | | | | | all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 &
% 159.49/28.12 | | | | | | op(e0, e3) = e0)
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | BETA: splitting (48) gives:
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | Case 1:
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | (49) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) &
% 159.49/28.12 | | | | | | | op(e3, e0) = e3 & op(e0, e3) = e3
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | ALPHA: (49) implies:
% 159.49/28.12 | | | | | | | (50) all_56_9 = e3
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | COMBINE_EQS: (26), (50) imply:
% 159.49/28.12 | | | | | | | (51) e3 = e0
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | SIMP: (51) implies:
% 159.49/28.12 | | | | | | | (52) e3 = e0
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | REDUCE: (7), (52) imply:
% 159.49/28.12 | | | | | | | (53) $false
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | CLOSE: (53) is inconsistent.
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | Case 2:
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | (54) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) &
% 159.49/28.12 | | | | | | | op(e3, e0) = e0 & op(e0, e3) = e0
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | ALPHA: (54) implies:
% 159.49/28.12 | | | | | | | (55) ~ (all_56_12 = e3)
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | REDUCE: (17), (55) imply:
% 159.49/28.12 | | | | | | | (56) $false
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | | CLOSE: (56) is inconsistent.
% 159.49/28.12 | | | | | | |
% 159.49/28.12 | | | | | | End of split
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | End of split
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | End of split
% 159.49/28.12 | | | |
% 159.49/28.12 | | | Case 2:
% 159.49/28.12 | | | |
% 159.49/28.12 | | | | (57) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2,
% 159.49/28.12 | | | | e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1
% 159.49/28.12 | | | | & ~ (all_56_13 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 159.49/28.12 | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2,
% 159.49/28.12 | | | | e0) = e2 & op(e0, e2) = e2) | (all_56_5 = e0 & all_56_10 =
% 159.49/28.12 | | | | e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 159.49/28.12 | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1,
% 159.49/28.12 | | | | e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 =
% 159.49/28.12 | | | | e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.49/28.12 | | | |
% 159.49/28.12 | | | | BETA: splitting (57) gives:
% 159.49/28.12 | | | |
% 159.49/28.12 | | | | Case 1:
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | (58) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2,
% 159.49/28.12 | | | | | e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 =
% 159.49/28.12 | | | | | e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 159.49/28.12 | | | | | e1) | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0)
% 159.49/28.12 | | | | | & op(e2, e0) = e2 & op(e0, e2) = e2)
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | REF_CLOSE: (5), (9), (15), (20), (21), (24), (25), (28), (58) are
% 159.49/28.12 | | | | | inconsistent by sub-proof #1015.
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | Case 2:
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | (59) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.49/28.12 | | | | | e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 =
% 159.49/28.12 | | | | | e1 & ~ (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 159.49/28.12 | | | | | e1) | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1)
% 159.49/28.12 | | | | | & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | BETA: splitting (59) gives:
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | | Case 1:
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | (60) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) &
% 159.49/28.12 | | | | | | op(e2, e0) = e0 & op(e0, e2) = e0
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | ALPHA: (60) implies:
% 159.49/28.12 | | | | | | (61) ~ (all_56_13 = e2)
% 159.49/28.12 | | | | | | (62) op(e0, e2) = e0
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | ALPHA: (12) implies:
% 159.49/28.12 | | | | | | (63) all_58_13 = e1
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | GROUND_INST: instantiating (28) with all_52_7, e0, e2, e0,
% 159.49/28.12 | | | | | | simplifying with (25), (62) gives:
% 159.49/28.12 | | | | | | (64) all_52_7 = e0
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | GROUND_INST: instantiating (28) with all_52_7, e1, e2, e0,
% 159.49/28.12 | | | | | | simplifying with (9), (25) gives:
% 159.49/28.12 | | | | | | (65) all_52_7 = e1
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | COMBINE_EQS: (64), (65) imply:
% 159.49/28.12 | | | | | | (66) e1 = e0
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | COMBINE_EQS: (63), (66) imply:
% 159.49/28.12 | | | | | | (67) all_58_13 = e0
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (13),
% 159.49/28.12 | | | | | | (14), (21), (22), (25), (27), (28), (29), (30), (62),
% 159.49/28.12 | | | | | | (67) are inconsistent by sub-proof #621.
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | Case 2:
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | (68) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) &
% 159.49/28.12 | | | | | | op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 &
% 159.49/28.12 | | | | | | all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 &
% 159.49/28.12 | | | | | | op(e0, e1) = e0)
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | | REF_CLOSE: (11), (18), (21), (28), (34), (68) are inconsistent by
% 159.49/28.12 | | | | | | sub-proof #1293.
% 159.49/28.12 | | | | | |
% 159.49/28.12 | | | | | End of split
% 159.49/28.12 | | | | |
% 159.49/28.12 | | | | End of split
% 159.49/28.12 | | | |
% 159.49/28.12 | | | End of split
% 159.49/28.12 | | |
% 159.49/28.12 | | Case 2:
% 159.49/28.12 | | |
% 159.49/28.12 | | | (69) all_58_15 = e2 & op(e0, e0) = e2
% 159.49/28.12 | | |
% 159.49/28.12 | | | ALPHA: (69) implies:
% 159.49/28.12 | | | (70) op(e0, e0) = e2
% 159.49/28.12 | | |
% 159.49/28.12 | | | REF_CLOSE: (28), (29), (30), (70) are inconsistent by sub-proof #1382.
% 159.49/28.12 | | |
% 159.49/28.12 | | End of split
% 159.49/28.12 | |
% 159.49/28.12 | End of split
% 159.49/28.12 |
% 159.49/28.12 End of proof
% 159.49/28.12
% 159.49/28.12 Sub-proof #604 shows that the following formulas are inconsistent:
% 159.49/28.12 ----------------------------------------------------------------
% 159.49/28.12 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.49/28.12 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.49/28.12 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.49/28.12 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.49/28.12 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.49/28.12 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.49/28.12 (4) ~ (all_52_7 = e3)
% 159.52/28.12 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.12 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.12 (6) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.12 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.12 (7) all_58_7 = e2
% 159.52/28.12 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.12 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.12 (9) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.12 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.12 (10) op(e3, e2) = all_52_4
% 159.52/28.12 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.12 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.12 (12) all_58_14 = e2
% 159.52/28.12 (13) op(e2, e3) = all_52_1
% 159.52/28.12 (14) ~ (all_52_13 = e3)
% 159.52/28.12 (15) ~ (e3 = e0)
% 159.52/28.12 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.12 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.12 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.12 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.12 (18) ~ (e2 = e0)
% 159.52/28.12 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.12 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.12 (20) op(e2, e0) = all_52_13
% 159.52/28.12 (21) op(e2, e3) = e2
% 159.52/28.12 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.12 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.12 (23) ~ (e3 = e1)
% 159.52/28.12 (24) op(e1, e2) = all_52_6
% 159.52/28.12 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.12 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.12 (26) op(e0, e0) = e2
% 159.52/28.12 (27) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.12 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.12 (28) ~ (all_52_4 = e3)
% 159.52/28.12 (29) op(e0, e2) = e0
% 159.52/28.12 (30) ~ (e2 = e1)
% 159.52/28.12 (31) ~ (e1 = e0)
% 159.52/28.12 (32) all_58_3 = e3
% 159.52/28.12 (33) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.12 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.12 e3)
% 159.52/28.13 (34) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.13 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.13 (35) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.13 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.13 (36) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.13 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.13 (37) op(e0, e2) = all_52_7
% 159.52/28.13 (38) ~ (all_52_6 = e3)
% 159.52/28.13 (39) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.13 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.13 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.13 (41) ~ (e3 = e2)
% 159.52/28.13 (42) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.13 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.13 (43) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.13 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.13 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.13 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.13
% 159.52/28.13 Begin of proof
% 159.52/28.13 |
% 159.52/28.13 | BETA: splitting (33) gives:
% 159.52/28.13 |
% 159.52/28.13 | Case 1:
% 159.52/28.13 | |
% 159.52/28.13 | | (44) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 159.52/28.13 | | e3)
% 159.52/28.13 | |
% 159.52/28.13 | | BETA: splitting (44) gives:
% 159.52/28.13 | |
% 159.52/28.13 | | Case 1:
% 159.52/28.13 | | |
% 159.52/28.13 | | | (45) all_58_12 = e3 & op(e0, e3) = e3
% 159.52/28.13 | | |
% 159.52/28.13 | | | ALPHA: (45) implies:
% 159.52/28.13 | | | (46) all_58_12 = e3
% 159.52/28.13 | | |
% 159.52/28.13 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.52/28.13 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.52/28.13 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 159.52/28.13 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (46) are
% 159.52/28.13 | | | inconsistent by sub-proof #605.
% 159.52/28.13 | | |
% 159.52/28.13 | | Case 2:
% 159.52/28.13 | | |
% 159.52/28.13 | | | (47) all_58_13 = e3 & op(e0, e2) = e3
% 159.52/28.13 | | |
% 159.52/28.13 | | | REF_CLOSE: (4), (37), (40), (47) are inconsistent by sub-proof #1449.
% 159.52/28.13 | | |
% 159.52/28.13 | | End of split
% 159.52/28.13 | |
% 159.52/28.13 | Case 2:
% 159.52/28.13 | |
% 159.52/28.13 | | (48) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.13 | | e3)
% 159.52/28.13 | |
% 159.52/28.13 | | REF_CLOSE: (12), (26), (40), (41), (48) are inconsistent by sub-proof #1381.
% 159.52/28.13 | |
% 159.52/28.13 | End of split
% 159.52/28.13 |
% 159.52/28.13 End of proof
% 159.52/28.13
% 159.52/28.13 Sub-proof #605 shows that the following formulas are inconsistent:
% 159.52/28.13 ----------------------------------------------------------------
% 159.52/28.13 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.13 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.13 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.13 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.13 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.13 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.13 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.13 (5) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.13 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.13 (6) all_58_12 = e3
% 159.52/28.13 (7) all_58_7 = e2
% 159.52/28.13 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.13 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.13 (9) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.13 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.13 (10) op(e3, e2) = all_52_4
% 159.52/28.13 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.13 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.13 (12) all_58_14 = e2
% 159.52/28.13 (13) op(e2, e3) = all_52_1
% 159.52/28.13 (14) ~ (all_52_13 = e3)
% 159.52/28.13 (15) ~ (e3 = e0)
% 159.52/28.13 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.13 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.13 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.13 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.13 (18) ~ (e2 = e0)
% 159.52/28.13 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.13 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.13 (20) op(e2, e0) = all_52_13
% 159.52/28.13 (21) op(e2, e3) = e2
% 159.52/28.13 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.13 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.13 (23) ~ (e3 = e1)
% 159.52/28.13 (24) op(e1, e2) = all_52_6
% 159.52/28.13 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.13 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.13 (26) op(e0, e0) = e2
% 159.52/28.13 (27) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.13 (28) ~ (all_52_4 = e3)
% 159.52/28.13 (29) op(e0, e2) = e0
% 159.52/28.13 (30) ~ (e2 = e1)
% 159.52/28.13 (31) ~ (e1 = e0)
% 159.52/28.13 (32) all_58_3 = e3
% 159.52/28.13 (33) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.13 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.13 (34) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.13 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.13 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.13 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.13 (36) op(e0, e2) = all_52_7
% 159.52/28.13 (37) ~ (all_52_6 = e3)
% 159.52/28.13 (38) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.13 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.13 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.13 (40) ~ (e3 = e2)
% 159.52/28.13 (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.13 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.13 (42) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.13 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.13 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.13 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.13
% 159.52/28.13 Begin of proof
% 159.52/28.13 |
% 159.52/28.13 | BETA: splitting (9) gives:
% 159.52/28.13 |
% 159.52/28.13 | Case 1:
% 159.52/28.13 | |
% 159.52/28.13 | | (43) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 159.52/28.13 | | e2)
% 159.52/28.13 | |
% 159.52/28.13 | | BETA: splitting (43) gives:
% 159.52/28.13 | |
% 159.52/28.13 | | Case 1:
% 159.52/28.13 | | |
% 159.52/28.13 | | | (44) all_58_9 = e2 & op(e3, e0) = e2
% 159.52/28.13 | | |
% 159.52/28.13 | | | ALPHA: (44) implies:
% 159.52/28.13 | | | (45) all_58_9 = e2
% 159.52/28.13 | | |
% 159.52/28.13 | | | BETA: splitting (38) gives:
% 159.52/28.13 | | |
% 159.52/28.13 | | | Case 1:
% 159.52/28.13 | | | |
% 159.52/28.13 | | | | (46) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 159.52/28.13 | | | | = e0)
% 159.52/28.13 | | | |
% 159.52/28.13 | | | | BETA: splitting (46) gives:
% 159.52/28.13 | | | |
% 159.52/28.13 | | | | Case 1:
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | (47) all_58_0 = e0 & op(e3, e3) = e0
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | ALPHA: (47) implies:
% 159.52/28.13 | | | | | (48) all_58_0 = e0
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | BETA: splitting (35) gives:
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | Case 1:
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | (49) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 159.52/28.13 | | | | | | e2) = e3)
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | REF_CLOSE: (10), (15), (28), (39), (48), (49) are inconsistent by
% 159.52/28.13 | | | | | | sub-proof #645.
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | Case 2:
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | (50) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 159.52/28.13 | | | | | | e0) = e3)
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | BETA: splitting (50) gives:
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | Case 1:
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | (51) all_58_4 = e3 & op(e3, e1) = e3
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | ALPHA: (51) implies:
% 159.52/28.13 | | | | | | | (52) all_58_4 = e3
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (12), (13), (14), (15), (16),
% 159.52/28.13 | | | | | | | (18), (19), (20), (21), (23), (25), (26), (27), (30),
% 159.52/28.13 | | | | | | | (31), (32), (39), (40), (45), (48), (52) are
% 159.52/28.13 | | | | | | | inconsistent by sub-proof #608.
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | Case 2:
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | (53) all_58_9 = e3 & op(e3, e0) = e3
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | ALPHA: (53) implies:
% 159.52/28.13 | | | | | | | (54) all_58_9 = e3
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | COMBINE_EQS: (45), (54) imply:
% 159.52/28.13 | | | | | | | (55) e3 = e2
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | REF_CLOSE: (6), (8), (13), (15), (16), (21), (23), (30), (31),
% 159.52/28.13 | | | | | | | (39), (40), (48), (55) are inconsistent by sub-proof
% 159.52/28.13 | | | | | | | #777.
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | End of split
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | End of split
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | Case 2:
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | (56) all_58_2 = e0 & op(e2, e3) = e0
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | ALPHA: (56) implies:
% 159.52/28.13 | | | | | (57) op(e2, e3) = e0
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | REF_CLOSE: (18), (21), (39), (57) are inconsistent by sub-proof #1156.
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | End of split
% 159.52/28.13 | | | |
% 159.52/28.13 | | | Case 2:
% 159.52/28.13 | | | |
% 159.52/28.13 | | | | (58) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 159.52/28.13 | | | | = e0)
% 159.52/28.13 | | | |
% 159.52/28.13 | | | | BETA: splitting (58) gives:
% 159.52/28.13 | | | |
% 159.52/28.13 | | | | Case 1:
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | (59) all_58_6 = e0 & op(e1, e3) = e0
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | ALPHA: (59) implies:
% 159.52/28.13 | | | | | (60) all_58_6 = e0
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | BETA: splitting (16) gives:
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | Case 1:
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | (61) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 159.52/28.13 | | | | | | e3) = e1)
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | BETA: splitting (61) gives:
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | Case 1:
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | (62) all_58_0 = e1 & op(e3, e3) = e1
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | ALPHA: (62) implies:
% 159.52/28.13 | | | | | | | (63) all_58_0 = e1
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | BETA: splitting (35) gives:
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | |
% 159.52/28.13 | | | | | | | | (64) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 159.52/28.13 | | | | | | | | op(e3, e2) = e3)
% 159.52/28.13 | | | | | | | |
% 159.52/28.13 | | | | | | | | REF_CLOSE: (10), (23), (28), (39), (63), (64) are inconsistent
% 159.52/28.13 | | | | | | | | by sub-proof #1306.
% 159.52/28.13 | | | | | | | |
% 159.52/28.13 | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | |
% 159.52/28.13 | | | | | | | | (65) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 159.52/28.13 | | | | | | | | op(e3, e0) = e3)
% 159.52/28.13 | | | | | | | |
% 159.52/28.13 | | | | | | | | BETA: splitting (65) gives:
% 159.52/28.13 | | | | | | | |
% 159.52/28.13 | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | (66) all_58_4 = e3 & op(e3, e1) = e3
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | ALPHA: (66) implies:
% 159.52/28.13 | | | | | | | | | (67) all_58_4 = e3
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | BETA: splitting (41) gives:
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | (68) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 159.52/28.13 | | | | | | | | | | op(e3, e2) = e0)
% 159.52/28.13 | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | BETA: splitting (68) gives:
% 159.52/28.13 | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | (69) all_58_0 = e0 & op(e3, e3) = e0
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | ALPHA: (69) implies:
% 159.52/28.13 | | | | | | | | | | | (70) all_58_0 = e0
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (12), (13), (14), (15),
% 159.52/28.13 | | | | | | | | | | | (16), (18), (19), (20), (21), (23), (25), (26),
% 159.52/28.13 | | | | | | | | | | | (27), (30), (31), (32), (39), (40), (45), (67),
% 159.52/28.13 | | | | | | | | | | | (70) are inconsistent by sub-proof #608.
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | (71) all_58_1 = e0 & op(e3, e2) = e0
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | ALPHA: (71) implies:
% 159.52/28.13 | | | | | | | | | | | (72) all_58_1 = e0
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | BETA: splitting (5) gives:
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | (73) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 159.52/28.13 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 159.52/28.13 | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | BETA: splitting (73) gives:
% 159.52/28.13 | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | (74) all_58_9 = e3 & op(e3, e0) = e3
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | ALPHA: (74) implies:
% 159.52/28.13 | | | | | | | | | | | | | (75) all_58_9 = e3
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | COMBINE_EQS: (45), (75) imply:
% 159.52/28.13 | | | | | | | | | | | | | (76) e3 = e2
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | SIMP: (76) implies:
% 159.52/28.13 | | | | | | | | | | | | | (77) e3 = e2
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | COMBINE_EQS: (6), (77) imply:
% 159.52/28.13 | | | | | | | | | | | | | (78) all_58_12 = e2
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | REF_CLOSE: (8), (13), (15), (21), (23), (39), (40), (60),
% 159.52/28.13 | | | | | | | | | | | | | (63), (78) are inconsistent by sub-proof #1065.
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | (79) all_58_10 = e3 & op(e2, e0) = e3
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | ALPHA: (79) implies:
% 159.52/28.13 | | | | | | | | | | | | | (80) op(e2, e0) = e3
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | REF_CLOSE: (14), (20), (39), (80) are inconsistent by
% 159.52/28.13 | | | | | | | | | | | | | sub-proof #1364.
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | (81) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 159.52/28.13 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 159.52/28.13 | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | BETA: splitting (81) gives:
% 159.52/28.13 | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | (82) all_58_11 = e3 & op(e1, e0) = e3
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | ALPHA: (82) implies:
% 159.52/28.13 | | | | | | | | | | | | | (83) all_58_11 = e3
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | BETA: splitting (2) gives:
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | (84) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 159.52/28.13 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.52/28.13 | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 159.52/28.13 | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | (85) all_58_9 = e1 & op(e3, e0) = e1
% 159.52/28.13 | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (12), (13), (15), (16), (18),
% 159.52/28.13 | | | | | | | | | | | | | | | (21), (22), (23), (26), (30), (31), (32), (34),
% 159.52/28.13 | | | | | | | | | | | | | | | (39), (40), (45), (60), (63), (85) are
% 159.52/28.13 | | | | | | | | | | | | | | | inconsistent by sub-proof #607.
% 159.52/28.13 | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | (86) all_58_10 = e1 & op(e2, e0) = e1
% 159.52/28.13 | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | ALPHA: (86) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | (87) all_58_10 = e1
% 159.52/28.13 | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 159.52/28.13 | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | (88) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 159.52/28.13 | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.52/28.13 | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | (89) all_58_12 = e1 & op(e0, e3) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (89) are inconsistent by sub-proof
% 159.52/28.13 | | | | | | | | | | | | | | | | | #1388.
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | (90) all_58_13 = e1 & op(e0, e2) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | (91) op(e0, e2) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | (92) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 159.52/28.13 | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (21), (32), (39), (92) are
% 159.52/28.13 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #909.
% 159.52/28.13 | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | (93) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 159.52/28.13 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 159.52/28.13 | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | (94) all_58_5 = e0 & op(e2, e1) = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | (95) all_58_5 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | (96) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (97) all_58_6 = e1 & op(e1, e3) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (98) all_58_6 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (98) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (99) e1 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (99) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (100) all_58_0 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (12), (15), (16), (18), (19), (21),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (23), (27), (30), (31), (39), (67), (83), (95),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (100) are inconsistent by sub-proof #713.
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (101) all_58_7 = e1 & op(e1, e2) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (102) all_58_7 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (12), (13), (15), (16), (18), (21),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (22), (23), (26), (30), (31), (32), (34), (39),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (40), (60), (63), (102) are inconsistent by
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | sub-proof #701.
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | (103) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (104) all_58_8 = e1 & op(e1, e1) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (105) all_58_8 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | (106) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_52_7, e0, e2, e0,
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (29), (36) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (107) all_52_7 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_52_7, e1, e2, e0,
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (36), (91) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (108) all_52_7 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (108) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (109) e1 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (109) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (110) all_58_0 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (15), (16), (18), (19), (21), (23),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (30), (31), (39), (83), (105), (110) are
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (111) all_58_1 = e1 & op(e3, e2) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (112) all_58_1 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (112) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (113) e1 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (113) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (114) e1 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (114) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (115) all_58_0 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (15), (16), (18), (19), (21), (23),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (30), (31), (39), (83), (105), (115) are
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | (116) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (117) all_58_4 = e1 & op(e3, e1) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (67), (117) are inconsistent by sub-proof
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | #1345.
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (118) all_58_9 = e1 & op(e3, e0) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (12), (13), (15), (16), (18),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (21), (22), (23), (26), (30), (31), (32), (34),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | (39), (40), (45), (60), (63), (118) are
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #607.
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | (119) all_58_11 = e1 & op(e1, e0) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (83), (119) are inconsistent by sub-proof
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | | #610.
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | (120) all_58_10 = e0 & op(e2, e0) = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | (121) all_58_10 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (121) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | (122) e1 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (122) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | (123) all_58_0 = e0
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (12), (15), (16), (18), (19), (21),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | (23), (25), (27), (30), (31), (32), (39), (67),
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | (83), (87), (123) are inconsistent by sub-proof
% 159.52/28.13 | | | | | | | | | | | | | | | | | | | #712.
% 159.52/28.13 | | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | (124) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 159.52/28.13 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.52/28.13 | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 159.52/28.13 | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | (125) all_58_14 = e1 & op(e0, e1) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | (126) all_58_14 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (126) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | (127) e2 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | SIMP: (127) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | (128) e2 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (128) imply:
% 159.52/28.13 | | | | | | | | | | | | | | | | | (129) all_58_7 = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (12), (13), (15), (16), (18), (21),
% 159.52/28.13 | | | | | | | | | | | | | | | | | (22), (23), (26), (30), (31), (32), (34), (39),
% 159.52/28.13 | | | | | | | | | | | | | | | | | (40), (60), (63), (129) are inconsistent by
% 159.52/28.13 | | | | | | | | | | | | | | | | | sub-proof #701.
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | (130) all_58_15 = e1 & op(e0, e0) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 159.52/28.13 | | | | | | | | | | | | | | | | | (131) op(e0, e0) = e1
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (30), (39), (131) are inconsistent by
% 159.52/28.13 | | | | | | | | | | | | | | | | | sub-proof #1386.
% 159.52/28.13 | | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | (132) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 159.52/28.13 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.52/28.13 | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | | REF_CLOSE: (23), (26), (30), (39), (83), (132) are
% 159.52/28.13 | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 159.52/28.13 | | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | (133) all_58_15 = e3 & op(e0, e0) = e3
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | ALPHA: (133) implies:
% 159.52/28.13 | | | | | | | | | | | | | (134) op(e0, e0) = e3
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | | REF_CLOSE: (26), (39), (40), (134) are inconsistent by
% 159.52/28.13 | | | | | | | | | | | | | sub-proof #1382.
% 159.52/28.13 | | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | (135) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 159.52/28.13 | | | | | | | | | | & op(e3, e0) = e0)
% 159.52/28.13 | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | | REF_CLOSE: (15), (18), (45), (67), (135) are inconsistent by
% 159.52/28.13 | | | | | | | | | | sub-proof #606.
% 159.52/28.13 | | | | | | | | | |
% 159.52/28.13 | | | | | | | | | End of split
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | Case 2:
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | (136) all_58_9 = e3 & op(e3, e0) = e3
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | ALPHA: (136) implies:
% 159.52/28.13 | | | | | | | | | (137) all_58_9 = e3
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | COMBINE_EQS: (45), (137) imply:
% 159.52/28.13 | | | | | | | | | (138) e3 = e2
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | COMBINE_EQS: (6), (138) imply:
% 159.52/28.13 | | | | | | | | | (139) all_58_12 = e2
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | | REF_CLOSE: (8), (13), (15), (21), (23), (39), (40), (60),
% 159.52/28.13 | | | | | | | | | (63), (139) are inconsistent by sub-proof #1065.
% 159.52/28.13 | | | | | | | | |
% 159.52/28.13 | | | | | | | | End of split
% 159.52/28.13 | | | | | | | |
% 159.52/28.13 | | | | | | | End of split
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | Case 2:
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | (140) all_58_2 = e1 & op(e2, e3) = e1
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | ALPHA: (140) implies:
% 159.52/28.13 | | | | | | | (141) op(e2, e3) = e1
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | | REF_CLOSE: (21), (30), (39), (141) are inconsistent by sub-proof
% 159.52/28.13 | | | | | | | #1430.
% 159.52/28.13 | | | | | | |
% 159.52/28.13 | | | | | | End of split
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | Case 2:
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | (142) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 159.52/28.13 | | | | | | op(e0, e3) = e1)
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | | REF_CLOSE: (6), (23), (31), (60), (142) are inconsistent by
% 159.52/28.13 | | | | | | sub-proof #1056.
% 159.52/28.13 | | | | | |
% 159.52/28.13 | | | | | End of split
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | Case 2:
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | (143) all_58_12 = e0 & op(e0, e3) = e0
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | | REF_CLOSE: (6), (15), (143) are inconsistent by sub-proof #1505.
% 159.52/28.13 | | | | |
% 159.52/28.13 | | | | End of split
% 159.52/28.13 | | | |
% 159.52/28.13 | | | End of split
% 159.52/28.13 | | |
% 159.52/28.13 | | Case 2:
% 159.52/28.13 | | |
% 159.52/28.13 | | | (144) all_58_10 = e2 & op(e2, e0) = e2
% 159.52/28.13 | | |
% 159.52/28.13 | | | ALPHA: (144) implies:
% 159.52/28.13 | | | (145) all_58_10 = e2
% 159.52/28.13 | | |
% 159.52/28.13 | | | REF_CLOSE: (3), (15), (18), (21), (23), (25), (30), (31), (32), (39),
% 159.52/28.13 | | | (145) are inconsistent by sub-proof #906.
% 159.52/28.13 | | |
% 159.52/28.13 | | End of split
% 159.52/28.13 | |
% 159.52/28.13 | Case 2:
% 159.52/28.13 | |
% 159.52/28.13 | | (146) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.13 | | e2)
% 159.52/28.13 | |
% 159.52/28.13 | | BETA: splitting (146) gives:
% 159.52/28.13 | |
% 159.52/28.13 | | Case 1:
% 159.52/28.13 | | |
% 159.52/28.13 | | | (147) all_58_11 = e2 & op(e1, e0) = e2
% 159.52/28.13 | | |
% 159.52/28.13 | | | ALPHA: (147) implies:
% 159.52/28.13 | | | (148) all_58_11 = e2
% 159.52/28.13 | | |
% 159.52/28.13 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (11), (12), (13), (14), (15),
% 159.52/28.13 | | | (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 159.52/28.13 | | | (27), (29), (30), (31), (32), (34), (36), (37), (38), (39),
% 159.52/28.13 | | | (40), (148) are inconsistent by sub-proof #697.
% 159.52/28.13 | | |
% 159.52/28.13 | | Case 2:
% 159.52/28.13 | | |
% 159.52/28.13 | | | (149) all_58_15 = e2 & op(e0, e0) = e2
% 159.52/28.13 | | |
% 159.52/28.13 | | | ALPHA: (149) implies:
% 159.52/28.13 | | | (150) all_58_15 = e2
% 159.52/28.13 | | |
% 159.52/28.13 | | | REF_CLOSE: (4), (6), (12), (15), (18), (23), (26), (30), (31), (39), (42),
% 159.52/28.13 | | | (150) are inconsistent by sub-proof #1383.
% 159.52/28.13 | | |
% 159.52/28.13 | | End of split
% 159.52/28.13 | |
% 159.52/28.13 | End of split
% 159.52/28.13 |
% 159.52/28.13 End of proof
% 159.52/28.13
% 159.52/28.13 Sub-proof #606 shows that the following formulas are inconsistent:
% 159.52/28.13 ----------------------------------------------------------------
% 159.52/28.13 (1) ~ (e3 = e0)
% 159.52/28.13 (2) ~ (e2 = e0)
% 159.52/28.13 (3) all_58_4 = e3
% 159.52/28.13 (4) all_58_9 = e2
% 159.52/28.13 (5) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.13
% 159.52/28.13 Begin of proof
% 159.52/28.13 |
% 159.52/28.13 | BETA: splitting (5) gives:
% 159.52/28.13 |
% 159.52/28.13 | Case 1:
% 159.52/28.13 | |
% 159.52/28.13 | | (6) all_58_4 = e0 & op(e3, e1) = e0
% 159.52/28.13 | |
% 159.52/28.13 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #1344.
% 159.52/28.13 | |
% 159.52/28.13 | Case 2:
% 159.52/28.13 | |
% 159.52/28.13 | | (7) all_58_9 = e0 & op(e3, e0) = e0
% 159.52/28.13 | |
% 159.52/28.13 | | ALPHA: (7) implies:
% 159.52/28.13 | | (8) all_58_9 = e0
% 159.52/28.13 | |
% 159.52/28.13 | | COMBINE_EQS: (4), (8) imply:
% 159.52/28.13 | | (9) e2 = e0
% 159.52/28.13 | |
% 159.52/28.13 | | SIMP: (9) implies:
% 159.52/28.13 | | (10) e2 = e0
% 159.52/28.13 | |
% 159.52/28.13 | | REDUCE: (2), (10) imply:
% 159.52/28.13 | | (11) $false
% 159.52/28.13 | |
% 159.52/28.13 | | CLOSE: (11) is inconsistent.
% 159.52/28.13 | |
% 159.52/28.13 | End of split
% 159.52/28.13 |
% 159.52/28.13 End of proof
% 159.52/28.13
% 159.52/28.13 Sub-proof #607 shows that the following formulas are inconsistent:
% 159.52/28.13 ----------------------------------------------------------------
% 159.52/28.14 (1) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.14 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.14 (2) all_58_12 = e3
% 159.52/28.14 (3) all_58_7 = e2
% 159.52/28.14 (4) all_58_0 = e1
% 159.52/28.14 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.14 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.14 (6) all_58_14 = e2
% 159.52/28.14 (7) op(e2, e3) = all_52_1
% 159.52/28.14 (8) all_58_9 = e1 & op(e3, e0) = e1
% 159.52/28.14 (9) ~ (e3 = e0)
% 159.52/28.14 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.14 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.14 (11) ~ (e2 = e0)
% 159.52/28.14 (12) all_58_6 = e0
% 159.52/28.14 (13) op(e2, e3) = e2
% 159.52/28.14 (14) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.14 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.14 (15) ~ (e3 = e1)
% 159.52/28.14 (16) op(e0, e0) = e2
% 159.52/28.14 (17) ~ (e2 = e1)
% 159.52/28.14 (18) ~ (e1 = e0)
% 159.52/28.14 (19) all_58_3 = e3
% 159.52/28.14 (20) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.14 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.14 (21) all_58_9 = e2
% 159.52/28.14 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.14 (23) ~ (e3 = e2)
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | ALPHA: (8) implies:
% 159.52/28.14 | (24) all_58_9 = e1
% 159.52/28.14 |
% 159.52/28.14 | COMBINE_EQS: (21), (24) imply:
% 159.52/28.14 | (25) e2 = e1
% 159.52/28.14 |
% 159.52/28.14 | COMBINE_EQS: (3), (25) imply:
% 159.52/28.14 | (26) all_58_7 = e1
% 159.52/28.14 |
% 159.52/28.14 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 159.52/28.14 | (15), (16), (17), (18), (19), (20), (22), (23), (26) are
% 159.52/28.14 | inconsistent by sub-proof #701.
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #608 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.14 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.14 (2) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.14 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.14 (3) all_58_12 = e3
% 159.52/28.14 (4) all_58_7 = e2
% 159.52/28.14 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.14 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.14 (6) all_58_14 = e2
% 159.52/28.14 (7) op(e2, e3) = all_52_1
% 159.52/28.14 (8) ~ (all_52_13 = e3)
% 159.52/28.14 (9) ~ (e3 = e0)
% 159.52/28.14 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.14 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.14 (11) ~ (e2 = e0)
% 159.52/28.14 (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.14 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.14 (13) op(e2, e0) = all_52_13
% 159.52/28.14 (14) op(e2, e3) = e2
% 159.52/28.14 (15) ~ (e3 = e1)
% 159.52/28.14 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.14 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.14 (17) op(e0, e0) = e2
% 159.52/28.14 (18) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.14 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.14 (19) ~ (e2 = e1)
% 159.52/28.14 (20) ~ (e1 = e0)
% 159.52/28.14 (21) all_58_4 = e3
% 159.52/28.14 (22) all_58_3 = e3
% 159.52/28.14 (23) all_58_9 = e2
% 159.52/28.14 (24) all_58_0 = e0
% 159.52/28.14 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.14 (26) ~ (e3 = e2)
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | BETA: splitting (2) gives:
% 159.52/28.14 |
% 159.52/28.14 | Case 1:
% 159.52/28.14 | |
% 159.52/28.14 | | (27) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 159.52/28.14 | | e3)
% 159.52/28.14 | |
% 159.52/28.14 | | BETA: splitting (27) gives:
% 159.52/28.14 | |
% 159.52/28.14 | | Case 1:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (28) all_58_9 = e3 & op(e3, e0) = e3
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (28) implies:
% 159.52/28.14 | | | (29) all_58_9 = e3
% 159.52/28.14 | | |
% 159.52/28.14 | | | COMBINE_EQS: (23), (29) imply:
% 159.52/28.14 | | | (30) e3 = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | COMBINE_EQS: (3), (30) imply:
% 159.52/28.14 | | | (31) all_58_12 = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (5), (7), (9), (10), (14), (15), (19), (20), (24), (25), (26),
% 159.52/28.14 | | | (31) are inconsistent by sub-proof #1066.
% 159.52/28.14 | | |
% 159.52/28.14 | | Case 2:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (32) all_58_10 = e3 & op(e2, e0) = e3
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (32) implies:
% 159.52/28.14 | | | (33) op(e2, e0) = e3
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (8), (13), (25), (33) are inconsistent by sub-proof #1364.
% 159.52/28.14 | | |
% 159.52/28.14 | | End of split
% 159.52/28.14 | |
% 159.52/28.14 | Case 2:
% 159.52/28.14 | |
% 159.52/28.14 | | (34) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.14 | | e3)
% 159.52/28.14 | |
% 159.52/28.14 | | BETA: splitting (34) gives:
% 159.52/28.14 | |
% 159.52/28.14 | | Case 1:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (35) all_58_11 = e3 & op(e1, e0) = e3
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (35) implies:
% 159.52/28.14 | | | (36) all_58_11 = e3
% 159.52/28.14 | | |
% 159.52/28.14 | | | BETA: splitting (1) gives:
% 159.52/28.14 | | |
% 159.52/28.14 | | | Case 1:
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | (37) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 159.52/28.14 | | | | = e1)
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | BETA: splitting (37) gives:
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | Case 1:
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | (38) all_58_9 = e1 & op(e3, e0) = e1
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | ALPHA: (38) implies:
% 159.52/28.14 | | | | | (39) all_58_9 = e1
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | REF_CLOSE: (19), (23), (39) are inconsistent by sub-proof #1324.
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | Case 2:
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | (40) all_58_10 = e1 & op(e2, e0) = e1
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | ALPHA: (40) implies:
% 159.52/28.14 | | | | | (41) all_58_10 = e1
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | REF_CLOSE: (3), (4), (6), (9), (10), (11), (12), (14), (15), (16),
% 159.52/28.14 | | | | | (18), (19), (20), (21), (22), (24), (25), (36), (41) are
% 159.52/28.14 | | | | | inconsistent by sub-proof #712.
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | End of split
% 159.52/28.14 | | | |
% 159.52/28.14 | | | Case 2:
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | (42) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 159.52/28.14 | | | | e0) = e1)
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | REF_CLOSE: (15), (17), (19), (25), (36), (42) are inconsistent by
% 159.52/28.14 | | | | sub-proof #609.
% 159.52/28.14 | | | |
% 159.52/28.14 | | | End of split
% 159.52/28.14 | | |
% 159.52/28.14 | | Case 2:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (43) all_58_15 = e3 & op(e0, e0) = e3
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (43) implies:
% 159.52/28.14 | | | (44) op(e0, e0) = e3
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (17), (25), (26), (44) are inconsistent by sub-proof #1382.
% 159.52/28.14 | | |
% 159.52/28.14 | | End of split
% 159.52/28.14 | |
% 159.52/28.14 | End of split
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #609 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) ~ (e3 = e1)
% 159.52/28.14 (2) op(e0, e0) = e2
% 159.52/28.14 (3) ~ (e2 = e1)
% 159.52/28.14 (4) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.14 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.14 (6) all_58_11 = e3
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | BETA: splitting (4) gives:
% 159.52/28.14 |
% 159.52/28.14 | Case 1:
% 159.52/28.14 | |
% 159.52/28.14 | | (7) all_58_11 = e1 & op(e1, e0) = e1
% 159.52/28.14 | |
% 159.52/28.14 | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #610.
% 159.52/28.14 | |
% 159.52/28.14 | Case 2:
% 159.52/28.14 | |
% 159.52/28.14 | | (8) all_58_15 = e1 & op(e0, e0) = e1
% 159.52/28.14 | |
% 159.52/28.14 | | ALPHA: (8) implies:
% 159.52/28.14 | | (9) op(e0, e0) = e1
% 159.52/28.14 | |
% 159.52/28.14 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1386.
% 159.52/28.14 | |
% 159.52/28.14 | End of split
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #610 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) all_58_11 = e1 & op(e1, e0) = e1
% 159.52/28.14 (2) all_58_11 = e3
% 159.52/28.14 (3) ~ (e3 = e1)
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | ALPHA: (1) implies:
% 159.52/28.14 | (4) all_58_11 = e1
% 159.52/28.14 |
% 159.52/28.14 | COMBINE_EQS: (2), (4) imply:
% 159.52/28.14 | (5) e3 = e1
% 159.52/28.14 |
% 159.52/28.14 | REDUCE: (3), (5) imply:
% 159.52/28.14 | (6) $false
% 159.52/28.14 |
% 159.52/28.14 | CLOSE: (6) is inconsistent.
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #611 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) all_58_13 = e0
% 159.52/28.14 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.14 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.14 (3) all_58_7 = e2
% 159.52/28.14 (4) all_58_6 = e1 & op(e1, e3) = e1
% 159.52/28.14 (5) all_58_6 = e0
% 159.52/28.14 (6) ~ (e3 = e1)
% 159.52/28.14 (7) all_58_1 = e1
% 159.52/28.14 (8) ~ (e2 = e1)
% 159.52/28.14 (9) ~ (e1 = e0)
% 159.52/28.14 (10) all_58_3 = e3
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | ALPHA: (4) implies:
% 159.52/28.14 | (11) all_58_6 = e1
% 159.52/28.14 |
% 159.52/28.14 | COMBINE_EQS: (5), (11) imply:
% 159.52/28.14 | (12) e1 = e0
% 159.52/28.14 |
% 159.52/28.14 | SIMP: (12) implies:
% 159.52/28.14 | (13) e1 = e0
% 159.52/28.14 |
% 159.52/28.14 | COMBINE_EQS: (7), (13) imply:
% 159.52/28.14 | (14) all_58_1 = e0
% 159.52/28.14 |
% 159.52/28.14 | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (14) are inconsistent by
% 159.52/28.14 | sub-proof #857.
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #612 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.14 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.14 (2) all_58_14 = e2
% 159.52/28.14 (3) op(e2, e3) = all_52_1
% 159.52/28.14 (4) ~ (e3 = e0)
% 159.52/28.14 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.14 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.14 (6) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 159.52/28.14 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.14 (7) ~ (e2 = e0)
% 159.52/28.14 (8) all_58_6 = e0
% 159.52/28.14 (9) op(e2, e3) = e2
% 159.52/28.14 (10) ~ (e3 = e1)
% 159.52/28.14 (11) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.14 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.14 (12) ~ (e2 = e1)
% 159.52/28.14 (13) ~ (e1 = e0)
% 159.52/28.14 (14) e2 = e1
% 159.52/28.14 (15) op(e0, e2) = all_52_7
% 159.52/28.14 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.14 (17) ~ (e3 = e2)
% 159.52/28.14 (18) all_58_12 = e1
% 159.52/28.14 (19) op(e0, e0) = e3
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | SIMP: (14) implies:
% 159.52/28.14 | (20) e2 = e1
% 159.52/28.14 |
% 159.52/28.14 | COMBINE_EQS: (2), (20) imply:
% 159.52/28.14 | (21) all_58_14 = e1
% 159.52/28.14 |
% 159.52/28.14 | BETA: splitting (6) gives:
% 159.52/28.14 |
% 159.52/28.14 | Case 1:
% 159.52/28.14 | |
% 159.52/28.14 | | (22) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 159.52/28.14 | | e2)
% 159.52/28.14 | |
% 159.52/28.14 | | BETA: splitting (22) gives:
% 159.52/28.14 | |
% 159.52/28.14 | | Case 1:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (23) all_58_12 = e2 & op(e0, e3) = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (23) implies:
% 159.52/28.14 | | | (24) all_58_12 = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (12), (13), (16), (17),
% 159.52/28.14 | | | (24) are inconsistent by sub-proof #1063.
% 159.52/28.14 | | |
% 159.52/28.14 | | Case 2:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (25) all_58_13 = e2 & op(e0, e2) = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (25) implies:
% 159.52/28.14 | | | (26) op(e0, e2) = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (7), (11), (13), (15), (16), (18), (21), (26) are inconsistent
% 159.52/28.14 | | | by sub-proof #613.
% 159.52/28.14 | | |
% 159.52/28.14 | | End of split
% 159.52/28.14 | |
% 159.52/28.14 | Case 2:
% 159.52/28.14 | |
% 159.52/28.14 | | (27) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.14 | | e2)
% 159.52/28.14 | |
% 159.52/28.14 | | REF_CLOSE: (12), (16), (17), (19), (21), (27) are inconsistent by sub-proof
% 159.52/28.14 | | #1038.
% 159.52/28.14 | |
% 159.52/28.14 | End of split
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #613 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) all_58_14 = e1
% 159.52/28.14 (2) ~ (e2 = e0)
% 159.52/28.14 (3) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 159.52/28.14 (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.14 (4) ~ (e1 = e0)
% 159.52/28.14 (5) op(e0, e2) = e2
% 159.52/28.14 (6) op(e0, e2) = all_52_7
% 159.52/28.14 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.14 (8) all_58_12 = e1
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | BETA: splitting (3) gives:
% 159.52/28.14 |
% 159.52/28.14 | Case 1:
% 159.52/28.14 | |
% 159.52/28.14 | | (9) all_58_12 = e0 & op(e0, e3) = e0
% 159.52/28.14 | |
% 159.52/28.14 | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #1260.
% 159.52/28.14 | |
% 159.52/28.14 | Case 2:
% 159.52/28.14 | |
% 159.52/28.14 | | (10) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 159.52/28.14 | | e0)
% 159.52/28.14 | |
% 159.52/28.14 | | BETA: splitting (10) gives:
% 159.52/28.14 | |
% 159.52/28.14 | | Case 1:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (11) all_58_13 = e0 & op(e0, e2) = e0
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (11) implies:
% 159.52/28.14 | | | (12) op(e0, e2) = e0
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (2), (5), (6), (7), (12) are inconsistent by sub-proof #1040.
% 159.52/28.14 | | |
% 159.52/28.14 | | Case 2:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (13) all_58_14 = e0 & op(e0, e1) = e0
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (13) implies:
% 159.52/28.14 | | | (14) all_58_14 = e0
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (1), (4), (14) are inconsistent by sub-proof #614.
% 159.52/28.14 | | |
% 159.52/28.14 | | End of split
% 159.52/28.14 | |
% 159.52/28.14 | End of split
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #614 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) all_58_14 = e1
% 159.52/28.14 (2) all_58_14 = e0
% 159.52/28.14 (3) ~ (e1 = e0)
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | COMBINE_EQS: (1), (2) imply:
% 159.52/28.14 | (4) e1 = e0
% 159.52/28.14 |
% 159.52/28.14 | SIMP: (4) implies:
% 159.52/28.14 | (5) e1 = e0
% 159.52/28.14 |
% 159.52/28.14 | REDUCE: (3), (5) imply:
% 159.52/28.14 | (6) $false
% 159.52/28.14 |
% 159.52/28.14 | CLOSE: (6) is inconsistent.
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #615 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 159.52/28.14 (2) ~ (e3 = e0)
% 159.52/28.14 (3) ~ (e2 = e0)
% 159.52/28.14 (4) op(e2, e3) = e2
% 159.52/28.14 (5) all_58_0 = e3
% 159.52/28.14 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | BETA: splitting (1) gives:
% 159.52/28.14 |
% 159.52/28.14 | Case 1:
% 159.52/28.14 | |
% 159.52/28.14 | | (7) all_58_0 = e0 & op(e3, e3) = e0
% 159.52/28.14 | |
% 159.52/28.14 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #859.
% 159.52/28.14 | |
% 159.52/28.14 | Case 2:
% 159.52/28.14 | |
% 159.52/28.14 | | (8) all_58_2 = e0 & op(e2, e3) = e0
% 159.52/28.14 | |
% 159.52/28.14 | | ALPHA: (8) implies:
% 159.52/28.14 | | (9) op(e2, e3) = e0
% 159.52/28.14 | |
% 159.52/28.14 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1156.
% 159.52/28.14 | |
% 159.52/28.14 | End of split
% 159.52/28.14 |
% 159.52/28.14 End of proof
% 159.52/28.14
% 159.52/28.14 Sub-proof #616 shows that the following formulas are inconsistent:
% 159.52/28.14 ----------------------------------------------------------------
% 159.52/28.14 (1) op(e1, e1) = e3
% 159.52/28.14 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.14 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.14 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.14 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.14 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.14 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.14 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.14 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.14 (6) op(e3, e3) = all_10_2
% 159.52/28.14 (7) ~ (all_10_2 = e1)
% 159.52/28.14 (8) op(e1, e1) = all_6_2
% 159.52/28.14 (9) ~ (all_52_7 = e3)
% 159.52/28.14 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.14 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.14 e1)
% 159.52/28.14 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.14 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.14 (12) op(e3, e3) = all_28_1
% 159.52/28.14 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.14 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.14 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.14 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.14 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.14 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.14 (16) op(e3, e2) = all_52_4
% 159.52/28.14 (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.14 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.14 (18) all_54_0 = all_10_2
% 159.52/28.14 (19) op(e2, e3) = all_52_1
% 159.52/28.14 (20) ~ (all_52_13 = e3)
% 159.52/28.14 (21) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.14 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.14 (22) ~ (all_10_2 = e0)
% 159.52/28.14 (23) ~ (e3 = e0)
% 159.52/28.14 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.14 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.14 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.14 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.14 (26) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.14 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.14 e2)
% 159.52/28.14 (27) ~ (e2 = e0)
% 159.52/28.14 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.14 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.14 (29) op(e1, e3) = all_52_2
% 159.52/28.14 (30) op(e2, e0) = all_52_13
% 159.52/28.14 (31) op(e2, e3) = e2
% 159.52/28.14 (32) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.14 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.14 (33) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.14 (34) ~ (e3 = e1)
% 159.52/28.14 (35) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.14 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.14 (36) op(e1, e2) = all_52_6
% 159.52/28.14 (37) ~ (all_52_4 = all_10_2)
% 159.52/28.14 (38) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.14 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.14 (39) op(e0, e1) = all_52_11
% 159.52/28.14 (40) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.14 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.14 (41) ~ (all_52_4 = e3)
% 159.52/28.14 (42) ~ (all_10_2 = e2)
% 159.52/28.14 (43) ~ (e2 = e1)
% 159.52/28.14 (44) ~ (e1 = e0)
% 159.52/28.14 (45) all_58_4 = e3
% 159.52/28.14 (46) all_58_3 = e3
% 159.52/28.14 (47) ~ (all_6_2 = e2)
% 159.52/28.14 (48) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.14 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.14 e3)
% 159.52/28.14 (49) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.14 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.14 (50) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.14 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.14 (51) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.14 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.14 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.14 (52) op(e1, e3) = e1
% 159.52/28.14 (53) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.14 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.14 (54) op(e0, e2) = all_52_7
% 159.52/28.14 (55) ~ (all_52_6 = e3)
% 159.52/28.14 (56) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.14 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.14 (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.14 (58) ~ (e3 = e2)
% 159.52/28.14 (59) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.14 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.14 (60) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.14 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.14 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.14 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.14
% 159.52/28.14 Begin of proof
% 159.52/28.14 |
% 159.52/28.14 | BETA: splitting (14) gives:
% 159.52/28.14 |
% 159.52/28.14 | Case 1:
% 159.52/28.14 | |
% 159.52/28.14 | | (61) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 159.52/28.14 | | e2)
% 159.52/28.14 | |
% 159.52/28.14 | | BETA: splitting (61) gives:
% 159.52/28.14 | |
% 159.52/28.14 | | Case 1:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (62) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (62) implies:
% 159.52/28.14 | | | (63) all_58_4 = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (45), (58), (63) are inconsistent by sub-proof #1467.
% 159.52/28.14 | | |
% 159.52/28.14 | | Case 2:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (64) all_58_5 = e2 & op(e2, e1) = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (64) implies:
% 159.52/28.14 | | | (65) all_58_5 = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (5), (23), (27), (31), (34), (38), (43), (44), (46), (57), (65)
% 159.52/28.14 | | | are inconsistent by sub-proof #898.
% 159.52/28.14 | | |
% 159.52/28.14 | | End of split
% 159.52/28.14 | |
% 159.52/28.14 | Case 2:
% 159.52/28.14 | |
% 159.52/28.14 | | (66) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 159.52/28.14 | | e2)
% 159.52/28.14 | |
% 159.52/28.14 | | BETA: splitting (66) gives:
% 159.52/28.14 | |
% 159.52/28.14 | | Case 1:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (67) all_58_8 = e2 & op(e1, e1) = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | REF_CLOSE: (8), (47), (57), (67) are inconsistent by sub-proof #1440.
% 159.52/28.14 | | |
% 159.52/28.14 | | Case 2:
% 159.52/28.14 | | |
% 159.52/28.14 | | | (68) all_58_14 = e2 & op(e0, e1) = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | ALPHA: (68) implies:
% 159.52/28.14 | | | (69) all_58_14 = e2
% 159.52/28.14 | | | (70) op(e0, e1) = e2
% 159.52/28.14 | | |
% 159.52/28.14 | | | BETA: splitting (17) gives:
% 159.52/28.14 | | |
% 159.52/28.14 | | | Case 1:
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | (71) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 159.52/28.14 | | | | = e3)
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | BETA: splitting (71) gives:
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | Case 1:
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | (72) all_58_6 = e3 & op(e1, e3) = e3
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.52/28.14 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 159.52/28.14 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 159.52/28.14 | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 159.52/28.14 | | | | | (42), (43), (44), (46), (47), (48), (49), (50), (51), (52),
% 159.52/28.14 | | | | | (53), (54), (55), (56), (57), (58), (59), (60), (70), (72)
% 159.52/28.14 | | | | | are inconsistent by sub-proof #619.
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | Case 2:
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | (73) all_58_7 = e3 & op(e1, e2) = e3
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | | REF_CLOSE: (36), (55), (57), (73) are inconsistent by sub-proof #1184.
% 159.52/28.14 | | | | |
% 159.52/28.14 | | | | End of split
% 159.52/28.14 | | | |
% 159.52/28.14 | | | Case 2:
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | (74) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 159.52/28.14 | | | | = e3)
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | BETA: splitting (74) gives:
% 159.52/28.14 | | | |
% 159.52/28.14 | | | | Case 1:
% 159.52/28.14 | | | | |
% 159.52/28.15 | | | | | (75) all_58_8 = e3 & op(e1, e1) = e3
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | ALPHA: (75) implies:
% 159.52/28.15 | | | | | (76) all_58_8 = e3
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | REF_CLOSE: (23), (27), (34), (35), (40), (43), (44), (45), (69), (76)
% 159.52/28.15 | | | | | are inconsistent by sub-proof #739.
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | Case 2:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | (77) all_58_11 = e3 & op(e1, e0) = e3
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | ALPHA: (77) implies:
% 159.52/28.15 | | | | | (78) all_58_11 = e3
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | BETA: splitting (21) gives:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | Case 1:
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | (79) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 159.52/28.15 | | | | | | e2) = e2)
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | BETA: splitting (79) gives:
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | Case 1:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | (80) all_58_6 = e2 & op(e1, e3) = e2
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | ALPHA: (80) implies:
% 159.52/28.15 | | | | | | | (81) all_58_6 = e2
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | REF_CLOSE: (13), (19), (23), (24), (27), (31), (34), (43), (44),
% 159.52/28.15 | | | | | | | (56), (57), (58), (81) are inconsistent by sub-proof
% 159.52/28.15 | | | | | | | #1152.
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | Case 2:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | (82) all_58_7 = e2 & op(e1, e2) = e2
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | ALPHA: (82) implies:
% 159.52/28.15 | | | | | | | (83) all_58_7 = e2
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | BETA: splitting (15) gives:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | Case 1:
% 159.52/28.15 | | | | | | | |
% 159.52/28.15 | | | | | | | | (84) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 159.52/28.15 | | | | | | | | op(e2, e0) = e2)
% 159.52/28.15 | | | | | | | |
% 159.52/28.15 | | | | | | | | BETA: splitting (84) gives:
% 159.52/28.15 | | | | | | | |
% 159.52/28.15 | | | | | | | | Case 1:
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | (85) all_58_9 = e2 & op(e3, e0) = e2
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | ALPHA: (85) implies:
% 159.52/28.15 | | | | | | | | | (86) all_58_9 = e2
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | BETA: splitting (28) gives:
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | Case 1:
% 159.52/28.15 | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | (87) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 159.52/28.15 | | | | | | | | | | op(e1, e2) = e0)
% 159.52/28.15 | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | BETA: splitting (87) gives:
% 159.52/28.15 | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | Case 1:
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | (88) all_58_6 = e0 & op(e1, e3) = e0
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | ALPHA: (88) implies:
% 159.52/28.15 | | | | | | | | | | | (89) all_58_6 = e0
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | BETA: splitting (51) gives:
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | Case 1:
% 159.52/28.15 | | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | | (90) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 159.52/28.15 | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 159.52/28.15 | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.15 | | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | | ALPHA: (90) implies:
% 159.52/28.15 | | | | | | | | | | | | (91) op(e3, e3) = all_22_1
% 159.52/28.15 | | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.15 | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 159.52/28.15 | | | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 159.52/28.15 | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 159.52/28.15 | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.52/28.15 | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (49), (50),
% 159.52/28.15 | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58),
% 159.52/28.15 | | | | | | | | | | | | (59), (60), (69), (70), (78), (83), (86), (89),
% 159.52/28.15 | | | | | | | | | | | | (91) are inconsistent by sub-proof #617.
% 159.52/28.15 | | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | Case 2:
% 159.52/28.15 | | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | | (92) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 159.52/28.15 | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.15 | | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | | ALPHA: (92) implies:
% 159.52/28.15 | | | | | | | | | | | | (93) op(e3, e3) = all_22_1
% 159.52/28.15 | | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.15 | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 159.52/28.15 | | | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 159.52/28.15 | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 159.52/28.15 | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.52/28.15 | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (49), (50),
% 159.52/28.15 | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58),
% 159.52/28.15 | | | | | | | | | | | | (59), (60), (69), (70), (78), (83), (86), (89),
% 159.52/28.15 | | | | | | | | | | | | (93) are inconsistent by sub-proof #617.
% 159.52/28.15 | | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | End of split
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | Case 2:
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | (94) all_58_7 = e0 & op(e1, e2) = e0
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | REF_CLOSE: (27), (83), (94) are inconsistent by sub-proof
% 159.52/28.15 | | | | | | | | | | | #1468.
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | End of split
% 159.52/28.15 | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | Case 2:
% 159.52/28.15 | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | (95) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 159.52/28.15 | | | | | | | | | | & op(e1, e0) = e0)
% 159.52/28.15 | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | BETA: splitting (95) gives:
% 159.52/28.15 | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | Case 1:
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | (96) all_58_8 = e0 & op(e1, e1) = e0
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | ALPHA: (96) implies:
% 159.52/28.15 | | | | | | | | | | | (97) op(e1, e1) = e0
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | REF_CLOSE: (1), (23), (57), (97) are inconsistent by
% 159.52/28.15 | | | | | | | | | | | sub-proof #1466.
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | Case 2:
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | (98) all_58_11 = e0 & op(e1, e0) = e0
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | ALPHA: (98) implies:
% 159.52/28.15 | | | | | | | | | | | (99) all_58_11 = e0
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | | REF_CLOSE: (23), (78), (99) are inconsistent by sub-proof
% 159.52/28.15 | | | | | | | | | | | #1216.
% 159.52/28.15 | | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | | End of split
% 159.52/28.15 | | | | | | | | | |
% 159.52/28.15 | | | | | | | | | End of split
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | Case 2:
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | (100) all_58_10 = e2 & op(e2, e0) = e2
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | ALPHA: (100) implies:
% 159.52/28.15 | | | | | | | | | (101) all_58_10 = e2
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | REF_CLOSE: (5), (23), (27), (31), (34), (38), (43), (44),
% 159.52/28.15 | | | | | | | | | (46), (57), (101) are inconsistent by sub-proof
% 159.52/28.15 | | | | | | | | | #906.
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | End of split
% 159.52/28.15 | | | | | | | |
% 159.52/28.15 | | | | | | | Case 2:
% 159.52/28.15 | | | | | | | |
% 159.52/28.15 | | | | | | | | (102) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 159.52/28.15 | | | | | | | | op(e0, e0) = e2)
% 159.52/28.15 | | | | | | | |
% 159.52/28.15 | | | | | | | | BETA: splitting (102) gives:
% 159.52/28.15 | | | | | | | |
% 159.52/28.15 | | | | | | | | Case 1:
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | (103) all_58_11 = e2 & op(e1, e0) = e2
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | ALPHA: (103) implies:
% 159.52/28.15 | | | | | | | | | (104) all_58_11 = e2
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | REF_CLOSE: (58), (78), (104) are inconsistent by sub-proof
% 159.52/28.15 | | | | | | | | | #1049.
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | Case 2:
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | (105) all_58_15 = e2 & op(e0, e0) = e2
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | ALPHA: (105) implies:
% 159.52/28.15 | | | | | | | | | (106) all_58_15 = e2
% 159.52/28.15 | | | | | | | | | (107) op(e0, e0) = e2
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | | REF_CLOSE: (9), (10), (23), (27), (34), (43), (44), (48),
% 159.52/28.15 | | | | | | | | | (54), (57), (58), (60), (69), (106), (107) are
% 159.52/28.15 | | | | | | | | | inconsistent by sub-proof #1380.
% 159.52/28.15 | | | | | | | | |
% 159.52/28.15 | | | | | | | | End of split
% 159.52/28.15 | | | | | | | |
% 159.52/28.15 | | | | | | | End of split
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | End of split
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | Case 2:
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | (108) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 159.52/28.15 | | | | | | op(e1, e0) = e2)
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | BETA: splitting (108) gives:
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | Case 1:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | (109) all_58_8 = e2 & op(e1, e1) = e2
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | REF_CLOSE: (23), (27), (34), (35), (40), (43), (44), (45), (69),
% 159.52/28.15 | | | | | | | (109) are inconsistent by sub-proof #1338.
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | Case 2:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | (110) all_58_11 = e2 & op(e1, e0) = e2
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | REF_CLOSE: (58), (78), (110) are inconsistent by sub-proof #852.
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | End of split
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | End of split
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | End of split
% 159.52/28.15 | | | |
% 159.52/28.15 | | | End of split
% 159.52/28.15 | | |
% 159.52/28.15 | | End of split
% 159.52/28.15 | |
% 159.52/28.15 | End of split
% 159.52/28.15 |
% 159.52/28.15 End of proof
% 159.52/28.15
% 159.52/28.15 Sub-proof #617 shows that the following formulas are inconsistent:
% 159.52/28.15 ----------------------------------------------------------------
% 159.52/28.15 (1) op(e1, e1) = e3
% 159.52/28.15 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.15 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.15 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.15 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.15 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.15 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.15 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.15 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.15 (6) op(e3, e3) = all_10_2
% 159.52/28.15 (7) ~ (all_10_2 = e1)
% 159.52/28.15 (8) op(e1, e1) = all_6_2
% 159.52/28.15 (9) ~ (all_52_7 = e3)
% 159.52/28.15 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.15 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.15 e1)
% 159.52/28.15 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.15 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.15 (12) op(e3, e3) = all_28_1
% 159.52/28.15 (13) all_58_7 = e2
% 159.52/28.15 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.15 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.15 (15) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.15 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.15 (16) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.15 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.15 (17) op(e3, e2) = all_52_4
% 159.52/28.15 (18) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.15 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.15 (19) all_58_14 = e2
% 159.52/28.15 (20) all_54_0 = all_10_2
% 159.52/28.15 (21) op(e2, e3) = all_52_1
% 159.52/28.15 (22) ~ (all_52_13 = e3)
% 159.52/28.15 (23) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.15 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.15 (24) ~ (all_10_2 = e0)
% 159.52/28.15 (25) ~ (e3 = e0)
% 159.52/28.15 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.15 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.15 (27) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.15 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.15 (28) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.15 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.15 e2)
% 159.52/28.15 (29) ~ (e2 = e0)
% 159.52/28.15 (30) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.15 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.15 (31) all_58_6 = e0
% 159.52/28.15 (32) op(e1, e3) = all_52_2
% 159.52/28.15 (33) op(e2, e0) = all_52_13
% 159.52/28.15 (34) op(e2, e3) = e2
% 159.52/28.15 (35) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.15 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.15 (36) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.15 (37) ~ (e3 = e1)
% 159.52/28.15 (38) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.15 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.15 (39) op(e1, e2) = all_52_6
% 159.52/28.15 (40) ~ (all_52_4 = all_10_2)
% 159.52/28.15 (41) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.15 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.15 (42) op(e0, e1) = e2
% 159.52/28.15 (43) op(e0, e1) = all_52_11
% 159.52/28.15 (44) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.15 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.15 (45) ~ (all_52_4 = e3)
% 159.52/28.15 (46) ~ (all_10_2 = e2)
% 159.52/28.15 (47) ~ (e2 = e1)
% 159.52/28.15 (48) ~ (e1 = e0)
% 159.52/28.15 (49) all_58_4 = e3
% 159.52/28.15 (50) all_58_3 = e3
% 159.52/28.15 (51) ~ (all_6_2 = e2)
% 159.52/28.15 (52) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.15 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.15 e3)
% 159.52/28.15 (53) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.15 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.15 (54) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.15 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.15 (55) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.15 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.15 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.15 (56) op(e1, e3) = e1
% 159.52/28.15 (57) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.15 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.15 (58) all_58_9 = e2
% 159.52/28.15 (59) op(e0, e2) = all_52_7
% 159.52/28.15 (60) op(e3, e3) = all_22_1
% 159.52/28.15 (61) ~ (all_52_6 = e3)
% 159.52/28.15 (62) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.15 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.15 (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.15 (64) ~ (e3 = e2)
% 159.52/28.15 (65) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.15 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.15 (66) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.15 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.15 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.15 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.15 (67) all_58_11 = e3
% 159.52/28.15
% 159.52/28.15 Begin of proof
% 159.52/28.15 |
% 159.52/28.15 | BETA: splitting (14) gives:
% 159.52/28.15 |
% 159.52/28.15 | Case 1:
% 159.52/28.15 | |
% 159.52/28.15 | | (68) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 159.52/28.15 | | e3)
% 159.52/28.15 | |
% 159.52/28.15 | | BETA: splitting (68) gives:
% 159.52/28.15 | |
% 159.52/28.15 | | Case 1:
% 159.52/28.15 | | |
% 159.52/28.15 | | | (69) all_58_0 = e3 & op(e3, e3) = e3
% 159.52/28.15 | | |
% 159.52/28.15 | | | ALPHA: (69) implies:
% 159.52/28.15 | | | (70) all_58_0 = e3
% 159.52/28.15 | | |
% 159.52/28.15 | | | BETA: splitting (53) gives:
% 159.52/28.15 | | |
% 159.52/28.15 | | | Case 1:
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 159.52/28.15 | | | | = e1)
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | BETA: splitting (71) gives:
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | Case 1:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | (72) all_58_0 = e1 & op(e3, e3) = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | ALPHA: (72) implies:
% 159.52/28.15 | | | | | (73) all_58_0 = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | REF_CLOSE: (6), (7), (12), (14), (20), (21), (24), (25), (26), (29),
% 159.52/28.15 | | | | | (31), (32), (34), (36), (37), (46), (47), (48), (55), (56),
% 159.52/28.15 | | | | | (62), (63), (64), (73) are inconsistent by sub-proof #660.
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | Case 2:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | (74) all_58_1 = e1 & op(e3, e2) = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | ALPHA: (74) implies:
% 159.52/28.15 | | | | | (75) all_58_1 = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | BETA: splitting (35) gives:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | Case 1:
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | (76) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 159.52/28.15 | | | | | | e2) = e0)
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | BETA: splitting (76) gives:
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | Case 1:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | (77) all_58_1 = e0 & op(e3, e2) = e0
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | REF_CLOSE: (48), (75), (77) are inconsistent by sub-proof #1327.
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | Case 2:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | (78) all_58_3 = e0 & op(e2, e2) = e0
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | REF_CLOSE: (25), (50), (78) are inconsistent by sub-proof #910.
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | End of split
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | Case 2:
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | (79) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 159.52/28.15 | | | | | | e2) = e0)
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | BETA: splitting (79) gives:
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | | Case 1:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | (80) all_58_7 = e0 & op(e1, e2) = e0
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | ALPHA: (80) implies:
% 159.52/28.15 | | | | | | | (81) all_58_7 = e0
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | REF_CLOSE: (13), (29), (81) are inconsistent by sub-proof #1086.
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | Case 2:
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | (82) all_58_13 = e0 & op(e0, e2) = e0
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | | REF_CLOSE: (3), (14), (19), (21), (23), (25), (26), (29), (34),
% 159.52/28.15 | | | | | | | (37), (38), (44), (47), (48), (49), (50), (58), (62),
% 159.52/28.15 | | | | | | | (63), (64), (65), (67), (70), (82) are inconsistent by
% 159.52/28.15 | | | | | | | sub-proof #618.
% 159.52/28.15 | | | | | | |
% 159.52/28.15 | | | | | | End of split
% 159.52/28.15 | | | | | |
% 159.52/28.15 | | | | | End of split
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | End of split
% 159.52/28.15 | | | |
% 159.52/28.15 | | | Case 2:
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | (83) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 159.52/28.15 | | | | = e1)
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | BETA: splitting (83) gives:
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | Case 1:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | (84) all_58_4 = e1 & op(e3, e1) = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | ALPHA: (84) implies:
% 159.52/28.15 | | | | | (85) all_58_4 = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | COMBINE_EQS: (49), (85) imply:
% 159.52/28.15 | | | | | (86) e3 = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | COMBINE_EQS: (70), (86) imply:
% 159.52/28.15 | | | | | (87) all_58_0 = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | REF_CLOSE: (6), (7), (12), (14), (20), (21), (24), (25), (26), (29),
% 159.52/28.15 | | | | | (31), (32), (34), (36), (37), (46), (47), (48), (55), (56),
% 159.52/28.15 | | | | | (62), (63), (64), (87) are inconsistent by sub-proof #660.
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | Case 2:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | (88) all_58_9 = e1 & op(e3, e0) = e1
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | REF_CLOSE: (47), (58), (88) are inconsistent by sub-proof #1325.
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | End of split
% 159.52/28.15 | | | |
% 159.52/28.15 | | | End of split
% 159.52/28.15 | | |
% 159.52/28.15 | | Case 2:
% 159.52/28.15 | | |
% 159.52/28.15 | | | (89) all_58_2 = e3 & op(e2, e3) = e3
% 159.52/28.15 | | |
% 159.52/28.15 | | | ALPHA: (89) implies:
% 159.52/28.15 | | | (90) op(e2, e3) = e3
% 159.52/28.15 | | |
% 159.52/28.15 | | | REF_CLOSE: (21), (34), (63), (64), (90) are inconsistent by sub-proof
% 159.52/28.15 | | | #1159.
% 159.52/28.15 | | |
% 159.52/28.15 | | End of split
% 159.52/28.15 | |
% 159.52/28.15 | Case 2:
% 159.52/28.15 | |
% 159.52/28.15 | | (91) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 159.52/28.15 | | e3)
% 159.52/28.15 | |
% 159.52/28.15 | | BETA: splitting (91) gives:
% 159.52/28.15 | |
% 159.52/28.15 | | Case 1:
% 159.52/28.15 | | |
% 159.52/28.15 | | | (92) all_58_6 = e3 & op(e1, e3) = e3
% 159.52/28.15 | | |
% 159.52/28.15 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.52/28.15 | | | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 159.52/28.15 | | | (25), (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 159.52/28.15 | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 159.52/28.15 | | | (46), (47), (48), (50), (51), (52), (53), (54), (55), (56),
% 159.52/28.15 | | | (57), (59), (61), (62), (63), (64), (65), (66), (92) are
% 159.52/28.15 | | | inconsistent by sub-proof #619.
% 159.52/28.15 | | |
% 159.52/28.15 | | Case 2:
% 159.52/28.15 | | |
% 159.52/28.15 | | | (93) all_58_12 = e3 & op(e0, e3) = e3
% 159.52/28.15 | | |
% 159.52/28.15 | | | ALPHA: (93) implies:
% 159.52/28.15 | | | (94) all_58_12 = e3
% 159.52/28.15 | | |
% 159.52/28.15 | | | REF_CLOSE: (6), (7), (12), (20), (24), (26), (29), (32), (34), (36), (46),
% 159.52/28.15 | | | (47), (48), (56), (60), (62), (63), (93), (94) are inconsistent
% 159.52/28.15 | | | by sub-proof #663.
% 159.52/28.15 | | |
% 159.52/28.15 | | End of split
% 159.52/28.15 | |
% 159.52/28.15 | End of split
% 159.52/28.15 |
% 159.52/28.15 End of proof
% 159.52/28.15
% 159.52/28.15 Sub-proof #618 shows that the following formulas are inconsistent:
% 159.52/28.15 ----------------------------------------------------------------
% 159.52/28.15 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.15 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.15 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.15 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.15 (3) all_58_14 = e2
% 159.52/28.15 (4) op(e2, e3) = all_52_1
% 159.52/28.15 (5) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.15 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.15 (6) ~ (e3 = e0)
% 159.52/28.15 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.15 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.15 (8) ~ (e2 = e0)
% 159.52/28.15 (9) op(e2, e3) = e2
% 159.52/28.15 (10) ~ (e3 = e1)
% 159.52/28.15 (11) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.15 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.15 (12) all_58_13 = e0 & op(e0, e2) = e0
% 159.52/28.15 (13) all_58_0 = e3
% 159.52/28.15 (14) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.15 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.15 (15) ~ (e2 = e1)
% 159.52/28.15 (16) ~ (e1 = e0)
% 159.52/28.15 (17) all_58_4 = e3
% 159.52/28.15 (18) all_58_3 = e3
% 159.52/28.15 (19) all_58_9 = e2
% 159.52/28.15 (20) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.15 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.15 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.15 (22) ~ (e3 = e2)
% 159.52/28.15 (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.15 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.15 (24) all_58_11 = e3
% 159.52/28.15
% 159.52/28.15 Begin of proof
% 159.52/28.15 |
% 159.52/28.15 | ALPHA: (12) implies:
% 159.52/28.15 | (25) all_58_13 = e0
% 159.52/28.15 |
% 159.52/28.15 | BETA: splitting (5) gives:
% 159.52/28.15 |
% 159.52/28.15 | Case 1:
% 159.52/28.15 | |
% 159.52/28.15 | | (26) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 159.52/28.15 | | e2)
% 159.52/28.15 | |
% 159.52/28.15 | | BETA: splitting (26) gives:
% 159.52/28.15 | |
% 159.52/28.15 | | Case 1:
% 159.52/28.15 | | |
% 159.52/28.15 | | | (27) all_58_6 = e2 & op(e1, e3) = e2
% 159.52/28.15 | | |
% 159.52/28.15 | | | ALPHA: (27) implies:
% 159.52/28.15 | | | (28) all_58_6 = e2
% 159.52/28.15 | | |
% 159.52/28.15 | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (15), (16), (20), (21),
% 159.52/28.15 | | | (22), (28) are inconsistent by sub-proof #1152.
% 159.52/28.15 | | |
% 159.52/28.15 | | Case 2:
% 159.52/28.15 | | |
% 159.52/28.15 | | | (29) all_58_7 = e2 & op(e1, e2) = e2
% 159.52/28.15 | | |
% 159.52/28.15 | | | ALPHA: (29) implies:
% 159.52/28.15 | | | (30) all_58_7 = e2
% 159.52/28.15 | | |
% 159.52/28.15 | | | BETA: splitting (23) gives:
% 159.52/28.15 | | |
% 159.52/28.15 | | | Case 1:
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | (31) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 159.52/28.15 | | | | = e0)
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | REF_CLOSE: (1), (6), (10), (13), (15), (16), (18), (25), (30), (31) are
% 159.52/28.15 | | | | inconsistent by sub-proof #856.
% 159.52/28.15 | | | |
% 159.52/28.15 | | | Case 2:
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | (32) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 159.52/28.15 | | | | = e0)
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | BETA: splitting (32) gives:
% 159.52/28.15 | | | |
% 159.52/28.15 | | | | Case 1:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | (33) all_58_4 = e0 & op(e3, e1) = e0
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | REF_CLOSE: (6), (17), (33) are inconsistent by sub-proof #1344.
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | Case 2:
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | (34) all_58_9 = e0 & op(e3, e0) = e0
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | | REF_CLOSE: (8), (19), (34) are inconsistent by sub-proof #1252.
% 159.52/28.15 | | | | |
% 159.52/28.15 | | | | End of split
% 159.52/28.15 | | | |
% 159.52/28.15 | | | End of split
% 159.52/28.15 | | |
% 159.52/28.15 | | End of split
% 159.52/28.15 | |
% 159.52/28.15 | Case 2:
% 159.52/28.15 | |
% 159.52/28.15 | | (35) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 159.52/28.15 | | e2)
% 159.52/28.15 | |
% 159.52/28.15 | | BETA: splitting (35) gives:
% 159.52/28.15 | |
% 159.52/28.15 | | Case 1:
% 159.52/28.15 | | |
% 159.52/28.15 | | | (36) all_58_8 = e2 & op(e1, e1) = e2
% 159.52/28.15 | | |
% 159.52/28.15 | | | REF_CLOSE: (3), (6), (8), (10), (11), (14), (15), (16), (17), (36) are
% 159.52/28.15 | | | inconsistent by sub-proof #1338.
% 159.52/28.15 | | |
% 159.52/28.15 | | Case 2:
% 159.52/28.15 | | |
% 159.52/28.15 | | | (37) all_58_11 = e2 & op(e1, e0) = e2
% 159.52/28.15 | | |
% 159.52/28.15 | | | REF_CLOSE: (22), (24), (37) are inconsistent by sub-proof #852.
% 159.52/28.15 | | |
% 159.52/28.15 | | End of split
% 159.52/28.15 | |
% 159.52/28.15 | End of split
% 159.52/28.15 |
% 159.52/28.15 End of proof
% 159.52/28.15
% 159.52/28.15 Sub-proof #619 shows that the following formulas are inconsistent:
% 159.52/28.15 ----------------------------------------------------------------
% 159.52/28.15 (1) op(e1, e1) = e3
% 159.52/28.15 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.15 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.15 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.15 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.15 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.15 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.15 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.15 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.15 (6) op(e3, e3) = all_10_2
% 159.52/28.15 (7) ~ (all_10_2 = e1)
% 159.52/28.15 (8) op(e1, e1) = all_6_2
% 159.52/28.15 (9) ~ (all_52_7 = e3)
% 159.52/28.15 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.15 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.15 e1)
% 159.52/28.15 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.15 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.15 (12) op(e3, e3) = all_28_1
% 159.52/28.15 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.15 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.15 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.15 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.15 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.15 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.15 (16) op(e3, e2) = all_52_4
% 159.52/28.15 (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.15 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.15 (18) all_58_6 = e3 & op(e1, e3) = e3
% 159.52/28.15 (19) all_54_0 = all_10_2
% 159.52/28.15 (20) op(e2, e3) = all_52_1
% 159.52/28.15 (21) ~ (all_52_13 = e3)
% 159.52/28.15 (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.15 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.15 (23) ~ (all_10_2 = e0)
% 159.52/28.16 (24) ~ (e3 = e0)
% 159.52/28.16 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.16 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.16 (26) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.16 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.16 (27) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.16 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.16 e2)
% 159.52/28.16 (28) ~ (e2 = e0)
% 159.52/28.16 (29) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.16 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.16 (30) op(e1, e3) = all_52_2
% 159.52/28.16 (31) op(e2, e0) = all_52_13
% 159.52/28.16 (32) op(e2, e3) = e2
% 159.52/28.16 (33) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.16 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.16 (34) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.16 (35) ~ (e3 = e1)
% 159.52/28.16 (36) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.16 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.16 (37) op(e1, e2) = all_52_6
% 159.52/28.16 (38) ~ (all_52_4 = all_10_2)
% 159.52/28.16 (39) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.16 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.16 (40) op(e0, e1) = e2
% 159.52/28.16 (41) op(e0, e1) = all_52_11
% 159.52/28.16 (42) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.16 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.16 (43) ~ (all_52_4 = e3)
% 159.52/28.16 (44) ~ (all_10_2 = e2)
% 159.52/28.16 (45) ~ (e2 = e1)
% 159.52/28.16 (46) ~ (e1 = e0)
% 159.52/28.16 (47) all_58_3 = e3
% 159.52/28.16 (48) ~ (all_6_2 = e2)
% 159.52/28.16 (49) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.16 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.16 e3)
% 159.52/28.16 (50) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.16 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.16 (51) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.16 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.16 (52) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.16 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.16 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.16 (53) op(e1, e3) = e1
% 159.52/28.16 (54) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.16 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.16 (55) op(e0, e2) = all_52_7
% 159.52/28.16 (56) ~ (all_52_6 = e3)
% 159.52/28.16 (57) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.16 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.16 (58) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.16 (59) ~ (e3 = e2)
% 159.52/28.16 (60) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.16 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.16 (61) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.16 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.16 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.16 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.16
% 159.52/28.16 Begin of proof
% 159.52/28.16 |
% 159.52/28.16 | ALPHA: (18) implies:
% 159.52/28.16 | (62) all_58_6 = e3
% 159.52/28.16 |
% 159.52/28.16 | BETA: splitting (25) gives:
% 159.52/28.16 |
% 159.52/28.16 | Case 1:
% 159.52/28.16 | |
% 159.52/28.16 | | (63) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 159.52/28.16 | | e1)
% 159.52/28.16 | |
% 159.52/28.16 | | BETA: splitting (63) gives:
% 159.52/28.16 | |
% 159.52/28.16 | | Case 1:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (64) all_58_0 = e1 & op(e3, e3) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | ALPHA: (64) implies:
% 159.52/28.16 | | | (65) op(e3, e3) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | BETA: splitting (34) gives:
% 159.52/28.16 | | |
% 159.52/28.16 | | | Case 1:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | (66) all_54_0 = e3
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | COMBINE_EQS: (19), (66) imply:
% 159.52/28.16 | | | | (67) all_10_2 = e3
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | SIMP: (67) implies:
% 159.52/28.16 | | | | (68) all_10_2 = e3
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | REDUCE: (6), (68) imply:
% 159.52/28.16 | | | | (69) op(e3, e3) = e3
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | BETA: splitting (52) gives:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | Case 1:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | (70) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3)
% 159.52/28.16 | | | | | = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | ALPHA: (70) implies:
% 159.52/28.16 | | | | | (71) op(e3, e3) = all_22_1
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | REF_CLOSE: (12), (35), (58), (65), (69), (71) are inconsistent by
% 159.52/28.16 | | | | | sub-proof #667.
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | Case 2:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | (72) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | ALPHA: (72) implies:
% 159.52/28.16 | | | | | (73) op(e3, e3) = all_22_1
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | REF_CLOSE: (12), (35), (58), (65), (69), (73) are inconsistent by
% 159.52/28.16 | | | | | sub-proof #667.
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | End of split
% 159.52/28.16 | | | |
% 159.52/28.16 | | | Case 2:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | (74) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | REF_CLOSE: (7), (19), (23), (44), (74) are inconsistent by sub-proof
% 159.52/28.16 | | | | #1307.
% 159.52/28.16 | | | |
% 159.52/28.16 | | | End of split
% 159.52/28.16 | | |
% 159.52/28.16 | | Case 2:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (75) all_58_2 = e1 & op(e2, e3) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | ALPHA: (75) implies:
% 159.52/28.16 | | | (76) op(e2, e3) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | REF_CLOSE: (32), (45), (58), (76) are inconsistent by sub-proof #1430.
% 159.52/28.16 | | |
% 159.52/28.16 | | End of split
% 159.52/28.16 | |
% 159.52/28.16 | Case 2:
% 159.52/28.16 | |
% 159.52/28.16 | | (77) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 159.52/28.16 | | e1)
% 159.52/28.16 | |
% 159.52/28.16 | | BETA: splitting (77) gives:
% 159.52/28.16 | |
% 159.52/28.16 | | Case 1:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (78) all_58_6 = e1 & op(e1, e3) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | ALPHA: (78) implies:
% 159.52/28.16 | | | (79) all_58_6 = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | REF_CLOSE: (35), (62), (79) are inconsistent by sub-proof #1073.
% 159.52/28.16 | | |
% 159.52/28.16 | | Case 2:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (80) all_58_12 = e1 & op(e0, e3) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | ALPHA: (80) implies:
% 159.52/28.16 | | | (81) all_58_12 = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | BETA: splitting (49) gives:
% 159.52/28.16 | | |
% 159.52/28.16 | | | Case 1:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | (82) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 159.52/28.16 | | | | e2) = e3)
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | BETA: splitting (82) gives:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | Case 1:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | (83) all_58_12 = e3 & op(e0, e3) = e3
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | REF_CLOSE: (6), (7), (12), (19), (23), (25), (28), (30), (32), (34),
% 159.52/28.16 | | | | | (44), (45), (46), (52), (53), (57), (58), (83) are
% 159.52/28.16 | | | | | inconsistent by sub-proof #662.
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | Case 2:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | (84) all_58_13 = e3 & op(e0, e2) = e3
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | REF_CLOSE: (9), (55), (58), (84) are inconsistent by sub-proof #1449.
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | End of split
% 159.52/28.16 | | | |
% 159.52/28.16 | | | Case 2:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | (85) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 159.52/28.16 | | | | e0) = e3)
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | BETA: splitting (85) gives:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | Case 1:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | (86) all_58_14 = e3 & op(e0, e1) = e3
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | ALPHA: (86) implies:
% 159.52/28.16 | | | | | (87) all_58_14 = e3
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.52/28.16 | | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21), (22),
% 159.52/28.16 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 159.52/28.16 | | | | | (33), (34), (35), (36), (37), (38), (39), (42), (43), (44),
% 159.52/28.16 | | | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 159.52/28.16 | | | | | (55), (56), (57), (58), (59), (60), (61), (87) are
% 159.52/28.16 | | | | | inconsistent by sub-proof #622.
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | Case 2:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | (88) all_58_15 = e3 & op(e0, e0) = e3
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | ALPHA: (88) implies:
% 159.52/28.16 | | | | | (89) all_58_15 = e3
% 159.52/28.16 | | | | | (90) op(e0, e0) = e3
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | BETA: splitting (61) gives:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | Case 1:
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | (91) all_58_15 = e0 & op(e0, e0) = e0
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | REF_CLOSE: (24), (89), (91) are inconsistent by sub-proof #1013.
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | Case 2:
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | (92) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 159.52/28.16 | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 159.52/28.16 | | | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.16 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | ALPHA: (92) implies:
% 159.52/28.16 | | | | | | (93) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.16 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | BETA: splitting (52) gives:
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | Case 1:
% 159.52/28.16 | | | | | | |
% 159.52/28.16 | | | | | | | (94) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3,
% 159.52/28.16 | | | | | | | e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 159.52/28.16 | | | | | | |
% 159.52/28.16 | | | | | | | ALPHA: (94) implies:
% 159.52/28.16 | | | | | | | (95) op(e3, e3) = all_22_1
% 159.52/28.16 | | | | | | |
% 159.52/28.16 | | | | | | | REF_CLOSE: (6), (7), (10), (12), (13), (19), (20), (23), (25),
% 159.52/28.16 | | | | | | | (27), (28), (32), (34), (40), (41), (44), (45), (46),
% 159.52/28.16 | | | | | | | (55), (57), (58), (62), (81), (89), (90), (93), (95)
% 159.52/28.16 | | | | | | | are inconsistent by sub-proof #620.
% 159.52/28.16 | | | | | | |
% 159.52/28.16 | | | | | | Case 2:
% 159.52/28.16 | | | | | | |
% 159.52/28.16 | | | | | | | (96) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 159.52/28.16 | | | | | | |
% 159.52/28.16 | | | | | | | ALPHA: (96) implies:
% 159.52/28.16 | | | | | | | (97) op(e3, e3) = all_22_1
% 159.52/28.16 | | | | | | |
% 159.52/28.16 | | | | | | | REF_CLOSE: (6), (7), (10), (12), (13), (19), (20), (23), (25),
% 159.52/28.16 | | | | | | | (27), (28), (32), (34), (40), (41), (44), (45), (46),
% 159.52/28.16 | | | | | | | (55), (57), (58), (62), (81), (89), (90), (93), (97)
% 159.52/28.16 | | | | | | | are inconsistent by sub-proof #620.
% 159.52/28.16 | | | | | | |
% 159.52/28.16 | | | | | | End of split
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | End of split
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | End of split
% 159.52/28.16 | | | |
% 159.52/28.16 | | | End of split
% 159.52/28.16 | | |
% 159.52/28.16 | | End of split
% 159.52/28.16 | |
% 159.52/28.16 | End of split
% 159.52/28.16 |
% 159.52/28.16 End of proof
% 159.52/28.16
% 159.52/28.16 Sub-proof #620 shows that the following formulas are inconsistent:
% 159.52/28.16 ----------------------------------------------------------------
% 159.52/28.16 (1) all_58_15 = e3
% 159.52/28.16 (2) op(e3, e3) = all_10_2
% 159.52/28.16 (3) ~ (all_10_2 = e1)
% 159.52/28.16 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.16 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.16 (5) op(e3, e3) = all_28_1
% 159.52/28.16 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.16 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.16 (7) all_58_6 = e3
% 159.52/28.16 (8) all_54_0 = all_10_2
% 159.52/28.16 (9) op(e2, e3) = all_52_1
% 159.52/28.16 (10) ~ (all_10_2 = e0)
% 159.52/28.16 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.16 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.16 (12) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.16 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.16 e2)
% 159.52/28.16 (13) ~ (e2 = e0)
% 159.52/28.16 (14) op(e2, e3) = e2
% 159.52/28.16 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.16 (16) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.16 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.16 (17) op(e0, e1) = e2
% 159.52/28.16 (18) op(e0, e1) = all_52_11
% 159.52/28.16 (19) ~ (all_10_2 = e2)
% 159.52/28.16 (20) ~ (e2 = e1)
% 159.52/28.16 (21) ~ (e1 = e0)
% 159.52/28.16 (22) op(e0, e2) = all_52_7
% 159.52/28.16 (23) op(e3, e3) = all_22_1
% 159.52/28.16 (24) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.16 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.16 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.16 (26) all_58_12 = e1
% 159.52/28.16 (27) op(e0, e0) = e3
% 159.52/28.16
% 159.52/28.16 Begin of proof
% 159.52/28.16 |
% 159.52/28.16 | BETA: splitting (16) gives:
% 159.52/28.16 |
% 159.52/28.16 | Case 1:
% 159.52/28.16 | |
% 159.52/28.16 | | (28) all_58_12 = e0 & op(e0, e3) = e0
% 159.52/28.16 | |
% 159.52/28.16 | | ALPHA: (28) implies:
% 159.52/28.16 | | (29) all_58_12 = e0
% 159.52/28.16 | |
% 159.52/28.16 | | REF_CLOSE: (21), (26), (29) are inconsistent by sub-proof #1513.
% 159.52/28.16 | |
% 159.52/28.16 | Case 2:
% 159.52/28.16 | |
% 159.52/28.16 | | (30) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 159.52/28.16 | | e0)
% 159.52/28.16 | |
% 159.52/28.16 | | BETA: splitting (30) gives:
% 159.52/28.16 | |
% 159.52/28.16 | | Case 1:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (31) all_58_13 = e0 & op(e0, e2) = e0
% 159.52/28.16 | | |
% 159.52/28.16 | | | ALPHA: (31) implies:
% 159.52/28.16 | | | (32) all_58_13 = e0
% 159.52/28.16 | | | (33) op(e0, e2) = e0
% 159.52/28.16 | | |
% 159.52/28.16 | | | BETA: splitting (15) gives:
% 159.52/28.16 | | |
% 159.52/28.16 | | | Case 1:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | (34) all_54_0 = e3
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | COMBINE_EQS: (8), (34) imply:
% 159.52/28.16 | | | | (35) all_10_2 = e3
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | REDUCE: (19), (35) imply:
% 159.52/28.16 | | | | (36) ~ (e3 = e2)
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | REDUCE: (3), (35) imply:
% 159.52/28.16 | | | | (37) ~ (e3 = e1)
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | REDUCE: (10), (35) imply:
% 159.52/28.16 | | | | (38) ~ (e3 = e0)
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | REDUCE: (2), (35) imply:
% 159.52/28.16 | | | | (39) op(e3, e3) = e3
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | BETA: splitting (24) gives:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | Case 1:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 159.52/28.16 | | | | | e3) = e0)
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | REF_CLOSE: (5), (13), (14), (23), (25), (38), (39), (40) are
% 159.52/28.16 | | | | | inconsistent by sub-proof #665.
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | Case 2:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | (41) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 159.52/28.16 | | | | | e3) = e0)
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | BETA: splitting (41) gives:
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | | Case 1:
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | (42) all_58_6 = e0 & op(e1, e3) = e0
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | REF_CLOSE: (7), (38), (42) are inconsistent by sub-proof #1350.
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | Case 2:
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | (43) all_58_12 = e0 & op(e0, e3) = e0
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | ALPHA: (43) implies:
% 159.52/28.16 | | | | | | (44) all_58_12 = e0
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | | REF_CLOSE: (1), (4), (6), (9), (11), (12), (13), (14), (20), (21),
% 159.52/28.16 | | | | | | (22), (24), (25), (27), (32), (33), (36), (37), (38),
% 159.52/28.16 | | | | | | (44) are inconsistent by sub-proof #621.
% 159.52/28.16 | | | | | |
% 159.52/28.16 | | | | | End of split
% 159.52/28.16 | | | | |
% 159.52/28.16 | | | | End of split
% 159.52/28.16 | | | |
% 159.52/28.16 | | | Case 2:
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | (45) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.16 | | | |
% 159.52/28.16 | | | | REF_CLOSE: (3), (8), (10), (19), (45) are inconsistent by sub-proof
% 159.52/28.16 | | | | #1307.
% 159.52/28.16 | | | |
% 159.52/28.16 | | | End of split
% 159.52/28.16 | | |
% 159.52/28.16 | | Case 2:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (46) all_58_14 = e0 & op(e0, e1) = e0
% 159.52/28.16 | | |
% 159.52/28.16 | | | ALPHA: (46) implies:
% 159.52/28.16 | | | (47) op(e0, e1) = e0
% 159.52/28.16 | | |
% 159.52/28.16 | | | REF_CLOSE: (13), (17), (18), (25), (47) are inconsistent by sub-proof
% 159.52/28.16 | | | #1372.
% 159.52/28.16 | | |
% 159.52/28.16 | | End of split
% 159.52/28.16 | |
% 159.52/28.16 | End of split
% 159.52/28.16 |
% 159.52/28.16 End of proof
% 159.52/28.16
% 159.52/28.16 Sub-proof #621 shows that the following formulas are inconsistent:
% 159.52/28.16 ----------------------------------------------------------------
% 159.52/28.16 (1) all_58_15 = e3
% 159.52/28.16 (2) all_58_13 = e0
% 159.52/28.16 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.16 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.16 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.16 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.16 (5) all_58_12 = e0
% 159.52/28.16 (6) op(e2, e3) = all_52_1
% 159.52/28.16 (7) ~ (e3 = e0)
% 159.52/28.16 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.16 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.16 (9) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 159.52/28.16 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.16 (10) ~ (e2 = e0)
% 159.52/28.16 (11) op(e2, e3) = e2
% 159.52/28.16 (12) ~ (e3 = e1)
% 159.52/28.16 (13) op(e0, e2) = e0
% 159.52/28.16 (14) ~ (e2 = e1)
% 159.52/28.16 (15) ~ (e1 = e0)
% 159.52/28.16 (16) op(e0, e2) = all_52_7
% 159.52/28.16 (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.16 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.16 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.16 (19) ~ (e3 = e2)
% 159.52/28.16 (20) op(e0, e0) = e3
% 159.52/28.16
% 159.52/28.16 Begin of proof
% 159.52/28.16 |
% 159.52/28.16 | BETA: splitting (3) gives:
% 159.52/28.16 |
% 159.52/28.16 | Case 1:
% 159.52/28.16 | |
% 159.52/28.16 | | (21) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 159.52/28.16 | | e1)
% 159.52/28.16 | |
% 159.52/28.16 | | BETA: splitting (21) gives:
% 159.52/28.16 | |
% 159.52/28.16 | | Case 1:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (22) all_58_12 = e1 & op(e0, e3) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | REF_CLOSE: (5), (15), (22) are inconsistent by sub-proof #1422.
% 159.52/28.16 | | |
% 159.52/28.16 | | Case 2:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (23) all_58_13 = e1 & op(e0, e2) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | ALPHA: (23) implies:
% 159.52/28.16 | | | (24) all_58_13 = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | REF_CLOSE: (2), (15), (24) are inconsistent by sub-proof #988.
% 159.52/28.16 | | |
% 159.52/28.16 | | End of split
% 159.52/28.16 | |
% 159.52/28.16 | Case 2:
% 159.52/28.16 | |
% 159.52/28.16 | | (25) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.16 | | e1)
% 159.52/28.16 | |
% 159.52/28.16 | | BETA: splitting (25) gives:
% 159.52/28.16 | |
% 159.52/28.16 | | Case 1:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (26) all_58_14 = e1 & op(e0, e1) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | ALPHA: (26) implies:
% 159.52/28.16 | | | (27) all_58_14 = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | REF_CLOSE: (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 159.52/28.16 | | | (16), (17), (18), (19), (20), (27) are inconsistent by
% 159.52/28.16 | | | sub-proof #1037.
% 159.52/28.16 | | |
% 159.52/28.16 | | Case 2:
% 159.52/28.16 | | |
% 159.52/28.16 | | | (28) all_58_15 = e1 & op(e0, e0) = e1
% 159.52/28.16 | | |
% 159.52/28.16 | | | REF_CLOSE: (1), (12), (28) are inconsistent by sub-proof #1010.
% 159.52/28.16 | | |
% 159.52/28.16 | | End of split
% 159.52/28.16 | |
% 159.52/28.16 | End of split
% 159.52/28.16 |
% 159.52/28.16 End of proof
% 159.52/28.16
% 159.52/28.16 Sub-proof #622 shows that the following formulas are inconsistent:
% 159.52/28.16 ----------------------------------------------------------------
% 159.52/28.16 (1) op(e1, e1) = e3
% 159.52/28.16 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.16 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.16 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.16 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.16 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.16 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.16 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.16 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.16 (6) op(e3, e3) = all_10_2
% 159.52/28.16 (7) ~ (all_10_2 = e1)
% 159.52/28.16 (8) all_58_14 = e3
% 159.52/28.16 (9) op(e1, e1) = all_6_2
% 159.52/28.16 (10) ~ (all_52_7 = e3)
% 159.52/28.16 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.16 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.16 e1)
% 159.52/28.16 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.16 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.16 (13) op(e3, e3) = all_28_1
% 159.52/28.16 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.16 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.16 (15) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.16 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.16 (16) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.16 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.16 (17) op(e3, e2) = all_52_4
% 159.52/28.16 (18) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.16 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.16 (19) all_54_0 = all_10_2
% 159.52/28.16 (20) op(e2, e3) = all_52_1
% 159.52/28.16 (21) ~ (all_52_13 = e3)
% 159.52/28.16 (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.16 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.16 (23) ~ (all_10_2 = e0)
% 159.52/28.16 (24) ~ (e3 = e0)
% 159.52/28.16 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.16 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.16 (26) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.16 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.16 (27) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.16 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.16 e2)
% 159.52/28.16 (28) ~ (e2 = e0)
% 159.52/28.16 (29) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.16 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.16 (30) op(e1, e3) = all_52_2
% 159.52/28.16 (31) op(e2, e0) = all_52_13
% 159.52/28.16 (32) op(e2, e3) = e2
% 159.52/28.16 (33) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.16 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.16 (34) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.16 (35) ~ (e3 = e1)
% 159.52/28.16 (36) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.16 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.16 (37) op(e1, e2) = all_52_6
% 159.52/28.16 (38) ~ (all_52_4 = all_10_2)
% 159.52/28.16 (39) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.16 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.16 (40) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.16 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.16 (41) ~ (all_52_4 = e3)
% 159.52/28.16 (42) ~ (all_10_2 = e2)
% 159.52/28.16 (43) ~ (e2 = e1)
% 159.52/28.16 (44) ~ (e1 = e0)
% 159.52/28.16 (45) all_58_3 = e3
% 159.52/28.16 (46) ~ (all_6_2 = e2)
% 159.52/28.16 (47) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.16 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.16 e3)
% 159.52/28.16 (48) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.16 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.16 (49) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.16 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.16 (50) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.16 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.16 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.16 (51) op(e1, e3) = e1
% 159.52/28.16 (52) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.16 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.16 (53) op(e0, e2) = all_52_7
% 159.52/28.16 (54) ~ (all_52_6 = e3)
% 159.52/28.16 (55) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.16 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.16 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.16 (57) ~ (e3 = e2)
% 159.52/28.16 (58) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.16 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.16 (59) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.16 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.16 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.16 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.16
% 159.52/28.16 Begin of proof
% 159.52/28.16 |
% 159.52/28.16 | BETA: splitting (15) gives:
% 159.52/28.16 |
% 159.52/28.16 | Case 1:
% 159.52/28.16 | |
% 159.52/28.16 | | (60) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 159.52/28.16 | | e2)
% 159.52/28.17 | |
% 159.52/28.17 | | BETA: splitting (60) gives:
% 159.52/28.17 | |
% 159.52/28.17 | | Case 1:
% 159.52/28.17 | | |
% 159.52/28.17 | | | (61) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.17 | | |
% 159.52/28.17 | | | ALPHA: (61) implies:
% 159.52/28.17 | | | (62) all_58_4 = e2
% 159.52/28.17 | | |
% 159.52/28.17 | | | BETA: splitting (18) gives:
% 159.52/28.17 | | |
% 159.52/28.17 | | | Case 1:
% 159.52/28.17 | | | |
% 159.52/28.17 | | | | (63) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 159.52/28.17 | | | | = e3)
% 159.52/28.17 | | | |
% 159.52/28.17 | | | | BETA: splitting (63) gives:
% 159.52/28.17 | | | |
% 159.52/28.17 | | | | Case 1:
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | (64) all_58_6 = e3 & op(e1, e3) = e3
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | ALPHA: (64) implies:
% 159.52/28.17 | | | | | (65) all_58_6 = e3
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | BETA: splitting (36) gives:
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | Case 1:
% 159.52/28.17 | | | | | |
% 159.52/28.17 | | | | | | (66) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 159.52/28.17 | | | | | | e1) = e0)
% 159.52/28.17 | | | | | |
% 159.52/28.17 | | | | | | BETA: splitting (66) gives:
% 159.52/28.17 | | | | | |
% 159.52/28.17 | | | | | | Case 1:
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | | (67) all_58_4 = e0 & op(e3, e1) = e0
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | | ALPHA: (67) implies:
% 159.52/28.17 | | | | | | | (68) all_58_4 = e0
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | | REF_CLOSE: (5), (8), (9), (15), (24), (28), (32), (35), (39),
% 159.52/28.17 | | | | | | | (43), (44), (45), (46), (56), (57), (68) are
% 159.52/28.17 | | | | | | | inconsistent by sub-proof #854.
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | Case 2:
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | | (69) all_58_5 = e0 & op(e2, e1) = e0
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | | ALPHA: (69) implies:
% 159.52/28.17 | | | | | | | (70) all_58_5 = e0
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | | BETA: splitting (25) gives:
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | |
% 159.52/28.17 | | | | | | | | (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 159.52/28.17 | | | | | | | | op(e2, e3) = e1)
% 159.52/28.17 | | | | | | | |
% 159.52/28.17 | | | | | | | | BETA: splitting (71) gives:
% 159.52/28.17 | | | | | | | |
% 159.52/28.17 | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | (72) all_58_0 = e1 & op(e3, e3) = e1
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | ALPHA: (72) implies:
% 159.52/28.17 | | | | | | | | | (73) all_58_0 = e1
% 159.52/28.17 | | | | | | | | | (74) op(e3, e3) = e1
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | BETA: splitting (27) gives:
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | (75) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2
% 159.52/28.17 | | | | | | | | | | & op(e0, e2) = e2)
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | BETA: splitting (75) gives:
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | (76) all_58_12 = e2 & op(e0, e3) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | ALPHA: (76) implies:
% 159.52/28.17 | | | | | | | | | | | (77) all_58_12 = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | REF_CLOSE: (14), (20), (24), (25), (28), (32), (35), (43),
% 159.52/28.17 | | | | | | | | | | | (44), (55), (56), (57), (77) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | sub-proof #1062.
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | (78) all_58_13 = e2 & op(e0, e2) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | ALPHA: (78) implies:
% 159.52/28.17 | | | | | | | | | | | (79) all_58_13 = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | BETA: splitting (34) gives:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | (80) all_54_0 = e3
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | COMBINE_EQS: (19), (80) imply:
% 159.52/28.17 | | | | | | | | | | | | (81) all_10_2 = e3
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | REDUCE: (6), (81) imply:
% 159.52/28.17 | | | | | | | | | | | | (82) op(e3, e3) = e3
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | BETA: splitting (12) gives:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | (83) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 159.52/28.17 | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | BETA: splitting (83) gives:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | (84) all_58_9 = e3 & op(e3, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | ALPHA: (84) implies:
% 159.52/28.17 | | | | | | | | | | | | | | (85) all_58_9 = e3
% 159.52/28.17 | | | | | | | | | | | | | | (86) op(e3, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | (87) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 159.52/28.17 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (20), (24), (25), (28), (32), (35),
% 159.52/28.17 | | | | | | | | | | | | | | | (39), (43), (44), (45), (55), (56), (57), (65),
% 159.52/28.17 | | | | | | | | | | | | | | | (85), (87) are inconsistent by sub-proof #661.
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | (88) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 159.52/28.17 | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | (89) all_58_11 = e2 & op(e1, e0) = e2
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 159.52/28.17 | | | | | | | | | | | | | | | | (90) all_58_11 = e2
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | | (91) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 159.52/28.17 | | | | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 159.52/28.17 | | | | | | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.17 | | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 159.52/28.17 | | | | | | | | | | | | | | | | | (92) op(e3, e3) = all_22_1
% 159.52/28.17 | | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (13), (14),
% 159.52/28.17 | | | | | | | | | | | | | | | | | (15), (19), (20), (23), (24), (25), (28), (29),
% 159.52/28.17 | | | | | | | | | | | | | | | | | (30), (32), (34), (35), (39), (42), (43), (44),
% 159.52/28.17 | | | | | | | | | | | | | | | | | (45), (46), (50), (51), (55), (56), (57), (58),
% 159.52/28.17 | | | | | | | | | | | | | | | | | (62), (73), (74), (79), (82), (86), (90), (92) are
% 159.52/28.17 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #657.
% 159.52/28.17 | | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | | (93) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 159.52/28.17 | | | | | | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.17 | | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 159.52/28.17 | | | | | | | | | | | | | | | | | (94) op(e3, e3) = all_22_1
% 159.52/28.17 | | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (13), (14),
% 159.52/28.17 | | | | | | | | | | | | | | | | | (15), (19), (20), (23), (24), (25), (28), (29),
% 159.52/28.17 | | | | | | | | | | | | | | | | | (30), (32), (34), (35), (39), (42), (43), (44),
% 159.52/28.17 | | | | | | | | | | | | | | | | | (45), (46), (50), (51), (55), (56), (57), (58),
% 159.52/28.17 | | | | | | | | | | | | | | | | | (62), (73), (74), (79), (82), (86), (90), (94) are
% 159.52/28.17 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #657.
% 159.52/28.17 | | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | (95) all_58_15 = e2 & op(e0, e0) = e2
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 159.52/28.17 | | | | | | | | | | | | | | | | (96) all_58_15 = e2
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (13), (14), (15),
% 159.52/28.17 | | | | | | | | | | | | | | | | (17), (19), (20), (22), (23), (25), (28), (30),
% 159.52/28.17 | | | | | | | | | | | | | | | | (32), (34), (38), (39), (42), (43), (44), (45),
% 159.52/28.17 | | | | | | | | | | | | | | | | (46), (50), (51), (52), (55), (56), (59), (65),
% 159.52/28.17 | | | | | | | | | | | | | | | | (70), (72), (73), (85), (96) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | | | | | | sub-proof #654.
% 159.52/28.17 | | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | (97) all_58_10 = e3 & op(e2, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | ALPHA: (97) implies:
% 159.52/28.17 | | | | | | | | | | | | | | (98) op(e2, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | REF_CLOSE: (21), (31), (56), (98) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | | | | sub-proof #1364.
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | (99) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 159.52/28.17 | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | BETA: splitting (99) gives:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | (100) all_58_11 = e3 & op(e1, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | ALPHA: (100) implies:
% 159.52/28.17 | | | | | | | | | | | | | | (101) all_58_11 = e3
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.17 | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (17), (18), (19),
% 159.52/28.17 | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27),
% 159.52/28.17 | | | | | | | | | | | | | | (28), (29), (30), (31), (32), (33), (34), (35),
% 159.52/28.17 | | | | | | | | | | | | | | (36), (37), (39), (40), (41), (42), (43), (44),
% 159.52/28.17 | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 159.52/28.17 | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (59), (61), (62),
% 159.52/28.17 | | | | | | | | | | | | | | (101) are inconsistent by sub-proof #633.
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | (102) all_58_15 = e3 & op(e0, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | ALPHA: (102) implies:
% 159.52/28.17 | | | | | | | | | | | | | | (103) all_58_15 = e3
% 159.52/28.17 | | | | | | | | | | | | | | (104) op(e0, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | (105) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 159.52/28.17 | | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 159.52/28.17 | | | | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 159.52/28.17 | | | | | | | | | | | | | | | (106) op(e3, e3) = all_22_1
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (14), (19), (20), (23),
% 159.52/28.17 | | | | | | | | | | | | | | | (24), (25), (27), (28), (30), (32), (34), (35),
% 159.52/28.17 | | | | | | | | | | | | | | | (42), (43), (44), (50), (51), (55), (56), (57),
% 159.52/28.17 | | | | | | | | | | | | | | | (65), (73), (82), (103), (104), (106) are
% 159.52/28.17 | | | | | | | | | | | | | | | inconsistent by sub-proof #632.
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | (107) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 159.52/28.17 | | | | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 159.52/28.17 | | | | | | | | | | | | | | | (108) op(e3, e3) = all_22_1
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (14), (19), (20), (23),
% 159.52/28.17 | | | | | | | | | | | | | | | (24), (25), (27), (28), (30), (32), (34), (35),
% 159.52/28.17 | | | | | | | | | | | | | | | (42), (43), (44), (50), (51), (55), (56), (57),
% 159.52/28.17 | | | | | | | | | | | | | | | (65), (73), (82), (103), (104), (108) are
% 159.52/28.17 | | | | | | | | | | | | | | | inconsistent by sub-proof #632.
% 159.52/28.17 | | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | (109) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | REF_CLOSE: (7), (19), (23), (42), (109) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | | sub-proof #1307.
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | (110) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 159.52/28.17 | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | BETA: splitting (110) gives:
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | (111) all_58_14 = e2 & op(e0, e1) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | REF_CLOSE: (8), (14), (20), (24), (25), (28), (32), (35),
% 159.52/28.17 | | | | | | | | | | | (43), (44), (55), (56), (57), (65), (111) are
% 159.52/28.17 | | | | | | | | | | | inconsistent by sub-proof #631.
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | (112) all_58_15 = e2 & op(e0, e0) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | ALPHA: (112) implies:
% 159.52/28.17 | | | | | | | | | | | (113) all_58_15 = e2
% 159.52/28.17 | | | | | | | | | | | (114) op(e0, e0) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | BETA: splitting (12) gives:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | (115) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 159.52/28.17 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | BETA: splitting (115) gives:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | (116) all_58_9 = e3 & op(e3, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | ALPHA: (116) implies:
% 159.52/28.17 | | | | | | | | | | | | | (117) all_58_9 = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (13), (14), (15),
% 159.52/28.17 | | | | | | | | | | | | | (17), (19), (20), (22), (23), (25), (28), (30),
% 159.52/28.17 | | | | | | | | | | | | | (32), (34), (38), (39), (42), (43), (44), (45),
% 159.52/28.17 | | | | | | | | | | | | | (46), (50), (51), (52), (55), (56), (59), (65),
% 159.52/28.17 | | | | | | | | | | | | | (70), (72), (73), (113), (117) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | | | sub-proof #654.
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | (118) all_58_10 = e3 & op(e2, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | ALPHA: (118) implies:
% 159.52/28.17 | | | | | | | | | | | | | (119) op(e2, e0) = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | REF_CLOSE: (21), (31), (56), (119) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | | | sub-proof #1364.
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | (120) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 159.52/28.17 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.17 | | | | | | | | | | | | (11), (12), (13), (14), (15), (17), (18), (19),
% 159.52/28.17 | | | | | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27),
% 159.52/28.17 | | | | | | | | | | | | (28), (29), (30), (31), (32), (33), (34), (35),
% 159.52/28.17 | | | | | | | | | | | | (36), (37), (39), (40), (41), (42), (43), (44),
% 159.52/28.17 | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 159.52/28.17 | | | | | | | | | | | | (53), (54), (55), (56), (57), (59), (61), (62),
% 159.52/28.17 | | | | | | | | | | | | (114), (120) are inconsistent by sub-proof #630.
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | (121) all_58_2 = e1 & op(e2, e3) = e1
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | ALPHA: (121) implies:
% 159.52/28.17 | | | | | | | | | (122) op(e2, e3) = e1
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | REF_CLOSE: (32), (43), (56), (122) are inconsistent by
% 159.52/28.17 | | | | | | | | | sub-proof #1430.
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | End of split
% 159.52/28.17 | | | | | | | |
% 159.52/28.17 | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | |
% 159.52/28.17 | | | | | | | | (123) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 159.52/28.17 | | | | | | | | op(e0, e3) = e1)
% 159.52/28.17 | | | | | | | |
% 159.52/28.17 | | | | | | | | BETA: splitting (123) gives:
% 159.52/28.17 | | | | | | | |
% 159.52/28.17 | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | (124) all_58_6 = e1 & op(e1, e3) = e1
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | ALPHA: (124) implies:
% 159.52/28.17 | | | | | | | | | (125) all_58_6 = e1
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | REF_CLOSE: (35), (65), (125) are inconsistent by sub-proof
% 159.52/28.17 | | | | | | | | | #1073.
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | (126) all_58_12 = e1 & op(e0, e3) = e1
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | ALPHA: (126) implies:
% 159.52/28.17 | | | | | | | | | (127) all_58_12 = e1
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | BETA: splitting (27) gives:
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | (128) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 159.52/28.17 | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | BETA: splitting (128) gives:
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | (129) all_58_12 = e2 & op(e0, e3) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | ALPHA: (129) implies:
% 159.52/28.17 | | | | | | | | | | | (130) all_58_12 = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | REF_CLOSE: (14), (20), (24), (25), (28), (32), (35), (43),
% 159.52/28.17 | | | | | | | | | | | (44), (55), (56), (57), (130) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | sub-proof #1062.
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | (131) all_58_13 = e2 & op(e0, e2) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | ALPHA: (131) implies:
% 159.52/28.17 | | | | | | | | | | | (132) all_58_13 = e2
% 159.52/28.17 | | | | | | | | | | | (133) op(e0, e2) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | BETA: splitting (59) gives:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | (134) all_58_15 = e0 & op(e0, e0) = e0
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | ALPHA: (134) implies:
% 159.52/28.17 | | | | | | | | | | | | (135) all_58_15 = e0
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | BETA: splitting (34) gives:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | (136) all_54_0 = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | COMBINE_EQS: (19), (136) imply:
% 159.52/28.17 | | | | | | | | | | | | | (137) all_10_2 = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | REDUCE: (6), (137) imply:
% 159.52/28.17 | | | | | | | | | | | | | (138) op(e3, e3) = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | BETA: splitting (50) gives:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | (139) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 159.52/28.17 | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 159.52/28.17 | | | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | ALPHA: (139) implies:
% 159.52/28.17 | | | | | | | | | | | | | | (140) op(e3, e3) = all_22_1
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.17 | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 159.52/28.17 | | | | | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 159.52/28.17 | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 159.52/28.17 | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.52/28.17 | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (49), (50),
% 159.52/28.17 | | | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58),
% 159.52/28.17 | | | | | | | | | | | | | | (59), (61), (62), (65), (127), (132), (135),
% 159.52/28.17 | | | | | | | | | | | | | | (138), (140) are inconsistent by sub-proof #625.
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | (141) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 159.52/28.17 | | | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | ALPHA: (141) implies:
% 159.52/28.17 | | | | | | | | | | | | | | (142) op(e3, e3) = all_22_1
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.17 | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 159.52/28.17 | | | | | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 159.52/28.17 | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 159.52/28.17 | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.52/28.17 | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (49), (50),
% 159.52/28.17 | | | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58),
% 159.52/28.17 | | | | | | | | | | | | | | (59), (61), (62), (65), (127), (132), (135),
% 159.52/28.17 | | | | | | | | | | | | | | (138), (142) are inconsistent by sub-proof #625.
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | (143) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | REF_CLOSE: (7), (19), (23), (42), (143) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | | | sub-proof #1307.
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | (144) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.52/28.17 | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.52/28.17 | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 159.52/28.17 | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.52/28.17 | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | ALPHA: (144) implies:
% 159.52/28.17 | | | | | | | | | | | | (145) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 159.52/28.17 | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 159.52/28.17 | | | | | | | | | | | | e1) = e0)
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | BETA: splitting (34) gives:
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | (146) all_54_0 = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | COMBINE_EQS: (19), (146) imply:
% 159.52/28.17 | | | | | | | | | | | | | (147) all_10_2 = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | SIMP: (147) implies:
% 159.52/28.17 | | | | | | | | | | | | | (148) all_10_2 = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | REDUCE: (6), (148) imply:
% 159.52/28.17 | | | | | | | | | | | | | (149) op(e3, e3) = e3
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | BETA: splitting (50) gives:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | (150) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 &
% 159.52/28.17 | | | | | | | | | | | | | | op(e3, e3) = all_22_1 & $i(all_22_0) &
% 159.52/28.17 | | | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | ALPHA: (150) implies:
% 159.52/28.17 | | | | | | | | | | | | | | (151) op(e3, e3) = all_22_1
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.17 | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 159.52/28.17 | | | | | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 159.52/28.17 | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 159.52/28.17 | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.52/28.17 | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (49), (50),
% 159.52/28.17 | | | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58),
% 159.52/28.17 | | | | | | | | | | | | | | (59), (61), (62), (65), (127), (132), (133),
% 159.52/28.17 | | | | | | | | | | | | | | (145), (149), (151) are inconsistent by sub-proof
% 159.52/28.17 | | | | | | | | | | | | | | #623.
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | (152) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 159.52/28.17 | | | | | | | | | | | | | | $i(all_22_1)
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | ALPHA: (152) implies:
% 159.52/28.17 | | | | | | | | | | | | | | (153) op(e3, e3) = all_22_1
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.17 | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 159.52/28.17 | | | | | | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 159.52/28.17 | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 159.52/28.17 | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 159.52/28.17 | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (49), (50),
% 159.52/28.17 | | | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58),
% 159.52/28.17 | | | | | | | | | | | | | | (59), (61), (62), (65), (127), (132), (133),
% 159.52/28.17 | | | | | | | | | | | | | | (145), (149), (153) are inconsistent by sub-proof
% 159.52/28.17 | | | | | | | | | | | | | | #623.
% 159.52/28.17 | | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | (154) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | | REF_CLOSE: (7), (19), (23), (42), (154) are inconsistent by
% 159.52/28.17 | | | | | | | | | | | | | sub-proof #1307.
% 159.52/28.17 | | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | (155) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 159.52/28.17 | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | BETA: splitting (155) gives:
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | Case 1:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | (156) all_58_14 = e2 & op(e0, e1) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | REF_CLOSE: (8), (14), (20), (24), (25), (28), (32), (35),
% 159.52/28.17 | | | | | | | | | | | (43), (44), (55), (56), (57), (65), (156) are
% 159.52/28.17 | | | | | | | | | | | inconsistent by sub-proof #631.
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | Case 2:
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | (157) all_58_15 = e2 & op(e0, e0) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | ALPHA: (157) implies:
% 159.52/28.17 | | | | | | | | | | | (158) all_58_15 = e2
% 159.52/28.17 | | | | | | | | | | | (159) op(e0, e0) = e2
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.52/28.17 | | | | | | | | | | | (11), (12), (13), (14), (15), (17), (18), (19),
% 159.52/28.17 | | | | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27),
% 159.52/28.17 | | | | | | | | | | | (28), (29), (30), (31), (32), (33), (34), (35),
% 159.52/28.17 | | | | | | | | | | | (36), (37), (38), (39), (40), (42), (43), (44),
% 159.52/28.17 | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 159.52/28.17 | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (61),
% 159.52/28.17 | | | | | | | | | | | (62), (65), (127), (158), (159) are inconsistent
% 159.52/28.17 | | | | | | | | | | | by sub-proof #626.
% 159.52/28.17 | | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | | |
% 159.52/28.17 | | | | | | | | | End of split
% 159.52/28.17 | | | | | | | | |
% 159.52/28.17 | | | | | | | | End of split
% 159.52/28.17 | | | | | | | |
% 159.52/28.17 | | | | | | | End of split
% 159.52/28.17 | | | | | | |
% 159.52/28.17 | | | | | | End of split
% 159.52/28.17 | | | | | |
% 159.52/28.17 | | | | | Case 2:
% 159.52/28.17 | | | | | |
% 159.52/28.17 | | | | | | (160) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 159.52/28.17 | | | | | | op(e0, e1) = e0)
% 159.52/28.17 | | | | | |
% 159.52/28.17 | | | | | | REF_CLOSE: (1), (8), (24), (56), (160) are inconsistent by sub-proof
% 159.52/28.17 | | | | | | #926.
% 159.52/28.17 | | | | | |
% 159.52/28.17 | | | | | End of split
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | Case 2:
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | (161) all_58_7 = e3 & op(e1, e2) = e3
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | REF_CLOSE: (37), (54), (56), (161) are inconsistent by sub-proof
% 159.52/28.17 | | | | | #1184.
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | End of split
% 159.52/28.17 | | | |
% 159.52/28.17 | | | Case 2:
% 159.52/28.17 | | | |
% 159.52/28.17 | | | | (162) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 159.52/28.17 | | | | e0) = e3)
% 159.52/28.17 | | | |
% 159.52/28.17 | | | | BETA: splitting (162) gives:
% 159.52/28.17 | | | |
% 159.52/28.17 | | | | Case 1:
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | (163) all_58_8 = e3 & op(e1, e1) = e3
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | ALPHA: (163) implies:
% 159.52/28.17 | | | | | (164) all_58_8 = e3
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | REF_CLOSE: (5), (8), (9), (15), (24), (28), (32), (35), (36), (39),
% 159.52/28.17 | | | | | (40), (43), (44), (45), (46), (56), (57), (164) are
% 159.52/28.17 | | | | | inconsistent by sub-proof #780.
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | Case 2:
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | (165) all_58_11 = e3 & op(e1, e0) = e3
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | ALPHA: (165) implies:
% 159.52/28.17 | | | | | (166) all_58_11 = e3
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.52/28.17 | | | | | (12), (13), (14), (15), (17), (18), (19), (20), (21), (22),
% 159.52/28.17 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 159.52/28.17 | | | | | (33), (34), (35), (36), (37), (39), (40), (41), (42), (43),
% 159.52/28.17 | | | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 159.52/28.17 | | | | | (54), (55), (56), (57), (59), (61), (62), (166) are
% 159.52/28.17 | | | | | inconsistent by sub-proof #633.
% 159.52/28.17 | | | | |
% 159.52/28.17 | | | | End of split
% 159.52/28.17 | | | |
% 159.52/28.17 | | | End of split
% 159.52/28.17 | | |
% 159.52/28.17 | | Case 2:
% 159.52/28.17 | | |
% 159.52/28.17 | | | (167) all_58_5 = e2 & op(e2, e1) = e2
% 159.52/28.17 | | |
% 159.52/28.17 | | | ALPHA: (167) implies:
% 159.52/28.17 | | | (168) all_58_5 = e2
% 159.52/28.17 | | |
% 159.52/28.17 | | | REF_CLOSE: (5), (24), (28), (32), (35), (39), (43), (44), (45), (56),
% 159.52/28.17 | | | (168) are inconsistent by sub-proof #898.
% 159.52/28.17 | | |
% 159.52/28.17 | | End of split
% 159.52/28.17 | |
% 159.52/28.17 | Case 2:
% 159.52/28.17 | |
% 159.52/28.17 | | (169) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 159.52/28.17 | | e2)
% 159.52/28.17 | |
% 159.52/28.17 | | REF_CLOSE: (8), (9), (46), (56), (57), (169) are inconsistent by sub-proof
% 159.52/28.17 | | #917.
% 159.52/28.17 | |
% 159.52/28.17 | End of split
% 159.52/28.17 |
% 159.52/28.17 End of proof
% 159.52/28.17
% 159.52/28.17 Sub-proof #623 shows that the following formulas are inconsistent:
% 159.52/28.17 ----------------------------------------------------------------
% 159.52/28.17 (1) op(e1, e1) = e3
% 159.52/28.17 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.17 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.17 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.17 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.17 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.17 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.17 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.17 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.17 (6) op(e3, e3) = all_10_2
% 159.52/28.17 (7) ~ (all_10_2 = e1)
% 159.52/28.17 (8) all_58_14 = e3
% 159.52/28.17 (9) op(e1, e1) = all_6_2
% 159.52/28.17 (10) ~ (all_52_7 = e3)
% 159.52/28.17 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.17 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.17 e1)
% 159.52/28.17 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.17 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.17 (13) op(e3, e3) = all_28_1
% 159.52/28.18 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.18 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.18 (15) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.18 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.18 (16) all_58_6 = e3
% 159.52/28.18 (17) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.18 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.18 (18) op(e3, e2) = all_52_4
% 159.52/28.18 (19) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.18 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.18 (20) all_54_0 = all_10_2
% 159.52/28.18 (21) op(e2, e3) = all_52_1
% 159.52/28.18 (22) ~ (all_52_13 = e3)
% 159.52/28.18 (23) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.18 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.18 (24) ~ (all_10_2 = e0)
% 159.52/28.18 (25) ~ (e3 = e0)
% 159.52/28.18 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.18 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.18 (27) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.18 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.18 (28) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.18 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.18 e2)
% 159.52/28.18 (29) ~ (e2 = e0)
% 159.52/28.18 (30) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.18 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.18 (31) op(e1, e3) = all_52_2
% 159.52/28.18 (32) op(e2, e0) = all_52_13
% 159.52/28.18 (33) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.18 (34) op(e2, e3) = e2
% 159.52/28.18 (35) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.18 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.18 (36) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.18 (37) ~ (e3 = e1)
% 159.52/28.18 (38) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.18 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.18 (39) op(e1, e2) = all_52_6
% 159.52/28.18 (40) ~ (all_52_4 = all_10_2)
% 159.52/28.18 (41) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.18 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.18 (42) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.18 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.18 (43) all_58_4 = e2
% 159.52/28.18 (44) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.18 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.18 (45) ~ (all_52_4 = e3)
% 159.52/28.18 (46) ~ (all_10_2 = e2)
% 159.52/28.18 (47) ~ (e2 = e1)
% 159.52/28.18 (48) op(e3, e3) = e3
% 159.52/28.18 (49) ~ (e1 = e0)
% 159.52/28.18 (50) all_58_3 = e3
% 159.52/28.18 (51) op(e0, e2) = e2
% 159.52/28.18 (52) ~ (all_6_2 = e2)
% 159.52/28.18 (53) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.18 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.18 e3)
% 159.52/28.18 (54) all_58_13 = e2
% 159.52/28.18 (55) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.18 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.18 (56) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.18 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.18 (57) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.18 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.18 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.18 (58) op(e1, e3) = e1
% 159.52/28.18 (59) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.18 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.18 (60) op(e0, e2) = all_52_7
% 159.52/28.18 (61) op(e3, e3) = all_22_1
% 159.52/28.18 (62) ~ (all_52_6 = e3)
% 159.52/28.18 (63) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.18 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.18 (64) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.18 (65) ~ (e3 = e2)
% 159.52/28.18 (66) all_58_12 = e1
% 159.52/28.18 (67) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.18 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.18 (68) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.18 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.18 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.18 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.18
% 159.52/28.18 Begin of proof
% 159.52/28.18 |
% 159.52/28.18 | BETA: splitting (12) gives:
% 159.52/28.18 |
% 159.52/28.18 | Case 1:
% 159.52/28.18 | |
% 159.52/28.18 | | (69) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 159.52/28.18 | | e3)
% 159.52/28.18 | |
% 159.52/28.18 | | REF_CLOSE: (3), (5), (8), (9), (13), (14), (15), (16), (21), (22), (25),
% 159.52/28.18 | | (26), (29), (32), (34), (37), (41), (42), (43), (47), (48), (49),
% 159.52/28.18 | | (50), (52), (56), (60), (61), (63), (64), (65), (66), (67), (69)
% 159.52/28.18 | | are inconsistent by sub-proof #627.
% 159.52/28.18 | |
% 159.52/28.18 | Case 2:
% 159.52/28.18 | |
% 159.52/28.18 | | (70) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.18 | | e3)
% 159.52/28.18 | |
% 159.52/28.18 | | BETA: splitting (70) gives:
% 159.52/28.18 | |
% 159.52/28.18 | | Case 1:
% 159.52/28.18 | | |
% 159.52/28.18 | | | (71) all_58_11 = e3 & op(e1, e0) = e3
% 159.52/28.18 | | |
% 159.52/28.18 | | | ALPHA: (71) implies:
% 159.52/28.18 | | | (72) all_58_11 = e3
% 159.52/28.18 | | |
% 159.52/28.18 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.52/28.18 | | | (13), (14), (15), (18), (19), (20), (21), (22), (23), (24),
% 159.52/28.18 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 159.52/28.18 | | | (35), (36), (37), (38), (39), (41), (43), (44), (45), (46),
% 159.52/28.18 | | | (47), (49), (50), (52), (53), (55), (56), (57), (58), (59),
% 159.52/28.18 | | | (60), (62), (63), (64), (65), (68), (72) are inconsistent by
% 159.52/28.18 | | | sub-proof #633.
% 159.52/28.18 | | |
% 159.52/28.18 | | Case 2:
% 159.52/28.18 | | |
% 159.52/28.18 | | | (73) all_58_15 = e3 & op(e0, e0) = e3
% 159.52/28.18 | | |
% 159.52/28.18 | | | ALPHA: (73) implies:
% 159.52/28.18 | | | (74) all_58_15 = e3
% 159.52/28.18 | | | (75) op(e0, e0) = e3
% 159.52/28.18 | | |
% 159.52/28.18 | | | BETA: splitting (36) gives:
% 159.52/28.18 | | |
% 159.52/28.18 | | | Case 1:
% 159.52/28.18 | | | |
% 159.52/28.18 | | | | (76) all_54_0 = e3
% 159.52/28.18 | | | |
% 159.52/28.18 | | | | COMBINE_EQS: (20), (76) imply:
% 159.52/28.18 | | | | (77) all_10_2 = e3
% 159.52/28.18 | | | |
% 159.52/28.18 | | | | BETA: splitting (57) gives:
% 159.52/28.18 | | | |
% 159.52/28.18 | | | | Case 1:
% 159.52/28.18 | | | | |
% 159.52/28.18 | | | | | (78) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3)
% 159.52/28.18 | | | | | = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 159.52/28.18 | | | | |
% 159.52/28.18 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.52/28.18 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 159.52/28.18 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 159.52/28.18 | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 159.52/28.18 | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 159.52/28.18 | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 159.52/28.18 | | | | | (62), (63), (64), (65), (66), (67), (68), (74), (75) are
% 159.52/28.18 | | | | | inconsistent by sub-proof #624.
% 159.52/28.18 | | | | |
% 159.52/28.18 | | | | Case 2:
% 159.52/28.18 | | | | |
% 159.52/28.18 | | | | | (79) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 159.52/28.18 | | | | |
% 159.52/28.18 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.52/28.18 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 159.52/28.18 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 159.52/28.18 | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 159.52/28.18 | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 159.52/28.18 | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 159.52/28.18 | | | | | (62), (63), (64), (65), (66), (67), (68), (74), (75) are
% 159.52/28.18 | | | | | inconsistent by sub-proof #624.
% 159.52/28.18 | | | | |
% 159.52/28.18 | | | | End of split
% 159.52/28.18 | | | |
% 159.52/28.18 | | | Case 2:
% 159.52/28.18 | | | |
% 159.52/28.18 | | | | (80) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.18 | | | |
% 159.52/28.18 | | | | REF_CLOSE: (7), (20), (24), (46), (80) are inconsistent by sub-proof
% 159.52/28.18 | | | | #1307.
% 159.52/28.18 | | | |
% 159.52/28.18 | | | End of split
% 159.52/28.18 | | |
% 159.52/28.18 | | End of split
% 159.52/28.18 | |
% 159.52/28.18 | End of split
% 159.52/28.18 |
% 159.52/28.18 End of proof
% 159.52/28.18
% 159.52/28.18 Sub-proof #624 shows that the following formulas are inconsistent:
% 159.52/28.18 ----------------------------------------------------------------
% 159.52/28.18 (1) op(e1, e1) = e3
% 159.52/28.18 (2) all_58_15 = e3
% 159.52/28.18 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.18 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.18 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.18 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.18 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.18 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.18 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.18 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.18 (7) op(e3, e3) = all_10_2
% 159.52/28.18 (8) ~ (all_10_2 = e1)
% 159.52/28.18 (9) all_58_14 = e3
% 159.52/28.18 (10) op(e1, e1) = all_6_2
% 159.52/28.18 (11) ~ (all_52_7 = e3)
% 159.52/28.18 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.18 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.18 e1)
% 159.52/28.18 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.18 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.18 (14) op(e3, e3) = all_28_1
% 159.52/28.18 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.18 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.18 (16) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.18 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.18 (17) all_58_6 = e3
% 159.52/28.18 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.18 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.18 (19) op(e3, e2) = all_52_4
% 159.52/28.18 (20) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.18 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.18 (21) all_54_0 = all_10_2
% 159.52/28.18 (22) op(e2, e3) = all_52_1
% 159.52/28.18 (23) ~ (all_52_13 = e3)
% 159.52/28.18 (24) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.18 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.18 (25) ~ (all_10_2 = e0)
% 159.52/28.18 (26) ~ (e3 = e0)
% 159.52/28.18 (27) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.18 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.18 (28) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.18 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.18 (29) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.18 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.18 e2)
% 159.52/28.18 (30) ~ (e2 = e0)
% 159.52/28.18 (31) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.18 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.18 (32) op(e1, e3) = all_52_2
% 159.52/28.18 (33) op(e2, e0) = all_52_13
% 159.52/28.18 (34) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.18 (35) op(e2, e3) = e2
% 159.52/28.18 (36) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.18 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.18 (37) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.18 (38) ~ (e3 = e1)
% 159.52/28.18 (39) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.18 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.18 (40) op(e1, e2) = all_52_6
% 159.52/28.18 (41) ~ (all_52_4 = all_10_2)
% 159.52/28.18 (42) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.18 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.18 (43) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.18 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.18 (44) all_58_4 = e2
% 159.52/28.18 (45) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.18 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.18 (46) ~ (all_52_4 = e3)
% 159.52/28.18 (47) ~ (all_10_2 = e2)
% 159.52/28.18 (48) ~ (e2 = e1)
% 159.52/28.18 (49) op(e3, e3) = e3
% 159.52/28.18 (50) ~ (e1 = e0)
% 159.52/28.18 (51) all_58_3 = e3
% 159.52/28.18 (52) op(e0, e2) = e2
% 159.52/28.18 (53) ~ (all_6_2 = e2)
% 159.52/28.18 (54) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.18 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.18 e3)
% 159.52/28.18 (55) all_58_13 = e2
% 159.52/28.18 (56) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.18 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.18 (57) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.18 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.18 (58) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.18 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.18 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.18 (59) op(e1, e3) = e1
% 159.52/28.18 (60) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.18 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.18 (61) op(e0, e2) = all_52_7
% 159.52/28.18 (62) op(e3, e3) = all_22_1
% 159.52/28.18 (63) ~ (all_52_6 = e3)
% 159.52/28.18 (64) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.18 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.18 (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.18 (66) ~ (e3 = e2)
% 159.52/28.18 (67) all_58_12 = e1
% 159.52/28.18 (68) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.18 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.18 (69) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.18 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.18 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.18 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.18 (70) op(e0, e0) = e3
% 159.52/28.18
% 159.52/28.18 Begin of proof
% 159.52/28.18 |
% 159.52/28.18 | BETA: splitting (43) gives:
% 159.52/28.18 |
% 159.52/28.18 | Case 1:
% 159.52/28.18 | |
% 159.52/28.18 | | (71) all_58_12 = e0 & op(e0, e3) = e0
% 159.52/28.18 | |
% 159.52/28.18 | | ALPHA: (71) implies:
% 159.52/28.18 | | (72) all_58_12 = e0
% 159.52/28.18 | |
% 159.52/28.18 | | REF_CLOSE: (2), (9), (12), (15), (17), (22), (26), (27), (29), (30), (35),
% 159.52/28.18 | | (38), (48), (50), (64), (65), (66), (70), (72) are inconsistent
% 159.52/28.18 | | by sub-proof #786.
% 159.52/28.18 | |
% 159.52/28.18 | Case 2:
% 159.52/28.18 | |
% 159.52/28.18 | | (73) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 159.52/28.18 | | e0)
% 159.52/28.18 | |
% 159.52/28.18 | | BETA: splitting (73) gives:
% 159.52/28.18 | |
% 159.52/28.18 | | Case 1:
% 159.52/28.18 | | |
% 159.52/28.18 | | | (74) all_58_13 = e0 & op(e0, e2) = e0
% 159.52/28.18 | | |
% 159.52/28.18 | | | ALPHA: (74) implies:
% 159.52/28.18 | | | (75) op(e0, e2) = e0
% 159.52/28.18 | | |
% 159.52/28.18 | | | REF_CLOSE: (30), (52), (61), (65), (75) are inconsistent by sub-proof
% 159.52/28.18 | | | #1040.
% 159.52/28.18 | | |
% 159.52/28.18 | | Case 2:
% 159.52/28.18 | | |
% 159.52/28.18 | | | (76) all_58_14 = e0 & op(e0, e1) = e0
% 159.52/28.18 | | |
% 159.52/28.18 | | | ALPHA: (76) implies:
% 159.52/28.18 | | | (77) all_58_14 = e0
% 159.52/28.18 | | |
% 159.52/28.18 | | | COMBINE_EQS: (9), (77) imply:
% 159.52/28.18 | | | (78) e3 = e0
% 159.52/28.18 | | |
% 159.52/28.18 | | | COMBINE_EQS: (2), (78) imply:
% 159.52/28.18 | | | (79) all_58_15 = e0
% 159.52/28.18 | | |
% 159.52/28.18 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.52/28.18 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.52/28.18 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 159.52/28.18 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (44),
% 159.52/28.18 | | | (45), (46), (47), (48), (49), (50), (51), (53), (54), (55),
% 159.52/28.18 | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 159.52/28.18 | | | (66), (67), (68), (69), (79) are inconsistent by sub-proof
% 159.52/28.18 | | | #625.
% 159.52/28.18 | | |
% 159.52/28.18 | | End of split
% 159.52/28.18 | |
% 159.52/28.18 | End of split
% 159.52/28.18 |
% 159.52/28.18 End of proof
% 159.52/28.18
% 159.52/28.18 Sub-proof #625 shows that the following formulas are inconsistent:
% 159.52/28.18 ----------------------------------------------------------------
% 159.52/28.18 (1) op(e1, e1) = e3
% 159.52/28.18 (2) all_58_15 = e0
% 159.52/28.18 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.18 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.18 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.18 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.18 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.18 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.18 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.18 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.18 (7) op(e3, e3) = all_10_2
% 159.52/28.18 (8) ~ (all_10_2 = e1)
% 159.52/28.18 (9) all_58_14 = e3
% 159.52/28.18 (10) op(e1, e1) = all_6_2
% 159.52/28.18 (11) ~ (all_52_7 = e3)
% 159.52/28.18 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.18 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.18 e1)
% 159.52/28.18 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.18 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.18 (14) op(e3, e3) = all_28_1
% 159.52/28.18 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.18 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.18 (16) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.18 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.18 (17) all_58_6 = e3
% 159.52/28.18 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.52/28.18 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.52/28.18 (19) op(e3, e2) = all_52_4
% 159.52/28.18 (20) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.18 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.18 (21) all_54_0 = all_10_2
% 159.52/28.18 (22) op(e2, e3) = all_52_1
% 159.52/28.18 (23) ~ (all_52_13 = e3)
% 159.52/28.18 (24) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.18 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.18 (25) ~ (all_10_2 = e0)
% 159.52/28.18 (26) ~ (e3 = e0)
% 159.52/28.18 (27) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.18 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.18 (28) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.18 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.18 (29) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.18 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.18 e2)
% 159.52/28.18 (30) ~ (e2 = e0)
% 159.52/28.18 (31) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.18 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.18 (32) op(e1, e3) = all_52_2
% 159.52/28.18 (33) op(e2, e0) = all_52_13
% 159.52/28.18 (34) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.18 (35) op(e2, e3) = e2
% 159.52/28.18 (36) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.18 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.18 (37) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.18 (38) ~ (e3 = e1)
% 159.52/28.18 (39) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.18 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.18 (40) op(e1, e2) = all_52_6
% 159.52/28.18 (41) ~ (all_52_4 = all_10_2)
% 159.52/28.18 (42) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.18 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.18 (43) all_58_4 = e2
% 159.52/28.18 (44) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.18 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.18 (45) ~ (all_52_4 = e3)
% 159.52/28.18 (46) ~ (all_10_2 = e2)
% 159.52/28.18 (47) ~ (e2 = e1)
% 159.52/28.18 (48) op(e3, e3) = e3
% 159.52/28.18 (49) ~ (e1 = e0)
% 159.52/28.18 (50) all_58_3 = e3
% 159.52/28.18 (51) ~ (all_6_2 = e2)
% 159.52/28.18 (52) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.18 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.18 e3)
% 159.52/28.18 (53) all_58_13 = e2
% 159.52/28.18 (54) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.18 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.18 (55) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.18 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.18 (56) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.18 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.18 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.18 (57) op(e1, e3) = e1
% 159.52/28.18 (58) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.18 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.18 (59) op(e0, e2) = all_52_7
% 159.52/28.18 (60) op(e3, e3) = all_22_1
% 159.52/28.18 (61) ~ (all_52_6 = e3)
% 159.52/28.18 (62) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.18 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.19 (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.19 (64) ~ (e3 = e2)
% 159.52/28.19 (65) all_58_12 = e1
% 159.52/28.19 (66) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.19 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.19 (67) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.19 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.19 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.19 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.19
% 159.52/28.19 Begin of proof
% 159.52/28.19 |
% 159.52/28.19 | BETA: splitting (13) gives:
% 159.52/28.19 |
% 159.52/28.19 | Case 1:
% 159.52/28.19 | |
% 159.52/28.19 | | (68) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 159.52/28.19 | | e3)
% 159.52/28.19 | |
% 159.52/28.19 | | BETA: splitting (68) gives:
% 159.52/28.19 | |
% 159.52/28.19 | | Case 1:
% 159.52/28.19 | | |
% 159.52/28.19 | | | (69) all_58_9 = e3 & op(e3, e0) = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | ALPHA: (69) implies:
% 159.52/28.19 | | | (70) all_58_9 = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | BETA: splitting (66) gives:
% 159.52/28.19 | | |
% 159.52/28.19 | | | Case 1:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | (71) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 159.52/28.19 | | | | = e0)
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | BETA: splitting (71) gives:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | Case 1:
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | (72) all_58_0 = e0 & op(e3, e3) = e0
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | REF_CLOSE: (14), (26), (48), (60), (63), (72) are inconsistent by
% 159.52/28.19 | | | | | sub-proof #666.
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | Case 2:
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | (73) all_58_1 = e0 & op(e3, e2) = e0
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | ALPHA: (73) implies:
% 159.52/28.19 | | | | | (74) all_58_1 = e0
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | BETA: splitting (18) gives:
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | Case 1:
% 159.52/28.19 | | | | | |
% 159.52/28.19 | | | | | | (75) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 159.52/28.19 | | | | | | e0) = e2)
% 159.52/28.19 | | | | | |
% 159.52/28.19 | | | | | | REF_CLOSE: (6), (15), (17), (22), (26), (27), (30), (35), (38),
% 159.52/28.19 | | | | | | (42), (47), (49), (50), (62), (63), (64), (70), (75) are
% 159.52/28.19 | | | | | | inconsistent by sub-proof #661.
% 159.52/28.19 | | | | | |
% 159.52/28.19 | | | | | Case 2:
% 159.52/28.19 | | | | | |
% 159.52/28.19 | | | | | | (76) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 159.52/28.19 | | | | | | op(e0, e0) = e2)
% 159.52/28.19 | | | | | |
% 159.52/28.19 | | | | | | BETA: splitting (76) gives:
% 159.52/28.19 | | | | | |
% 159.52/28.19 | | | | | | Case 1:
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | | (77) all_58_11 = e2 & op(e1, e0) = e2
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | | ALPHA: (77) implies:
% 159.52/28.19 | | | | | | | (78) all_58_11 = e2
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | | BETA: splitting (31) gives:
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | | Case 1:
% 159.52/28.19 | | | | | | | |
% 159.52/28.19 | | | | | | | | (79) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 159.52/28.19 | | | | | | | | op(e1, e2) = e0)
% 159.52/28.19 | | | | | | | |
% 159.52/28.19 | | | | | | | | BETA: splitting (79) gives:
% 159.52/28.19 | | | | | | | |
% 159.52/28.19 | | | | | | | | Case 1:
% 159.52/28.19 | | | | | | | | |
% 159.52/28.19 | | | | | | | | | (80) all_58_6 = e0 & op(e1, e3) = e0
% 159.52/28.19 | | | | | | | | |
% 159.52/28.19 | | | | | | | | | ALPHA: (80) implies:
% 159.52/28.19 | | | | | | | | | (81) all_58_6 = e0
% 159.52/28.19 | | | | | | | | |
% 159.52/28.19 | | | | | | | | | REF_CLOSE: (17), (26), (81) are inconsistent by sub-proof
% 159.52/28.19 | | | | | | | | | #1321.
% 159.52/28.19 | | | | | | | | |
% 159.52/28.19 | | | | | | | | Case 2:
% 159.52/28.19 | | | | | | | | |
% 159.52/28.19 | | | | | | | | | (82) all_58_7 = e0 & op(e1, e2) = e0
% 159.52/28.19 | | | | | | | | |
% 159.52/28.19 | | | | | | | | | ALPHA: (82) implies:
% 159.52/28.19 | | | | | | | | | (83) all_58_7 = e0
% 159.52/28.19 | | | | | | | | |
% 159.52/28.19 | | | | | | | | | REF_CLOSE: (4), (38), (47), (49), (50), (53), (74), (83) are
% 159.52/28.19 | | | | | | | | | inconsistent by sub-proof #752.
% 159.52/28.19 | | | | | | | | |
% 159.52/28.19 | | | | | | | | End of split
% 159.52/28.19 | | | | | | | |
% 159.52/28.19 | | | | | | | Case 2:
% 159.52/28.19 | | | | | | | |
% 159.52/28.19 | | | | | | | | (84) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 159.52/28.19 | | | | | | | | op(e1, e0) = e0)
% 159.52/28.19 | | | | | | | |
% 159.52/28.19 | | | | | | | | REF_CLOSE: (1), (6), (9), (10), (16), (26), (30), (35), (38),
% 159.52/28.19 | | | | | | | | (42), (43), (47), (49), (50), (51), (63), (64), (78),
% 159.52/28.19 | | | | | | | | (84) are inconsistent by sub-proof #658.
% 159.52/28.19 | | | | | | | |
% 159.52/28.19 | | | | | | | End of split
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | Case 2:
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | | (85) all_58_15 = e2 & op(e0, e0) = e2
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | | ALPHA: (85) implies:
% 159.52/28.19 | | | | | | | (86) all_58_15 = e2
% 159.52/28.19 | | | | | | | (87) op(e0, e0) = e2
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.52/28.19 | | | | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21),
% 159.52/28.19 | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 159.52/28.19 | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 159.52/28.19 | | | | | | | (40), (41), (42), (43), (44), (46), (47), (49), (50),
% 159.52/28.19 | | | | | | | (51), (52), (54), (55), (56), (57), (58), (59), (61),
% 159.52/28.19 | | | | | | | (62), (63), (64), (65), (66), (67), (86), (87) are
% 159.52/28.19 | | | | | | | inconsistent by sub-proof #626.
% 159.52/28.19 | | | | | | |
% 159.52/28.19 | | | | | | End of split
% 159.52/28.19 | | | | | |
% 159.52/28.19 | | | | | End of split
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | End of split
% 159.52/28.19 | | | |
% 159.52/28.19 | | | Case 2:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | (88) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 159.52/28.19 | | | | = e0)
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | REF_CLOSE: (6), (9), (10), (16), (26), (30), (35), (38), (42), (47),
% 159.52/28.19 | | | | (49), (50), (51), (63), (64), (70), (88) are inconsistent by
% 159.52/28.19 | | | | sub-proof #628.
% 159.52/28.19 | | | |
% 159.52/28.19 | | | End of split
% 159.52/28.19 | | |
% 159.52/28.19 | | Case 2:
% 159.52/28.19 | | |
% 159.52/28.19 | | | (89) all_58_10 = e3 & op(e2, e0) = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | ALPHA: (89) implies:
% 159.52/28.19 | | | (90) op(e2, e0) = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | REF_CLOSE: (23), (33), (63), (90) are inconsistent by sub-proof #1364.
% 159.52/28.19 | | |
% 159.52/28.19 | | End of split
% 159.52/28.19 | |
% 159.52/28.19 | Case 2:
% 159.52/28.19 | |
% 159.52/28.19 | | (91) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.19 | | e3)
% 159.52/28.19 | |
% 159.52/28.19 | | BETA: splitting (91) gives:
% 159.52/28.19 | |
% 159.52/28.19 | | Case 1:
% 159.52/28.19 | | |
% 159.52/28.19 | | | (92) all_58_11 = e3 & op(e1, e0) = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | ALPHA: (92) implies:
% 159.52/28.19 | | | (93) all_58_11 = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.52/28.19 | | | (14), (15), (16), (19), (20), (21), (22), (23), (24), (25),
% 159.52/28.19 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 159.52/28.19 | | | (36), (37), (38), (39), (40), (42), (43), (44), (45), (46),
% 159.52/28.19 | | | (47), (49), (50), (51), (52), (54), (55), (56), (57), (58),
% 159.52/28.19 | | | (59), (61), (62), (63), (64), (67), (93) are inconsistent by
% 159.52/28.19 | | | sub-proof #633.
% 159.52/28.19 | | |
% 159.52/28.19 | | Case 2:
% 159.52/28.19 | | |
% 159.52/28.19 | | | (94) all_58_15 = e3 & op(e0, e0) = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | ALPHA: (94) implies:
% 159.52/28.19 | | | (95) all_58_15 = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | REF_CLOSE: (2), (26), (95) are inconsistent by sub-proof #1318.
% 159.52/28.19 | | |
% 159.52/28.19 | | End of split
% 159.52/28.19 | |
% 159.52/28.19 | End of split
% 159.52/28.19 |
% 159.52/28.19 End of proof
% 159.52/28.19
% 159.52/28.19 Sub-proof #626 shows that the following formulas are inconsistent:
% 159.52/28.19 ----------------------------------------------------------------
% 159.52/28.19 (1) op(e1, e1) = e3
% 159.52/28.19 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.19 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.19 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.19 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.19 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.19 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.19 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.19 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.19 (6) op(e3, e3) = all_10_2
% 159.52/28.19 (7) ~ (all_10_2 = e1)
% 159.52/28.19 (8) all_58_14 = e3
% 159.52/28.19 (9) op(e1, e1) = all_6_2
% 159.52/28.19 (10) ~ (all_52_7 = e3)
% 159.52/28.19 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.19 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.19 e1)
% 159.52/28.19 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.19 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.19 (13) op(e3, e3) = all_28_1
% 159.52/28.19 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.19 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.19 (15) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.19 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.19 (16) all_58_6 = e3
% 159.52/28.19 (17) op(e3, e2) = all_52_4
% 159.52/28.19 (18) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.19 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.19 (19) all_54_0 = all_10_2
% 159.52/28.19 (20) op(e2, e3) = all_52_1
% 159.52/28.19 (21) ~ (all_52_13 = e3)
% 159.52/28.19 (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.19 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.19 (23) ~ (all_10_2 = e0)
% 159.52/28.19 (24) ~ (e3 = e0)
% 159.52/28.19 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.19 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.19 (26) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.19 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.19 (27) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.19 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.19 e2)
% 159.52/28.19 (28) ~ (e2 = e0)
% 159.52/28.19 (29) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.19 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.19 (30) op(e1, e3) = all_52_2
% 159.52/28.19 (31) op(e2, e0) = all_52_13
% 159.52/28.19 (32) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.19 (33) op(e2, e3) = e2
% 159.52/28.19 (34) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.19 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.19 (35) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.19 (36) ~ (e3 = e1)
% 159.52/28.19 (37) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.19 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.19 (38) op(e1, e2) = all_52_6
% 159.52/28.19 (39) ~ (all_52_4 = all_10_2)
% 159.52/28.19 (40) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.19 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.19 (41) op(e0, e0) = e2
% 159.52/28.19 (42) all_58_4 = e2
% 159.52/28.19 (43) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.19 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.19 (44) ~ (all_10_2 = e2)
% 159.52/28.19 (45) all_58_15 = e2
% 159.52/28.19 (46) ~ (e2 = e1)
% 159.52/28.19 (47) ~ (e1 = e0)
% 159.52/28.19 (48) all_58_3 = e3
% 159.52/28.19 (49) ~ (all_6_2 = e2)
% 159.52/28.19 (50) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.19 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.19 e3)
% 159.52/28.19 (51) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.19 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.19 (52) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.19 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.19 (53) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.19 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.19 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.19 (54) op(e1, e3) = e1
% 159.52/28.19 (55) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.19 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.19 (56) op(e0, e2) = all_52_7
% 159.52/28.19 (57) ~ (all_52_6 = e3)
% 159.52/28.19 (58) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.19 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.19 (59) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.19 (60) ~ (e3 = e2)
% 159.52/28.19 (61) all_58_12 = e1
% 159.52/28.19 (62) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.19 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.19 (63) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.19 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.19 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.19 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.19
% 159.52/28.19 Begin of proof
% 159.52/28.19 |
% 159.52/28.19 | BETA: splitting (63) gives:
% 159.52/28.19 |
% 159.52/28.19 | Case 1:
% 159.52/28.19 | |
% 159.52/28.19 | | (64) all_58_15 = e0 & op(e0, e0) = e0
% 159.52/28.19 | |
% 159.52/28.19 | | REF_CLOSE: (5), (8), (9), (15), (24), (28), (33), (36), (40), (42), (45),
% 159.52/28.19 | | (46), (47), (48), (49), (59), (60), (64) are inconsistent by
% 159.52/28.19 | | sub-proof #629.
% 159.52/28.19 | |
% 159.52/28.19 | Case 2:
% 159.52/28.19 | |
% 159.52/28.19 | | (65) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 159.52/28.19 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 159.52/28.19 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 159.52/28.19 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.52/28.19 | |
% 159.52/28.19 | | ALPHA: (65) implies:
% 159.52/28.19 | | (66) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.52/28.19 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.19 | |
% 159.52/28.19 | | BETA: splitting (35) gives:
% 159.52/28.19 | |
% 159.52/28.19 | | Case 1:
% 159.52/28.19 | | |
% 159.52/28.19 | | | (67) all_54_0 = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | COMBINE_EQS: (19), (67) imply:
% 159.52/28.19 | | | (68) all_10_2 = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | SIMP: (68) implies:
% 159.52/28.19 | | | (69) all_10_2 = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | REDUCE: (39), (69) imply:
% 159.52/28.19 | | | (70) ~ (all_52_4 = e3)
% 159.52/28.19 | | |
% 159.52/28.19 | | | REDUCE: (6), (69) imply:
% 159.52/28.19 | | | (71) op(e3, e3) = e3
% 159.52/28.19 | | |
% 159.52/28.19 | | | BETA: splitting (53) gives:
% 159.52/28.19 | | |
% 159.52/28.19 | | | Case 1:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | (72) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.19 | | | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | ALPHA: (72) implies:
% 159.52/28.19 | | | | (73) op(e3, e3) = all_22_1
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | BETA: splitting (12) gives:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | Case 1:
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | (74) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2,
% 159.52/28.19 | | | | | e0) = e3)
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | REF_CLOSE: (3), (5), (8), (9), (13), (14), (15), (16), (20), (21),
% 159.52/28.19 | | | | | (24), (25), (28), (31), (33), (36), (40), (42), (46), (47),
% 159.52/28.19 | | | | | (48), (49), (52), (56), (58), (59), (60), (61), (62), (66),
% 159.52/28.19 | | | | | (71), (73), (74) are inconsistent by sub-proof #627.
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | Case 2:
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | (75) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 159.52/28.19 | | | | | e0) = e3)
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.52/28.19 | | | | | (12), (13), (14), (15), (17), (18), (19), (20), (21), (22),
% 159.52/28.19 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 159.52/28.19 | | | | | (33), (34), (35), (36), (37), (38), (40), (41), (42), (43),
% 159.52/28.19 | | | | | (44), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 159.52/28.19 | | | | | (55), (56), (57), (58), (59), (60), (63), (70), (75) are
% 159.52/28.19 | | | | | inconsistent by sub-proof #630.
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | End of split
% 159.52/28.19 | | | |
% 159.52/28.19 | | | Case 2:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | (76) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | ALPHA: (76) implies:
% 159.52/28.19 | | | | (77) op(e3, e3) = all_22_1
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | BETA: splitting (12) gives:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | Case 1:
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | (78) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2,
% 159.52/28.19 | | | | | e0) = e3)
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | REF_CLOSE: (3), (5), (8), (9), (13), (14), (15), (16), (20), (21),
% 159.52/28.19 | | | | | (24), (25), (28), (31), (33), (36), (40), (42), (46), (47),
% 159.52/28.19 | | | | | (48), (49), (52), (56), (58), (59), (60), (61), (62), (66),
% 159.52/28.19 | | | | | (71), (77), (78) are inconsistent by sub-proof #627.
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | Case 2:
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | (79) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 159.52/28.19 | | | | | e0) = e3)
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.52/28.19 | | | | | (12), (13), (14), (15), (17), (18), (19), (20), (21), (22),
% 159.52/28.19 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 159.52/28.19 | | | | | (33), (34), (35), (36), (37), (38), (40), (41), (42), (43),
% 159.52/28.19 | | | | | (44), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 159.52/28.19 | | | | | (55), (56), (57), (58), (59), (60), (63), (70), (79) are
% 159.52/28.19 | | | | | inconsistent by sub-proof #630.
% 159.52/28.19 | | | | |
% 159.52/28.19 | | | | End of split
% 159.52/28.19 | | | |
% 159.52/28.19 | | | End of split
% 159.52/28.19 | | |
% 159.52/28.19 | | Case 2:
% 159.52/28.19 | | |
% 159.52/28.19 | | | (80) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.19 | | |
% 159.52/28.19 | | | REF_CLOSE: (7), (19), (23), (44), (80) are inconsistent by sub-proof
% 159.52/28.19 | | | #1307.
% 159.52/28.19 | | |
% 159.52/28.19 | | End of split
% 159.52/28.19 | |
% 159.52/28.19 | End of split
% 159.52/28.19 |
% 159.52/28.19 End of proof
% 159.52/28.19
% 159.52/28.19 Sub-proof #627 shows that the following formulas are inconsistent:
% 159.52/28.19 ----------------------------------------------------------------
% 159.52/28.19 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.19 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.19 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.19 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.19 (3) all_58_14 = e3
% 159.52/28.19 (4) op(e1, e1) = all_6_2
% 159.52/28.19 (5) op(e3, e3) = all_28_1
% 159.52/28.19 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.19 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.19 (7) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.19 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.19 (8) all_58_6 = e3
% 159.52/28.19 (9) op(e2, e3) = all_52_1
% 159.52/28.19 (10) ~ (all_52_13 = e3)
% 159.52/28.19 (11) ~ (e3 = e0)
% 159.52/28.19 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.19 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.19 (13) ~ (e2 = e0)
% 159.52/28.19 (14) op(e2, e0) = all_52_13
% 159.52/28.19 (15) op(e2, e3) = e2
% 159.52/28.19 (16) ~ (e3 = e1)
% 159.52/28.19 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.19 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.19 (18) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.19 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.19 (19) all_58_4 = e2
% 159.52/28.19 (20) ~ (e2 = e1)
% 159.52/28.19 (21) op(e3, e3) = e3
% 159.52/28.19 (22) ~ (e1 = e0)
% 159.52/28.19 (23) all_58_3 = e3
% 159.52/28.19 (24) ~ (all_6_2 = e2)
% 159.52/28.19 (25) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 159.52/28.19 (26) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.19 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.19 (27) op(e0, e2) = all_52_7
% 159.52/28.19 (28) op(e3, e3) = all_22_1
% 159.52/28.19 (29) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.19 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.19 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.19 (31) ~ (e3 = e2)
% 159.52/28.19 (32) all_58_12 = e1
% 159.52/28.19 (33) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.52/28.19 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.19
% 159.52/28.19 Begin of proof
% 159.52/28.19 |
% 159.52/28.19 | BETA: splitting (25) gives:
% 159.52/28.19 |
% 159.52/28.19 | Case 1:
% 159.52/28.19 | |
% 159.52/28.19 | | (34) all_58_9 = e3 & op(e3, e0) = e3
% 159.52/28.19 | |
% 159.52/28.19 | | ALPHA: (34) implies:
% 159.52/28.19 | | (35) all_58_9 = e3
% 159.52/28.19 | |
% 159.52/28.19 | | BETA: splitting (33) gives:
% 159.52/28.19 | |
% 159.52/28.19 | | Case 1:
% 159.52/28.19 | | |
% 159.52/28.19 | | | (36) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 159.52/28.19 | | | e0)
% 159.52/28.19 | | |
% 159.52/28.19 | | | BETA: splitting (36) gives:
% 159.52/28.19 | | |
% 159.52/28.19 | | | Case 1:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | (37) all_58_0 = e0 & op(e3, e3) = e0
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | REF_CLOSE: (5), (11), (21), (28), (30), (37) are inconsistent by
% 159.52/28.19 | | | | sub-proof #666.
% 159.52/28.19 | | | |
% 159.52/28.19 | | | Case 2:
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | (38) all_58_1 = e0 & op(e3, e2) = e0
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | ALPHA: (38) implies:
% 159.52/28.19 | | | | (39) all_58_1 = e0
% 159.52/28.19 | | | |
% 159.52/28.19 | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13),
% 159.52/28.19 | | | | (15), (16), (17), (18), (19), (20), (22), (23), (24), (26),
% 159.52/28.19 | | | | (27), (29), (30), (31), (32), (39) are inconsistent by
% 159.52/28.19 | | | | sub-proof #817.
% 159.52/28.19 | | | |
% 159.52/28.19 | | | End of split
% 159.52/28.19 | | |
% 159.52/28.19 | | Case 2:
% 159.52/28.19 | | |
% 159.52/28.19 | | | (40) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 159.52/28.19 | | | e0)
% 159.52/28.19 | | |
% 159.52/28.19 | | | REF_CLOSE: (2), (3), (4), (7), (11), (13), (15), (16), (17), (20), (22),
% 159.52/28.19 | | | (23), (24), (30), (31), (35), (40) are inconsistent by
% 159.52/28.19 | | | sub-proof #628.
% 159.52/28.19 | | |
% 159.52/28.19 | | End of split
% 159.52/28.19 | |
% 159.52/28.19 | Case 2:
% 159.52/28.19 | |
% 159.52/28.19 | | (41) all_58_10 = e3 & op(e2, e0) = e3
% 159.52/28.19 | |
% 159.52/28.19 | | ALPHA: (41) implies:
% 159.52/28.19 | | (42) op(e2, e0) = e3
% 159.52/28.19 | |
% 159.52/28.19 | | REF_CLOSE: (10), (14), (30), (42) are inconsistent by sub-proof #1364.
% 159.52/28.19 | |
% 159.52/28.19 | End of split
% 159.52/28.19 |
% 159.52/28.19 End of proof
% 159.52/28.19
% 159.52/28.19 Sub-proof #628 shows that the following formulas are inconsistent:
% 159.52/28.19 ----------------------------------------------------------------
% 159.52/28.19 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.19 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.19 (2) all_58_14 = e3
% 159.52/28.19 (3) op(e1, e1) = all_6_2
% 159.52/28.19 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.19 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.19 (5) ~ (e3 = e0)
% 159.52/28.19 (6) ~ (e2 = e0)
% 159.52/28.19 (7) all_58_9 = e3
% 159.52/28.19 (8) op(e2, e3) = e2
% 159.52/28.19 (9) ~ (e3 = e1)
% 159.52/28.19 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.19 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.19 (11) ~ (e2 = e1)
% 159.52/28.19 (12) ~ (e1 = e0)
% 159.52/28.19 (13) all_58_3 = e3
% 159.52/28.19 (14) ~ (all_6_2 = e2)
% 159.52/28.19 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.19 (16) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.19 (17) ~ (e3 = e2)
% 159.52/28.19
% 159.52/28.19 Begin of proof
% 159.52/28.19 |
% 159.52/28.19 | BETA: splitting (16) gives:
% 159.52/28.19 |
% 159.52/28.19 | Case 1:
% 159.52/28.19 | |
% 159.52/28.19 | | (18) all_58_4 = e0 & op(e3, e1) = e0
% 159.52/28.19 | |
% 159.52/28.19 | | ALPHA: (18) implies:
% 159.52/28.19 | | (19) all_58_4 = e0
% 159.52/28.19 | |
% 159.52/28.19 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 159.52/28.19 | | (14), (15), (17), (19) are inconsistent by sub-proof #854.
% 159.52/28.19 | |
% 159.52/28.19 | Case 2:
% 159.52/28.19 | |
% 159.52/28.19 | | (20) all_58_9 = e0 & op(e3, e0) = e0
% 159.52/28.19 | |
% 159.52/28.19 | | ALPHA: (20) implies:
% 159.52/28.19 | | (21) all_58_9 = e0
% 159.52/28.19 | |
% 159.52/28.19 | | REF_CLOSE: (5), (7), (21) are inconsistent by sub-proof #1315.
% 159.52/28.19 | |
% 159.52/28.19 | End of split
% 159.52/28.19 |
% 159.52/28.19 End of proof
% 159.52/28.19
% 159.52/28.19 Sub-proof #629 shows that the following formulas are inconsistent:
% 159.52/28.19 ----------------------------------------------------------------
% 159.52/28.19 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.19 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.19 (2) all_58_14 = e3
% 159.52/28.19 (3) op(e1, e1) = all_6_2
% 159.52/28.19 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.19 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.19 (5) ~ (e3 = e0)
% 159.52/28.20 (6) ~ (e2 = e0)
% 159.52/28.20 (7) op(e2, e3) = e2
% 159.52/28.20 (8) ~ (e3 = e1)
% 159.52/28.20 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.20 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.20 (10) all_58_15 = e0 & op(e0, e0) = e0
% 159.52/28.20 (11) all_58_4 = e2
% 159.52/28.20 (12) all_58_15 = e2
% 159.52/28.20 (13) ~ (e2 = e1)
% 159.52/28.20 (14) ~ (e1 = e0)
% 159.52/28.20 (15) all_58_3 = e3
% 159.52/28.20 (16) ~ (all_6_2 = e2)
% 159.52/28.20 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.20 (18) ~ (e3 = e2)
% 159.52/28.20
% 159.52/28.20 Begin of proof
% 159.52/28.20 |
% 159.52/28.20 | ALPHA: (10) implies:
% 159.52/28.20 | (19) all_58_15 = e0
% 159.52/28.20 |
% 159.52/28.20 | COMBINE_EQS: (12), (19) imply:
% 159.52/28.20 | (20) e2 = e0
% 159.52/28.20 |
% 159.52/28.20 | COMBINE_EQS: (11), (20) imply:
% 159.52/28.20 | (21) all_58_4 = e0
% 159.52/28.20 |
% 159.52/28.20 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (13), (14), (15),
% 159.52/28.20 | (16), (17), (18), (21) are inconsistent by sub-proof #854.
% 159.52/28.20 |
% 159.52/28.20 End of proof
% 159.52/28.20
% 159.52/28.20 Sub-proof #630 shows that the following formulas are inconsistent:
% 159.52/28.20 ----------------------------------------------------------------
% 159.52/28.20 (1) op(e1, e1) = e3
% 159.52/28.20 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.20 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.20 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.20 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.20 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.20 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.20 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.20 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.20 (6) op(e3, e3) = all_10_2
% 159.52/28.20 (7) ~ (all_10_2 = e1)
% 159.52/28.20 (8) all_58_14 = e3
% 159.52/28.20 (9) op(e1, e1) = all_6_2
% 159.52/28.20 (10) ~ (all_52_7 = e3)
% 159.52/28.20 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.20 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.20 e1)
% 159.52/28.20 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.20 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.20 (13) op(e3, e3) = all_28_1
% 159.52/28.20 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.20 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.20 (15) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.20 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.20 (16) op(e3, e2) = all_52_4
% 159.52/28.20 (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.20 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.20 (18) all_54_0 = all_10_2
% 159.52/28.20 (19) op(e2, e3) = all_52_1
% 159.52/28.20 (20) ~ (all_52_13 = e3)
% 159.52/28.20 (21) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.20 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.20 (22) ~ (all_10_2 = e0)
% 159.52/28.20 (23) ~ (e3 = e0)
% 159.52/28.20 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.20 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.20 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.20 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.20 (26) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.20 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.20 e2)
% 159.52/28.20 (27) ~ (e2 = e0)
% 159.52/28.20 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.20 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.20 (29) op(e1, e3) = all_52_2
% 159.52/28.20 (30) op(e2, e0) = all_52_13
% 159.52/28.20 (31) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.20 (32) op(e2, e3) = e2
% 159.52/28.20 (33) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.20 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.20 (34) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.20 (35) ~ (e3 = e1)
% 159.52/28.20 (36) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.20 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.20 (37) op(e1, e2) = all_52_6
% 159.52/28.20 (38) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.20 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.20 (39) op(e0, e0) = e2
% 159.52/28.20 (40) all_58_4 = e2
% 159.52/28.20 (41) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.20 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.20 (42) ~ (all_52_4 = e3)
% 159.52/28.20 (43) ~ (all_10_2 = e2)
% 159.52/28.20 (44) ~ (e2 = e1)
% 159.52/28.20 (45) ~ (e1 = e0)
% 159.52/28.20 (46) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.20 (47) all_58_3 = e3
% 159.52/28.20 (48) ~ (all_6_2 = e2)
% 159.52/28.20 (49) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.20 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.20 e3)
% 159.52/28.20 (50) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.20 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.20 (51) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.20 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.20 (52) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.20 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.20 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.20 (53) op(e1, e3) = e1
% 159.52/28.20 (54) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.20 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.20 (55) op(e0, e2) = all_52_7
% 159.52/28.20 (56) ~ (all_52_6 = e3)
% 159.52/28.20 (57) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.20 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.20 (58) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.20 (59) ~ (e3 = e2)
% 159.52/28.20 (60) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.20 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.20 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.20 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.20
% 159.52/28.20 Begin of proof
% 159.52/28.20 |
% 159.52/28.20 | BETA: splitting (46) gives:
% 159.52/28.20 |
% 159.52/28.20 | Case 1:
% 159.52/28.20 | |
% 159.52/28.20 | | (61) all_58_11 = e3 & op(e1, e0) = e3
% 159.52/28.20 | |
% 159.52/28.20 | | ALPHA: (61) implies:
% 159.52/28.20 | | (62) all_58_11 = e3
% 159.52/28.20 | |
% 159.52/28.20 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.52/28.20 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.52/28.20 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 159.52/28.20 | | (35), (36), (37), (38), (40), (41), (42), (43), (44), (45), (47),
% 159.52/28.20 | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 159.52/28.20 | | (59), (60), (62) are inconsistent by sub-proof #633.
% 159.52/28.20 | |
% 159.52/28.20 | Case 2:
% 159.52/28.20 | |
% 159.52/28.20 | | (63) all_58_15 = e3 & op(e0, e0) = e3
% 159.52/28.20 | |
% 159.52/28.20 | | ALPHA: (63) implies:
% 159.52/28.20 | | (64) op(e0, e0) = e3
% 159.52/28.20 | |
% 159.52/28.20 | | REF_CLOSE: (39), (58), (59), (64) are inconsistent by sub-proof #1382.
% 159.52/28.20 | |
% 159.52/28.20 | End of split
% 159.52/28.20 |
% 159.52/28.20 End of proof
% 159.52/28.20
% 159.52/28.20 Sub-proof #631 shows that the following formulas are inconsistent:
% 159.52/28.20 ----------------------------------------------------------------
% 159.52/28.20 (1) all_58_14 = e3
% 159.52/28.20 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.20 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.20 (3) all_58_6 = e3
% 159.52/28.20 (4) op(e2, e3) = all_52_1
% 159.52/28.20 (5) ~ (e3 = e0)
% 159.52/28.20 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.20 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.20 (7) ~ (e2 = e0)
% 159.52/28.20 (8) op(e2, e3) = e2
% 159.52/28.20 (9) ~ (e3 = e1)
% 159.52/28.20 (10) ~ (e2 = e1)
% 159.52/28.20 (11) ~ (e1 = e0)
% 159.52/28.20 (12) all_58_14 = e2 & op(e0, e1) = e2
% 159.52/28.20 (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.20 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.20 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.20 (15) ~ (e3 = e2)
% 159.52/28.20
% 159.52/28.20 Begin of proof
% 159.52/28.20 |
% 159.52/28.20 | ALPHA: (12) implies:
% 159.52/28.20 | (16) all_58_14 = e2
% 159.52/28.20 |
% 159.52/28.20 | COMBINE_EQS: (1), (16) imply:
% 159.52/28.20 | (17) e3 = e2
% 159.52/28.20 |
% 159.52/28.20 | SIMP: (17) implies:
% 159.52/28.20 | (18) e3 = e2
% 159.52/28.20 |
% 159.52/28.20 | COMBINE_EQS: (3), (18) imply:
% 159.52/28.20 | (19) all_58_6 = e2
% 159.52/28.20 |
% 159.52/28.20 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 159.52/28.20 | (19) are inconsistent by sub-proof #1152.
% 159.52/28.20 |
% 159.52/28.20 End of proof
% 159.52/28.20
% 159.52/28.20 Sub-proof #632 shows that the following formulas are inconsistent:
% 159.52/28.20 ----------------------------------------------------------------
% 159.52/28.20 (1) all_58_15 = e3
% 159.52/28.20 (2) op(e3, e3) = all_10_2
% 159.52/28.20 (3) ~ (all_10_2 = e1)
% 159.52/28.20 (4) all_58_14 = e3
% 159.52/28.20 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.20 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.20 (6) op(e3, e3) = all_28_1
% 159.52/28.20 (7) all_58_0 = e1
% 159.52/28.20 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.20 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.20 (9) all_58_6 = e3
% 159.52/28.20 (10) all_54_0 = all_10_2
% 159.52/28.20 (11) op(e2, e3) = all_52_1
% 159.52/28.20 (12) ~ (all_10_2 = e0)
% 159.52/28.20 (13) ~ (e3 = e0)
% 159.52/28.20 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.20 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.20 (15) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.20 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.20 e2)
% 159.52/28.20 (16) ~ (e2 = e0)
% 159.52/28.20 (17) op(e1, e3) = all_52_2
% 159.52/28.20 (18) op(e2, e3) = e2
% 159.52/28.20 (19) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.20 (20) ~ (e3 = e1)
% 159.52/28.20 (21) ~ (all_10_2 = e2)
% 159.52/28.20 (22) ~ (e2 = e1)
% 159.52/28.20 (23) op(e3, e3) = e3
% 159.52/28.20 (24) ~ (e1 = e0)
% 159.52/28.20 (25) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.20 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.20 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.20 (26) op(e1, e3) = e1
% 159.52/28.20 (27) op(e3, e3) = all_22_1
% 159.52/28.20 (28) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.20 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.20 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.20 (30) ~ (e3 = e2)
% 159.52/28.20 (31) op(e0, e0) = e3
% 159.52/28.20
% 159.52/28.20 Begin of proof
% 159.52/28.20 |
% 159.52/28.20 | BETA: splitting (28) gives:
% 159.52/28.20 |
% 159.52/28.20 | Case 1:
% 159.52/28.20 | |
% 159.52/28.20 | | (32) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.52/28.20 | | e0)
% 159.52/28.20 | |
% 159.52/28.20 | | REF_CLOSE: (6), (13), (16), (18), (23), (27), (29), (32) are inconsistent by
% 159.52/28.20 | | sub-proof #665.
% 159.52/28.20 | |
% 159.52/28.20 | Case 2:
% 159.52/28.20 | |
% 159.52/28.20 | | (33) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.52/28.20 | | e0)
% 159.52/28.20 | |
% 159.52/28.20 | | BETA: splitting (33) gives:
% 159.52/28.20 | |
% 159.52/28.20 | | Case 1:
% 159.52/28.20 | | |
% 159.52/28.20 | | | (34) all_58_6 = e0 & op(e1, e3) = e0
% 159.52/28.20 | | |
% 159.52/28.20 | | | ALPHA: (34) implies:
% 159.52/28.20 | | | (35) all_58_6 = e0
% 159.52/28.20 | | |
% 159.52/28.20 | | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (11), (12), (13), (14), (16),
% 159.52/28.20 | | | (17), (18), (19), (20), (21), (22), (24), (25), (26), (28),
% 159.52/28.20 | | | (29), (30), (35) are inconsistent by sub-proof #660.
% 159.52/28.20 | | |
% 159.52/28.20 | | Case 2:
% 159.52/28.20 | | |
% 159.52/28.20 | | | (36) all_58_12 = e0 & op(e0, e3) = e0
% 159.52/28.20 | | |
% 159.52/28.20 | | | ALPHA: (36) implies:
% 159.52/28.20 | | | (37) all_58_12 = e0
% 159.52/28.20 | | |
% 159.52/28.20 | | | REF_CLOSE: (1), (4), (5), (8), (9), (11), (13), (14), (15), (16), (18),
% 159.52/28.20 | | | (20), (22), (24), (28), (29), (30), (31), (37) are inconsistent
% 159.52/28.20 | | | by sub-proof #786.
% 159.52/28.20 | | |
% 159.52/28.20 | | End of split
% 159.52/28.20 | |
% 159.52/28.20 | End of split
% 159.52/28.20 |
% 159.52/28.20 End of proof
% 159.52/28.20
% 159.52/28.20 Sub-proof #633 shows that the following formulas are inconsistent:
% 159.52/28.20 ----------------------------------------------------------------
% 159.52/28.20 (1) op(e1, e1) = e3
% 159.52/28.20 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.20 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.20 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.20 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.20 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.20 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.20 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.20 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.20 (6) op(e3, e3) = all_10_2
% 159.52/28.20 (7) ~ (all_10_2 = e1)
% 159.52/28.20 (8) all_58_14 = e3
% 159.52/28.20 (9) op(e1, e1) = all_6_2
% 159.52/28.20 (10) ~ (all_52_7 = e3)
% 159.52/28.20 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.52/28.20 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.52/28.20 e1)
% 159.52/28.20 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.20 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.20 (13) op(e3, e3) = all_28_1
% 159.52/28.20 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.20 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.20 (15) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.20 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.20 (16) op(e3, e2) = all_52_4
% 159.52/28.20 (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.20 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.20 (18) all_54_0 = all_10_2
% 159.52/28.20 (19) op(e2, e3) = all_52_1
% 159.52/28.20 (20) ~ (all_52_13 = e3)
% 159.52/28.20 (21) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.20 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.20 (22) ~ (all_10_2 = e0)
% 159.52/28.20 (23) ~ (e3 = e0)
% 159.52/28.20 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.20 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.20 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.20 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.20 (26) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.20 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.20 e2)
% 159.52/28.20 (27) ~ (e2 = e0)
% 159.52/28.20 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.52/28.20 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.52/28.20 (29) op(e1, e3) = all_52_2
% 159.52/28.20 (30) op(e2, e0) = all_52_13
% 159.52/28.20 (31) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.20 (32) op(e2, e3) = e2
% 159.52/28.20 (33) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.20 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.20 (34) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.52/28.20 (35) ~ (e3 = e1)
% 159.52/28.20 (36) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.52/28.20 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.52/28.20 (37) op(e1, e2) = all_52_6
% 159.52/28.20 (38) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.20 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.20 (39) all_58_4 = e2
% 159.52/28.20 (40) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.20 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.20 (41) ~ (all_52_4 = e3)
% 159.52/28.20 (42) ~ (all_10_2 = e2)
% 159.52/28.20 (43) ~ (e2 = e1)
% 159.52/28.20 (44) ~ (e1 = e0)
% 159.52/28.20 (45) all_58_3 = e3
% 159.52/28.20 (46) ~ (all_6_2 = e2)
% 159.52/28.20 (47) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.20 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.20 e3)
% 159.52/28.20 (48) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.52/28.20 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.52/28.20 (49) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.52/28.20 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.20 (50) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.52/28.20 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.52/28.20 e3) = all_22_1 & $i(all_22_1))
% 159.52/28.20 (51) op(e1, e3) = e1
% 159.52/28.20 (52) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.52/28.20 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.52/28.20 (53) op(e0, e2) = all_52_7
% 159.52/28.20 (54) ~ (all_52_6 = e3)
% 159.52/28.20 (55) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.20 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.20 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.20 (57) ~ (e3 = e2)
% 159.52/28.20 (58) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.20 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.20 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.20 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.20 (59) all_58_11 = e3
% 159.52/28.20
% 159.52/28.20 Begin of proof
% 159.52/28.20 |
% 159.52/28.20 | BETA: splitting (21) gives:
% 159.52/28.20 |
% 159.52/28.20 | Case 1:
% 159.52/28.20 | |
% 159.52/28.20 | | (60) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 159.52/28.20 | | e2)
% 159.52/28.20 | |
% 159.52/28.20 | | BETA: splitting (60) gives:
% 159.52/28.20 | |
% 159.52/28.20 | | Case 1:
% 159.52/28.20 | | |
% 159.52/28.20 | | | (61) all_58_6 = e2 & op(e1, e3) = e2
% 159.52/28.20 | | |
% 159.52/28.20 | | | ALPHA: (61) implies:
% 159.52/28.20 | | | (62) all_58_6 = e2
% 159.52/28.20 | | |
% 159.52/28.20 | | | REF_CLOSE: (14), (19), (23), (24), (27), (32), (35), (43), (44), (55),
% 159.52/28.20 | | | (56), (57), (62) are inconsistent by sub-proof #1152.
% 159.52/28.20 | | |
% 159.52/28.20 | | Case 2:
% 159.52/28.20 | | |
% 159.52/28.20 | | | (63) all_58_7 = e2 & op(e1, e2) = e2
% 159.52/28.20 | | |
% 159.52/28.20 | | | ALPHA: (63) implies:
% 159.52/28.20 | | | (64) all_58_7 = e2
% 159.52/28.20 | | |
% 159.52/28.20 | | | BETA: splitting (26) gives:
% 159.52/28.20 | | |
% 159.52/28.20 | | | Case 1:
% 159.52/28.20 | | | |
% 159.52/28.20 | | | | (65) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 159.52/28.20 | | | | e2) = e2)
% 159.52/28.20 | | | |
% 159.52/28.20 | | | | BETA: splitting (65) gives:
% 159.52/28.20 | | | |
% 159.52/28.20 | | | | Case 1:
% 159.52/28.20 | | | | |
% 159.52/28.20 | | | | | (66) all_58_12 = e2 & op(e0, e3) = e2
% 159.52/28.20 | | | | |
% 159.52/28.20 | | | | | ALPHA: (66) implies:
% 159.52/28.20 | | | | | (67) all_58_12 = e2
% 159.52/28.20 | | | | |
% 159.52/28.20 | | | | | REF_CLOSE: (14), (19), (23), (24), (27), (32), (35), (43), (44), (55),
% 159.52/28.20 | | | | | (56), (57), (67) are inconsistent by sub-proof #1062.
% 159.52/28.20 | | | | |
% 159.52/28.20 | | | | Case 2:
% 159.52/28.20 | | | | |
% 159.52/28.20 | | | | | (68) all_58_13 = e2 & op(e0, e2) = e2
% 159.52/28.20 | | | | |
% 159.52/28.20 | | | | | ALPHA: (68) implies:
% 159.52/28.20 | | | | | (69) all_58_13 = e2
% 159.52/28.20 | | | | | (70) op(e0, e2) = e2
% 159.52/28.20 | | | | |
% 159.52/28.20 | | | | | BETA: splitting (33) gives:
% 159.52/28.20 | | | | |
% 159.52/28.20 | | | | | Case 1:
% 159.52/28.20 | | | | | |
% 159.52/28.20 | | | | | | (71) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 159.52/28.20 | | | | | | e2) = e0)
% 159.52/28.20 | | | | | |
% 159.52/28.20 | | | | | | BETA: splitting (71) gives:
% 159.52/28.20 | | | | | |
% 159.52/28.20 | | | | | | Case 1:
% 159.52/28.20 | | | | | | |
% 159.52/28.20 | | | | | | | (72) all_58_1 = e0 & op(e3, e2) = e0
% 159.52/28.20 | | | | | | |
% 159.52/28.20 | | | | | | | ALPHA: (72) implies:
% 159.52/28.20 | | | | | | | (73) all_58_1 = e0
% 159.52/28.20 | | | | | | |
% 159.52/28.20 | | | | | | | BETA: splitting (36) gives:
% 159.52/28.20 | | | | | | |
% 159.52/28.20 | | | | | | | Case 1:
% 159.52/28.20 | | | | | | | |
% 159.52/28.20 | | | | | | | | (74) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 159.52/28.20 | | | | | | | | op(e2, e1) = e0)
% 159.52/28.20 | | | | | | | |
% 159.52/28.20 | | | | | | | | BETA: splitting (74) gives:
% 159.52/28.20 | | | | | | | |
% 159.52/28.20 | | | | | | | | Case 1:
% 159.52/28.20 | | | | | | | | |
% 159.52/28.20 | | | | | | | | | (75) all_58_4 = e0 & op(e3, e1) = e0
% 159.52/28.20 | | | | | | | | |
% 159.52/28.20 | | | | | | | | | ALPHA: (75) implies:
% 159.52/28.20 | | | | | | | | | (76) all_58_4 = e0
% 159.52/28.20 | | | | | | | | |
% 159.52/28.20 | | | | | | | | | REF_CLOSE: (5), (8), (9), (15), (23), (27), (32), (35), (38),
% 159.52/28.20 | | | | | | | | | (43), (44), (45), (46), (56), (57), (76) are
% 159.52/28.20 | | | | | | | | | inconsistent by sub-proof #854.
% 159.52/28.20 | | | | | | | | |
% 159.52/28.20 | | | | | | | | Case 2:
% 159.52/28.20 | | | | | | | | |
% 159.52/28.20 | | | | | | | | | (77) all_58_5 = e0 & op(e2, e1) = e0
% 159.52/28.20 | | | | | | | | |
% 159.52/28.20 | | | | | | | | | ALPHA: (77) implies:
% 159.52/28.20 | | | | | | | | | (78) all_58_5 = e0
% 159.52/28.20 | | | | | | | | |
% 159.52/28.20 | | | | | | | | | BETA: splitting (28) gives:
% 159.52/28.20 | | | | | | | | |
% 159.52/28.20 | | | | | | | | | Case 1:
% 159.52/28.20 | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | (79) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 159.52/28.20 | | | | | | | | | | op(e1, e2) = e0)
% 159.52/28.20 | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | BETA: splitting (79) gives:
% 159.52/28.20 | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | Case 1:
% 159.52/28.20 | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | (80) all_58_6 = e0 & op(e1, e3) = e0
% 159.52/28.20 | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | ALPHA: (80) implies:
% 159.52/28.20 | | | | | | | | | | | (81) all_58_6 = e0
% 159.52/28.20 | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | BETA: splitting (24) gives:
% 159.52/28.20 | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | Case 1:
% 159.52/28.20 | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | (82) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 159.52/28.20 | | | | | | | | | | | | & op(e2, e3) = e1)
% 159.52/28.20 | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | REF_CLOSE: (6), (7), (13), (14), (18), (19), (22), (23),
% 159.52/28.20 | | | | | | | | | | | | (24), (27), (29), (32), (34), (35), (42), (43),
% 159.52/28.20 | | | | | | | | | | | | (44), (50), (51), (55), (56), (57), (81), (82) are
% 159.52/28.20 | | | | | | | | | | | | inconsistent by sub-proof #653.
% 159.52/28.20 | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | Case 2:
% 159.52/28.20 | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | (83) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 159.52/28.20 | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 159.52/28.20 | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | BETA: splitting (83) gives:
% 159.52/28.20 | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | Case 1:
% 159.52/28.20 | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | (84) all_58_6 = e1 & op(e1, e3) = e1
% 159.52/28.20 | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | REF_CLOSE: (44), (81), (84) are inconsistent by sub-proof
% 159.52/28.20 | | | | | | | | | | | | | #1064.
% 159.52/28.20 | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | Case 2:
% 159.52/28.20 | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | (85) all_58_12 = e1 & op(e0, e3) = e1
% 159.52/28.20 | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | ALPHA: (85) implies:
% 159.52/28.20 | | | | | | | | | | | | | (86) all_58_12 = e1
% 159.52/28.20 | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | BETA: splitting (5) gives:
% 159.52/28.20 | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | Case 1:
% 159.52/28.20 | | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | | (87) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 159.52/28.20 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.52/28.20 | | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | | REF_CLOSE: (32), (35), (43), (45), (56), (87) are
% 159.52/28.20 | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 159.52/28.20 | | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | Case 2:
% 159.52/28.20 | | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | | (88) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 159.52/28.20 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.52/28.20 | | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 159.52/28.20 | | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | | Case 1:
% 159.52/28.20 | | | | | | | | | | | | | | |
% 159.52/28.20 | | | | | | | | | | | | | | | (89) all_58_5 = e1 & op(e2, e1) = e1
% 159.52/28.20 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (8), (9), (15), (23), (27), (32), (35),
% 159.52/28.21 | | | | | | | | | | | | | | | (36), (38), (43), (44), (45), (46), (56), (57),
% 159.52/28.21 | | | | | | | | | | | | | | | (89) are inconsistent by sub-proof #651.
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | (90) all_58_10 = e1 & op(e2, e0) = e1
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | (91) all_58_10 = e1
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (8), (9), (14), (15), (19), (23), (24),
% 159.52/28.21 | | | | | | | | | | | | | | | (26), (27), (32), (33), (35), (38), (39), (43),
% 159.52/28.21 | | | | | | | | | | | | | | | (44), (45), (46), (55), (56), (57), (58), (64),
% 159.52/28.21 | | | | | | | | | | | | | | | (73), (78), (86), (91) are inconsistent by
% 159.52/28.21 | | | | | | | | | | | | | | | sub-proof #646.
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | (92) all_58_7 = e0 & op(e1, e2) = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | ALPHA: (92) implies:
% 159.52/28.21 | | | | | | | | | | | (93) all_58_7 = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | REF_CLOSE: (3), (35), (43), (44), (45), (69), (73), (93) are
% 159.52/28.21 | | | | | | | | | | | inconsistent by sub-proof #752.
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | (94) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 159.52/28.21 | | | | | | | | | | & op(e1, e0) = e0)
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | REF_CLOSE: (1), (23), (56), (59), (94) are inconsistent by
% 159.52/28.21 | | | | | | | | | | sub-proof #940.
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | End of split
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | | (95) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 159.52/28.21 | | | | | | | | op(e0, e1) = e0)
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | | BETA: splitting (95) gives:
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | (96) all_58_8 = e0 & op(e1, e1) = e0
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | ALPHA: (96) implies:
% 159.52/28.21 | | | | | | | | | (97) op(e1, e1) = e0
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | REF_CLOSE: (1), (23), (56), (97) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | #1466.
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | (98) all_58_14 = e0 & op(e0, e1) = e0
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | REF_CLOSE: (8), (23), (98) are inconsistent by sub-proof #882.
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | End of split
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | End of split
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | Case 2:
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | (99) all_58_3 = e0 & op(e2, e2) = e0
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | REF_CLOSE: (23), (45), (99) are inconsistent by sub-proof #910.
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | End of split
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | Case 2:
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | (100) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 159.52/28.21 | | | | | | op(e0, e2) = e0)
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | BETA: splitting (100) gives:
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | Case 1:
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | (101) all_58_7 = e0 & op(e1, e2) = e0
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | ALPHA: (101) implies:
% 159.52/28.21 | | | | | | | (102) all_58_7 = e0
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | COMBINE_EQS: (64), (102) imply:
% 159.52/28.21 | | | | | | | (103) e2 = e0
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | COMBINE_EQS: (39), (103) imply:
% 159.52/28.21 | | | | | | | (104) all_58_4 = e0
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | REF_CLOSE: (5), (8), (9), (15), (23), (27), (32), (35), (38),
% 159.52/28.21 | | | | | | | (43), (44), (45), (46), (56), (57), (104) are
% 159.52/28.21 | | | | | | | inconsistent by sub-proof #854.
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | Case 2:
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | (105) all_58_13 = e0 & op(e0, e2) = e0
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | ALPHA: (105) implies:
% 159.52/28.21 | | | | | | | (106) op(e0, e2) = e0
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | REF_CLOSE: (27), (53), (56), (70), (106) are inconsistent by
% 159.52/28.21 | | | | | | | sub-proof #1040.
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | End of split
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | End of split
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | End of split
% 159.52/28.21 | | | |
% 159.52/28.21 | | | Case 2:
% 159.52/28.21 | | | |
% 159.52/28.21 | | | | (107) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 159.52/28.21 | | | | e0) = e2)
% 159.52/28.21 | | | |
% 159.52/28.21 | | | | BETA: splitting (107) gives:
% 159.52/28.21 | | | |
% 159.52/28.21 | | | | Case 1:
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | | (108) all_58_14 = e2 & op(e0, e1) = e2
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | | ALPHA: (108) implies:
% 159.52/28.21 | | | | | (109) all_58_14 = e2
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | | REF_CLOSE: (8), (57), (109) are inconsistent by sub-proof #1405.
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | Case 2:
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | | (110) all_58_15 = e2 & op(e0, e0) = e2
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | | ALPHA: (110) implies:
% 159.52/28.21 | | | | | (111) all_58_15 = e2
% 159.52/28.21 | | | | | (112) op(e0, e0) = e2
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | | BETA: splitting (40) gives:
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | | Case 1:
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | (113) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 159.52/28.21 | | | | | | e1) = e1)
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | BETA: splitting (113) gives:
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | Case 1:
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | (114) all_58_4 = e1 & op(e3, e1) = e1
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | ALPHA: (114) implies:
% 159.52/28.21 | | | | | | | (115) all_58_4 = e1
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | REF_CLOSE: (5), (8), (9), (15), (23), (27), (32), (35), (38),
% 159.52/28.21 | | | | | | | (43), (44), (45), (46), (56), (57), (115) are
% 159.52/28.21 | | | | | | | inconsistent by sub-proof #850.
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | Case 2:
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | (116) all_58_5 = e1 & op(e2, e1) = e1
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | REF_CLOSE: (1), (5), (8), (9), (15), (23), (27), (32), (35), (36),
% 159.52/28.21 | | | | | | | (38), (43), (44), (45), (46), (56), (57), (116) are
% 159.52/28.21 | | | | | | | inconsistent by sub-proof #651.
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | End of split
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | Case 2:
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | (117) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 159.52/28.21 | | | | | | op(e0, e1) = e1)
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | BETA: splitting (117) gives:
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | | Case 1:
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | (118) all_58_8 = e1 & op(e1, e1) = e1
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | ALPHA: (118) implies:
% 159.52/28.21 | | | | | | | (119) all_58_8 = e1
% 159.52/28.21 | | | | | | | (120) op(e1, e1) = e1
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | BETA: splitting (36) gives:
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | | (121) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 159.52/28.21 | | | | | | | | op(e2, e1) = e0)
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | | BETA: splitting (121) gives:
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | (122) all_58_4 = e0 & op(e3, e1) = e0
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | ALPHA: (122) implies:
% 159.52/28.21 | | | | | | | | | (123) all_58_4 = e0
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | REF_CLOSE: (5), (8), (9), (15), (23), (27), (32), (35), (38),
% 159.52/28.21 | | | | | | | | | (43), (44), (45), (46), (56), (57), (123) are
% 159.52/28.21 | | | | | | | | | inconsistent by sub-proof #854.
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | (124) all_58_5 = e0 & op(e2, e1) = e0
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | ALPHA: (124) implies:
% 159.52/28.21 | | | | | | | | | (125) all_58_5 = e0
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | BETA: splitting (28) gives:
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | (126) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 159.52/28.21 | | | | | | | | | | & op(e1, e2) = e0)
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | BETA: splitting (126) gives:
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | (127) all_58_6 = e0 & op(e1, e3) = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | ALPHA: (127) implies:
% 159.52/28.21 | | | | | | | | | | | (128) all_58_6 = e0
% 159.52/28.21 | | | | | | | | | | | (129) op(e1, e3) = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | BETA: splitting (24) gives:
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | (130) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 159.52/28.21 | | | | | | | | | | | | & op(e2, e3) = e1)
% 159.52/28.21 | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | REF_CLOSE: (6), (7), (13), (14), (18), (19), (22), (23),
% 159.52/28.21 | | | | | | | | | | | | (24), (27), (29), (32), (34), (35), (42), (43),
% 159.52/28.21 | | | | | | | | | | | | (44), (50), (51), (55), (56), (57), (128), (130)
% 159.52/28.21 | | | | | | | | | | | | are inconsistent by sub-proof #653.
% 159.52/28.21 | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | (131) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 159.52/28.21 | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 159.52/28.21 | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | BETA: splitting (131) gives:
% 159.52/28.21 | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | (132) all_58_6 = e1 & op(e1, e3) = e1
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | ALPHA: (132) implies:
% 159.52/28.21 | | | | | | | | | | | | | (133) all_58_6 = e1
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | REF_CLOSE: (44), (128), (133) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | | | | | #735.
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | (134) all_58_12 = e1 & op(e0, e3) = e1
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | ALPHA: (134) implies:
% 159.52/28.21 | | | | | | | | | | | | | (135) all_58_12 = e1
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | BETA: splitting (5) gives:
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | (136) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 159.52/28.21 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.52/28.21 | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | REF_CLOSE: (32), (35), (43), (45), (56), (136) are
% 159.52/28.21 | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 159.52/28.21 | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | (137) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 159.52/28.21 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.52/28.21 | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 159.52/28.21 | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | (138) all_58_5 = e1 & op(e2, e1) = e1
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | (139) all_58_5 = e1
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | REF_CLOSE: (44), (125), (139) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | | | | | | | #935.
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | (140) all_58_10 = e1 & op(e2, e0) = e1
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | (141) all_58_10 = e1
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | (142) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 159.52/28.21 | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 159.52/28.21 | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | (143) all_58_0 = e3 & op(e3, e3) = e3
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | (144) all_58_0 = e3
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (145) all_58_15 = e0 & op(e0, e0) = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (146) all_58_15 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (146) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (147) e2 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | SIMP: (147) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (148) e2 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (148) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (149) all_58_4 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (15), (23), (27), (32), (35), (38),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (56), (57), (149) are
% 159.52/28.21 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (150) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.52/28.21 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.52/28.21 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 159.52/28.21 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.52/28.21 | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (151) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 159.52/28.21 | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 159.52/28.21 | | | | | | | | | | | | | | | | | | e1) = e0)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | (152) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.52/28.21 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 159.52/28.21 | | | | | | | | | | | | | | | | | | e0) = e0)
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | (153) all_58_12 = e0 & op(e0, e3) = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | (154) all_58_12 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (154) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | (155) e1 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (155) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | (156) all_58_10 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (32), (35), (43), (44), (45), (56), (125),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | (156) are inconsistent by sub-proof #839.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | (157) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | (158) all_58_13 = e0 & op(e0, e2) = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | (159) all_58_13 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | (160) op(e0, e2) = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | (161) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (162) all_58_1 = e1 & op(e3, e2) = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (163) all_58_1 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | (164) all_58_9 = e0 & op(e3, e0) = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | (165) all_58_9 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | (166) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_58_0 = e1 & op(e3, e3) = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_58_0 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (13), (14), (18), (19), (22), (23),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (24), (27), (29), (32), (34), (35), (42), (43),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (44), (50), (51), (55), (56), (57), (128), (168)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #660.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with e1, e3, e1, e1,
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1), (120) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (169) e3 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with all_52_2, e0, e3, e1,
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (29), (129) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_52_2 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with all_52_2, e1, e3, e1,
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (29), (51) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_52_2 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (171) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (172) e1 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (172) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (173) e1 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (173) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (174) e3 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (173) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_58_1 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (174) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_58_0 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (10), (11), (12), (14), (16), (17),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (23), (24), (25), (26), (27), (30),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (32), (33), (35), (37), (38), (39), (40), (41),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (47), (48), (49), (52), (53),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (54), (55), (56), (57), (58), (59), (64), (112),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (160), (175), (176) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | #639.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | (177) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_58_4 = e1 & op(e3, e1) = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (179) all_58_4 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (15), (23), (27), (32), (35), (38),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (56), (57), (179) are
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #850.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_58_9 = e1 & op(e3, e0) = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_58_9 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (181) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (182) e1 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (182) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (183) e1 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (183) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_58_1 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (35), (43), (44), (45), (64), (159), (184)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #857.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | (185) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (23), (32), (35), (43), (44), (45), (56),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | (59), (125), (185) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | | #838.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (186) all_58_3 = e1 & op(e2, e2) = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (187) all_58_3 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (187) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (188) e3 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | SIMP: (188) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (189) e3 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (189) imply:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (190) all_58_0 = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (13), (14), (18), (19), (22), (23),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (24), (27), (29), (32), (34), (35), (42), (43),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (44), (50), (51), (55), (56), (57), (128), (190)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #660.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | (191) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (192) all_58_7 = e1 & op(e1, e2) = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (12), (14),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (15), (17), (19), (20), (21), (23), (24), (25),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (26), (27), (30), (32), (33), (35), (37), (38),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (40), (43), (44), (45), (46), (47), (49), (53),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (54), (55), (56), (57), (58), (111), (112), (160),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (192) are inconsistent by sub-proof #637.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (193) all_58_13 = e1 & op(e0, e2) = e1
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (14), (19), (23), (24), (26), (27),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (32), (33), (35), (43), (44), (45), (55), (56),
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | (57), (58), (64), (135), (193) are inconsistent by
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | | sub-proof #647.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | (194) all_58_14 = e0 & op(e0, e1) = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | (195) all_58_14 = e0
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23), (195) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | | #1444.
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | (196) all_58_2 = e3 & op(e2, e3) = e3
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | (197) op(e2, e3) = e3
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (32), (56), (57), (197) are inconsistent by
% 159.52/28.21 | | | | | | | | | | | | | | | | | sub-proof #1159.
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | (198) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 159.52/28.21 | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 159.52/28.21 | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 159.52/28.21 | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | (199) all_58_6 = e3 & op(e1, e3) = e3
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 159.52/28.21 | | | | | | | | | | | | | | | | | (200) all_58_6 = e3
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (128), (200) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | | | | | | | | | #1321.
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | (201) all_58_12 = e3 & op(e0, e3) = e3
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (13), (18), (22), (24), (27), (29),
% 159.52/28.21 | | | | | | | | | | | | | | | | | (32), (34), (42), (43), (44), (50), (51), (55),
% 159.52/28.21 | | | | | | | | | | | | | | | | | (56), (201) are inconsistent by sub-proof #662.
% 159.52/28.21 | | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | (202) all_58_7 = e0 & op(e1, e2) = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | ALPHA: (202) implies:
% 159.52/28.21 | | | | | | | | | | | (203) all_58_7 = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (14), (15), (19), (21),
% 159.52/28.21 | | | | | | | | | | | (23), (24), (27), (32), (35), (38), (43), (44),
% 159.52/28.21 | | | | | | | | | | | (45), (46), (47), (53), (55), (56), (57), (58),
% 159.52/28.21 | | | | | | | | | | | (59), (111), (112), (203) are inconsistent by
% 159.52/28.21 | | | | | | | | | | | sub-proof #634.
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | (204) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 159.52/28.21 | | | | | | | | | | & op(e1, e0) = e0)
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | BETA: splitting (204) gives:
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | Case 1:
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | (205) all_58_8 = e0 & op(e1, e1) = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | ALPHA: (205) implies:
% 159.52/28.21 | | | | | | | | | | | (206) all_58_8 = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | REF_CLOSE: (44), (119), (206) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | | | #1445.
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | (207) all_58_11 = e0 & op(e1, e0) = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | ALPHA: (207) implies:
% 159.52/28.21 | | | | | | | | | | | (208) all_58_11 = e0
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | | REF_CLOSE: (23), (59), (208) are inconsistent by sub-proof
% 159.52/28.21 | | | | | | | | | | | #1216.
% 159.52/28.21 | | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | | |
% 159.52/28.21 | | | | | | | | | End of split
% 159.52/28.21 | | | | | | | | |
% 159.52/28.21 | | | | | | | | End of split
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | Case 2:
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | | (209) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 159.52/28.21 | | | | | | | | op(e0, e1) = e0)
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | | REF_CLOSE: (8), (23), (44), (119), (209) are inconsistent by
% 159.52/28.21 | | | | | | | | sub-proof #1443.
% 159.52/28.21 | | | | | | | |
% 159.52/28.21 | | | | | | | End of split
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | Case 2:
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | (210) all_58_14 = e1 & op(e0, e1) = e1
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | ALPHA: (210) implies:
% 159.52/28.21 | | | | | | | (211) all_58_14 = e1
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | | REF_CLOSE: (8), (35), (211) are inconsistent by sub-proof #1147.
% 159.52/28.21 | | | | | | |
% 159.52/28.21 | | | | | | End of split
% 159.52/28.21 | | | | | |
% 159.52/28.21 | | | | | End of split
% 159.52/28.21 | | | | |
% 159.52/28.21 | | | | End of split
% 159.52/28.21 | | | |
% 159.52/28.21 | | | End of split
% 159.52/28.21 | | |
% 159.52/28.21 | | End of split
% 159.52/28.21 | |
% 159.52/28.21 | Case 2:
% 159.52/28.21 | |
% 159.52/28.21 | | (212) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 159.52/28.21 | | e2)
% 159.52/28.21 | |
% 159.52/28.21 | | BETA: splitting (212) gives:
% 159.52/28.21 | |
% 159.52/28.21 | | Case 1:
% 159.52/28.21 | | |
% 159.52/28.21 | | | (213) all_58_8 = e2 & op(e1, e1) = e2
% 159.52/28.21 | | |
% 159.52/28.21 | | | REF_CLOSE: (9), (46), (56), (213) are inconsistent by sub-proof #1440.
% 159.52/28.21 | | |
% 159.52/28.21 | | Case 2:
% 159.52/28.21 | | |
% 159.52/28.21 | | | (214) all_58_11 = e2 & op(e1, e0) = e2
% 159.52/28.21 | | |
% 159.52/28.21 | | | REF_CLOSE: (57), (59), (214) are inconsistent by sub-proof #852.
% 159.52/28.21 | | |
% 159.52/28.21 | | End of split
% 159.52/28.21 | |
% 159.52/28.21 | End of split
% 159.52/28.21 |
% 159.52/28.21 End of proof
% 159.52/28.21
% 159.52/28.21 Sub-proof #634 shows that the following formulas are inconsistent:
% 159.52/28.21 ----------------------------------------------------------------
% 159.52/28.21 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.21 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.21 (2) all_58_14 = e3
% 159.52/28.21 (3) op(e1, e1) = all_6_2
% 159.52/28.21 (4) ~ (all_52_7 = e3)
% 159.52/28.21 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.21 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.21 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.21 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.21 (7) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.21 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.21 (8) all_58_7 = e0
% 159.52/28.21 (9) op(e2, e3) = all_52_1
% 159.52/28.21 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.21 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.21 (11) ~ (e3 = e0)
% 159.52/28.21 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.21 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.21 (13) ~ (e2 = e0)
% 159.52/28.21 (14) op(e2, e3) = e2
% 159.52/28.21 (15) ~ (e3 = e1)
% 159.52/28.21 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.21 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.21 (17) op(e0, e0) = e2
% 159.52/28.21 (18) all_58_15 = e2
% 159.52/28.21 (19) ~ (e2 = e1)
% 159.52/28.21 (20) ~ (e1 = e0)
% 159.52/28.21 (21) all_58_3 = e3
% 159.52/28.21 (22) ~ (all_6_2 = e2)
% 159.52/28.21 (23) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.21 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.21 e3)
% 159.52/28.21 (24) op(e0, e2) = all_52_7
% 159.52/28.21 (25) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.21 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.21 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.21 (27) ~ (e3 = e2)
% 159.52/28.21 (28) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.21 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.21 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.21 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.21 (29) all_58_11 = e3
% 159.52/28.21
% 159.52/28.21 Begin of proof
% 159.52/28.21 |
% 159.52/28.21 | BETA: splitting (7) gives:
% 159.52/28.21 |
% 159.52/28.21 | Case 1:
% 159.52/28.21 | |
% 159.52/28.21 | | (30) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 159.52/28.21 | | e2)
% 159.52/28.21 | |
% 159.52/28.21 | | BETA: splitting (30) gives:
% 159.52/28.21 | |
% 159.52/28.21 | | Case 1:
% 159.52/28.21 | | |
% 159.52/28.21 | | | (31) all_58_4 = e2 & op(e3, e1) = e2
% 159.52/28.21 | | |
% 159.52/28.21 | | | ALPHA: (31) implies:
% 159.52/28.21 | | | (32) all_58_4 = e2
% 159.52/28.21 | | |
% 159.52/28.21 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.52/28.21 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 159.52/28.21 | | | (23), (24), (25), (26), (27), (28), (29), (32) are inconsistent
% 159.52/28.21 | | | by sub-proof #635.
% 159.52/28.21 | | |
% 159.52/28.21 | | Case 2:
% 159.52/28.21 | | |
% 159.52/28.21 | | | (33) all_58_5 = e2 & op(e2, e1) = e2
% 159.52/28.21 | | |
% 159.52/28.21 | | | ALPHA: (33) implies:
% 159.52/28.21 | | | (34) all_58_5 = e2
% 159.52/28.21 | | |
% 159.52/28.21 | | | REF_CLOSE: (1), (11), (13), (14), (15), (16), (19), (20), (21), (26), (34)
% 159.52/28.21 | | | are inconsistent by sub-proof #898.
% 159.52/28.21 | | |
% 159.52/28.21 | | End of split
% 159.52/28.21 | |
% 159.52/28.21 | Case 2:
% 159.52/28.21 | |
% 159.52/28.21 | | (35) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 159.52/28.21 | | e2)
% 159.52/28.21 | |
% 159.52/28.21 | | REF_CLOSE: (3), (4), (5), (11), (13), (15), (17), (18), (19), (20), (22),
% 159.52/28.21 | | (23), (24), (26), (27), (28), (35) are inconsistent by sub-proof
% 159.52/28.21 | | #891.
% 159.52/28.21 | |
% 159.52/28.21 | End of split
% 159.52/28.21 |
% 159.52/28.21 End of proof
% 159.52/28.21
% 159.52/28.21 Sub-proof #635 shows that the following formulas are inconsistent:
% 159.52/28.21 ----------------------------------------------------------------
% 159.52/28.21 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.21 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.21 (2) all_58_14 = e3
% 159.52/28.21 (3) op(e1, e1) = all_6_2
% 159.52/28.21 (4) ~ (all_52_7 = e3)
% 159.52/28.21 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.21 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.21 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.21 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.21 (7) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.21 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.21 (8) all_58_7 = e0
% 159.52/28.21 (9) op(e2, e3) = all_52_1
% 159.52/28.21 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.21 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.21 (11) ~ (e3 = e0)
% 159.52/28.22 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.22 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.22 (13) ~ (e2 = e0)
% 159.52/28.22 (14) op(e2, e3) = e2
% 159.52/28.22 (15) ~ (e3 = e1)
% 159.52/28.22 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.22 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.22 (17) op(e0, e0) = e2
% 159.52/28.22 (18) all_58_4 = e2
% 159.52/28.22 (19) all_58_15 = e2
% 159.52/28.22 (20) ~ (e2 = e1)
% 159.52/28.22 (21) ~ (e1 = e0)
% 159.52/28.22 (22) all_58_3 = e3
% 159.52/28.22 (23) ~ (all_6_2 = e2)
% 159.52/28.22 (24) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.52/28.22 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.52/28.22 e3)
% 159.52/28.22 (25) op(e0, e2) = all_52_7
% 159.52/28.22 (26) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.52/28.22 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.52/28.22 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.22 (28) ~ (e3 = e2)
% 159.52/28.22 (29) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.52/28.22 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.52/28.22 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.52/28.22 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.52/28.22 (30) all_58_11 = e3
% 159.52/28.22
% 159.52/28.22 Begin of proof
% 159.52/28.22 |
% 159.52/28.22 | BETA: splitting (10) gives:
% 159.52/28.22 |
% 159.52/28.22 | Case 1:
% 159.52/28.22 | |
% 159.52/28.22 | | (31) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 159.52/28.22 | | e2)
% 159.52/28.22 | |
% 159.52/28.22 | | BETA: splitting (31) gives:
% 159.52/28.22 | |
% 159.52/28.22 | | Case 1:
% 159.52/28.22 | | |
% 159.52/28.22 | | | (32) all_58_6 = e2 & op(e1, e3) = e2
% 159.52/28.22 | | |
% 159.52/28.22 | | | ALPHA: (32) implies:
% 159.52/28.22 | | | (33) all_58_6 = e2
% 159.52/28.22 | | |
% 159.52/28.22 | | | REF_CLOSE: (6), (9), (11), (12), (13), (14), (15), (20), (21), (26), (27),
% 159.52/28.22 | | | (28), (33) are inconsistent by sub-proof #1152.
% 159.52/28.22 | | |
% 159.52/28.22 | | Case 2:
% 159.52/28.22 | | |
% 159.52/28.22 | | | (34) all_58_7 = e2 & op(e1, e2) = e2
% 159.52/28.22 | | |
% 159.52/28.22 | | | REF_CLOSE: (1), (2), (3), (7), (8), (11), (13), (14), (15), (16), (18),
% 159.52/28.22 | | | (20), (21), (22), (23), (27), (28), (34) are inconsistent by
% 159.52/28.22 | | | sub-proof #636.
% 159.52/28.22 | | |
% 159.52/28.22 | | End of split
% 159.52/28.22 | |
% 159.52/28.22 | Case 2:
% 159.52/28.22 | |
% 159.52/28.22 | | (35) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 159.52/28.22 | | e2)
% 159.52/28.22 | |
% 159.52/28.22 | | BETA: splitting (35) gives:
% 159.52/28.22 | |
% 159.52/28.22 | | Case 1:
% 159.52/28.22 | | |
% 159.52/28.22 | | | (36) all_58_8 = e2 & op(e1, e1) = e2
% 159.52/28.22 | | |
% 159.52/28.22 | | | REF_CLOSE: (3), (23), (27), (36) are inconsistent by sub-proof #1440.
% 159.52/28.22 | | |
% 159.52/28.22 | | Case 2:
% 159.52/28.22 | | |
% 159.52/28.22 | | | (37) all_58_11 = e2 & op(e1, e0) = e2
% 159.52/28.22 | | |
% 159.52/28.22 | | | ALPHA: (37) implies:
% 159.52/28.22 | | | (38) all_58_11 = e2
% 159.52/28.22 | | |
% 159.52/28.22 | | | COMBINE_EQS: (30), (38) imply:
% 159.52/28.22 | | | (39) e3 = e2
% 159.52/28.22 | | |
% 159.52/28.22 | | | COMBINE_EQS: (2), (39) imply:
% 159.52/28.22 | | | (40) all_58_14 = e2
% 159.52/28.22 | | |
% 159.52/28.22 | | | REF_CLOSE: (4), (5), (11), (13), (15), (17), (19), (20), (21), (24), (25),
% 159.52/28.22 | | | (27), (28), (29), (40) are inconsistent by sub-proof #1380.
% 159.52/28.22 | | |
% 159.52/28.22 | | End of split
% 159.52/28.22 | |
% 159.52/28.22 | End of split
% 159.52/28.22 |
% 159.52/28.22 End of proof
% 159.52/28.22
% 159.52/28.22 Sub-proof #636 shows that the following formulas are inconsistent:
% 159.52/28.22 ----------------------------------------------------------------
% 159.52/28.22 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.22 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.22 (2) all_58_14 = e3
% 159.52/28.22 (3) op(e1, e1) = all_6_2
% 159.52/28.22 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.22 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.22 (5) all_58_7 = e0
% 159.52/28.22 (6) ~ (e3 = e0)
% 159.52/28.22 (7) ~ (e2 = e0)
% 159.52/28.22 (8) all_58_7 = e2 & op(e1, e2) = e2
% 159.52/28.22 (9) op(e2, e3) = e2
% 159.52/28.22 (10) ~ (e3 = e1)
% 159.52/28.22 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.22 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.22 (12) all_58_4 = e2
% 159.52/28.22 (13) ~ (e2 = e1)
% 159.52/28.22 (14) ~ (e1 = e0)
% 159.52/28.22 (15) all_58_3 = e3
% 159.52/28.22 (16) ~ (all_6_2 = e2)
% 159.52/28.22 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.52/28.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.52/28.22 (18) ~ (e3 = e2)
% 159.52/28.22
% 159.52/28.22 Begin of proof
% 159.52/28.22 |
% 159.52/28.22 | ALPHA: (8) implies:
% 159.52/28.22 | (19) all_58_7 = e2
% 159.52/28.22 |
% 159.52/28.22 | COMBINE_EQS: (5), (19) imply:
% 159.52/28.22 | (20) e2 = e0
% 159.52/28.22 |
% 159.52/28.22 | COMBINE_EQS: (12), (20) imply:
% 159.52/28.22 | (21) all_58_4 = e0
% 159.52/28.22 |
% 159.52/28.22 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (13), (14), (15),
% 159.52/28.22 | (16), (17), (18), (21) are inconsistent by sub-proof #854.
% 159.52/28.22 |
% 159.52/28.22 End of proof
% 159.52/28.22
% 159.52/28.22 Sub-proof #637 shows that the following formulas are inconsistent:
% 159.52/28.22 ----------------------------------------------------------------
% 159.52/28.22 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.52/28.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.52/28.22 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.52/28.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.22 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.52/28.22 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.52/28.22 (4) all_58_14 = e3
% 159.52/28.22 (5) op(e1, e1) = all_6_2
% 159.52/28.22 (6) ~ (all_52_7 = e3)
% 159.52/28.22 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.52/28.22 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.52/28.22 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.52/28.22 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.52/28.22 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.52/28.22 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.52/28.22 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.52/28.22 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.52/28.22 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.52/28.22 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.52/28.22 (12) op(e2, e3) = all_52_1
% 159.52/28.22 (13) ~ (all_52_13 = e3)
% 159.52/28.22 (14) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.52/28.22 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.52/28.22 (15) ~ (e3 = e0)
% 159.52/28.22 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.52/28.22 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.52/28.22 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.52/28.22 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.52/28.22 (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.52/28.22 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.52/28.22 e2)
% 159.52/28.22 (19) ~ (e2 = e0)
% 159.52/28.22 (20) op(e2, e0) = all_52_13
% 159.52/28.22 (21) all_58_7 = e1 & op(e1, e2) = e1
% 159.52/28.22 (22) op(e2, e3) = e2
% 159.52/28.22 (23) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.22 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.52/28.22 (24) ~ (e3 = e1)
% 159.52/28.22 (25) op(e1, e2) = all_52_6
% 159.52/28.22 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.52/28.22 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.52/28.22 (27) op(e0, e0) = e2
% 159.52/28.22 (28) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.52/28.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.52/28.22 (29) op(e0, e2) = e0
% 159.62/28.22 (30) all_58_15 = e2
% 159.62/28.22 (31) ~ (e2 = e1)
% 159.62/28.22 (32) ~ (e1 = e0)
% 159.62/28.22 (33) all_58_3 = e3
% 159.62/28.22 (34) ~ (all_6_2 = e2)
% 159.62/28.22 (35) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.62/28.22 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.62/28.22 e3)
% 159.62/28.22 (36) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.62/28.22 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.22 (37) op(e0, e2) = all_52_7
% 159.62/28.22 (38) ~ (all_52_6 = e3)
% 159.62/28.22 (39) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.22 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.22 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.22 (41) ~ (e3 = e2)
% 159.62/28.22 (42) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.22 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.22 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.22 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.22
% 159.62/28.22 Begin of proof
% 159.62/28.22 |
% 159.62/28.22 | ALPHA: (21) implies:
% 159.62/28.22 | (43) all_58_7 = e1
% 159.62/28.22 |
% 159.62/28.22 | BETA: splitting (10) gives:
% 159.62/28.22 |
% 159.62/28.22 | Case 1:
% 159.62/28.22 | |
% 159.62/28.22 | | (44) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 159.62/28.22 | | e2)
% 159.62/28.22 | |
% 159.62/28.22 | | BETA: splitting (44) gives:
% 159.62/28.22 | |
% 159.62/28.22 | | Case 1:
% 159.62/28.22 | | |
% 159.62/28.22 | | | (45) all_58_4 = e2 & op(e3, e1) = e2
% 159.62/28.22 | | |
% 159.62/28.22 | | | ALPHA: (45) implies:
% 159.62/28.22 | | | (46) all_58_4 = e2
% 159.62/28.22 | | |
% 159.62/28.22 | | | BETA: splitting (14) gives:
% 159.62/28.22 | | |
% 159.62/28.22 | | | Case 1:
% 159.62/28.22 | | | |
% 159.62/28.22 | | | | (47) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 159.62/28.22 | | | | = e2)
% 159.62/28.22 | | | |
% 159.62/28.22 | | | | REF_CLOSE: (3), (4), (5), (9), (10), (12), (15), (16), (19), (22), (24),
% 159.62/28.22 | | | | (26), (31), (32), (33), (34), (39), (40), (41), (43), (46),
% 159.62/28.22 | | | | (47) are inconsistent by sub-proof #762.
% 159.62/28.22 | | | |
% 159.62/28.22 | | | Case 2:
% 159.62/28.22 | | | |
% 159.62/28.22 | | | | (48) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 159.62/28.22 | | | | = e2)
% 159.62/28.22 | | | |
% 159.62/28.22 | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 159.62/28.22 | | | | (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 159.62/28.22 | | | | (27), (28), (29), (31), (32), (33), (34), (35), (36), (37),
% 159.62/28.22 | | | | (38), (39), (40), (41), (42), (48) are inconsistent by
% 159.62/28.22 | | | | sub-proof #638.
% 159.62/28.22 | | | |
% 159.62/28.22 | | | End of split
% 159.62/28.22 | | |
% 159.62/28.22 | | Case 2:
% 159.62/28.22 | | |
% 159.62/28.22 | | | (49) all_58_5 = e2 & op(e2, e1) = e2
% 159.62/28.22 | | |
% 159.62/28.22 | | | ALPHA: (49) implies:
% 159.62/28.22 | | | (50) all_58_5 = e2
% 159.62/28.22 | | |
% 159.62/28.22 | | | REF_CLOSE: (3), (15), (19), (22), (24), (26), (31), (32), (33), (40), (50)
% 159.62/28.22 | | | are inconsistent by sub-proof #898.
% 159.62/28.22 | | |
% 159.62/28.22 | | End of split
% 159.62/28.22 | |
% 159.62/28.22 | Case 2:
% 159.62/28.22 | |
% 159.62/28.22 | | (51) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 159.62/28.22 | | e2)
% 159.62/28.22 | |
% 159.62/28.22 | | REF_CLOSE: (5), (6), (7), (15), (19), (24), (27), (30), (31), (32), (34),
% 159.62/28.22 | | (35), (37), (40), (41), (42), (51) are inconsistent by sub-proof
% 159.62/28.22 | | #891.
% 159.62/28.22 | |
% 159.62/28.22 | End of split
% 159.62/28.22 |
% 159.62/28.22 End of proof
% 159.62/28.22
% 159.62/28.22 Sub-proof #638 shows that the following formulas are inconsistent:
% 159.62/28.22 ----------------------------------------------------------------
% 159.62/28.22 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.62/28.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.62/28.22 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.22 (3) op(e1, e1) = all_6_2
% 159.62/28.22 (4) ~ (all_52_7 = e3)
% 159.62/28.22 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.62/28.22 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.22 (6) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.62/28.22 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.62/28.22 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.22 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.22 (8) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.62/28.22 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.62/28.22 (9) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.62/28.22 (10) op(e2, e3) = all_52_1
% 159.62/28.22 (11) ~ (all_52_13 = e3)
% 159.62/28.22 (12) ~ (e3 = e0)
% 159.62/28.22 (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.22 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.22 (14) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.62/28.22 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.62/28.22 (15) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.22 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.22 e2)
% 159.62/28.22 (16) ~ (e2 = e0)
% 159.62/28.22 (17) op(e2, e0) = all_52_13
% 159.62/28.22 (18) op(e2, e3) = e2
% 159.62/28.22 (19) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.22 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.22 (20) ~ (e3 = e1)
% 159.62/28.22 (21) op(e1, e2) = all_52_6
% 159.62/28.22 (22) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.22 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.22 (23) op(e0, e0) = e2
% 159.62/28.22 (24) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.62/28.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.62/28.22 (25) op(e0, e2) = e0
% 159.62/28.22 (26) ~ (e2 = e1)
% 159.62/28.22 (27) ~ (e1 = e0)
% 159.62/28.22 (28) all_58_3 = e3
% 159.62/28.22 (29) ~ (all_6_2 = e2)
% 159.62/28.22 (30) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.62/28.22 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.62/28.22 e3)
% 159.62/28.22 (31) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.62/28.22 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.22 (32) op(e0, e2) = all_52_7
% 159.62/28.22 (33) ~ (all_52_6 = e3)
% 159.62/28.22 (34) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.22 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.22 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.22 (36) ~ (e3 = e2)
% 159.62/28.22 (37) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.22 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.22 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.22 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.22
% 159.62/28.22 Begin of proof
% 159.62/28.22 |
% 159.62/28.22 | BETA: splitting (9) gives:
% 159.62/28.22 |
% 159.62/28.22 | Case 1:
% 159.62/28.22 | |
% 159.62/28.22 | | (38) all_58_8 = e2 & op(e1, e1) = e2
% 159.62/28.22 | |
% 159.62/28.22 | | REF_CLOSE: (3), (29), (35), (38) are inconsistent by sub-proof #1440.
% 159.62/28.22 | |
% 159.62/28.22 | Case 2:
% 159.62/28.22 | |
% 159.62/28.22 | | (39) all_58_11 = e2 & op(e1, e0) = e2
% 159.62/28.22 | |
% 159.62/28.22 | | ALPHA: (39) implies:
% 159.62/28.22 | | (40) all_58_11 = e2
% 159.62/28.22 | |
% 159.62/28.22 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 159.62/28.22 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 159.62/28.22 | | (26), (27), (28), (30), (31), (32), (33), (34), (35), (36), (37),
% 159.62/28.22 | | (40) are inconsistent by sub-proof #696.
% 159.62/28.22 | |
% 159.62/28.22 | End of split
% 159.62/28.22 |
% 159.62/28.22 End of proof
% 159.62/28.22
% 159.62/28.22 Sub-proof #639 shows that the following formulas are inconsistent:
% 159.62/28.22 ----------------------------------------------------------------
% 159.62/28.22 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.62/28.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.62/28.22 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.22 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.22 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.22 (4) all_58_1 = e0
% 159.62/28.22 (5) ~ (all_52_7 = e3)
% 159.62/28.22 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.62/28.22 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.22 (7) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.62/28.22 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.62/28.22 (8) all_58_7 = e2
% 159.62/28.22 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.22 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.22 (10) op(e3, e2) = all_52_4
% 159.62/28.22 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.62/28.22 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.62/28.22 (12) op(e2, e3) = all_52_1
% 159.62/28.22 (13) ~ (all_52_13 = e3)
% 159.62/28.22 (14) ~ (e3 = e0)
% 159.62/28.22 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.22 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.22 (16) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.62/28.22 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.62/28.22 (17) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.22 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.22 e2)
% 159.62/28.22 (18) ~ (e2 = e0)
% 159.62/28.22 (19) op(e2, e0) = all_52_13
% 159.62/28.22 (20) op(e2, e3) = e2
% 159.62/28.22 (21) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.22 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.22 (22) ~ (e3 = e1)
% 159.62/28.22 (23) op(e1, e2) = all_52_6
% 159.62/28.22 (24) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.22 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.22 (25) op(e0, e0) = e2
% 159.62/28.22 (26) all_58_4 = e2
% 159.62/28.22 (27) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.62/28.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.62/28.22 (28) ~ (all_52_4 = e3)
% 159.62/28.22 (29) op(e0, e2) = e0
% 159.62/28.22 (30) ~ (e2 = e1)
% 159.62/28.22 (31) ~ (e1 = e0)
% 159.62/28.22 (32) all_58_3 = e3
% 159.62/28.22 (33) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.62/28.22 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.62/28.22 e3)
% 159.62/28.22 (34) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.62/28.22 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.62/28.22 (35) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.62/28.22 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.22 (36) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.62/28.22 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.62/28.22 (37) op(e0, e2) = all_52_7
% 159.62/28.22 (38) all_58_0 = e0
% 159.62/28.22 (39) ~ (all_52_6 = e3)
% 159.62/28.22 (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.22 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.22 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.22 (42) ~ (e3 = e2)
% 159.62/28.22 (43) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.22 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.22 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.22 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.22 (44) all_58_11 = e3
% 159.62/28.22
% 159.62/28.22 Begin of proof
% 159.62/28.22 |
% 159.62/28.22 | BETA: splitting (2) gives:
% 159.62/28.22 |
% 159.62/28.22 | Case 1:
% 159.62/28.22 | |
% 159.62/28.22 | | (45) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 159.62/28.22 | | e1)
% 159.62/28.22 | |
% 159.62/28.22 | | BETA: splitting (45) gives:
% 159.62/28.22 | |
% 159.62/28.22 | | Case 1:
% 159.62/28.22 | | |
% 159.62/28.22 | | | (46) all_58_1 = e1 & op(e3, e2) = e1
% 159.62/28.22 | | |
% 159.62/28.22 | | | REF_CLOSE: (4), (31), (46) are inconsistent by sub-proof #1424.
% 159.62/28.22 | | |
% 159.62/28.22 | | Case 2:
% 159.62/28.22 | | |
% 159.62/28.22 | | | (47) all_58_3 = e1 & op(e2, e2) = e1
% 159.62/28.22 | | |
% 159.62/28.22 | | | REF_CLOSE: (22), (32), (47) are inconsistent by sub-proof #912.
% 159.62/28.22 | | |
% 159.62/28.22 | | End of split
% 159.62/28.22 | |
% 159.62/28.22 | Case 2:
% 159.62/28.22 | |
% 159.62/28.22 | | (48) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 159.62/28.22 | | e1)
% 159.62/28.22 | |
% 159.62/28.22 | | BETA: splitting (48) gives:
% 159.62/28.22 | |
% 159.62/28.22 | | Case 1:
% 159.62/28.22 | | |
% 159.62/28.22 | | | (49) all_58_7 = e1 & op(e1, e2) = e1
% 159.62/28.22 | | |
% 159.62/28.22 | | | REF_CLOSE: (8), (30), (49) are inconsistent by sub-proof #1045.
% 159.62/28.22 | | |
% 159.62/28.22 | | Case 2:
% 159.62/28.22 | | |
% 159.62/28.22 | | | (50) all_58_13 = e1 & op(e0, e2) = e1
% 159.62/28.22 | | |
% 159.62/28.22 | | | ALPHA: (50) implies:
% 159.62/28.22 | | | (51) all_58_13 = e1
% 159.62/28.22 | | |
% 159.62/28.22 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.22 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 159.62/28.22 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 159.62/28.22 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 159.62/28.22 | | | (43), (44), (51) are inconsistent by sub-proof #640.
% 159.62/28.22 | | |
% 159.62/28.22 | | End of split
% 159.62/28.22 | |
% 159.62/28.22 | End of split
% 159.62/28.22 |
% 159.62/28.22 End of proof
% 159.62/28.22
% 159.62/28.22 Sub-proof #640 shows that the following formulas are inconsistent:
% 159.62/28.22 ----------------------------------------------------------------
% 159.62/28.22 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.62/28.22 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.62/28.22 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.22 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.22 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.22 (4) all_58_1 = e0
% 159.62/28.22 (5) ~ (all_52_7 = e3)
% 159.62/28.22 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.62/28.22 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.22 (7) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.62/28.22 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.62/28.22 (8) all_58_7 = e2
% 159.62/28.22 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.22 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.22 (10) op(e3, e2) = all_52_4
% 159.62/28.22 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.62/28.22 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.62/28.23 (12) op(e2, e3) = all_52_1
% 159.62/28.23 (13) ~ (all_52_13 = e3)
% 159.62/28.23 (14) all_58_13 = e1
% 159.62/28.23 (15) ~ (e3 = e0)
% 159.62/28.23 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.23 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.23 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.62/28.23 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.62/28.23 (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.23 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.23 e2)
% 159.62/28.23 (19) ~ (e2 = e0)
% 159.62/28.23 (20) op(e2, e0) = all_52_13
% 159.62/28.23 (21) op(e2, e3) = e2
% 159.62/28.23 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.23 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.23 (23) ~ (e3 = e1)
% 159.62/28.23 (24) op(e1, e2) = all_52_6
% 159.62/28.23 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.23 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.23 (26) op(e0, e0) = e2
% 159.62/28.23 (27) all_58_4 = e2
% 159.62/28.23 (28) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.62/28.23 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.62/28.23 (29) ~ (all_52_4 = e3)
% 159.62/28.23 (30) op(e0, e2) = e0
% 159.62/28.23 (31) ~ (e2 = e1)
% 159.62/28.23 (32) ~ (e1 = e0)
% 159.62/28.23 (33) all_58_3 = e3
% 159.62/28.23 (34) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.62/28.23 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.62/28.23 e3)
% 159.62/28.23 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.62/28.23 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.62/28.23 (36) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.62/28.23 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.23 (37) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.62/28.23 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.62/28.23 (38) op(e0, e2) = all_52_7
% 159.62/28.23 (39) all_58_0 = e0
% 159.62/28.23 (40) ~ (all_52_6 = e3)
% 159.62/28.23 (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.23 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.23 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.23 (43) ~ (e3 = e2)
% 159.62/28.23 (44) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.23 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.23 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.23 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.23 (45) all_58_11 = e3
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | BETA: splitting (37) gives:
% 159.62/28.23 |
% 159.62/28.23 | Case 1:
% 159.62/28.23 | |
% 159.62/28.23 | | (46) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 159.62/28.23 | | e3)
% 159.62/28.23 | |
% 159.62/28.23 | | REF_CLOSE: (10), (15), (29), (39), (42), (46) are inconsistent by sub-proof
% 159.62/28.23 | | #645.
% 159.62/28.23 | |
% 159.62/28.23 | Case 2:
% 159.62/28.23 | |
% 159.62/28.23 | | (47) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 159.62/28.23 | | e3)
% 159.62/28.23 | |
% 159.62/28.23 | | BETA: splitting (47) gives:
% 159.62/28.23 | |
% 159.62/28.23 | | Case 1:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (48) all_58_4 = e3 & op(e3, e1) = e3
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (11), (12), (13), (15), (16),
% 159.62/28.23 | | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 159.62/28.23 | | | (27), (28), (30), (31), (32), (33), (34), (36), (38), (40),
% 159.62/28.23 | | | (41), (42), (43), (44), (45), (48) are inconsistent by
% 159.62/28.23 | | | sub-proof #644.
% 159.62/28.23 | | |
% 159.62/28.23 | | Case 2:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (49) all_58_9 = e3 & op(e3, e0) = e3
% 159.62/28.23 | | |
% 159.62/28.23 | | | ALPHA: (49) implies:
% 159.62/28.23 | | | (50) all_58_9 = e3
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (2), (4), (8), (14), (23), (27), (31), (32), (33), (35), (39),
% 159.62/28.23 | | | (50) are inconsistent by sub-proof #641.
% 159.62/28.23 | | |
% 159.62/28.23 | | End of split
% 159.62/28.23 | |
% 159.62/28.23 | End of split
% 159.62/28.23 |
% 159.62/28.23 End of proof
% 159.62/28.23
% 159.62/28.23 Sub-proof #641 shows that the following formulas are inconsistent:
% 159.62/28.23 ----------------------------------------------------------------
% 159.62/28.23 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.23 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.23 (2) all_58_1 = e0
% 159.62/28.23 (3) all_58_7 = e2
% 159.62/28.23 (4) all_58_13 = e1
% 159.62/28.23 (5) all_58_9 = e3
% 159.62/28.23 (6) ~ (e3 = e1)
% 159.62/28.23 (7) all_58_4 = e2
% 159.62/28.23 (8) ~ (e2 = e1)
% 159.62/28.23 (9) ~ (e1 = e0)
% 159.62/28.23 (10) all_58_3 = e3
% 159.62/28.23 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.62/28.23 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.62/28.23 (12) all_58_0 = e0
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | BETA: splitting (11) gives:
% 159.62/28.23 |
% 159.62/28.23 | Case 1:
% 159.62/28.23 | |
% 159.62/28.23 | | (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 159.62/28.23 | | e1)
% 159.62/28.23 | |
% 159.62/28.23 | | BETA: splitting (13) gives:
% 159.62/28.23 | |
% 159.62/28.23 | | Case 1:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (14) all_58_0 = e1 & op(e3, e3) = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | ALPHA: (14) implies:
% 159.62/28.23 | | | (15) all_58_0 = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | COMBINE_EQS: (12), (15) imply:
% 159.62/28.23 | | | (16) e1 = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | SIMP: (16) implies:
% 159.62/28.23 | | | (17) e1 = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | COMBINE_EQS: (4), (17) imply:
% 159.62/28.23 | | | (18) all_58_13 = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (18) are inconsistent by
% 159.62/28.23 | | | sub-proof #857.
% 159.62/28.23 | | |
% 159.62/28.23 | | Case 2:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (19) all_58_1 = e1 & op(e3, e2) = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (19) are inconsistent
% 159.62/28.23 | | | by sub-proof #643.
% 159.62/28.23 | | |
% 159.62/28.23 | | End of split
% 159.62/28.23 | |
% 159.62/28.23 | Case 2:
% 159.62/28.23 | |
% 159.62/28.23 | | (20) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 159.62/28.23 | | e1)
% 159.62/28.23 | |
% 159.62/28.23 | | REF_CLOSE: (5), (6), (7), (8), (20) are inconsistent by sub-proof #642.
% 159.62/28.23 | |
% 159.62/28.23 | End of split
% 159.62/28.23 |
% 159.62/28.23 End of proof
% 159.62/28.23
% 159.62/28.23 Sub-proof #642 shows that the following formulas are inconsistent:
% 159.62/28.23 ----------------------------------------------------------------
% 159.62/28.23 (1) all_58_9 = e3
% 159.62/28.23 (2) ~ (e3 = e1)
% 159.62/28.23 (3) all_58_4 = e2
% 159.62/28.23 (4) ~ (e2 = e1)
% 159.62/28.23 (5) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | BETA: splitting (5) gives:
% 159.62/28.23 |
% 159.62/28.23 | Case 1:
% 159.62/28.23 | |
% 159.62/28.23 | | (6) all_58_4 = e1 & op(e3, e1) = e1
% 159.62/28.23 | |
% 159.62/28.23 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #1476.
% 159.62/28.23 | |
% 159.62/28.23 | Case 2:
% 159.62/28.23 | |
% 159.62/28.23 | | (7) all_58_9 = e1 & op(e3, e0) = e1
% 159.62/28.23 | |
% 159.62/28.23 | | ALPHA: (7) implies:
% 159.62/28.23 | | (8) all_58_9 = e1
% 159.62/28.23 | |
% 159.62/28.23 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #1461.
% 159.62/28.23 | |
% 159.62/28.23 | End of split
% 159.62/28.23 |
% 159.62/28.23 End of proof
% 159.62/28.23
% 159.62/28.23 Sub-proof #643 shows that the following formulas are inconsistent:
% 159.62/28.23 ----------------------------------------------------------------
% 159.62/28.23 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.23 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.23 (2) all_58_1 = e0
% 159.62/28.23 (3) all_58_1 = e1 & op(e3, e2) = e1
% 159.62/28.23 (4) all_58_7 = e2
% 159.62/28.23 (5) all_58_13 = e1
% 159.62/28.23 (6) ~ (e3 = e1)
% 159.62/28.23 (7) ~ (e2 = e1)
% 159.62/28.23 (8) ~ (e1 = e0)
% 159.62/28.23 (9) all_58_3 = e3
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | ALPHA: (3) implies:
% 159.62/28.23 | (10) all_58_1 = e1
% 159.62/28.23 |
% 159.62/28.23 | COMBINE_EQS: (2), (10) imply:
% 159.62/28.23 | (11) e1 = e0
% 159.62/28.23 |
% 159.62/28.23 | SIMP: (11) implies:
% 159.62/28.23 | (12) e1 = e0
% 159.62/28.23 |
% 159.62/28.23 | COMBINE_EQS: (5), (12) imply:
% 159.62/28.23 | (13) all_58_13 = e0
% 159.62/28.23 |
% 159.62/28.23 | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (13) are inconsistent by
% 159.62/28.23 | sub-proof #857.
% 159.62/28.23 |
% 159.62/28.23 End of proof
% 159.62/28.23
% 159.62/28.23 Sub-proof #644 shows that the following formulas are inconsistent:
% 159.62/28.23 ----------------------------------------------------------------
% 159.62/28.23 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.62/28.23 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.62/28.23 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.23 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.23 (3) ~ (all_52_7 = e3)
% 159.62/28.23 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.62/28.23 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.23 (5) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.62/28.23 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.62/28.23 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.23 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.23 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.62/28.23 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.62/28.23 (8) op(e2, e3) = all_52_1
% 159.62/28.23 (9) ~ (all_52_13 = e3)
% 159.62/28.23 (10) ~ (e3 = e0)
% 159.62/28.23 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.23 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.23 (12) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.62/28.23 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.62/28.23 (13) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.23 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.23 e2)
% 159.62/28.23 (14) ~ (e2 = e0)
% 159.62/28.23 (15) op(e2, e0) = all_52_13
% 159.62/28.23 (16) op(e2, e3) = e2
% 159.62/28.23 (17) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.23 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.23 (18) ~ (e3 = e1)
% 159.62/28.23 (19) op(e1, e2) = all_52_6
% 159.62/28.23 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.23 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.23 (21) op(e0, e0) = e2
% 159.62/28.23 (22) all_58_4 = e2
% 159.62/28.23 (23) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.62/28.23 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.62/28.23 (24) op(e0, e2) = e0
% 159.62/28.23 (25) ~ (e2 = e1)
% 159.62/28.23 (26) ~ (e1 = e0)
% 159.62/28.23 (27) all_58_3 = e3
% 159.62/28.23 (28) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.62/28.23 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.62/28.23 e3)
% 159.62/28.23 (29) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.62/28.23 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.23 (30) op(e0, e2) = all_52_7
% 159.62/28.23 (31) all_58_4 = e3 & op(e3, e1) = e3
% 159.62/28.23 (32) ~ (all_52_6 = e3)
% 159.62/28.23 (33) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.23 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.23 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.23 (35) ~ (e3 = e2)
% 159.62/28.23 (36) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.23 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.23 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.23 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.23 (37) all_58_11 = e3
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | ALPHA: (31) implies:
% 159.62/28.23 | (38) all_58_4 = e3
% 159.62/28.23 |
% 159.62/28.23 | COMBINE_EQS: (22), (38) imply:
% 159.62/28.23 | (39) e3 = e2
% 159.62/28.23 |
% 159.62/28.23 | SIMP: (39) implies:
% 159.62/28.23 | (40) e3 = e2
% 159.62/28.23 |
% 159.62/28.23 | COMBINE_EQS: (37), (40) imply:
% 159.62/28.23 | (41) all_58_11 = e2
% 159.62/28.23 |
% 159.62/28.23 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.23 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 159.62/28.23 | (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 159.62/28.23 | (41) are inconsistent by sub-proof #696.
% 159.62/28.23 |
% 159.62/28.23 End of proof
% 159.62/28.23
% 159.62/28.23 Sub-proof #645 shows that the following formulas are inconsistent:
% 159.62/28.23 ----------------------------------------------------------------
% 159.62/28.23 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 159.62/28.23 (2) op(e3, e2) = all_52_4
% 159.62/28.23 (3) ~ (e3 = e0)
% 159.62/28.23 (4) ~ (all_52_4 = e3)
% 159.62/28.23 (5) all_58_0 = e0
% 159.62/28.23 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | BETA: splitting (1) gives:
% 159.62/28.23 |
% 159.62/28.23 | Case 1:
% 159.62/28.23 | |
% 159.62/28.23 | | (7) all_58_0 = e3 & op(e3, e3) = e3
% 159.62/28.23 | |
% 159.62/28.23 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #1496.
% 159.62/28.23 | |
% 159.62/28.23 | Case 2:
% 159.62/28.23 | |
% 159.62/28.23 | | (8) all_58_1 = e3 & op(e3, e2) = e3
% 159.62/28.23 | |
% 159.62/28.23 | | ALPHA: (8) implies:
% 159.62/28.23 | | (9) op(e3, e2) = e3
% 159.62/28.23 | |
% 159.62/28.23 | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #1540.
% 159.62/28.23 | |
% 159.62/28.23 | End of split
% 159.62/28.23 |
% 159.62/28.23 End of proof
% 159.62/28.23
% 159.62/28.23 Sub-proof #646 shows that the following formulas are inconsistent:
% 159.62/28.23 ----------------------------------------------------------------
% 159.62/28.23 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.23 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.23 (2) all_58_1 = e0
% 159.62/28.23 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.23 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.23 (4) all_58_14 = e3
% 159.62/28.23 (5) op(e1, e1) = all_6_2
% 159.62/28.23 (6) all_58_7 = e2
% 159.62/28.23 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.23 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.23 (8) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.23 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.23 (9) op(e2, e3) = all_52_1
% 159.62/28.23 (10) ~ (e3 = e0)
% 159.62/28.23 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.23 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.23 (12) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.23 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.23 e2)
% 159.62/28.23 (13) ~ (e2 = e0)
% 159.62/28.23 (14) op(e2, e3) = e2
% 159.62/28.23 (15) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.23 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.23 (16) ~ (e3 = e1)
% 159.62/28.23 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.23 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.23 (18) all_58_10 = e1
% 159.62/28.23 (19) all_58_5 = e0
% 159.62/28.23 (20) all_58_4 = e2
% 159.62/28.23 (21) ~ (e2 = e1)
% 159.62/28.23 (22) ~ (e1 = e0)
% 159.62/28.23 (23) all_58_3 = e3
% 159.62/28.23 (24) ~ (all_6_2 = e2)
% 159.62/28.23 (25) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.23 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.23 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.23 (27) ~ (e3 = e2)
% 159.62/28.23 (28) all_58_12 = e1
% 159.62/28.23 (29) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.23 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.23 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.23 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | BETA: splitting (1) gives:
% 159.62/28.23 |
% 159.62/28.23 | Case 1:
% 159.62/28.23 | |
% 159.62/28.23 | | (30) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 159.62/28.23 | | e1)
% 159.62/28.23 | |
% 159.62/28.23 | | BETA: splitting (30) gives:
% 159.62/28.23 | |
% 159.62/28.23 | | Case 1:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (31) all_58_1 = e1 & op(e3, e2) = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | ALPHA: (31) implies:
% 159.62/28.23 | | | (32) all_58_1 = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | COMBINE_EQS: (2), (32) imply:
% 159.62/28.23 | | | (33) e1 = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | SIMP: (33) implies:
% 159.62/28.23 | | | (34) e1 = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | COMBINE_EQS: (18), (34) imply:
% 159.62/28.23 | | | (35) all_58_10 = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (3), (14), (16), (19), (21), (22), (23), (26), (35) are
% 159.62/28.23 | | | inconsistent by sub-proof #839.
% 159.62/28.23 | | |
% 159.62/28.23 | | Case 2:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (36) all_58_3 = e1 & op(e2, e2) = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | ALPHA: (36) implies:
% 159.62/28.23 | | | (37) all_58_3 = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (16), (23), (37) are inconsistent by sub-proof #841.
% 159.62/28.23 | | |
% 159.62/28.23 | | End of split
% 159.62/28.23 | |
% 159.62/28.23 | Case 2:
% 159.62/28.23 | |
% 159.62/28.23 | | (38) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 159.62/28.23 | | e1)
% 159.62/28.23 | |
% 159.62/28.23 | | BETA: splitting (38) gives:
% 159.62/28.23 | |
% 159.62/28.23 | | Case 1:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (39) all_58_7 = e1 & op(e1, e2) = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (3), (4), (5), (6), (8), (10), (13), (14), (16), (17), (20),
% 159.62/28.23 | | | (21), (22), (23), (24), (26), (27), (39) are inconsistent by
% 159.62/28.23 | | | sub-proof #650.
% 159.62/28.23 | | |
% 159.62/28.23 | | Case 2:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (40) all_58_13 = e1 & op(e0, e2) = e1
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (1), (4), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 159.62/28.23 | | | (16), (21), (22), (23), (25), (26), (27), (28), (29), (40) are
% 159.62/28.23 | | | inconsistent by sub-proof #647.
% 159.62/28.23 | | |
% 159.62/28.23 | | End of split
% 159.62/28.23 | |
% 159.62/28.23 | End of split
% 159.62/28.23 |
% 159.62/28.23 End of proof
% 159.62/28.23
% 159.62/28.23 Sub-proof #647 shows that the following formulas are inconsistent:
% 159.62/28.23 ----------------------------------------------------------------
% 159.62/28.23 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.23 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.23 (2) all_58_14 = e3
% 159.62/28.23 (3) all_58_7 = e2
% 159.62/28.23 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.23 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.23 (5) op(e2, e3) = all_52_1
% 159.62/28.23 (6) ~ (e3 = e0)
% 159.62/28.23 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.23 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.23 (8) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 159.62/28.23 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.62/28.23 (9) ~ (e2 = e0)
% 159.62/28.23 (10) all_58_13 = e1 & op(e0, e2) = e1
% 159.62/28.23 (11) op(e2, e3) = e2
% 159.62/28.23 (12) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.23 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.23 (13) ~ (e3 = e1)
% 159.62/28.23 (14) ~ (e2 = e1)
% 159.62/28.23 (15) ~ (e1 = e0)
% 159.62/28.23 (16) all_58_3 = e3
% 159.62/28.23 (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.23 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.23 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.23 (19) ~ (e3 = e2)
% 159.62/28.23 (20) all_58_12 = e1
% 159.62/28.23 (21) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.23 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.23 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.23 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | ALPHA: (10) implies:
% 159.62/28.23 | (22) all_58_13 = e1
% 159.62/28.23 |
% 159.62/28.23 | BETA: splitting (12) gives:
% 159.62/28.23 |
% 159.62/28.23 | Case 1:
% 159.62/28.23 | |
% 159.62/28.23 | | (23) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 159.62/28.23 | | e0)
% 159.62/28.23 | |
% 159.62/28.23 | | BETA: splitting (23) gives:
% 159.62/28.23 | |
% 159.62/28.23 | | Case 1:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (24) all_58_1 = e0 & op(e3, e2) = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | ALPHA: (24) implies:
% 159.62/28.23 | | | (25) all_58_1 = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14),
% 159.62/28.23 | | | (15), (16), (17), (18), (19), (20), (21), (22), (25) are
% 159.62/28.23 | | | inconsistent by sub-proof #648.
% 159.62/28.23 | | |
% 159.62/28.23 | | Case 2:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (26) all_58_3 = e0 & op(e2, e2) = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (6), (16), (26) are inconsistent by sub-proof #756.
% 159.62/28.23 | | |
% 159.62/28.23 | | End of split
% 159.62/28.23 | |
% 159.62/28.23 | Case 2:
% 159.62/28.23 | |
% 159.62/28.23 | | (27) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.62/28.23 | | e0)
% 159.62/28.23 | |
% 159.62/28.23 | | BETA: splitting (27) gives:
% 159.62/28.23 | |
% 159.62/28.23 | | Case 1:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (28) all_58_7 = e0 & op(e1, e2) = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (3), (9), (28) are inconsistent by sub-proof #1468.
% 159.62/28.23 | | |
% 159.62/28.23 | | Case 2:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (29) all_58_13 = e0 & op(e0, e2) = e0
% 159.62/28.23 | | |
% 159.62/28.23 | | | REF_CLOSE: (15), (22), (29) are inconsistent by sub-proof #1409.
% 159.62/28.23 | | |
% 159.62/28.23 | | End of split
% 159.62/28.23 | |
% 159.62/28.23 | End of split
% 159.62/28.23 |
% 159.62/28.23 End of proof
% 159.62/28.23
% 159.62/28.23 Sub-proof #648 shows that the following formulas are inconsistent:
% 159.62/28.23 ----------------------------------------------------------------
% 159.62/28.23 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.23 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.23 (2) all_58_1 = e0
% 159.62/28.23 (3) all_58_14 = e3
% 159.62/28.23 (4) all_58_7 = e2
% 159.62/28.23 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.23 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.23 (6) op(e2, e3) = all_52_1
% 159.62/28.23 (7) all_58_13 = e1
% 159.62/28.23 (8) ~ (e3 = e0)
% 159.62/28.23 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.23 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.23 (10) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.23 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.23 e2)
% 159.62/28.23 (11) ~ (e2 = e0)
% 159.62/28.23 (12) op(e2, e3) = e2
% 159.62/28.23 (13) ~ (e3 = e1)
% 159.62/28.23 (14) ~ (e2 = e1)
% 159.62/28.23 (15) ~ (e1 = e0)
% 159.62/28.23 (16) all_58_3 = e3
% 159.62/28.23 (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.23 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.23 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.23 (19) ~ (e3 = e2)
% 159.62/28.23 (20) all_58_12 = e1
% 159.62/28.23 (21) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.23 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.23 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.23 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.23
% 159.62/28.23 Begin of proof
% 159.62/28.23 |
% 159.62/28.23 | BETA: splitting (10) gives:
% 159.62/28.23 |
% 159.62/28.23 | Case 1:
% 159.62/28.23 | |
% 159.62/28.23 | | (22) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 159.62/28.23 | | e2)
% 159.62/28.23 | |
% 159.62/28.23 | | REF_CLOSE: (5), (6), (7), (8), (9), (11), (12), (13), (14), (15), (17),
% 159.62/28.23 | | (18), (19), (22) are inconsistent by sub-proof #806.
% 159.62/28.23 | |
% 159.62/28.23 | Case 2:
% 159.62/28.23 | |
% 159.62/28.23 | | (23) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.23 | | e2)
% 159.62/28.23 | |
% 159.62/28.23 | | BETA: splitting (23) gives:
% 159.62/28.23 | |
% 159.62/28.23 | | Case 1:
% 159.62/28.23 | | |
% 159.62/28.23 | | | (24) all_58_14 = e2 & op(e0, e1) = e2
% 159.62/28.24 | | |
% 159.62/28.24 | | | ALPHA: (24) implies:
% 159.62/28.24 | | | (25) all_58_14 = e2
% 159.62/28.24 | | |
% 159.62/28.24 | | | REF_CLOSE: (3), (19), (25) are inconsistent by sub-proof #1405.
% 159.62/28.24 | | |
% 159.62/28.24 | | Case 2:
% 159.62/28.24 | | |
% 159.62/28.24 | | | (26) all_58_15 = e2 & op(e0, e0) = e2
% 159.62/28.24 | | |
% 159.62/28.24 | | | ALPHA: (26) implies:
% 159.62/28.24 | | | (27) all_58_15 = e2
% 159.62/28.24 | | |
% 159.62/28.24 | | | BETA: splitting (21) gives:
% 159.62/28.24 | | |
% 159.62/28.24 | | | Case 1:
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | (28) all_58_15 = e0 & op(e0, e0) = e0
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | ALPHA: (28) implies:
% 159.62/28.24 | | | | (29) all_58_15 = e0
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | REF_CLOSE: (11), (27), (29) are inconsistent by sub-proof #1462.
% 159.62/28.24 | | | |
% 159.62/28.24 | | | Case 2:
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | (30) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 159.62/28.24 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 159.62/28.24 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 159.62/28.24 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | ALPHA: (30) implies:
% 159.62/28.24 | | | | (31) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 159.62/28.24 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | BETA: splitting (31) gives:
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | Case 1:
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | (32) all_58_12 = e0 & op(e0, e3) = e0
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | ALPHA: (32) implies:
% 159.62/28.24 | | | | | (33) all_58_12 = e0
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | COMBINE_EQS: (20), (33) imply:
% 159.62/28.24 | | | | | (34) e1 = e0
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | COMBINE_EQS: (7), (34) imply:
% 159.62/28.24 | | | | | (35) all_58_13 = e0
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | REF_CLOSE: (1), (2), (4), (13), (14), (15), (16), (35) are
% 159.62/28.24 | | | | | inconsistent by sub-proof #857.
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | Case 2:
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | (36) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 159.62/28.24 | | | | | e1) = e0)
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | REF_CLOSE: (1), (2), (3), (4), (8), (13), (14), (15), (16), (36) are
% 159.62/28.24 | | | | | inconsistent by sub-proof #649.
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | End of split
% 159.62/28.24 | | | |
% 159.62/28.24 | | | End of split
% 159.62/28.24 | | |
% 159.62/28.24 | | End of split
% 159.62/28.24 | |
% 159.62/28.24 | End of split
% 159.62/28.24 |
% 159.62/28.24 End of proof
% 159.62/28.24
% 159.62/28.24 Sub-proof #649 shows that the following formulas are inconsistent:
% 159.62/28.24 ----------------------------------------------------------------
% 159.62/28.24 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.24 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.24 (2) all_58_1 = e0
% 159.62/28.24 (3) all_58_14 = e3
% 159.62/28.24 (4) all_58_7 = e2
% 159.62/28.24 (5) ~ (e3 = e0)
% 159.62/28.24 (6) ~ (e3 = e1)
% 159.62/28.24 (7) ~ (e2 = e1)
% 159.62/28.24 (8) ~ (e1 = e0)
% 159.62/28.24 (9) all_58_3 = e3
% 159.62/28.24 (10) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.62/28.24
% 159.62/28.24 Begin of proof
% 159.62/28.24 |
% 159.62/28.24 | BETA: splitting (10) gives:
% 159.62/28.24 |
% 159.62/28.24 | Case 1:
% 159.62/28.24 | |
% 159.62/28.24 | | (11) all_58_13 = e0 & op(e0, e2) = e0
% 159.62/28.24 | |
% 159.62/28.24 | | ALPHA: (11) implies:
% 159.62/28.24 | | (12) all_58_13 = e0
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (12) are inconsistent by
% 159.62/28.24 | | sub-proof #857.
% 159.62/28.24 | |
% 159.62/28.24 | Case 2:
% 159.62/28.24 | |
% 159.62/28.24 | | (13) all_58_14 = e0 & op(e0, e1) = e0
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #882.
% 159.62/28.24 | |
% 159.62/28.24 | End of split
% 159.62/28.24 |
% 159.62/28.24 End of proof
% 159.62/28.24
% 159.62/28.24 Sub-proof #650 shows that the following formulas are inconsistent:
% 159.62/28.24 ----------------------------------------------------------------
% 159.62/28.24 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.24 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.24 (2) all_58_14 = e3
% 159.62/28.24 (3) op(e1, e1) = all_6_2
% 159.62/28.24 (4) all_58_7 = e2
% 159.62/28.24 (5) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.24 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.24 (6) ~ (e3 = e0)
% 159.62/28.24 (7) ~ (e2 = e0)
% 159.62/28.24 (8) all_58_7 = e1 & op(e1, e2) = e1
% 159.62/28.24 (9) op(e2, e3) = e2
% 159.62/28.24 (10) ~ (e3 = e1)
% 159.62/28.24 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.24 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.24 (12) all_58_4 = e2
% 159.62/28.24 (13) ~ (e2 = e1)
% 159.62/28.24 (14) ~ (e1 = e0)
% 159.62/28.24 (15) all_58_3 = e3
% 159.62/28.24 (16) ~ (all_6_2 = e2)
% 159.62/28.24 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.24 (18) ~ (e3 = e2)
% 159.62/28.24
% 159.62/28.24 Begin of proof
% 159.62/28.24 |
% 159.62/28.24 | ALPHA: (8) implies:
% 159.62/28.24 | (19) all_58_7 = e1
% 159.62/28.24 |
% 159.62/28.24 | COMBINE_EQS: (4), (19) imply:
% 159.62/28.24 | (20) e2 = e1
% 159.62/28.24 |
% 159.62/28.24 | SIMP: (20) implies:
% 159.62/28.24 | (21) e2 = e1
% 159.62/28.24 |
% 159.62/28.24 | COMBINE_EQS: (12), (21) imply:
% 159.62/28.24 | (22) all_58_4 = e1
% 159.62/28.24 |
% 159.62/28.24 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (13), (14), (15),
% 159.62/28.24 | (16), (17), (18), (22) are inconsistent by sub-proof #850.
% 159.62/28.24 |
% 159.62/28.24 End of proof
% 159.62/28.24
% 159.62/28.24 Sub-proof #651 shows that the following formulas are inconsistent:
% 159.62/28.24 ----------------------------------------------------------------
% 159.62/28.24 (1) op(e1, e1) = e3
% 159.62/28.24 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.24 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.24 (3) all_58_14 = e3
% 159.62/28.24 (4) op(e1, e1) = all_6_2
% 159.62/28.24 (5) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.24 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.24 (6) ~ (e3 = e0)
% 159.62/28.24 (7) ~ (e2 = e0)
% 159.62/28.24 (8) op(e2, e3) = e2
% 159.62/28.24 (9) ~ (e3 = e1)
% 159.62/28.24 (10) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.62/28.24 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.62/28.24 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.24 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.24 (12) ~ (e2 = e1)
% 159.62/28.24 (13) ~ (e1 = e0)
% 159.62/28.24 (14) all_58_3 = e3
% 159.62/28.24 (15) ~ (all_6_2 = e2)
% 159.62/28.24 (16) all_58_5 = e1 & op(e2, e1) = e1
% 159.62/28.24 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.24 (18) ~ (e3 = e2)
% 159.62/28.24
% 159.62/28.24 Begin of proof
% 159.62/28.24 |
% 159.62/28.24 | ALPHA: (16) implies:
% 159.62/28.24 | (19) all_58_5 = e1
% 159.62/28.24 |
% 159.62/28.24 | BETA: splitting (10) gives:
% 159.62/28.24 |
% 159.62/28.24 | Case 1:
% 159.62/28.24 | |
% 159.62/28.24 | | (20) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 159.62/28.24 | | e0)
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 159.62/28.24 | | (15), (17), (18), (19), (20) are inconsistent by sub-proof #652.
% 159.62/28.24 | |
% 159.62/28.24 | Case 2:
% 159.62/28.24 | |
% 159.62/28.24 | | (21) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 159.62/28.24 | | e0)
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (1), (3), (6), (17), (21) are inconsistent by sub-proof #926.
% 159.62/28.24 | |
% 159.62/28.24 | End of split
% 159.62/28.24 |
% 159.62/28.24 End of proof
% 159.62/28.24
% 159.62/28.24 Sub-proof #652 shows that the following formulas are inconsistent:
% 159.62/28.24 ----------------------------------------------------------------
% 159.62/28.24 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.24 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.24 (2) all_58_14 = e3
% 159.62/28.24 (3) op(e1, e1) = all_6_2
% 159.62/28.24 (4) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.24 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.24 (5) ~ (e3 = e0)
% 159.62/28.24 (6) ~ (e2 = e0)
% 159.62/28.24 (7) op(e2, e3) = e2
% 159.62/28.24 (8) ~ (e3 = e1)
% 159.62/28.24 (9) all_58_5 = e1
% 159.62/28.24 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.24 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.24 (11) ~ (e2 = e1)
% 159.62/28.24 (12) ~ (e1 = e0)
% 159.62/28.24 (13) all_58_3 = e3
% 159.62/28.24 (14) ~ (all_6_2 = e2)
% 159.62/28.24 (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 159.62/28.24 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.24 (17) ~ (e3 = e2)
% 159.62/28.24
% 159.62/28.24 Begin of proof
% 159.62/28.24 |
% 159.62/28.24 | BETA: splitting (15) gives:
% 159.62/28.24 |
% 159.62/28.24 | Case 1:
% 159.62/28.24 | |
% 159.62/28.24 | | (18) all_58_4 = e0 & op(e3, e1) = e0
% 159.62/28.24 | |
% 159.62/28.24 | | ALPHA: (18) implies:
% 159.62/28.24 | | (19) all_58_4 = e0
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 159.62/28.24 | | (14), (16), (17), (19) are inconsistent by sub-proof #854.
% 159.62/28.24 | |
% 159.62/28.24 | Case 2:
% 159.62/28.24 | |
% 159.62/28.24 | | (20) all_58_5 = e0 & op(e2, e1) = e0
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (9), (12), (20) are inconsistent by sub-proof #1343.
% 159.62/28.24 | |
% 159.62/28.24 | End of split
% 159.62/28.24 |
% 159.62/28.24 End of proof
% 159.62/28.24
% 159.62/28.24 Sub-proof #653 shows that the following formulas are inconsistent:
% 159.62/28.24 ----------------------------------------------------------------
% 159.62/28.24 (1) op(e3, e3) = all_10_2
% 159.62/28.24 (2) ~ (all_10_2 = e1)
% 159.62/28.24 (3) op(e3, e3) = all_28_1
% 159.62/28.24 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.24 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.24 (5) all_54_0 = all_10_2
% 159.62/28.24 (6) op(e2, e3) = all_52_1
% 159.62/28.24 (7) ~ (all_10_2 = e0)
% 159.62/28.24 (8) ~ (e3 = e0)
% 159.62/28.24 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.24 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.24 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 159.62/28.24 (11) ~ (e2 = e0)
% 159.62/28.24 (12) all_58_6 = e0
% 159.62/28.24 (13) op(e1, e3) = all_52_2
% 159.62/28.24 (14) op(e2, e3) = e2
% 159.62/28.24 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.24 (16) ~ (e3 = e1)
% 159.62/28.24 (17) ~ (all_10_2 = e2)
% 159.62/28.24 (18) ~ (e2 = e1)
% 159.62/28.24 (19) ~ (e1 = e0)
% 159.62/28.24 (20) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.62/28.24 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.62/28.24 e3) = all_22_1 & $i(all_22_1))
% 159.62/28.24 (21) op(e1, e3) = e1
% 159.62/28.24 (22) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.24 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.24 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.24 (24) ~ (e3 = e2)
% 159.62/28.24
% 159.62/28.24 Begin of proof
% 159.62/28.24 |
% 159.62/28.24 | BETA: splitting (10) gives:
% 159.62/28.24 |
% 159.62/28.24 | Case 1:
% 159.62/28.24 | |
% 159.62/28.24 | | (25) all_58_0 = e1 & op(e3, e3) = e1
% 159.62/28.24 | |
% 159.62/28.24 | | ALPHA: (25) implies:
% 159.62/28.24 | | (26) all_58_0 = e1
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 159.62/28.24 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 159.62/28.24 | | (26) are inconsistent by sub-proof #660.
% 159.62/28.24 | |
% 159.62/28.24 | Case 2:
% 159.62/28.24 | |
% 159.62/28.24 | | (27) all_58_2 = e1 & op(e2, e3) = e1
% 159.62/28.24 | |
% 159.62/28.24 | | ALPHA: (27) implies:
% 159.62/28.24 | | (28) op(e2, e3) = e1
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (14), (18), (23), (28) are inconsistent by sub-proof #1430.
% 159.62/28.24 | |
% 159.62/28.24 | End of split
% 159.62/28.24 |
% 159.62/28.24 End of proof
% 159.62/28.24
% 159.62/28.24 Sub-proof #654 shows that the following formulas are inconsistent:
% 159.62/28.24 ----------------------------------------------------------------
% 159.62/28.24 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.24 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.24 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.24 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.24 (3) op(e3, e3) = all_10_2
% 159.62/28.24 (4) ~ (all_10_2 = e1)
% 159.62/28.24 (5) all_58_14 = e3
% 159.62/28.24 (6) op(e1, e1) = all_6_2
% 159.62/28.24 (7) op(e3, e3) = all_28_1
% 159.62/28.24 (8) all_58_0 = e1
% 159.62/28.24 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.24 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.24 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.24 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.24 (11) all_58_6 = e3
% 159.62/28.24 (12) op(e3, e2) = all_52_4
% 159.62/28.24 (13) all_54_0 = all_10_2
% 159.62/28.24 (14) op(e2, e3) = all_52_1
% 159.62/28.24 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.62/28.24 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.62/28.24 (16) ~ (all_10_2 = e0)
% 159.62/28.24 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.24 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.24 (18) ~ (e2 = e0)
% 159.62/28.24 (19) all_58_9 = e3
% 159.62/28.24 (20) op(e1, e3) = all_52_2
% 159.62/28.24 (21) all_58_0 = e1 & op(e3, e3) = e1
% 159.62/28.24 (22) op(e2, e3) = e2
% 159.62/28.24 (23) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.24 (24) ~ (all_52_4 = all_10_2)
% 159.62/28.24 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.24 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.24 (26) all_58_5 = e0
% 159.62/28.24 (27) ~ (all_10_2 = e2)
% 159.62/28.24 (28) all_58_15 = e2
% 159.62/28.24 (29) ~ (e2 = e1)
% 159.62/28.24 (30) ~ (e1 = e0)
% 159.62/28.24 (31) all_58_3 = e3
% 159.62/28.24 (32) ~ (all_6_2 = e2)
% 159.62/28.24 (33) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.62/28.24 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.62/28.24 e3) = all_22_1 & $i(all_22_1))
% 159.62/28.24 (34) op(e1, e3) = e1
% 159.62/28.24 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.62/28.24 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.62/28.24 (36) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.24 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.24 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.24 (38) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.24 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.24 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.24 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.24
% 159.62/28.24 Begin of proof
% 159.62/28.24 |
% 159.62/28.24 | BETA: splitting (23) gives:
% 159.62/28.24 |
% 159.62/28.24 | Case 1:
% 159.62/28.24 | |
% 159.62/28.24 | | (39) all_54_0 = e3
% 159.62/28.24 | |
% 159.62/28.24 | | COMBINE_EQS: (13), (39) imply:
% 159.62/28.24 | | (40) all_10_2 = e3
% 159.62/28.24 | |
% 159.62/28.24 | | REDUCE: (24), (40) imply:
% 159.62/28.24 | | (41) ~ (all_52_4 = e3)
% 159.62/28.24 | |
% 159.62/28.24 | | REDUCE: (27), (40) imply:
% 159.62/28.24 | | (42) ~ (e3 = e2)
% 159.62/28.24 | |
% 159.62/28.24 | | REDUCE: (4), (40) imply:
% 159.62/28.24 | | (43) ~ (e3 = e1)
% 159.62/28.24 | |
% 159.62/28.24 | | REDUCE: (16), (40) imply:
% 159.62/28.24 | | (44) ~ (e3 = e0)
% 159.62/28.24 | |
% 159.62/28.24 | | REDUCE: (3), (40) imply:
% 159.62/28.24 | | (45) op(e3, e3) = e3
% 159.62/28.24 | |
% 159.62/28.24 | | BETA: splitting (33) gives:
% 159.62/28.24 | |
% 159.62/28.24 | | Case 1:
% 159.62/28.24 | | |
% 159.62/28.24 | | | (46) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.62/28.24 | | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 159.62/28.24 | | |
% 159.62/28.24 | | | ALPHA: (46) implies:
% 159.62/28.24 | | | (47) op(e3, e3) = all_22_1
% 159.62/28.24 | | |
% 159.62/28.24 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.24 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 159.62/28.24 | | | (23), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 159.62/28.24 | | | (34), (35), (36), (37), (38), (41), (42), (43), (44), (45),
% 159.62/28.24 | | | (47) are inconsistent by sub-proof #655.
% 159.62/28.24 | | |
% 159.62/28.24 | | Case 2:
% 159.62/28.24 | | |
% 159.62/28.24 | | | (48) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 159.62/28.24 | | |
% 159.62/28.24 | | | ALPHA: (48) implies:
% 159.62/28.24 | | | (49) op(e3, e3) = all_22_1
% 159.62/28.24 | | |
% 159.62/28.24 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.24 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 159.62/28.24 | | | (23), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 159.62/28.24 | | | (34), (35), (36), (37), (38), (41), (42), (43), (44), (45),
% 159.62/28.24 | | | (49) are inconsistent by sub-proof #655.
% 159.62/28.24 | | |
% 159.62/28.24 | | End of split
% 159.62/28.24 | |
% 159.62/28.24 | Case 2:
% 159.62/28.24 | |
% 159.62/28.24 | | (50) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (4), (13), (16), (27), (50) are inconsistent by sub-proof #1307.
% 159.62/28.24 | |
% 159.62/28.24 | End of split
% 159.62/28.24 |
% 159.62/28.24 End of proof
% 159.62/28.24
% 159.62/28.24 Sub-proof #655 shows that the following formulas are inconsistent:
% 159.62/28.24 ----------------------------------------------------------------
% 159.62/28.24 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.24 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.24 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.24 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.24 (3) op(e3, e3) = all_10_2
% 159.62/28.24 (4) ~ (all_10_2 = e1)
% 159.62/28.24 (5) all_58_14 = e3
% 159.62/28.24 (6) op(e1, e1) = all_6_2
% 159.62/28.24 (7) op(e3, e3) = all_28_1
% 159.62/28.24 (8) all_58_0 = e1
% 159.62/28.24 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.24 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.24 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.24 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.24 (11) all_58_6 = e3
% 159.62/28.24 (12) op(e3, e2) = all_52_4
% 159.62/28.24 (13) all_54_0 = all_10_2
% 159.62/28.24 (14) op(e2, e3) = all_52_1
% 159.62/28.24 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.62/28.24 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.62/28.24 (16) ~ (all_10_2 = e0)
% 159.62/28.24 (17) ~ (e3 = e0)
% 159.62/28.24 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.24 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.24 (19) ~ (e2 = e0)
% 159.62/28.24 (20) all_58_9 = e3
% 159.62/28.24 (21) op(e1, e3) = all_52_2
% 159.62/28.24 (22) all_58_0 = e1 & op(e3, e3) = e1
% 159.62/28.24 (23) op(e2, e3) = e2
% 159.62/28.24 (24) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.24 (25) ~ (e3 = e1)
% 159.62/28.24 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.24 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.24 (27) all_58_5 = e0
% 159.62/28.24 (28) ~ (all_52_4 = e3)
% 159.62/28.24 (29) ~ (all_10_2 = e2)
% 159.62/28.24 (30) all_58_15 = e2
% 159.62/28.24 (31) ~ (e2 = e1)
% 159.62/28.24 (32) op(e3, e3) = e3
% 159.62/28.24 (33) ~ (e1 = e0)
% 159.62/28.24 (34) all_58_3 = e3
% 159.62/28.24 (35) ~ (all_6_2 = e2)
% 159.62/28.24 (36) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.62/28.24 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.62/28.24 e3) = all_22_1 & $i(all_22_1))
% 159.62/28.24 (37) op(e1, e3) = e1
% 159.62/28.24 (38) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.62/28.24 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.62/28.24 (39) op(e3, e3) = all_22_1
% 159.62/28.24 (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.24 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.24 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.24 (42) ~ (e3 = e2)
% 159.62/28.24 (43) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.24 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.24 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.24 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.24
% 159.62/28.24 Begin of proof
% 159.62/28.24 |
% 159.62/28.24 | BETA: splitting (40) gives:
% 159.62/28.24 |
% 159.62/28.24 | Case 1:
% 159.62/28.24 | |
% 159.62/28.24 | | (44) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.62/28.24 | | e0)
% 159.62/28.24 | |
% 159.62/28.24 | | REF_CLOSE: (7), (17), (19), (23), (32), (39), (41), (44) are inconsistent by
% 159.62/28.24 | | sub-proof #665.
% 159.62/28.24 | |
% 159.62/28.24 | Case 2:
% 159.62/28.24 | |
% 159.62/28.24 | | (45) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.62/28.24 | | e0)
% 159.62/28.24 | |
% 159.62/28.24 | | BETA: splitting (45) gives:
% 159.62/28.24 | |
% 159.62/28.24 | | Case 1:
% 159.62/28.24 | | |
% 159.62/28.24 | | | (46) all_58_6 = e0 & op(e1, e3) = e0
% 159.62/28.24 | | |
% 159.62/28.24 | | | ALPHA: (46) implies:
% 159.62/28.24 | | | (47) all_58_6 = e0
% 159.62/28.24 | | |
% 159.62/28.24 | | | REF_CLOSE: (3), (4), (7), (8), (9), (13), (14), (16), (17), (18), (19),
% 159.62/28.24 | | | (21), (23), (24), (25), (29), (31), (33), (36), (37), (40),
% 159.62/28.24 | | | (41), (42), (47) are inconsistent by sub-proof #660.
% 159.62/28.24 | | |
% 159.62/28.24 | | Case 2:
% 159.62/28.24 | | |
% 159.62/28.24 | | | (48) all_58_12 = e0 & op(e0, e3) = e0
% 159.62/28.24 | | |
% 159.62/28.24 | | | ALPHA: (48) implies:
% 159.62/28.24 | | | (49) all_58_12 = e0
% 159.62/28.24 | | |
% 159.62/28.24 | | | BETA: splitting (15) gives:
% 159.62/28.24 | | |
% 159.62/28.24 | | | Case 1:
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | (50) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 159.62/28.24 | | | | = e2)
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | BETA: splitting (50) gives:
% 159.62/28.24 | | | |
% 159.62/28.24 | | | | Case 1:
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | (51) all_58_6 = e2 & op(e1, e3) = e2
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | ALPHA: (51) implies:
% 159.62/28.24 | | | | | (52) all_58_6 = e2
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | REF_CLOSE: (9), (14), (17), (18), (23), (25), (31), (33), (41), (42),
% 159.62/28.24 | | | | | (49), (52) are inconsistent by sub-proof #1153.
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | Case 2:
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | ALPHA: (22) implies:
% 159.62/28.24 | | | | | (53) op(e3, e3) = e1
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | GROUND_INST: instantiating (41) with e3, all_22_1, e3, e3, simplifying
% 159.62/28.24 | | | | | with (32), (39) gives:
% 159.62/28.24 | | | | | (54) all_22_1 = e3
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | GROUND_INST: instantiating (41) with all_22_1, all_28_1, e3, e3,
% 159.62/28.24 | | | | | simplifying with (7), (39) gives:
% 159.62/28.24 | | | | | (55) all_28_1 = all_22_1
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | GROUND_INST: instantiating (41) with e1, all_28_1, e3, e3, simplifying
% 159.62/28.24 | | | | | with (7), (53) gives:
% 159.62/28.24 | | | | | (56) all_28_1 = e1
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | COMBINE_EQS: (55), (56) imply:
% 159.62/28.24 | | | | | (57) all_22_1 = e1
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | SIMP: (57) implies:
% 159.62/28.24 | | | | | (58) all_22_1 = e1
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | COMBINE_EQS: (54), (58) imply:
% 159.62/28.24 | | | | | (59) e3 = e1
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (10), (11), (12), (14), (17),
% 159.62/28.24 | | | | | (18), (19), (20), (23), (25), (26), (27), (28), (31), (33),
% 159.62/28.24 | | | | | (34), (35), (38), (41), (42), (49), (59) are inconsistent
% 159.62/28.24 | | | | | by sub-proof #825.
% 159.62/28.24 | | | | |
% 159.62/28.24 | | | | End of split
% 159.62/28.25 | | | |
% 159.62/28.25 | | | Case 2:
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | (60) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 159.62/28.25 | | | | = e2)
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | REF_CLOSE: (1), (6), (17), (19), (20), (25), (30), (31), (33), (35),
% 159.62/28.25 | | | | (41), (43), (60) are inconsistent by sub-proof #656.
% 159.62/28.25 | | | |
% 159.62/28.25 | | | End of split
% 159.62/28.25 | | |
% 159.62/28.25 | | End of split
% 159.62/28.25 | |
% 159.62/28.25 | End of split
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #656 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.25 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.25 (2) op(e1, e1) = all_6_2
% 159.62/28.25 (3) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.62/28.25 (4) ~ (e3 = e0)
% 159.62/28.25 (5) ~ (e2 = e0)
% 159.62/28.25 (6) all_58_9 = e3
% 159.62/28.25 (7) ~ (e3 = e1)
% 159.62/28.25 (8) all_58_15 = e2
% 159.62/28.25 (9) ~ (e2 = e1)
% 159.62/28.25 (10) ~ (e1 = e0)
% 159.62/28.25 (11) ~ (all_6_2 = e2)
% 159.62/28.25 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25 (13) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.25 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.25 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.25 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | BETA: splitting (3) gives:
% 159.62/28.25 |
% 159.62/28.25 | Case 1:
% 159.62/28.25 | |
% 159.62/28.25 | | (14) all_58_8 = e2 & op(e1, e1) = e2
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (2), (11), (12), (14) are inconsistent by sub-proof #1440.
% 159.62/28.25 | |
% 159.62/28.25 | Case 2:
% 159.62/28.25 | |
% 159.62/28.25 | | (15) all_58_11 = e2 & op(e1, e0) = e2
% 159.62/28.25 | |
% 159.62/28.25 | | ALPHA: (15) implies:
% 159.62/28.25 | | (16) all_58_11 = e2
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (13), (16) are
% 159.62/28.25 | | inconsistent by sub-proof #1453.
% 159.62/28.25 | |
% 159.62/28.25 | End of split
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #657 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) op(e1, e1) = e3
% 159.62/28.25 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.25 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.25 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.25 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.25 (4) op(e3, e3) = all_10_2
% 159.62/28.25 (5) ~ (all_10_2 = e1)
% 159.62/28.25 (6) all_58_14 = e3
% 159.62/28.25 (7) op(e1, e1) = all_6_2
% 159.62/28.25 (8) op(e3, e3) = all_28_1
% 159.62/28.25 (9) all_58_0 = e1
% 159.62/28.25 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.25 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.25 (11) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.25 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.25 (12) all_54_0 = all_10_2
% 159.62/28.25 (13) op(e2, e3) = all_52_1
% 159.62/28.25 (14) ~ (all_10_2 = e0)
% 159.62/28.25 (15) ~ (e3 = e0)
% 159.62/28.25 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.25 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.25 (17) ~ (e2 = e0)
% 159.62/28.25 (18) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.62/28.25 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.62/28.25 (19) op(e1, e3) = all_52_2
% 159.62/28.25 (20) op(e2, e3) = e2
% 159.62/28.25 (21) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.25 (22) ~ (e3 = e1)
% 159.62/28.25 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.25 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.25 (24) op(e3, e3) = e1
% 159.62/28.25 (25) all_58_11 = e2
% 159.62/28.25 (26) all_58_4 = e2
% 159.62/28.25 (27) ~ (all_10_2 = e2)
% 159.62/28.25 (28) ~ (e2 = e1)
% 159.62/28.25 (29) op(e3, e3) = e3
% 159.62/28.25 (30) ~ (e1 = e0)
% 159.62/28.25 (31) all_58_3 = e3
% 159.62/28.25 (32) ~ (all_6_2 = e2)
% 159.62/28.25 (33) all_58_13 = e2
% 159.62/28.25 (34) op(e3, e0) = e3
% 159.62/28.25 (35) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.62/28.25 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.62/28.25 e3) = all_22_1 & $i(all_22_1))
% 159.62/28.25 (36) op(e1, e3) = e1
% 159.62/28.25 (37) op(e3, e3) = all_22_1
% 159.62/28.25 (38) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.25 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.25 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25 (40) ~ (e3 = e2)
% 159.62/28.25 (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.62/28.25 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | BETA: splitting (18) gives:
% 159.62/28.25 |
% 159.62/28.25 | Case 1:
% 159.62/28.25 | |
% 159.62/28.25 | | (42) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 159.62/28.25 | | e0)
% 159.62/28.25 | |
% 159.62/28.25 | | BETA: splitting (42) gives:
% 159.62/28.25 | |
% 159.62/28.25 | | Case 1:
% 159.62/28.25 | | |
% 159.62/28.25 | | | (43) all_58_6 = e0 & op(e1, e3) = e0
% 159.62/28.25 | | |
% 159.62/28.25 | | | ALPHA: (43) implies:
% 159.62/28.25 | | | (44) all_58_6 = e0
% 159.62/28.25 | | |
% 159.62/28.25 | | | REF_CLOSE: (4), (5), (8), (9), (10), (12), (13), (14), (15), (16), (17),
% 159.62/28.25 | | | (19), (20), (21), (22), (27), (28), (30), (35), (36), (38),
% 159.62/28.25 | | | (39), (40), (44) are inconsistent by sub-proof #660.
% 159.62/28.25 | | |
% 159.62/28.25 | | Case 2:
% 159.62/28.25 | | |
% 159.62/28.25 | | | (45) all_58_7 = e0 & op(e1, e2) = e0
% 159.62/28.25 | | |
% 159.62/28.25 | | | ALPHA: (45) implies:
% 159.62/28.25 | | | (46) all_58_7 = e0
% 159.62/28.25 | | |
% 159.62/28.25 | | | BETA: splitting (41) gives:
% 159.62/28.25 | | |
% 159.62/28.25 | | | Case 1:
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | (47) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 159.62/28.25 | | | | = e0)
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | BETA: splitting (47) gives:
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | Case 1:
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | (48) all_58_0 = e0 & op(e3, e3) = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | REF_CLOSE: (8), (15), (29), (37), (39), (48) are inconsistent by
% 159.62/28.25 | | | | | sub-proof #666.
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | Case 2:
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | (49) all_58_1 = e0 & op(e3, e2) = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | ALPHA: (49) implies:
% 159.62/28.25 | | | | | (50) all_58_1 = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | REF_CLOSE: (2), (22), (28), (30), (31), (33), (46), (50) are
% 159.62/28.25 | | | | | inconsistent by sub-proof #752.
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | End of split
% 159.62/28.25 | | | |
% 159.62/28.25 | | | Case 2:
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | (51) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 159.62/28.25 | | | | = e0)
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | BETA: splitting (51) gives:
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | Case 1:
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | (52) all_58_4 = e0 & op(e3, e1) = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | ALPHA: (52) implies:
% 159.62/28.25 | | | | | (53) all_58_4 = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | REF_CLOSE: (3), (6), (7), (11), (15), (17), (20), (22), (23), (28),
% 159.62/28.25 | | | | | (30), (31), (32), (39), (40), (53) are inconsistent by
% 159.62/28.25 | | | | | sub-proof #854.
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | Case 2:
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | (54) all_58_9 = e0 & op(e3, e0) = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | ALPHA: (54) implies:
% 159.62/28.25 | | | | | (55) op(e3, e0) = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | GROUND_INST: instantiating (39) with e0, e3, e0, e3, simplifying with
% 159.62/28.25 | | | | | (34), (55) gives:
% 159.62/28.25 | | | | | (56) e3 = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | REF_CLOSE: (8), (24), (29), (30), (37), (39), (56) are inconsistent by
% 159.62/28.25 | | | | | sub-proof #659.
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | End of split
% 159.62/28.25 | | | |
% 159.62/28.25 | | | End of split
% 159.62/28.25 | | |
% 159.62/28.25 | | End of split
% 159.62/28.25 | |
% 159.62/28.25 | Case 2:
% 159.62/28.25 | |
% 159.62/28.25 | | (57) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.62/28.25 | | e0)
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (1), (3), (6), (7), (11), (15), (17), (20), (22), (23), (25),
% 159.62/28.25 | | (26), (28), (30), (31), (32), (39), (40), (57) are inconsistent
% 159.62/28.25 | | by sub-proof #658.
% 159.62/28.25 | |
% 159.62/28.25 | End of split
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #658 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) op(e1, e1) = e3
% 159.62/28.25 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.25 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.25 (3) all_58_14 = e3
% 159.62/28.25 (4) op(e1, e1) = all_6_2
% 159.62/28.25 (5) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.25 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.25 (6) ~ (e3 = e0)
% 159.62/28.25 (7) ~ (e2 = e0)
% 159.62/28.25 (8) op(e2, e3) = e2
% 159.62/28.25 (9) ~ (e3 = e1)
% 159.62/28.25 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.25 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.25 (11) all_58_11 = e2
% 159.62/28.25 (12) all_58_4 = e2
% 159.62/28.25 (13) ~ (e2 = e1)
% 159.62/28.25 (14) ~ (e1 = e0)
% 159.62/28.25 (15) all_58_3 = e3
% 159.62/28.25 (16) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.62/28.25 (17) ~ (all_6_2 = e2)
% 159.62/28.25 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25 (19) ~ (e3 = e2)
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | BETA: splitting (16) gives:
% 159.62/28.25 |
% 159.62/28.25 | Case 1:
% 159.62/28.25 | |
% 159.62/28.25 | | (20) all_58_8 = e0 & op(e1, e1) = e0
% 159.62/28.25 | |
% 159.62/28.25 | | ALPHA: (20) implies:
% 159.62/28.25 | | (21) op(e1, e1) = e0
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (1), (6), (18), (21) are inconsistent by sub-proof #1466.
% 159.62/28.25 | |
% 159.62/28.25 | Case 2:
% 159.62/28.25 | |
% 159.62/28.25 | | (22) all_58_11 = e0 & op(e1, e0) = e0
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.62/28.25 | | (14), (15), (17), (18), (19), (22) are inconsistent by sub-proof
% 159.62/28.25 | | #816.
% 159.62/28.25 | |
% 159.62/28.25 | End of split
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #659 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) op(e3, e3) = all_28_1
% 159.62/28.25 (2) e3 = e0
% 159.62/28.25 (3) op(e3, e3) = e1
% 159.62/28.25 (4) op(e3, e3) = e3
% 159.62/28.25 (5) ~ (e1 = e0)
% 159.62/28.25 (6) op(e3, e3) = all_22_1
% 159.62/28.25 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | GROUND_INST: instantiating (7) with all_22_1, all_28_1, e3, e3, simplifying
% 159.62/28.25 | with (1), (6) gives:
% 159.62/28.25 | (8) all_28_1 = all_22_1
% 159.62/28.25 |
% 159.62/28.25 | GROUND_INST: instantiating (7) with e3, all_28_1, e3, e3, simplifying with
% 159.62/28.25 | (1), (4) gives:
% 159.62/28.25 | (9) all_28_1 = e3
% 159.62/28.25 |
% 159.62/28.25 | GROUND_INST: instantiating (7) with e1, all_28_1, e3, e3, simplifying with
% 159.62/28.25 | (1), (3) gives:
% 159.62/28.25 | (10) all_28_1 = e1
% 159.62/28.25 |
% 159.62/28.25 | COMBINE_EQS: (8), (9) imply:
% 159.62/28.25 | (11) all_22_1 = e3
% 159.62/28.25 |
% 159.62/28.25 | COMBINE_EQS: (8), (10) imply:
% 159.62/28.25 | (12) all_22_1 = e1
% 159.62/28.25 |
% 159.62/28.25 | COMBINE_EQS: (11), (12) imply:
% 159.62/28.25 | (13) e3 = e1
% 159.62/28.25 |
% 159.62/28.25 | COMBINE_EQS: (2), (13) imply:
% 159.62/28.25 | (14) e1 = e0
% 159.62/28.25 |
% 159.62/28.25 | REDUCE: (5), (14) imply:
% 159.62/28.25 | (15) $false
% 159.62/28.25 |
% 159.62/28.25 | CLOSE: (15) is inconsistent.
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #660 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) op(e3, e3) = all_10_2
% 159.62/28.25 (2) ~ (all_10_2 = e1)
% 159.62/28.25 (3) op(e3, e3) = all_28_1
% 159.62/28.25 (4) all_58_0 = e1
% 159.62/28.25 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.25 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.25 (6) all_54_0 = all_10_2
% 159.62/28.25 (7) op(e2, e3) = all_52_1
% 159.62/28.25 (8) ~ (all_10_2 = e0)
% 159.62/28.25 (9) ~ (e3 = e0)
% 159.62/28.25 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.25 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.25 (11) ~ (e2 = e0)
% 159.62/28.25 (12) all_58_6 = e0
% 159.62/28.25 (13) op(e1, e3) = all_52_2
% 159.62/28.25 (14) op(e2, e3) = e2
% 159.62/28.25 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.25 (16) ~ (e3 = e1)
% 159.62/28.25 (17) ~ (all_10_2 = e2)
% 159.62/28.25 (18) ~ (e2 = e1)
% 159.62/28.25 (19) ~ (e1 = e0)
% 159.62/28.25 (20) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.62/28.25 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.62/28.25 e3) = all_22_1 & $i(all_22_1))
% 159.62/28.25 (21) op(e1, e3) = e1
% 159.62/28.25 (22) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.25 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.25 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25 (24) ~ (e3 = e2)
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | BETA: splitting (5) gives:
% 159.62/28.25 |
% 159.62/28.25 | Case 1:
% 159.62/28.25 | |
% 159.62/28.25 | | (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 159.62/28.25 | | e3)
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (4), (7), (14), (16), (23), (24), (25) are inconsistent by
% 159.62/28.25 | | sub-proof #1155.
% 159.62/28.25 | |
% 159.62/28.25 | Case 2:
% 159.62/28.25 | |
% 159.62/28.25 | | (26) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 159.62/28.25 | | e3)
% 159.62/28.25 | |
% 159.62/28.25 | | BETA: splitting (26) gives:
% 159.62/28.25 | |
% 159.62/28.25 | | Case 1:
% 159.62/28.25 | | |
% 159.62/28.25 | | | (27) all_58_6 = e3 & op(e1, e3) = e3
% 159.62/28.25 | | |
% 159.62/28.25 | | | REF_CLOSE: (9), (12), (27) are inconsistent by sub-proof #749.
% 159.62/28.25 | | |
% 159.62/28.25 | | Case 2:
% 159.62/28.25 | | |
% 159.62/28.25 | | | (28) all_58_12 = e3 & op(e0, e3) = e3
% 159.62/28.25 | | |
% 159.62/28.25 | | | REF_CLOSE: (1), (2), (3), (6), (8), (10), (11), (13), (14), (15), (17),
% 159.62/28.25 | | | (18), (19), (20), (21), (22), (23), (28) are inconsistent by
% 159.62/28.25 | | | sub-proof #662.
% 159.62/28.25 | | |
% 159.62/28.25 | | End of split
% 159.62/28.25 | |
% 159.62/28.25 | End of split
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #661 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.25 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.25 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.25 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.25 (3) all_58_6 = e3
% 159.62/28.25 (4) op(e2, e3) = all_52_1
% 159.62/28.25 (5) ~ (e3 = e0)
% 159.62/28.25 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.25 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.25 (7) ~ (e2 = e0)
% 159.62/28.25 (8) all_58_9 = e3
% 159.62/28.25 (9) op(e2, e3) = e2
% 159.62/28.25 (10) ~ (e3 = e1)
% 159.62/28.25 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.25 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.25 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 159.62/28.25 (13) ~ (e2 = e1)
% 159.62/28.25 (14) ~ (e1 = e0)
% 159.62/28.25 (15) all_58_3 = e3
% 159.62/28.25 (16) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.25 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.25 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25 (18) ~ (e3 = e2)
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | BETA: splitting (12) gives:
% 159.62/28.25 |
% 159.62/28.25 | Case 1:
% 159.62/28.25 | |
% 159.62/28.25 | | (19) all_58_9 = e2 & op(e3, e0) = e2
% 159.62/28.25 | |
% 159.62/28.25 | | ALPHA: (19) implies:
% 159.62/28.25 | | (20) all_58_9 = e2
% 159.62/28.25 | |
% 159.62/28.25 | | COMBINE_EQS: (8), (20) imply:
% 159.62/28.25 | | (21) e3 = e2
% 159.62/28.25 | |
% 159.62/28.25 | | COMBINE_EQS: (3), (21) imply:
% 159.62/28.25 | | (22) all_58_6 = e2
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (13), (14), (16), (17), (18),
% 159.62/28.25 | | (22) are inconsistent by sub-proof #1152.
% 159.62/28.25 | |
% 159.62/28.25 | Case 2:
% 159.62/28.25 | |
% 159.62/28.25 | | (23) all_58_10 = e2 & op(e2, e0) = e2
% 159.62/28.25 | |
% 159.62/28.25 | | ALPHA: (23) implies:
% 159.62/28.25 | | (24) all_58_10 = e2
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (1), (5), (7), (9), (10), (11), (13), (14), (15), (17), (24) are
% 159.62/28.25 | | inconsistent by sub-proof #906.
% 159.62/28.25 | |
% 159.62/28.25 | End of split
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #662 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) op(e3, e3) = all_10_2
% 159.62/28.25 (2) ~ (all_10_2 = e1)
% 159.62/28.25 (3) op(e3, e3) = all_28_1
% 159.62/28.25 (4) all_54_0 = all_10_2
% 159.62/28.25 (5) ~ (all_10_2 = e0)
% 159.62/28.25 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.25 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.25 (7) ~ (e2 = e0)
% 159.62/28.25 (8) op(e1, e3) = all_52_2
% 159.62/28.25 (9) op(e2, e3) = e2
% 159.62/28.25 (10) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.25 (11) ~ (all_10_2 = e2)
% 159.62/28.25 (12) ~ (e2 = e1)
% 159.62/28.25 (13) ~ (e1 = e0)
% 159.62/28.25 (14) ( ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.62/28.25 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e1) & op(e3,
% 159.62/28.25 e3) = all_22_1 & $i(all_22_1))
% 159.62/28.25 (15) op(e1, e3) = e1
% 159.62/28.25 (16) all_58_12 = e3 & op(e0, e3) = e3
% 159.62/28.25 (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.25 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.25 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | ALPHA: (16) implies:
% 159.62/28.25 | (19) all_58_12 = e3
% 159.62/28.25 |
% 159.62/28.25 | BETA: splitting (14) gives:
% 159.62/28.25 |
% 159.62/28.25 | Case 1:
% 159.62/28.25 | |
% 159.62/28.25 | | (20) ~ (all_22_0 = e0) & op(all_22_1, e2) = all_22_0 & op(e3, e3) =
% 159.62/28.25 | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 159.62/28.25 | |
% 159.62/28.25 | | ALPHA: (20) implies:
% 159.62/28.25 | | (21) op(e3, e3) = all_22_1
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.25 | | (13), (15), (16), (17), (18), (19), (21) are inconsistent by
% 159.62/28.25 | | sub-proof #663.
% 159.62/28.25 | |
% 159.62/28.25 | Case 2:
% 159.62/28.25 | |
% 159.62/28.25 | | (22) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 159.62/28.25 | |
% 159.62/28.25 | | ALPHA: (22) implies:
% 159.62/28.25 | | (23) op(e3, e3) = all_22_1
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.25 | | (13), (15), (16), (17), (18), (19), (23) are inconsistent by
% 159.62/28.25 | | sub-proof #663.
% 159.62/28.25 | |
% 159.62/28.25 | End of split
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #663 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) op(e3, e3) = all_10_2
% 159.62/28.25 (2) ~ (all_10_2 = e1)
% 159.62/28.25 (3) all_58_12 = e3
% 159.62/28.25 (4) op(e3, e3) = all_28_1
% 159.62/28.25 (5) all_54_0 = all_10_2
% 159.62/28.25 (6) ~ (all_10_2 = e0)
% 159.62/28.25 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.25 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.25 (8) ~ (e2 = e0)
% 159.62/28.25 (9) op(e1, e3) = all_52_2
% 159.62/28.25 (10) op(e2, e3) = e2
% 159.62/28.25 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.25 (12) ~ (all_10_2 = e2)
% 159.62/28.25 (13) ~ (e2 = e1)
% 159.62/28.25 (14) ~ (e1 = e0)
% 159.62/28.25 (15) op(e1, e3) = e1
% 159.62/28.25 (16) op(e3, e3) = all_22_1
% 159.62/28.25 (17) all_58_12 = e3 & op(e0, e3) = e3
% 159.62/28.25 (18) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.25 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.25 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | BETA: splitting (11) gives:
% 159.62/28.25 |
% 159.62/28.25 | Case 1:
% 159.62/28.25 | |
% 159.62/28.25 | | (20) all_54_0 = e3
% 159.62/28.25 | |
% 159.62/28.25 | | COMBINE_EQS: (5), (20) imply:
% 159.62/28.25 | | (21) all_10_2 = e3
% 159.62/28.25 | |
% 159.62/28.25 | | REDUCE: (2), (21) imply:
% 159.62/28.25 | | (22) ~ (e3 = e1)
% 159.62/28.25 | |
% 159.62/28.25 | | REDUCE: (6), (21) imply:
% 159.62/28.25 | | (23) ~ (e3 = e0)
% 159.62/28.25 | |
% 159.62/28.25 | | REDUCE: (1), (21) imply:
% 159.62/28.25 | | (24) op(e3, e3) = e3
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (13), (14), (15), (16), (17),
% 159.62/28.25 | | (18), (19), (22), (23), (24) are inconsistent by sub-proof #664.
% 159.62/28.25 | |
% 159.62/28.25 | Case 2:
% 159.62/28.25 | |
% 159.62/28.25 | | (25) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 159.62/28.25 | |
% 159.62/28.25 | | REF_CLOSE: (2), (5), (6), (12), (25) are inconsistent by sub-proof #1307.
% 159.62/28.25 | |
% 159.62/28.25 | End of split
% 159.62/28.25 |
% 159.62/28.25 End of proof
% 159.62/28.25
% 159.62/28.25 Sub-proof #664 shows that the following formulas are inconsistent:
% 159.62/28.25 ----------------------------------------------------------------
% 159.62/28.25 (1) all_58_12 = e3
% 159.62/28.25 (2) op(e3, e3) = all_28_1
% 159.62/28.25 (3) ~ (e3 = e0)
% 159.62/28.25 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.25 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.25 (5) ~ (e2 = e0)
% 159.62/28.25 (6) op(e1, e3) = all_52_2
% 159.62/28.25 (7) op(e2, e3) = e2
% 159.62/28.25 (8) ~ (e3 = e1)
% 159.62/28.25 (9) ~ (e2 = e1)
% 159.62/28.25 (10) op(e3, e3) = e3
% 159.62/28.25 (11) ~ (e1 = e0)
% 159.62/28.25 (12) op(e1, e3) = e1
% 159.62/28.25 (13) op(e3, e3) = all_22_1
% 159.62/28.25 (14) all_58_12 = e3 & op(e0, e3) = e3
% 159.62/28.25 (15) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.25 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.25 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.25
% 159.62/28.25 Begin of proof
% 159.62/28.25 |
% 159.62/28.25 | BETA: splitting (4) gives:
% 159.62/28.25 |
% 159.62/28.25 | Case 1:
% 159.62/28.25 | |
% 159.62/28.25 | | (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 159.62/28.25 | | e1)
% 159.62/28.25 | |
% 159.62/28.25 | | BETA: splitting (17) gives:
% 159.62/28.25 | |
% 159.62/28.25 | | Case 1:
% 159.62/28.25 | | |
% 159.62/28.25 | | | (18) all_58_0 = e1 & op(e3, e3) = e1
% 159.62/28.25 | | |
% 159.62/28.25 | | | ALPHA: (18) implies:
% 159.62/28.25 | | | (19) all_58_0 = e1
% 159.62/28.25 | | |
% 159.62/28.25 | | | BETA: splitting (15) gives:
% 159.62/28.25 | | |
% 159.62/28.25 | | | Case 1:
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | (20) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 159.62/28.25 | | | | = e0)
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | REF_CLOSE: (2), (3), (5), (7), (10), (13), (16), (20) are inconsistent
% 159.62/28.25 | | | | by sub-proof #665.
% 159.62/28.25 | | | |
% 159.62/28.25 | | | Case 2:
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 159.62/28.25 | | | | = e0)
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | BETA: splitting (21) gives:
% 159.62/28.25 | | | |
% 159.62/28.25 | | | | Case 1:
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | (22) all_58_6 = e0 & op(e1, e3) = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | ALPHA: (22) implies:
% 159.62/28.25 | | | | | (23) all_58_6 = e0
% 159.62/28.25 | | | | | (24) op(e1, e3) = e0
% 159.62/28.25 | | | | |
% 159.62/28.25 | | | | | GROUND_INST: instantiating (16) with all_52_2, e0, e3, e1, simplifying
% 159.62/28.25 | | | | | with (6), (24) gives:
% 159.62/28.25 | | | | | (25) all_52_2 = e0
% 159.62/28.25 | | | | |
% 159.62/28.26 | | | | | GROUND_INST: instantiating (16) with all_52_2, e1, e3, e1, simplifying
% 159.62/28.26 | | | | | with (6), (12) gives:
% 159.62/28.26 | | | | | (26) all_52_2 = e1
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | COMBINE_EQS: (25), (26) imply:
% 159.62/28.26 | | | | | (27) e1 = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | SIMP: (27) implies:
% 159.62/28.26 | | | | | (28) e1 = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | COMBINE_EQS: (19), (28) imply:
% 159.62/28.26 | | | | | (29) all_58_0 = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | REF_CLOSE: (1), (4), (7), (8), (9), (11), (16), (23), (29) are
% 159.62/28.26 | | | | | inconsistent by sub-proof #733.
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | Case 2:
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | (30) all_58_12 = e0 & op(e0, e3) = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | ALPHA: (30) implies:
% 159.62/28.26 | | | | | (31) all_58_12 = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | REF_CLOSE: (1), (3), (31) are inconsistent by sub-proof #1463.
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | End of split
% 159.62/28.26 | | | |
% 159.62/28.26 | | | End of split
% 159.62/28.26 | | |
% 159.62/28.26 | | Case 2:
% 159.62/28.26 | | |
% 159.62/28.26 | | | (32) all_58_2 = e1 & op(e2, e3) = e1
% 159.62/28.26 | | |
% 159.62/28.26 | | | ALPHA: (32) implies:
% 159.62/28.26 | | | (33) op(e2, e3) = e1
% 159.62/28.26 | | |
% 159.62/28.26 | | | REF_CLOSE: (7), (9), (16), (33) are inconsistent by sub-proof #1430.
% 159.62/28.26 | | |
% 159.62/28.26 | | End of split
% 159.62/28.26 | |
% 159.62/28.26 | Case 2:
% 159.62/28.26 | |
% 159.62/28.26 | | (34) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 159.62/28.26 | | e1)
% 159.62/28.26 | |
% 159.62/28.26 | | BETA: splitting (34) gives:
% 159.62/28.26 | |
% 159.62/28.26 | | Case 1:
% 159.62/28.26 | | |
% 159.62/28.26 | | | (35) all_58_6 = e1 & op(e1, e3) = e1
% 159.62/28.26 | | |
% 159.62/28.26 | | | ALPHA: (35) implies:
% 159.62/28.26 | | | (36) all_58_6 = e1
% 159.62/28.26 | | |
% 159.62/28.26 | | | BETA: splitting (15) gives:
% 159.62/28.26 | | |
% 159.62/28.26 | | | Case 1:
% 159.62/28.26 | | | |
% 159.62/28.26 | | | | (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 159.62/28.26 | | | | = e0)
% 159.62/28.26 | | | |
% 159.62/28.26 | | | | REF_CLOSE: (2), (3), (5), (7), (10), (13), (16), (37) are inconsistent
% 159.62/28.26 | | | | by sub-proof #665.
% 159.62/28.26 | | | |
% 159.62/28.26 | | | Case 2:
% 159.62/28.26 | | | |
% 159.62/28.26 | | | | (38) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 159.62/28.26 | | | | = e0)
% 159.62/28.26 | | | |
% 159.62/28.26 | | | | BETA: splitting (38) gives:
% 159.62/28.26 | | | |
% 159.62/28.26 | | | | Case 1:
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | (39) all_58_6 = e0 & op(e1, e3) = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | ALPHA: (39) implies:
% 159.62/28.26 | | | | | (40) all_58_6 = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | REF_CLOSE: (11), (36), (40) are inconsistent by sub-proof #735.
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | Case 2:
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | (41) all_58_12 = e0 & op(e0, e3) = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | ALPHA: (41) implies:
% 159.62/28.26 | | | | | (42) all_58_12 = e0
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | REF_CLOSE: (1), (3), (42) are inconsistent by sub-proof #1463.
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | End of split
% 159.62/28.26 | | | |
% 159.62/28.26 | | | End of split
% 159.62/28.26 | | |
% 159.62/28.26 | | Case 2:
% 159.62/28.26 | | |
% 159.62/28.26 | | | (43) all_58_12 = e1 & op(e0, e3) = e1
% 159.62/28.26 | | |
% 159.62/28.26 | | | REF_CLOSE: (1), (8), (43) are inconsistent by sub-proof #1388.
% 159.62/28.26 | | |
% 159.62/28.26 | | End of split
% 159.62/28.26 | |
% 159.62/28.26 | End of split
% 159.62/28.26 |
% 159.62/28.26 End of proof
% 159.62/28.26
% 159.62/28.26 Sub-proof #665 shows that the following formulas are inconsistent:
% 159.62/28.26 ----------------------------------------------------------------
% 159.62/28.26 (1) op(e3, e3) = all_28_1
% 159.62/28.26 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 159.62/28.26 (3) ~ (e3 = e0)
% 159.62/28.26 (4) ~ (e2 = e0)
% 159.62/28.26 (5) op(e2, e3) = e2
% 159.62/28.26 (6) op(e3, e3) = e3
% 159.62/28.26 (7) op(e3, e3) = all_22_1
% 159.62/28.26 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.26
% 159.62/28.26 Begin of proof
% 159.62/28.26 |
% 159.62/28.26 | BETA: splitting (2) gives:
% 159.62/28.26 |
% 159.62/28.26 | Case 1:
% 159.62/28.26 | |
% 159.62/28.26 | | (9) all_58_0 = e0 & op(e3, e3) = e0
% 159.62/28.26 | |
% 159.62/28.26 | | REF_CLOSE: (1), (3), (6), (7), (8), (9) are inconsistent by sub-proof #666.
% 159.62/28.26 | |
% 159.62/28.26 | Case 2:
% 159.62/28.26 | |
% 159.62/28.26 | | (10) all_58_2 = e0 & op(e2, e3) = e0
% 159.62/28.26 | |
% 159.62/28.26 | | ALPHA: (10) implies:
% 159.62/28.26 | | (11) op(e2, e3) = e0
% 159.62/28.26 | |
% 159.62/28.26 | | REF_CLOSE: (4), (5), (8), (11) are inconsistent by sub-proof #1156.
% 159.62/28.26 | |
% 159.62/28.26 | End of split
% 159.62/28.26 |
% 159.62/28.26 End of proof
% 159.62/28.26
% 159.62/28.26 Sub-proof #666 shows that the following formulas are inconsistent:
% 159.62/28.26 ----------------------------------------------------------------
% 159.62/28.26 (1) op(e3, e3) = all_28_1
% 159.62/28.26 (2) ~ (e3 = e0)
% 159.62/28.26 (3) all_58_0 = e0 & op(e3, e3) = e0
% 159.62/28.26 (4) op(e3, e3) = e3
% 159.62/28.26 (5) op(e3, e3) = all_22_1
% 159.62/28.26 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.26
% 159.62/28.26 Begin of proof
% 159.62/28.26 |
% 159.62/28.26 | ALPHA: (3) implies:
% 159.62/28.26 | (7) op(e3, e3) = e0
% 159.62/28.26 |
% 159.62/28.26 | GROUND_INST: instantiating (6) with all_22_1, all_28_1, e3, e3, simplifying
% 159.62/28.26 | with (1), (5) gives:
% 159.62/28.26 | (8) all_28_1 = all_22_1
% 159.62/28.26 |
% 159.62/28.26 | GROUND_INST: instantiating (6) with e3, all_28_1, e3, e3, simplifying with
% 159.62/28.26 | (1), (4) gives:
% 159.62/28.26 | (9) all_28_1 = e3
% 159.62/28.26 |
% 159.62/28.26 | GROUND_INST: instantiating (6) with e0, all_28_1, e3, e3, simplifying with
% 159.62/28.26 | (1), (7) gives:
% 159.62/28.26 | (10) all_28_1 = e0
% 159.62/28.26 |
% 159.62/28.26 | COMBINE_EQS: (8), (10) imply:
% 159.62/28.26 | (11) all_22_1 = e0
% 159.62/28.26 |
% 159.62/28.26 | COMBINE_EQS: (8), (9) imply:
% 159.62/28.26 | (12) all_22_1 = e3
% 159.62/28.26 |
% 159.62/28.26 | COMBINE_EQS: (11), (12) imply:
% 159.62/28.26 | (13) e3 = e0
% 159.62/28.26 |
% 159.62/28.26 | REDUCE: (2), (13) imply:
% 159.62/28.26 | (14) $false
% 159.62/28.26 |
% 159.62/28.26 | CLOSE: (14) is inconsistent.
% 159.62/28.26 |
% 159.62/28.26 End of proof
% 159.62/28.26
% 159.62/28.26 Sub-proof #667 shows that the following formulas are inconsistent:
% 159.62/28.26 ----------------------------------------------------------------
% 159.62/28.26 (1) op(e3, e3) = all_28_1
% 159.62/28.26 (2) ~ (e3 = e1)
% 159.62/28.26 (3) op(e3, e3) = e1
% 159.62/28.26 (4) op(e3, e3) = e3
% 159.62/28.26 (5) op(e3, e3) = all_22_1
% 159.62/28.26 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.26
% 159.62/28.26 Begin of proof
% 159.62/28.26 |
% 159.62/28.26 | GROUND_INST: instantiating (6) with all_22_1, all_28_1, e3, e3, simplifying
% 159.62/28.26 | with (1), (5) gives:
% 159.62/28.26 | (7) all_28_1 = all_22_1
% 159.62/28.26 |
% 159.62/28.26 | GROUND_INST: instantiating (6) with e3, all_28_1, e3, e3, simplifying with
% 159.62/28.26 | (1), (4) gives:
% 159.62/28.26 | (8) all_28_1 = e3
% 159.62/28.26 |
% 159.62/28.26 | GROUND_INST: instantiating (6) with e1, all_28_1, e3, e3, simplifying with
% 159.62/28.26 | (1), (3) gives:
% 159.62/28.26 | (9) all_28_1 = e1
% 159.62/28.26 |
% 159.62/28.26 | COMBINE_EQS: (7), (8) imply:
% 159.62/28.26 | (10) all_22_1 = e3
% 159.62/28.26 |
% 159.62/28.26 | COMBINE_EQS: (7), (9) imply:
% 159.62/28.26 | (11) all_22_1 = e1
% 159.62/28.26 |
% 159.62/28.26 | COMBINE_EQS: (10), (11) imply:
% 159.62/28.26 | (12) e3 = e1
% 159.62/28.26 |
% 159.62/28.26 | REDUCE: (2), (12) imply:
% 159.62/28.26 | (13) $false
% 159.62/28.26 |
% 159.62/28.26 | CLOSE: (13) is inconsistent.
% 159.62/28.26 |
% 159.62/28.26 End of proof
% 159.62/28.26
% 159.62/28.26 Sub-proof #668 shows that the following formulas are inconsistent:
% 159.62/28.26 ----------------------------------------------------------------
% 159.62/28.26 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.26 (2) op(e3, e3) = all_22_1
% 159.62/28.26 (3) op(e3, e3) = e1
% 159.62/28.26 (4) ~ (all_22_1 = e1)
% 159.62/28.26
% 159.62/28.26 Begin of proof
% 159.62/28.26 |
% 159.62/28.26 | GROUND_INST: instantiating (1) with e1, all_22_1, e3, e3, simplifying with
% 159.62/28.26 | (2), (3) gives:
% 159.62/28.26 | (5) all_22_1 = e1
% 159.62/28.26 |
% 159.62/28.26 | REDUCE: (4), (5) imply:
% 159.62/28.26 | (6) $false
% 159.62/28.26 |
% 159.62/28.26 | CLOSE: (6) is inconsistent.
% 159.62/28.26 |
% 159.62/28.26 End of proof
% 159.62/28.26
% 159.62/28.26 Sub-proof #669 shows that the following formulas are inconsistent:
% 159.62/28.26 ----------------------------------------------------------------
% 159.62/28.26 (1) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.62/28.26 (2) ~ (all_52_12 = e3)
% 159.62/28.26 (3) op(e3, e0) = all_52_12
% 159.62/28.26 (4) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.62/28.26 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.62/28.26 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.26 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.26 (6) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.26 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.26 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.26 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.26 (8) op(e1, e1) = all_6_2
% 159.62/28.26 (9) ~ (all_52_7 = e3)
% 159.62/28.26 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.26 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.62/28.26 e1)
% 159.62/28.26 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.62/28.26 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.62/28.26 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.62/28.26 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.62/28.26 (13) all_54_10 = all_6_2
% 159.62/28.26 (14) ~ (all_52_11 = e3)
% 159.62/28.26 (15) ~ (all_52_2 = all_52_3)
% 159.62/28.26 (16) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.62/28.26 (17) ~ (all_52_7 = all_52_11)
% 159.62/28.26 (18) all_58_0 = e1
% 159.62/28.26 (19) op(e1, e2) = all_14_0
% 159.62/28.26 (20) ~ (all_52_12 = all_4_2)
% 159.62/28.26 (21) ~ (all_52_14 = all_14_0)
% 159.62/28.26 (22) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 159.62/28.26 (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.26 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.26 (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.26 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.26 (25) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.62/28.26 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.62/28.26 (26) ~ (all_14_0 = all_6_2)
% 159.62/28.26 (27) all_54_1 = all_52_4
% 159.62/28.26 (28) op(e3, e2) = all_52_4
% 159.62/28.26 (29) ~ (all_4_2 = e2)
% 159.62/28.26 (30) ~ (all_14_0 = e3)
% 159.62/28.26 (31) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.62/28.26 (32) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.62/28.26 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.62/28.26 (33) ~ (all_52_12 = all_52_13)
% 159.62/28.26 (34) all_58_14 = e2
% 159.62/28.26 (35) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.62/28.26 (36) ~ (all_52_4 = all_52_12)
% 159.62/28.26 (37) op(e2, e1) = all_52_9
% 159.62/28.26 (38) op(e2, e3) = all_52_1
% 159.62/28.26 (39) ~ (all_52_13 = e3)
% 159.62/28.26 (40) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.62/28.26 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.62/28.26 (41) ~ (all_52_2 = all_6_2)
% 159.62/28.26 (42) ~ (all_52_2 = all_14_0)
% 159.62/28.26 (43) ~ (e3 = e0)
% 159.62/28.26 (44) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.26 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.26 (45) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.62/28.26 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.62/28.26 (46) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.26 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.26 e2)
% 159.62/28.26 (47) ~ (e2 = e0)
% 159.62/28.26 (48) ~ (all_52_9 = e3)
% 159.62/28.26 (49) ~ (all_52_11 = all_6_2)
% 159.62/28.26 (50) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 159.62/28.26 (51) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.62/28.26 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.62/28.26 (52) op(e2, e0) = all_52_13
% 159.62/28.26 (53) op(e2, e3) = e2
% 159.62/28.26 (54) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.26 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.26 (55) ~ (e3 = e1)
% 159.62/28.26 (56) ~ (all_52_7 = all_14_0)
% 159.62/28.26 (57) all_56_12 = e1
% 159.62/28.26 (58) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.62/28.26 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.62/28.26 (59) op(e1, e2) = all_52_6
% 159.62/28.26 (60) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 159.62/28.26 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.62/28.26 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 159.62/28.26 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.62/28.26 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.62/28.26 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.62/28.26 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 159.62/28.26 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 159.62/28.26 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 159.62/28.26 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.62/28.26 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.62/28.26 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 159.62/28.26 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.62/28.26 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.62/28.26 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 159.62/28.26 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 159.62/28.26 = e0)
% 159.62/28.26 (61) ~ (all_52_3 = all_4_2)
% 159.62/28.26 (62) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.26 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.26 (63) ~ (all_6_2 = e3)
% 159.62/28.26 (64) op(e0, e0) = all_4_2
% 159.62/28.26 (65) all_54_8 = all_52_2
% 159.62/28.26 (66) all_54_7 = all_52_13
% 159.62/28.26 (67) op(e3, e3) = e1
% 159.62/28.26 (68) ~ (all_52_13 = e2)
% 159.62/28.26 (69) all_56_15 = all_4_2
% 159.62/28.26 (70) op(e0, e1) = e2
% 159.62/28.26 (71) op(e0, e1) = all_52_11
% 159.62/28.26 (72) ~ (all_52_9 = all_52_11)
% 159.62/28.26 (73) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 159.62/28.26 (74) ~ (all_52_13 = all_4_2)
% 159.62/28.26 (75) ~ (all_52_2 = e1)
% 159.62/28.26 (76) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.62/28.26 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.62/28.26 (77) ~ (all_52_4 = e3)
% 159.62/28.26 (78) ~ (e2 = e1)
% 159.62/28.26 (79) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 159.62/28.26 (80) all_54_3 = all_52_12
% 159.62/28.26 (81) ~ (all_52_4 = all_52_7)
% 159.62/28.26 (82) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.62/28.26 (83) ~ (e1 = e0)
% 159.62/28.26 (84) op(e1, e2) = all_22_0
% 159.62/28.26 (85) ~ (all_22_0 = e0)
% 159.62/28.26 (86) all_58_3 = e3
% 159.62/28.26 (87) ~ (all_6_2 = e2)
% 159.62/28.26 (88) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.62/28.26 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.62/28.26 e3)
% 159.62/28.26 (89) all_56_14 = all_6_2
% 159.62/28.26 (90) all_54_9 = all_14_0
% 159.62/28.26 (91) all_56_13 = e3
% 159.62/28.26 (92) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.62/28.26 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.62/28.26 (93) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.62/28.26 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.26 (94) ~ (all_52_7 = all_4_2)
% 159.62/28.26 (95) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.62/28.26 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.62/28.26 (96) op(e0, e2) = all_52_7
% 159.62/28.26 (97) op(e1, e0) = all_52_14
% 159.62/28.26 (98) op(e3, e3) = all_22_1
% 159.62/28.26 (99) all_54_15 = all_4_2
% 159.62/28.26 (100) all_56_1 = e3
% 159.62/28.26 (101) ~ (all_52_6 = e3)
% 159.62/28.26 (102) ~ (all_52_14 = all_6_2)
% 159.62/28.26 (103) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.26 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.26 (104) ~ (all_52_12 = e1)
% 159.62/28.26 (105) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.26 (106) ~ (all_52_3 = all_52_11)
% 159.62/28.26 (107) ~ (all_52_11 = all_4_2)
% 159.62/28.26 (108) all_54_11 = all_52_14
% 159.62/28.26 (109) ~ (all_52_13 = all_52_14)
% 159.62/28.26 (110) ~ (e3 = e2)
% 159.62/28.26 (111) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.62/28.26 (112) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.62/28.26 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.26 (113) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 159.62/28.26 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.62/28.26 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 159.62/28.26 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 159.62/28.26 e0)))
% 159.62/28.26 (114) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 159.62/28.26 (115) all_54_12 = all_52_3
% 159.62/28.26 (116) ~ (all_52_4 = all_14_0)
% 159.62/28.26 (117) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.62/28.26 (118) ~ (all_52_3 = all_52_7)
% 159.62/28.26
% 159.62/28.26 Begin of proof
% 159.62/28.26 |
% 159.62/28.26 | BETA: splitting (12) gives:
% 159.62/28.26 |
% 159.62/28.26 | Case 1:
% 159.62/28.26 | |
% 159.62/28.26 | | (119) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 159.62/28.26 | | e3)
% 159.62/28.26 | |
% 159.62/28.26 | | BETA: splitting (119) gives:
% 159.62/28.26 | |
% 159.62/28.26 | | Case 1:
% 159.62/28.26 | | |
% 159.62/28.26 | | | (120) all_58_4 = e3 & op(e3, e1) = e3
% 159.62/28.26 | | |
% 159.62/28.26 | | | ALPHA: (120) implies:
% 159.62/28.26 | | | (121) all_58_4 = e3
% 159.62/28.26 | | | (122) op(e3, e1) = e3
% 159.62/28.26 | | |
% 159.62/28.26 | | | BETA: splitting (5) gives:
% 159.62/28.26 | | |
% 159.62/28.26 | | | Case 1:
% 159.62/28.26 | | | |
% 159.62/28.26 | | | | (123) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 159.62/28.26 | | | | = e1)
% 159.62/28.26 | | | |
% 159.62/28.26 | | | | BETA: splitting (123) gives:
% 159.62/28.26 | | | |
% 159.62/28.26 | | | | Case 1:
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | (124) all_58_1 = e1 & op(e3, e2) = e1
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | ALPHA: (124) implies:
% 159.62/28.26 | | | | | (125) all_58_1 = e1
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | BETA: splitting (45) gives:
% 159.62/28.26 | | | | |
% 159.62/28.26 | | | | | Case 1:
% 159.62/28.26 | | | | | |
% 159.62/28.26 | | | | | | (126) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 159.62/28.26 | | | | | | e2) = e2)
% 159.62/28.26 | | | | | |
% 159.62/28.26 | | | | | | BETA: splitting (126) gives:
% 159.62/28.26 | | | | | |
% 159.62/28.26 | | | | | | Case 1:
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | (127) all_58_0 = e2 & op(e3, e3) = e2
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | REF_CLOSE: (18), (78), (127) are inconsistent by sub-proof #802.
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | Case 2:
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | (128) all_58_1 = e2 & op(e3, e2) = e2
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | REF_CLOSE: (78), (125), (128) are inconsistent by sub-proof #1213.
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | End of split
% 159.62/28.26 | | | | | |
% 159.62/28.26 | | | | | Case 2:
% 159.62/28.26 | | | | | |
% 159.62/28.26 | | | | | | (129) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 159.62/28.26 | | | | | | e0) = e2)
% 159.62/28.26 | | | | | |
% 159.62/28.26 | | | | | | BETA: splitting (129) gives:
% 159.62/28.26 | | | | | |
% 159.62/28.26 | | | | | | Case 1:
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | (130) all_58_4 = e2 & op(e3, e1) = e2
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | ALPHA: (130) implies:
% 159.62/28.26 | | | | | | | (131) all_58_4 = e2
% 159.62/28.26 | | | | | | | (132) op(e3, e1) = e2
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12), (18),
% 159.62/28.26 | | | | | | | (23), (24), (25), (28), (29), (32), (37), (38), (39),
% 159.62/28.26 | | | | | | | (40), (43), (44), (45), (46), (47), (48), (51), (52),
% 159.62/28.26 | | | | | | | (53), (54), (55), (58), (59), (62), (63), (64), (67),
% 159.62/28.26 | | | | | | | (76), (77), (78), (83), (86), (87), (88), (92), (93),
% 159.62/28.26 | | | | | | | (95), (96), (98), (101), (103), (105), (110), (112),
% 159.62/28.26 | | | | | | | (113), (122), (131), (132) are inconsistent by
% 159.62/28.26 | | | | | | | sub-proof #751.
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | Case 2:
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | (133) all_58_9 = e2 & op(e3, e0) = e2
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | ALPHA: (133) implies:
% 159.62/28.26 | | | | | | | (134) all_58_9 = e2
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | BETA: splitting (10) gives:
% 159.62/28.26 | | | | | | |
% 159.62/28.26 | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | |
% 159.62/28.26 | | | | | | | | (135) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 159.62/28.26 | | | | | | | | op(e0, e2) = e1)
% 159.62/28.26 | | | | | | | |
% 159.62/28.26 | | | | | | | | BETA: splitting (135) gives:
% 159.62/28.26 | | | | | | | |
% 159.62/28.26 | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | |
% 159.62/28.26 | | | | | | | | | (136) all_58_12 = e1 & op(e0, e3) = e1
% 159.62/28.26 | | | | | | | | |
% 159.62/28.26 | | | | | | | | | ALPHA: (136) implies:
% 159.62/28.26 | | | | | | | | | (137) all_58_12 = e1
% 159.62/28.26 | | | | | | | | |
% 159.62/28.26 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.26 | | | | | | | | | (23), (24), (25), (28), (29), (32), (37), (38),
% 159.62/28.26 | | | | | | | | | (39), (40), (43), (44), (45), (46), (47), (48),
% 159.62/28.26 | | | | | | | | | (52), (53), (54), (55), (58), (59), (62), (63),
% 159.62/28.26 | | | | | | | | | (64), (67), (76), (77), (78), (83), (86), (87),
% 159.62/28.26 | | | | | | | | | (88), (92), (93), (95), (96), (98), (101), (103),
% 159.62/28.26 | | | | | | | | | (105), (110), (112), (113), (137) are inconsistent
% 159.62/28.26 | | | | | | | | | by sub-proof #747.
% 159.62/28.26 | | | | | | | | |
% 159.62/28.26 | | | | | | | | Case 2:
% 159.62/28.26 | | | | | | | | |
% 159.62/28.26 | | | | | | | | | (138) all_58_13 = e1 & op(e0, e2) = e1
% 159.62/28.26 | | | | | | | | |
% 159.62/28.26 | | | | | | | | | ALPHA: (138) implies:
% 159.62/28.26 | | | | | | | | | (139) all_58_13 = e1
% 159.62/28.26 | | | | | | | | | (140) op(e0, e2) = e1
% 159.62/28.26 | | | | | | | | |
% 159.62/28.26 | | | | | | | | | BETA: splitting (54) gives:
% 159.62/28.26 | | | | | | | | |
% 159.62/28.26 | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | (141) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 159.62/28.26 | | | | | | | | | | & op(e2, e2) = e0)
% 159.62/28.26 | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | BETA: splitting (141) gives:
% 159.62/28.26 | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | (142) all_58_1 = e0 & op(e3, e2) = e0
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | REF_CLOSE: (83), (125), (142) are inconsistent by sub-proof
% 159.62/28.26 | | | | | | | | | | | #1327.
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | Case 2:
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | (143) all_58_3 = e0 & op(e2, e2) = e0
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | REF_CLOSE: (43), (86), (143) are inconsistent by sub-proof
% 159.62/28.26 | | | | | | | | | | | #910.
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | End of split
% 159.62/28.26 | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | Case 2:
% 159.62/28.26 | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | (144) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0
% 159.62/28.26 | | | | | | | | | | & op(e0, e2) = e0)
% 159.62/28.26 | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | BETA: splitting (144) gives:
% 159.62/28.26 | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | (145) all_58_7 = e0 & op(e1, e2) = e0
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | ALPHA: (145) implies:
% 159.62/28.26 | | | | | | | | | | | (146) all_58_7 = e0
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | BETA: splitting (40) gives:
% 159.62/28.26 | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | (147) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 159.62/28.26 | | | | | | | | | | | | & op(e1, e2) = e2)
% 159.62/28.26 | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | REF_CLOSE: (23), (38), (43), (44), (47), (53), (55), (78),
% 159.62/28.26 | | | | | | | | | | | | (83), (103), (105), (110), (146), (147) are
% 159.62/28.26 | | | | | | | | | | | | inconsistent by sub-proof #745.
% 159.62/28.26 | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | Case 2:
% 159.62/28.26 | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | (148) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 159.62/28.26 | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 159.62/28.26 | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | BETA: splitting (148) gives:
% 159.62/28.26 | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | (149) all_58_8 = e2 & op(e1, e1) = e2
% 159.62/28.26 | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | REF_CLOSE: (34), (43), (47), (55), (58), (76), (78), (83),
% 159.62/28.26 | | | | | | | | | | | | | (121), (149) are inconsistent by sub-proof #1338.
% 159.62/28.26 | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | Case 2:
% 159.62/28.26 | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | (150) all_58_11 = e2 & op(e1, e0) = e2
% 159.62/28.26 | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | ALPHA: (150) implies:
% 159.62/28.26 | | | | | | | | | | | | | (151) all_58_11 = e2
% 159.62/28.26 | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | BETA: splitting (32) gives:
% 159.62/28.26 | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | (152) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 159.62/28.26 | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 159.62/28.26 | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 159.62/28.26 | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | (153) all_58_6 = e3 & op(e1, e3) = e3
% 159.62/28.26 | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 159.62/28.26 | | | | | | | | | | | | | | | (154) all_58_6 = e3
% 159.62/28.26 | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 159.62/28.26 | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | (155) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 159.62/28.26 | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 159.62/28.26 | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | REF_CLOSE: (47), (53), (67), (83), (98), (105), (155) are
% 159.62/28.26 | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 159.62/28.26 | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | Case 2:
% 159.62/28.26 | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | (156) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 159.62/28.26 | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 159.62/28.26 | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 159.62/28.26 | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | (157) all_58_6 = e0 & op(e1, e3) = e0
% 159.62/28.26 | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 159.62/28.26 | | | | | | | | | | | | | | | | | (158) all_58_6 = e0
% 159.62/28.26 | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (154), (158) are inconsistent by sub-proof
% 159.62/28.26 | | | | | | | | | | | | | | | | | #1321.
% 159.62/28.26 | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.26 | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | (159) all_58_12 = e0 & op(e0, e3) = e0
% 159.62/28.26 | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 159.62/28.26 | | | | | | | | | | | | | | | | | (160) all_58_12 = e0
% 159.62/28.26 | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 159.62/28.26 | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | (161) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.62/28.26 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.62/28.26 | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 159.62/28.26 | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.26 | | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | (162) all_58_1 = e2 & op(e3, e2) = e2
% 159.62/28.26 | | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23), (38), (40), (43), (44), (47), (53),
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | (55), (78), (83), (87), (103), (105), (110),
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | (125), (146), (151), (162) are inconsistent by
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 159.62/28.26 | | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.26 | | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | (163) all_58_3 = e2 & op(e2, e2) = e2
% 159.62/28.26 | | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (38), (43), (53), (55), (86), (105),
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | (110), (154), (160), (163) are inconsistent by
% 159.62/28.26 | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 159.62/28.26 | | | | | | | | | | | | | | | | | | |
% 159.62/28.26 | | | | | | | | | | | | | | | | | | End of split
% 159.62/28.26 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (164) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (78), (96), (105), (140), (146), (164) are
% 159.62/28.27 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #740.
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | (165) all_58_7 = e3 & op(e1, e2) = e3
% 159.62/28.27 | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | REF_CLOSE: (59), (101), (105), (165) are inconsistent by
% 159.62/28.27 | | | | | | | | | | | | | | | sub-proof #1184.
% 159.62/28.27 | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | (166) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 159.62/28.27 | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | REF_CLOSE: (34), (43), (47), (55), (58), (76), (78), (83),
% 159.62/28.27 | | | | | | | | | | | | | | (110), (121), (151), (166) are inconsistent by
% 159.62/28.27 | | | | | | | | | | | | | | sub-proof #738.
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (167) all_58_13 = e0 & op(e0, e2) = e0
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | ALPHA: (167) implies:
% 159.62/28.27 | | | | | | | | | | | (168) all_58_13 = e0
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | REF_CLOSE: (83), (139), (168) are inconsistent by sub-proof
% 159.62/28.27 | | | | | | | | | | | #988.
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | End of split
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | (169) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 159.62/28.27 | | | | | | | | op(e0, e0) = e1)
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | BETA: splitting (169) gives:
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | (170) all_58_14 = e1 & op(e0, e1) = e1
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | ALPHA: (170) implies:
% 159.62/28.27 | | | | | | | | | (171) op(e0, e1) = e1
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | REF_CLOSE: (70), (71), (78), (105), (171) are inconsistent by
% 159.62/28.27 | | | | | | | | | sub-proof #1473.
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | (172) all_58_15 = e1 & op(e0, e0) = e1
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | ALPHA: (172) implies:
% 159.62/28.27 | | | | | | | | | (173) all_58_15 = e1
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | BETA: splitting (88) gives:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | (174) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 159.62/28.27 | | | | | | | | | | e3 & op(e0, e2) = e3)
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | BETA: splitting (174) gives:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (175) all_58_12 = e3 & op(e0, e3) = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | ALPHA: (175) implies:
% 159.62/28.27 | | | | | | | | | | | (176) all_58_12 = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.27 | | | | | | | | | | | (18), (23), (24), (25), (28), (29), (32), (34),
% 159.62/28.27 | | | | | | | | | | | (37), (38), (39), (40), (43), (44), (45), (46),
% 159.62/28.27 | | | | | | | | | | | (47), (48), (51), (52), (53), (54), (55), (58),
% 159.62/28.27 | | | | | | | | | | | (59), (62), (63), (64), (67), (70), (71), (76),
% 159.62/28.27 | | | | | | | | | | | (77), (78), (83), (86), (87), (88), (92), (93),
% 159.62/28.27 | | | | | | | | | | | (95), (96), (98), (101), (103), (105), (110),
% 159.62/28.27 | | | | | | | | | | | (112), (113), (121), (122), (134), (173), (176)
% 159.62/28.27 | | | | | | | | | | | are inconsistent by sub-proof #729.
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (177) all_58_13 = e3 & op(e0, e2) = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | REF_CLOSE: (9), (96), (105), (177) are inconsistent by
% 159.62/28.27 | | | | | | | | | | | sub-proof #1449.
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | (178) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 159.62/28.27 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | BETA: splitting (178) gives:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (179) all_58_14 = e3 & op(e0, e1) = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | ALPHA: (179) implies:
% 159.62/28.27 | | | | | | | | | | | (180) all_58_14 = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | COMBINE_EQS: (34), (180) imply:
% 159.62/28.27 | | | | | | | | | | | (181) e3 = e2
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | COMBINE_EQS: (121), (181) imply:
% 159.62/28.27 | | | | | | | | | | | (182) all_58_4 = e2
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (23),
% 159.62/28.27 | | | | | | | | | | | (24), (25), (28), (29), (32), (38), (39), (40),
% 159.62/28.27 | | | | | | | | | | | (43), (44), (45), (46), (47), (52), (53), (54),
% 159.62/28.27 | | | | | | | | | | | (55), (58), (59), (62), (64), (67), (76), (77),
% 159.62/28.27 | | | | | | | | | | | (78), (83), (86), (87), (88), (92), (93), (95),
% 159.62/28.27 | | | | | | | | | | | (96), (98), (101), (103), (105), (110), (112),
% 159.62/28.27 | | | | | | | | | | | (113), (125), (180), (182) are inconsistent by
% 159.62/28.27 | | | | | | | | | | | sub-proof #764.
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (183) all_58_15 = e3 & op(e0, e0) = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | ALPHA: (183) implies:
% 159.62/28.27 | | | | | | | | | | | (184) all_58_15 = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | REF_CLOSE: (55), (173), (184) are inconsistent by sub-proof
% 159.62/28.27 | | | | | | | | | | | #1404.
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | End of split
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | End of split
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | End of split
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | End of split
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | Case 2:
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | (185) all_58_3 = e1 & op(e2, e2) = e1
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | ALPHA: (185) implies:
% 159.62/28.27 | | | | | (186) all_58_3 = e1
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REF_CLOSE: (55), (86), (186) are inconsistent by sub-proof #841.
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | End of split
% 159.62/28.27 | | | |
% 159.62/28.27 | | | Case 2:
% 159.62/28.27 | | | |
% 159.62/28.27 | | | | (187) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 159.62/28.27 | | | | e2) = e1)
% 159.62/28.27 | | | |
% 159.62/28.27 | | | | BETA: splitting (187) gives:
% 159.62/28.27 | | | |
% 159.62/28.27 | | | | Case 1:
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | (188) all_58_7 = e1 & op(e1, e2) = e1
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | ALPHA: (188) implies:
% 159.62/28.27 | | | | | (189) all_58_7 = e1
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | BETA: splitting (10) gives:
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | Case 1:
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | (190) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 159.62/28.27 | | | | | | op(e0, e2) = e1)
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | BETA: splitting (190) gives:
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | Case 1:
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | (191) all_58_12 = e1 & op(e0, e3) = e1
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | ALPHA: (191) implies:
% 159.62/28.27 | | | | | | | (192) all_58_12 = e1
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12), (23),
% 159.62/28.27 | | | | | | | (24), (25), (28), (29), (32), (37), (38), (39), (40),
% 159.62/28.27 | | | | | | | (43), (44), (45), (46), (47), (48), (52), (53), (54),
% 159.62/28.27 | | | | | | | (55), (58), (59), (62), (63), (64), (67), (76), (77),
% 159.62/28.27 | | | | | | | (78), (83), (86), (87), (88), (92), (93), (95), (96),
% 159.62/28.27 | | | | | | | (98), (101), (103), (105), (110), (112), (113), (192)
% 159.62/28.27 | | | | | | | are inconsistent by sub-proof #747.
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | Case 2:
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | (193) all_58_13 = e1 & op(e0, e2) = e1
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | ALPHA: (193) implies:
% 159.62/28.27 | | | | | | | (194) all_58_13 = e1
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12), (18),
% 159.62/28.27 | | | | | | | (23), (24), (25), (28), (29), (32), (34), (37), (38),
% 159.62/28.27 | | | | | | | (39), (40), (43), (44), (45), (46), (47), (48), (51),
% 159.62/28.27 | | | | | | | (52), (53), (54), (55), (58), (59), (62), (63), (64),
% 159.62/28.27 | | | | | | | (67), (70), (71), (76), (77), (78), (83), (86), (87),
% 159.62/28.27 | | | | | | | (88), (92), (93), (95), (96), (98), (101), (103),
% 159.62/28.27 | | | | | | | (105), (110), (112), (113), (121), (122), (189), (194)
% 159.62/28.27 | | | | | | | are inconsistent by sub-proof #722.
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | End of split
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | Case 2:
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | (195) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 159.62/28.27 | | | | | | op(e0, e0) = e1)
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | BETA: splitting (195) gives:
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | Case 1:
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | (196) all_58_14 = e1 & op(e0, e1) = e1
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | ALPHA: (196) implies:
% 159.62/28.27 | | | | | | | (197) op(e0, e1) = e1
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | REF_CLOSE: (70), (71), (78), (105), (197) are inconsistent by
% 159.62/28.27 | | | | | | | sub-proof #1473.
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | Case 2:
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | (198) all_58_15 = e1 & op(e0, e0) = e1
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | ALPHA: (198) implies:
% 159.62/28.27 | | | | | | | (199) all_58_15 = e1
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | BETA: splitting (88) gives:
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | (200) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 159.62/28.27 | | | | | | | | op(e0, e2) = e3)
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | BETA: splitting (200) gives:
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | (201) all_58_12 = e3 & op(e0, e3) = e3
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | ALPHA: (201) implies:
% 159.62/28.27 | | | | | | | | | (202) all_58_12 = e3
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | BETA: splitting (11) gives:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | (203) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3
% 159.62/28.27 | | | | | | | | | | & op(e2, e0) = e3)
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.27 | | | | | | | | | | (18), (23), (24), (25), (28), (29), (32), (37),
% 159.62/28.27 | | | | | | | | | | (38), (39), (40), (43), (44), (45), (46), (47),
% 159.62/28.27 | | | | | | | | | | (48), (51), (52), (53), (54), (55), (58), (59),
% 159.62/28.27 | | | | | | | | | | (62), (63), (64), (67), (76), (77), (78), (83),
% 159.62/28.27 | | | | | | | | | | (86), (87), (88), (92), (93), (95), (96), (98),
% 159.62/28.27 | | | | | | | | | | (101), (103), (105), (110), (112), (113), (121),
% 159.62/28.27 | | | | | | | | | | (122), (202), (203) are inconsistent by sub-proof
% 159.62/28.27 | | | | | | | | | | #736.
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | (204) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 159.62/28.27 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | BETA: splitting (204) gives:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (205) all_58_11 = e3 & op(e1, e0) = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | ALPHA: (205) implies:
% 159.62/28.27 | | | | | | | | | | | (206) all_58_11 = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | BETA: splitting (40) gives:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | (207) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 159.62/28.27 | | | | | | | | | | | | & op(e1, e2) = e2)
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | REF_CLOSE: (23), (38), (43), (44), (47), (53), (55), (78),
% 159.62/28.27 | | | | | | | | | | | | (83), (103), (105), (110), (189), (207) are
% 159.62/28.27 | | | | | | | | | | | | inconsistent by sub-proof #720.
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | (208) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 159.62/28.27 | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | BETA: splitting (208) gives:
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | (209) all_58_8 = e2 & op(e1, e1) = e2
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | REF_CLOSE: (34), (43), (47), (55), (58), (76), (78), (83),
% 159.62/28.27 | | | | | | | | | | | | | (121), (209) are inconsistent by sub-proof #1338.
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | (210) all_58_11 = e2 & op(e1, e0) = e2
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | REF_CLOSE: (23), (38), (43), (44), (47), (53), (55), (78),
% 159.62/28.27 | | | | | | | | | | | | | (83), (103), (105), (110), (202), (206), (210) are
% 159.62/28.27 | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (211) all_58_15 = e3 & op(e0, e0) = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | ALPHA: (211) implies:
% 159.62/28.27 | | | | | | | | | | | (212) all_58_15 = e3
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | COMBINE_EQS: (199), (212) imply:
% 159.62/28.27 | | | | | | | | | | | (213) e3 = e1
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | SIMP: (213) implies:
% 159.62/28.27 | | | | | | | | | | | (214) e3 = e1
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | COMBINE_EQS: (202), (214) imply:
% 159.62/28.27 | | | | | | | | | | | (215) all_58_12 = e1
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.27 | | | | | | | | | | | (23), (24), (25), (28), (29), (32), (37), (38),
% 159.62/28.27 | | | | | | | | | | | (39), (40), (43), (44), (45), (46), (47), (48),
% 159.62/28.27 | | | | | | | | | | | (52), (53), (54), (55), (58), (59), (62), (63),
% 159.62/28.27 | | | | | | | | | | | (64), (67), (76), (77), (78), (83), (86), (87),
% 159.62/28.27 | | | | | | | | | | | (88), (92), (93), (95), (96), (98), (101), (103),
% 159.62/28.27 | | | | | | | | | | | (105), (110), (112), (113), (215) are inconsistent
% 159.62/28.27 | | | | | | | | | | | by sub-proof #747.
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | (216) all_58_13 = e3 & op(e0, e2) = e3
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | REF_CLOSE: (9), (96), (105), (216) are inconsistent by
% 159.62/28.27 | | | | | | | | | sub-proof #1449.
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | End of split
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | (217) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 159.62/28.27 | | | | | | | | op(e0, e0) = e3)
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | BETA: splitting (217) gives:
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | (218) all_58_14 = e3 & op(e0, e1) = e3
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | REF_CLOSE: (34), (110), (218) are inconsistent by sub-proof
% 159.62/28.27 | | | | | | | | | #1465.
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | (219) all_58_15 = e3 & op(e0, e0) = e3
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | REF_CLOSE: (55), (199), (219) are inconsistent by sub-proof
% 159.62/28.27 | | | | | | | | | #1054.
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | End of split
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | End of split
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | End of split
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | End of split
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | Case 2:
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | (220) all_58_13 = e1 & op(e0, e2) = e1
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | ALPHA: (220) implies:
% 159.62/28.27 | | | | | (221) all_58_13 = e1
% 159.62/28.27 | | | | | (222) op(e0, e2) = e1
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | GROUND_INST: instantiating (105) with all_52_11, e2, e1, e0,
% 159.62/28.27 | | | | | simplifying with (70), (71) gives:
% 159.62/28.27 | | | | | (223) all_52_11 = e2
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | GROUND_INST: instantiating (105) with all_52_7, e1, e2, e0,
% 159.62/28.27 | | | | | simplifying with (96), (222) gives:
% 159.62/28.27 | | | | | (224) all_52_7 = e1
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | GROUND_INST: instantiating (105) with all_14_0, all_22_0, e2, e1,
% 159.62/28.27 | | | | | simplifying with (19), (84) gives:
% 159.62/28.27 | | | | | (225) all_22_0 = all_14_0
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (118), (224) imply:
% 159.62/28.27 | | | | | (226) ~ (all_52_3 = e1)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (106), (223) imply:
% 159.62/28.27 | | | | | (227) ~ (all_52_3 = e2)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (81), (224) imply:
% 159.62/28.27 | | | | | (228) ~ (all_52_4 = e1)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (17), (223), (224) imply:
% 159.62/28.27 | | | | | (229) ~ (e2 = e1)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (56), (224) imply:
% 159.62/28.27 | | | | | (230) ~ (all_14_0 = e1)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | SIMP: (230) implies:
% 159.62/28.27 | | | | | (231) ~ (all_14_0 = e1)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (94), (224) imply:
% 159.62/28.27 | | | | | (232) ~ (all_4_2 = e1)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | SIMP: (232) implies:
% 159.62/28.27 | | | | | (233) ~ (all_4_2 = e1)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (9), (224) imply:
% 159.62/28.27 | | | | | (234) ~ (e3 = e1)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (72), (223) imply:
% 159.62/28.27 | | | | | (235) ~ (all_52_9 = e2)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (49), (223) imply:
% 159.62/28.27 | | | | | (236) ~ (all_6_2 = e2)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (107), (223) imply:
% 159.62/28.27 | | | | | (237) ~ (all_4_2 = e2)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (14), (223) imply:
% 159.62/28.27 | | | | | (238) ~ (e3 = e2)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | REDUCE: (85), (225) imply:
% 159.62/28.27 | | | | | (239) ~ (all_14_0 = e0)
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | BETA: splitting (1) gives:
% 159.62/28.27 | | | | |
% 159.62/28.27 | | | | | Case 1:
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | (240) all_54_9 = e3
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | COMBINE_EQS: (90), (240) imply:
% 159.62/28.27 | | | | | | (241) all_14_0 = e3
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | SIMP: (241) implies:
% 159.62/28.27 | | | | | | (242) all_14_0 = e3
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | REDUCE: (30), (242) imply:
% 159.62/28.27 | | | | | | (243) $false
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | CLOSE: (243) is inconsistent.
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | Case 2:
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | (244) ~ (all_54_9 = e3)
% 159.62/28.27 | | | | | | (245) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | BETA: splitting (54) gives:
% 159.62/28.27 | | | | | |
% 159.62/28.27 | | | | | | Case 1:
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | (246) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 159.62/28.27 | | | | | | | op(e2, e2) = e0)
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | BETA: splitting (246) gives:
% 159.62/28.27 | | | | | | |
% 159.62/28.27 | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | (247) all_58_1 = e0 & op(e3, e2) = e0
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | ALPHA: (247) implies:
% 159.62/28.27 | | | | | | | | (248) all_58_1 = e0
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | BETA: splitting (245) gives:
% 159.62/28.27 | | | | | | | |
% 159.62/28.27 | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | (249) all_54_9 = e2
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | COMBINE_EQS: (90), (249) imply:
% 159.62/28.27 | | | | | | | | | (250) all_14_0 = e2
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | SIMP: (250) implies:
% 159.62/28.27 | | | | | | | | | (251) all_14_0 = e2
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | REDUCE: (42), (251) imply:
% 159.62/28.27 | | | | | | | | | (252) ~ (all_52_2 = e2)
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | REDUCE: (116), (251) imply:
% 159.62/28.27 | | | | | | | | | (253) ~ (all_52_4 = e2)
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | BETA: splitting (93) gives:
% 159.62/28.27 | | | | | | | | |
% 159.62/28.27 | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | (254) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.62/28.27 | | | | | | | | | | & op(e2, e2) = e2)
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | BETA: splitting (254) gives:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (255) all_58_1 = e2 & op(e3, e2) = e2
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | REF_CLOSE: (47), (248), (255) are inconsistent by sub-proof
% 159.62/28.27 | | | | | | | | | | | #801.
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (256) all_58_3 = e2 & op(e2, e2) = e2
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | REF_CLOSE: (86), (110), (256) are inconsistent by sub-proof
% 159.62/28.27 | | | | | | | | | | | #719.
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | (257) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2
% 159.62/28.27 | | | | | | | | | | & op(e0, e2) = e2)
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | BETA: splitting (257) gives:
% 159.62/28.27 | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | (258) all_58_7 = e2 & op(e1, e2) = e2
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | ALPHA: (258) implies:
% 159.62/28.27 | | | | | | | | | | | (259) all_58_7 = e2
% 159.62/28.27 | | | | | | | | | | | (260) op(e1, e2) = e2
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | BETA: splitting (31) gives:
% 159.62/28.27 | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | (261) all_54_1 = e3
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | COMBINE_EQS: (27), (261) imply:
% 159.62/28.27 | | | | | | | | | | | | (262) all_52_4 = e3
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | REDUCE: (77), (262) imply:
% 159.62/28.27 | | | | | | | | | | | | (263) $false
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | CLOSE: (263) is inconsistent.
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | (264) ~ (all_54_1 = e3)
% 159.62/28.27 | | | | | | | | | | | | (265) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | BETA: splitting (265) gives:
% 159.62/28.27 | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | (266) all_54_1 = e2
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | COMBINE_EQS: (27), (266) imply:
% 159.62/28.27 | | | | | | | | | | | | | (267) all_52_4 = e2
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | REDUCE: (253), (267) imply:
% 159.62/28.27 | | | | | | | | | | | | | (268) $false
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | CLOSE: (268) is inconsistent.
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | (269) ~ (all_54_1 = e2)
% 159.62/28.27 | | | | | | | | | | | | | (270) all_54_1 = e1 | all_54_1 = e0
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | BETA: splitting (270) gives:
% 159.62/28.27 | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | (271) all_54_1 = e1
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | COMBINE_EQS: (27), (271) imply:
% 159.62/28.27 | | | | | | | | | | | | | | (272) all_52_4 = e1
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | REDUCE: (228), (272) imply:
% 159.62/28.27 | | | | | | | | | | | | | | (273) $false
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | CLOSE: (273) is inconsistent.
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | (274) all_54_1 = e0
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | COMBINE_EQS: (27), (274) imply:
% 159.62/28.27 | | | | | | | | | | | | | | (275) all_52_4 = e0
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | REDUCE: (36), (275) imply:
% 159.62/28.27 | | | | | | | | | | | | | | (276) ~ (all_52_12 = e0)
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | SIMP: (276) implies:
% 159.62/28.27 | | | | | | | | | | | | | | (277) ~ (all_52_12 = e0)
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | REDUCE: (77), (275) imply:
% 159.62/28.27 | | | | | | | | | | | | | | (278) ~ (e3 = e0)
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | REDUCE: (253), (275) imply:
% 159.62/28.27 | | | | | | | | | | | | | | (279) ~ (e2 = e0)
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | REDUCE: (228), (275) imply:
% 159.62/28.27 | | | | | | | | | | | | | | (280) ~ (e1 = e0)
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | REDUCE: (28), (275) imply:
% 159.62/28.27 | | | | | | | | | | | | | | (281) op(e3, e2) = e0
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 159.62/28.27 | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | (282) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 159.62/28.27 | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 159.62/28.27 | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 159.62/28.27 | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 159.62/28.27 | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.62/28.27 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 159.62/28.27 | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.62/28.27 | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 159.62/28.27 | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.62/28.27 | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 159.62/28.27 | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | (283) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 159.62/28.27 | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 159.62/28.27 | | | | | | | | | | | | | | | | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 159.62/28.27 | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 159.62/28.27 | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 159.62/28.27 | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | (284) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 159.62/28.27 | | | | | | | | | | | | | | | | | (285) op(e2, e3) = e3
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (53), (105), (110), (285) are inconsistent
% 159.62/28.27 | | | | | | | | | | | | | | | | | by sub-proof #1159.
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | (286) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 159.62/28.27 | | | | | | | | | | | | | | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (287) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (288) ~ (all_56_12 = e3)
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (289) op(e3, e2) = e2
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (290) all_54_3 = e3
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (290) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (291) all_52_12 = e3
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | REDUCE: (2), (291) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (292) $false
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent.
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (293) ~ (all_54_3 = e3)
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (294) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (295) all_54_3 = e2
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (295) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (296) all_52_12 = e2
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (296) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (297) ~ (all_52_13 = e2)
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (105) with e0, e2, e2, e3,
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | simplifying with (281), (289) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (298) e2 = e0
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (298) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (299) all_58_7 = e0
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (13), (16), (18), (21), (23), (24), (25), (26),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (34), (37),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (43), (44), (45), (46), (47),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (48), (50), (51), (52), (53), (54), (55), (57),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (58), (59), (60), (62), (63), (64), (66), (67),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (68), (69), (70), (71), (73), (74), (76), (77),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (78), (79), (82), (83), (86), (87), (88), (89),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (90), (91), (92), (93), (95), (96), (97), (98),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (99), (100), (101), (102), (103), (105), (108),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (109), (110), (111), (112), (113), (116), (117),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (121), (122), (221), (222), (228), (231), (233),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (235), (239), (245), (299) are inconsistent by
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | sub-proof #675.
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (300) all_54_3 = e1 | all_54_3 = e0
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (104), (277), (300) are inconsistent by
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | sub-proof #1289.
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (301) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | | e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (22), (41), (55), (57), (61), (63),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (65), (69), (75), (79), (87), (89), (91), (110),
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (114), (115), (117), (226), (227), (252), (301)
% 159.62/28.27 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #673.
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | End of split
% 159.62/28.27 | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | (302) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 159.62/28.27 | | | | | | | | | | | | | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.62/28.27 | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 159.62/28.27 | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.62/28.27 | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | (303) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (100), (303) are inconsistent by sub-proof
% 159.62/28.27 | | | | | | | | | | | | | | | | | #672.
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | (304) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 159.62/28.27 | | | | | | | | | | | | | | | | | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (305) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | | e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (69), (73), (99), (111), (233), (305) are
% 159.62/28.27 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1294.
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (306) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 =
% 159.62/28.27 | | | | | | | | | | | | | | | | | | e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (307) ~ (all_56_12 = e3)
% 159.62/28.27 | | | | | | | | | | | | | | | | | | (308) op(e3, e0) = e0
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (309) all_54_3 = e3
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (309) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (310) all_52_12 = e3
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | REDUCE: (2), (310) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (311) $false
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | CLOSE: (311) is inconsistent.
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (312) ~ (all_54_3 = e3)
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | (313) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (314) all_54_3 = e2
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (314) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (315) all_52_12 = e2
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (315) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (316) ~ (all_52_13 = e2)
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (315) imply:
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | (317) op(e3, e0) = e2
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (105) with e0, e2, e0, e3,
% 159.62/28.27 | | | | | | | | | | | | | | | | | | | | simplifying with (308), (317) gives:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (318) e2 = e0
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (318) imply:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (319) all_58_7 = e0
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (13), (16), (18), (21), (23), (24), (25), (26),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (34), (37),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (43), (44), (45), (46), (47),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (48), (50), (51), (52), (53), (54), (55), (57),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (58), (59), (60), (62), (63), (64), (66), (67),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (68), (69), (70), (71), (73), (74), (76), (77),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (78), (79), (82), (83), (86), (87), (88), (89),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (90), (91), (92), (93), (95), (96), (97), (98),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (99), (100), (101), (102), (103), (105), (108),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (109), (110), (111), (112), (113), (116), (117),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (121), (122), (221), (222), (228), (231), (233),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (235), (239), (245), (319) are inconsistent by
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | sub-proof #675.
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | (320) all_54_3 = e1 | all_54_3 = e0
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (104), (277), (320) are inconsistent by
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | | sub-proof #1289.
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | (321) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 159.62/28.28 | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 159.62/28.28 | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.62/28.28 | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 159.62/28.28 | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 159.62/28.28 | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 159.62/28.28 | | | | | | | | | | | | | | | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 159.62/28.28 | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 159.62/28.28 | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 159.62/28.28 | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 159.62/28.28 | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 159.62/28.28 | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.62/28.28 | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 159.62/28.28 | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | Case 1:
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | (322) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 159.62/28.28 | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 159.62/28.28 | | | | | | | | | | | | | | | | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.62/28.28 | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 159.62/28.28 | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 159.62/28.28 | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | (323) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 =
% 159.62/28.28 | | | | | | | | | | | | | | | | | e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 159.62/28.28 | | | | | | | | | | | | | | | | | (324) op(e2, e1) = e2
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (105), (235), (324) are inconsistent by
% 159.62/28.28 | | | | | | | | | | | | | | | | | sub-proof #1441.
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | (325) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.62/28.28 | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 159.62/28.28 | | | | | | | | | | | | | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 159.62/28.28 | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (326) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.62/28.28 | | | | | | | | | | | | | | | | | | e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (327) op(e1, e2) = e1
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (328) all_54_3 = e3
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (328) imply:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (329) all_52_12 = e3
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | REDUCE: (2), (329) imply:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (330) $false
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent.
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (331) ~ (all_54_3 = e3)
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (332) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (12), (18), (20), (23), (24), (25), (28), (32),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (34), (37), (38), (39), (40), (43), (44), (45),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (46), (48), (51), (52), (53), (54), (55), (58),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (59), (62), (63), (64), (67), (70), (71), (76),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (77), (80), (83), (86), (87), (88), (92), (93),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (95), (96), (98), (101), (103), (104), (105),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (112), (113), (121), (122), (221), (248), (259),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | (260), (277), (327), (332) are inconsistent by
% 159.62/28.28 | | | | | | | | | | | | | | | | | | | sub-proof #671.
% 159.62/28.28 | | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (333) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 =
% 159.62/28.28 | | | | | | | | | | | | | | | | | | e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (334) op(e0, e2) = e2
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (96), (105), (222), (334) are inconsistent
% 159.62/28.28 | | | | | | | | | | | | | | | | | | by sub-proof #1319.
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | (335) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 159.62/28.28 | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 159.62/28.28 | | | | | | | | | | | | | | | | (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 159.62/28.28 | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 159.62/28.28 | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 159.62/28.28 | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | (336) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 =
% 159.62/28.28 | | | | | | | | | | | | | | | | | e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 159.62/28.28 | | | | | | | | | | | | | | | | | (337) op(e0, e2) = e0
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (338) all_54_3 = e3
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (338) imply:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (339) all_52_12 = e3
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | REDUCE: (2), (339) imply:
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (340) $false
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent.
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (341) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (55), (80), (83), (86), (104), (105), (221),
% 159.62/28.28 | | | | | | | | | | | | | | | | | | (222), (248), (259), (277), (337), (341) are
% 159.62/28.28 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #670.
% 159.62/28.28 | | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | (342) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 =
% 159.62/28.28 | | | | | | | | | | | | | | | | | e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 159.62/28.28 | | | | | | | | | | | | | | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 =
% 159.62/28.28 | | | | | | | | | | | | | | | | | e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (70), (71), (78), (105), (342) are
% 159.62/28.28 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1293.
% 159.62/28.28 | | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | (343) all_58_13 = e2 & op(e0, e2) = e2
% 159.62/28.28 | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | ALPHA: (343) implies:
% 159.62/28.28 | | | | | | | | | | | (344) op(e0, e2) = e2
% 159.62/28.28 | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | | REF_CLOSE: (78), (96), (105), (222), (344) are inconsistent
% 159.62/28.28 | | | | | | | | | | | by sub-proof #1319.
% 159.62/28.28 | | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | | |
% 159.62/28.28 | | | | | | | | | End of split
% 159.62/28.28 | | | | | | | | |
% 159.62/28.28 | | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | | |
% 159.62/28.28 | | | | | | | | | (345) all_54_9 = e1 | all_54_9 = e0
% 159.62/28.28 | | | | | | | | |
% 159.62/28.28 | | | | | | | | | REF_CLOSE: (90), (231), (239), (345) are inconsistent by
% 159.62/28.28 | | | | | | | | | sub-proof #676.
% 159.62/28.28 | | | | | | | | |
% 159.62/28.28 | | | | | | | | End of split
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | | (346) all_58_3 = e0 & op(e2, e2) = e0
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | | REF_CLOSE: (43), (86), (346) are inconsistent by sub-proof #756.
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | End of split
% 159.62/28.28 | | | | | | |
% 159.62/28.28 | | | | | | Case 2:
% 159.62/28.28 | | | | | | |
% 159.62/28.28 | | | | | | | (347) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 159.62/28.28 | | | | | | | op(e0, e2) = e0)
% 159.62/28.28 | | | | | | |
% 159.62/28.28 | | | | | | | BETA: splitting (347) gives:
% 159.62/28.28 | | | | | | |
% 159.62/28.28 | | | | | | | Case 1:
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | | (348) all_58_7 = e0 & op(e1, e2) = e0
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | | ALPHA: (348) implies:
% 159.62/28.28 | | | | | | | | (349) all_58_7 = e0
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.62/28.28 | | | | | | | | (16), (18), (21), (23), (24), (25), (26), (27), (28),
% 159.62/28.28 | | | | | | | | (29), (30), (31), (32), (34), (37), (38), (39), (40),
% 159.62/28.28 | | | | | | | | (43), (44), (45), (46), (47), (48), (50), (51), (52),
% 159.62/28.28 | | | | | | | | (53), (54), (55), (57), (58), (59), (60), (62), (63),
% 159.62/28.28 | | | | | | | | (64), (66), (67), (68), (69), (70), (71), (73), (74),
% 159.62/28.28 | | | | | | | | (76), (77), (78), (79), (82), (83), (86), (87), (88),
% 159.62/28.28 | | | | | | | | (89), (90), (91), (92), (93), (95), (96), (97), (98),
% 159.62/28.28 | | | | | | | | (99), (100), (101), (102), (103), (105), (108),
% 159.62/28.28 | | | | | | | | (109), (110), (111), (112), (113), (116), (117),
% 159.62/28.28 | | | | | | | | (121), (122), (221), (222), (228), (231), (233),
% 159.62/28.28 | | | | | | | | (235), (239), (245), (349) are inconsistent by
% 159.62/28.28 | | | | | | | | sub-proof #675.
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | Case 2:
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | | (350) all_58_13 = e0 & op(e0, e2) = e0
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | | REF_CLOSE: (83), (221), (350) are inconsistent by sub-proof
% 159.62/28.28 | | | | | | | | #1409.
% 159.62/28.28 | | | | | | | |
% 159.62/28.28 | | | | | | | End of split
% 159.62/28.28 | | | | | | |
% 159.62/28.28 | | | | | | End of split
% 159.62/28.28 | | | | | |
% 159.62/28.28 | | | | | End of split
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | End of split
% 159.62/28.28 | | | |
% 159.62/28.28 | | | End of split
% 159.62/28.28 | | |
% 159.62/28.28 | | Case 2:
% 159.62/28.28 | | |
% 159.62/28.28 | | | (351) all_58_5 = e3 & op(e2, e1) = e3
% 159.62/28.28 | | |
% 159.62/28.28 | | | ALPHA: (351) implies:
% 159.62/28.28 | | | (352) op(e2, e1) = e3
% 159.62/28.28 | | |
% 159.62/28.28 | | | REF_CLOSE: (37), (48), (105), (352) are inconsistent by sub-proof #1196.
% 159.62/28.28 | | |
% 159.62/28.28 | | End of split
% 159.62/28.28 | |
% 159.62/28.28 | Case 2:
% 159.62/28.28 | |
% 159.62/28.28 | | (353) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 159.62/28.28 | | e3)
% 159.62/28.28 | |
% 159.62/28.28 | | REF_CLOSE: (8), (34), (63), (105), (110), (353) are inconsistent by
% 159.62/28.28 | | sub-proof #1243.
% 159.62/28.28 | |
% 159.62/28.28 | End of split
% 159.62/28.28 |
% 159.62/28.28 End of proof
% 159.62/28.28
% 159.62/28.28 Sub-proof #670 shows that the following formulas are inconsistent:
% 159.62/28.28 ----------------------------------------------------------------
% 159.62/28.28 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.28 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.28 (2) all_58_1 = e0
% 159.62/28.28 (3) all_58_7 = e2
% 159.62/28.28 (4) all_58_13 = e1
% 159.62/28.28 (5) op(e0, e2) = e1
% 159.62/28.28 (6) ~ (e3 = e1)
% 159.62/28.28 (7) op(e0, e2) = e0
% 159.62/28.28 (8) all_54_3 = all_52_12
% 159.62/28.28 (9) ~ (all_52_12 = e0)
% 159.62/28.28 (10) ~ (e1 = e0)
% 159.62/28.28 (11) all_58_3 = e3
% 159.62/28.28 (12) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.62/28.28 (13) ~ (all_52_12 = e1)
% 159.62/28.28 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.28
% 159.62/28.28 Begin of proof
% 159.62/28.28 |
% 159.62/28.28 | BETA: splitting (12) gives:
% 159.62/28.28 |
% 159.62/28.28 | Case 1:
% 159.62/28.28 | |
% 159.62/28.28 | | (15) all_54_3 = e2
% 159.62/28.28 | |
% 159.62/28.28 | | COMBINE_EQS: (8), (15) imply:
% 159.62/28.28 | | (16) all_52_12 = e2
% 159.62/28.28 | |
% 159.62/28.28 | | REDUCE: (13), (16) imply:
% 159.62/28.28 | | (17) ~ (e2 = e1)
% 159.62/28.28 | |
% 159.62/28.28 | | GROUND_INST: instantiating (14) with e1, e0, e2, e0, simplifying with (5),
% 159.62/28.28 | | (7) gives:
% 159.62/28.28 | | (18) e1 = e0
% 159.62/28.28 | |
% 159.62/28.28 | | COMBINE_EQS: (4), (18) imply:
% 159.62/28.28 | | (19) all_58_13 = e0
% 159.62/28.28 | |
% 159.62/28.28 | | REF_CLOSE: (1), (2), (3), (6), (10), (11), (17), (19) are inconsistent by
% 159.62/28.28 | | sub-proof #857.
% 159.62/28.28 | |
% 159.62/28.28 | Case 2:
% 159.62/28.28 | |
% 159.62/28.28 | | (20) all_54_3 = e1 | all_54_3 = e0
% 159.62/28.28 | |
% 159.62/28.28 | | REF_CLOSE: (8), (9), (13), (20) are inconsistent by sub-proof #1289.
% 159.62/28.28 | |
% 159.62/28.28 | End of split
% 159.62/28.28 |
% 159.62/28.28 End of proof
% 159.62/28.28
% 159.62/28.28 Sub-proof #671 shows that the following formulas are inconsistent:
% 159.62/28.28 ----------------------------------------------------------------
% 159.62/28.28 (1) ~ (all_52_12 = e3)
% 159.62/28.28 (2) op(e3, e1) = e3
% 159.62/28.28 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.62/28.28 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.62/28.28 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.28 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.28 (5) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.28 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.28 (6) all_58_1 = e0
% 159.62/28.28 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.28 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.28 (8) op(e1, e1) = all_6_2
% 159.62/28.28 (9) ~ (all_52_7 = e3)
% 159.62/28.28 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.28 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.62/28.28 e1)
% 159.62/28.28 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.62/28.28 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.62/28.28 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.62/28.28 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.62/28.28 (13) all_58_7 = e2
% 159.62/28.28 (14) all_58_0 = e1
% 159.62/28.28 (15) ~ (all_52_12 = all_4_2)
% 159.62/28.28 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.28 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.28 (17) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.28 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.28 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.62/28.28 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.62/28.28 (19) op(e3, e2) = all_52_4
% 159.62/28.28 (20) op(e1, e2) = e2
% 159.62/28.28 (21) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.62/28.28 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.62/28.28 (22) all_58_14 = e2
% 159.62/28.28 (23) op(e2, e1) = all_52_9
% 159.62/28.28 (24) op(e2, e3) = all_52_1
% 159.62/28.28 (25) ~ (all_52_13 = e3)
% 159.62/28.28 (26) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.62/28.28 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.62/28.28 (27) all_58_13 = e1
% 159.62/28.28 (28) ~ (e3 = e0)
% 159.62/28.28 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.28 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.28 (30) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.62/28.28 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.62/28.28 (31) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.28 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.28 e2)
% 159.62/28.28 (32) ~ (all_52_9 = e3)
% 159.62/28.28 (33) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.62/28.28 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.62/28.28 (34) op(e2, e0) = all_52_13
% 159.62/28.28 (35) op(e2, e3) = e2
% 159.62/28.28 (36) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.28 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.28 (37) ~ (e3 = e1)
% 159.62/28.28 (38) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.62/28.28 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.62/28.28 (39) op(e1, e2) = all_52_6
% 159.62/28.28 (40) op(e1, e2) = e1
% 159.62/28.28 (41) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.28 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.28 (42) ~ (all_6_2 = e3)
% 159.62/28.28 (43) op(e0, e0) = all_4_2
% 159.62/28.28 (44) op(e3, e3) = e1
% 159.62/28.28 (45) op(e0, e1) = e2
% 159.62/28.28 (46) op(e0, e1) = all_52_11
% 159.62/28.28 (47) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.62/28.28 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.62/28.28 (48) ~ (all_52_4 = e3)
% 159.62/28.28 (49) all_54_3 = all_52_12
% 159.62/28.28 (50) ~ (all_52_12 = e0)
% 159.62/28.28 (51) ~ (e1 = e0)
% 159.62/28.28 (52) all_58_4 = e3
% 159.62/28.28 (53) all_58_3 = e3
% 159.62/28.28 (54) ~ (all_6_2 = e2)
% 159.62/28.28 (55) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.62/28.28 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.62/28.28 e3)
% 159.62/28.28 (56) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.62/28.28 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.62/28.28 (57) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.62/28.28 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.28 (58) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 159.62/28.28 (59) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.62/28.28 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.62/28.28 (60) op(e0, e2) = all_52_7
% 159.62/28.28 (61) op(e3, e3) = all_22_1
% 159.62/28.28 (62) ~ (all_52_6 = e3)
% 159.62/28.28 (63) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.28 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.28 (64) ~ (all_52_12 = e1)
% 159.62/28.28 (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.28 (66) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.62/28.28 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.28 (67) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.28 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.28 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.28 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.28
% 159.62/28.28 Begin of proof
% 159.62/28.28 |
% 159.62/28.28 | BETA: splitting (58) gives:
% 159.62/28.28 |
% 159.62/28.28 | Case 1:
% 159.62/28.28 | |
% 159.62/28.28 | | (68) all_54_3 = e2
% 159.62/28.28 | |
% 159.62/28.28 | | COMBINE_EQS: (49), (68) imply:
% 159.62/28.28 | | (69) all_52_12 = e2
% 159.62/28.28 | |
% 159.62/28.28 | | REDUCE: (15), (69) imply:
% 159.62/28.28 | | (70) ~ (all_4_2 = e2)
% 159.62/28.28 | |
% 159.62/28.28 | | SIMP: (70) implies:
% 159.62/28.28 | | (71) ~ (all_4_2 = e2)
% 159.62/28.28 | |
% 159.62/28.28 | | REDUCE: (1), (69) imply:
% 159.62/28.28 | | (72) ~ (e3 = e2)
% 159.62/28.28 | |
% 159.62/28.28 | | SIMP: (72) implies:
% 159.62/28.28 | | (73) ~ (e3 = e2)
% 159.62/28.28 | |
% 159.62/28.28 | | REDUCE: (64), (69) imply:
% 159.62/28.28 | | (74) ~ (e2 = e1)
% 159.62/28.28 | |
% 159.62/28.28 | | REDUCE: (50), (69) imply:
% 159.62/28.28 | | (75) ~ (e2 = e0)
% 159.62/28.28 | |
% 159.62/28.28 | | GROUND_INST: instantiating (65) with e1, e2, e2, e1, simplifying with (20),
% 159.62/28.28 | | (40) gives:
% 159.62/28.28 | | (76) e2 = e1
% 159.62/28.28 | |
% 159.62/28.28 | | COMBINE_EQS: (13), (76) imply:
% 159.62/28.28 | | (77) all_58_7 = e1
% 159.62/28.28 | |
% 159.62/28.28 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 159.62/28.28 | | (16), (17), (18), (19), (21), (22), (23), (24), (25), (26), (27),
% 159.62/28.28 | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 159.62/28.28 | | (39), (41), (42), (43), (44), (45), (46), (47), (48), (51), (52),
% 159.62/28.28 | | (53), (54), (55), (56), (57), (59), (60), (61), (62), (63), (65),
% 159.62/28.28 | | (66), (67), (71), (73), (74), (75), (77) are inconsistent by
% 159.62/28.28 | | sub-proof #723.
% 159.62/28.28 | |
% 159.62/28.28 | Case 2:
% 159.62/28.28 | |
% 159.62/28.28 | | (78) all_54_3 = e1 | all_54_3 = e0
% 159.62/28.28 | |
% 159.62/28.28 | | REF_CLOSE: (49), (50), (64), (78) are inconsistent by sub-proof #1289.
% 159.62/28.28 | |
% 159.62/28.28 | End of split
% 159.62/28.28 |
% 159.62/28.28 End of proof
% 159.62/28.28
% 159.62/28.28 Sub-proof #672 shows that the following formulas are inconsistent:
% 159.62/28.28 ----------------------------------------------------------------
% 159.62/28.28 (1) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.62/28.28 op(e1, e3) = e1
% 159.62/28.28 (2) all_56_1 = e3
% 159.62/28.28 (3) ~ (e3 = e1)
% 159.62/28.28
% 159.62/28.28 Begin of proof
% 159.62/28.28 |
% 159.62/28.28 | ALPHA: (1) implies:
% 159.62/28.28 | (4) all_56_1 = e1
% 159.62/28.28 |
% 159.62/28.28 | COMBINE_EQS: (2), (4) imply:
% 159.62/28.28 | (5) e3 = e1
% 159.62/28.28 |
% 159.62/28.28 | REDUCE: (3), (5) imply:
% 159.62/28.28 | (6) $false
% 159.62/28.28 |
% 159.62/28.28 | CLOSE: (6) is inconsistent.
% 159.62/28.28 |
% 159.62/28.28 End of proof
% 159.62/28.28
% 159.62/28.28 Sub-proof #673 shows that the following formulas are inconsistent:
% 159.62/28.28 ----------------------------------------------------------------
% 159.62/28.28 (1) ~ (all_52_3 = e1)
% 159.62/28.28 (2) all_54_10 = all_6_2
% 159.62/28.28 (3) ~ (all_52_2 = all_52_3)
% 159.62/28.28 (4) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 159.62/28.28 (5) ~ (all_52_2 = all_6_2)
% 159.62/28.28 (6) ~ (all_52_3 = e2)
% 159.62/28.28 (7) ~ (e3 = e1)
% 159.62/28.28 (8) all_56_12 = e1
% 159.62/28.28 (9) ~ (all_52_3 = all_4_2)
% 159.62/28.28 (10) ~ (all_6_2 = e3)
% 159.62/28.28 (11) all_54_8 = all_52_2
% 159.62/28.28 (12) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 &
% 159.62/28.28 op(e1, e3) = e3
% 159.62/28.28 (13) all_56_15 = all_4_2
% 159.62/28.28 (14) ~ (all_52_2 = e1)
% 159.62/28.28 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 159.62/28.28 (16) ~ (all_52_2 = e2)
% 159.62/28.28 (17) ~ (all_6_2 = e2)
% 159.62/28.28 (18) all_56_14 = all_6_2
% 159.62/28.28 (19) all_56_13 = e3
% 159.62/28.28 (20) ~ (e3 = e2)
% 159.62/28.28 (21) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 159.62/28.28 (22) all_54_12 = all_52_3
% 159.62/28.28 (23) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.62/28.28
% 159.62/28.28 Begin of proof
% 159.62/28.28 |
% 159.62/28.28 | ALPHA: (12) implies:
% 159.62/28.28 | (24) ~ (all_56_14 = e1)
% 159.62/28.28 |
% 159.62/28.28 | REDUCE: (18), (24) imply:
% 159.62/28.28 | (25) ~ (all_6_2 = e1)
% 159.62/28.28 |
% 159.62/28.28 | BETA: splitting (23) gives:
% 159.62/28.28 |
% 159.62/28.28 | Case 1:
% 159.62/28.28 | |
% 159.62/28.28 | | (26) all_56_12 = e3
% 159.62/28.28 | |
% 159.62/28.28 | | COMBINE_EQS: (8), (26) imply:
% 159.62/28.28 | | (27) e3 = e1
% 159.62/28.28 | |
% 159.62/28.28 | | REDUCE: (7), (27) imply:
% 159.62/28.28 | | (28) $false
% 159.62/28.28 | |
% 159.62/28.28 | | CLOSE: (28) is inconsistent.
% 159.62/28.28 | |
% 159.62/28.28 | Case 2:
% 159.62/28.28 | |
% 159.62/28.28 | | (29) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.62/28.28 | |
% 159.62/28.28 | | BETA: splitting (29) gives:
% 159.62/28.28 | |
% 159.62/28.28 | | Case 1:
% 159.62/28.28 | | |
% 159.62/28.28 | | | (30) all_56_13 = e2
% 159.62/28.28 | | |
% 159.62/28.28 | | | REF_CLOSE: (19), (20), (30) are inconsistent by sub-proof #674.
% 159.62/28.28 | | |
% 159.62/28.28 | | Case 2:
% 159.62/28.28 | | |
% 159.62/28.28 | | | (31) all_56_14 = e1 | all_56_15 = e0
% 159.62/28.28 | | |
% 159.62/28.28 | | | BETA: splitting (31) gives:
% 159.62/28.28 | | |
% 159.62/28.28 | | | Case 1:
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | (32) all_56_14 = e1
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | COMBINE_EQS: (18), (32) imply:
% 159.62/28.28 | | | | (33) all_6_2 = e1
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | REDUCE: (25), (33) imply:
% 159.62/28.28 | | | | (34) $false
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | CLOSE: (34) is inconsistent.
% 159.62/28.28 | | | |
% 159.62/28.28 | | | Case 2:
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | (35) all_56_15 = e0
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | COMBINE_EQS: (13), (35) imply:
% 159.62/28.28 | | | | (36) all_4_2 = e0
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | REDUCE: (9), (36) imply:
% 159.62/28.28 | | | | (37) ~ (all_52_3 = e0)
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | BETA: splitting (21) gives:
% 159.62/28.28 | | | |
% 159.62/28.28 | | | | Case 1:
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | | (38) all_54_12 = e3
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | | COMBINE_EQS: (22), (38) imply:
% 159.62/28.28 | | | | | (39) all_52_3 = e3
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | | SIMP: (39) implies:
% 159.62/28.28 | | | | | (40) all_52_3 = e3
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | | REDUCE: (3), (40) imply:
% 159.62/28.28 | | | | | (41) ~ (all_52_2 = e3)
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | | REF_CLOSE: (2), (4), (5), (10), (11), (14), (15), (16), (17), (25),
% 159.62/28.28 | | | | | (41) are inconsistent by sub-proof #1229.
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | Case 2:
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | | (42) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | | REF_CLOSE: (1), (6), (22), (37), (42) are inconsistent by sub-proof
% 159.62/28.28 | | | | | #1098.
% 159.62/28.28 | | | | |
% 159.62/28.28 | | | | End of split
% 159.62/28.28 | | | |
% 159.62/28.28 | | | End of split
% 159.62/28.28 | | |
% 159.62/28.28 | | End of split
% 159.62/28.28 | |
% 159.62/28.28 | End of split
% 159.62/28.28 |
% 159.62/28.28 End of proof
% 159.62/28.28
% 159.62/28.28 Sub-proof #674 shows that the following formulas are inconsistent:
% 159.62/28.28 ----------------------------------------------------------------
% 159.62/28.29 (1) all_56_13 = e3
% 159.62/28.29 (2) all_56_13 = e2
% 159.62/28.29 (3) ~ (e3 = e2)
% 159.62/28.29
% 159.62/28.29 Begin of proof
% 159.62/28.29 |
% 159.62/28.29 | COMBINE_EQS: (1), (2) imply:
% 159.62/28.29 | (4) e3 = e2
% 159.62/28.29 |
% 159.62/28.29 | SIMP: (4) implies:
% 159.62/28.29 | (5) e3 = e2
% 159.62/28.29 |
% 159.62/28.29 | REDUCE: (3), (5) imply:
% 159.62/28.29 | (6) $false
% 159.62/28.29 |
% 159.62/28.29 | CLOSE: (6) is inconsistent.
% 159.62/28.29 |
% 159.62/28.29 End of proof
% 159.62/28.29
% 159.62/28.29 Sub-proof #675 shows that the following formulas are inconsistent:
% 159.62/28.29 ----------------------------------------------------------------
% 159.62/28.29 (1) op(e3, e1) = e3
% 159.62/28.29 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.62/28.29 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.62/28.29 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.29 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.62/28.29 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.62/28.29 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.29 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.62/28.29 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.62/28.29 (6) op(e1, e1) = all_6_2
% 159.62/28.29 (7) ~ (all_52_7 = e3)
% 159.62/28.29 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.62/28.29 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.62/28.29 (9) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.62/28.29 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.62/28.29 (10) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.62/28.29 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.62/28.29 (11) ~ (all_14_0 = e0)
% 159.62/28.29 (12) all_54_10 = all_6_2
% 159.62/28.29 (13) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.62/28.29 (14) all_58_0 = e1
% 159.62/28.29 (15) ~ (all_52_14 = all_14_0)
% 159.62/28.29 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.62/28.29 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.62/28.29 (17) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.62/28.29 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.62/28.29 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.62/28.29 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.62/28.29 (19) ~ (all_14_0 = all_6_2)
% 159.62/28.29 (20) all_54_1 = all_52_4
% 159.62/28.29 (21) op(e3, e2) = all_52_4
% 159.62/28.29 (22) ~ (all_4_2 = e2)
% 159.62/28.29 (23) all_58_7 = e0
% 159.62/28.29 (24) ~ (all_14_0 = e3)
% 159.62/28.29 (25) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.62/28.29 (26) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.62/28.29 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.62/28.29 (27) all_58_14 = e2
% 159.62/28.29 (28) op(e2, e1) = all_52_9
% 159.62/28.29 (29) op(e2, e3) = all_52_1
% 159.62/28.29 (30) ~ (all_52_13 = e3)
% 159.62/28.29 (31) ~ (all_14_0 = e1)
% 159.62/28.29 (32) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.62/28.29 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.62/28.29 (33) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 159.62/28.29 (34) all_58_13 = e1
% 159.62/28.29 (35) ~ (e3 = e0)
% 159.62/28.29 (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.62/28.29 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.62/28.29 (37) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.62/28.29 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.62/28.29 (38) op(e0, e2) = e1
% 159.62/28.29 (39) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.29 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.62/28.29 e2)
% 159.62/28.29 (40) ~ (e2 = e0)
% 159.62/28.29 (41) ~ (all_52_9 = e3)
% 159.62/28.29 (42) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 159.62/28.29 (43) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.62/28.29 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.62/28.29 (44) op(e2, e0) = all_52_13
% 159.62/28.29 (45) op(e2, e3) = e2
% 159.62/28.29 (46) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.29 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.62/28.29 (47) ~ (e3 = e1)
% 159.62/28.29 (48) all_56_12 = e1
% 159.62/28.29 (49) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.62/28.29 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.62/28.29 (50) op(e1, e2) = all_52_6
% 159.62/28.29 (51) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 159.62/28.29 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.62/28.29 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 159.62/28.29 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.62/28.29 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.62/28.29 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.62/28.29 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 159.62/28.29 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 159.62/28.29 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 159.62/28.29 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.62/28.29 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.62/28.29 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 159.62/28.29 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.62/28.29 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.62/28.29 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 159.62/28.29 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 159.62/28.29 = e0)
% 159.62/28.29 (52) ~ (all_4_2 = e1)
% 159.62/28.29 (53) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.62/28.29 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.62/28.29 (54) ~ (all_6_2 = e3)
% 159.62/28.29 (55) op(e0, e0) = all_4_2
% 159.62/28.29 (56) all_54_7 = all_52_13
% 159.62/28.29 (57) op(e3, e3) = e1
% 159.62/28.29 (58) ~ (all_52_13 = e2)
% 159.62/28.29 (59) all_56_15 = all_4_2
% 159.62/28.29 (60) op(e0, e1) = e2
% 159.62/28.29 (61) op(e0, e1) = all_52_11
% 159.62/28.29 (62) ~ (all_52_4 = e1)
% 159.62/28.29 (63) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 159.62/28.29 (64) ~ (all_52_13 = all_4_2)
% 159.62/28.29 (65) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.62/28.29 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.62/28.29 (66) ~ (all_52_4 = e3)
% 159.62/28.29 (67) ~ (e2 = e1)
% 159.62/28.29 (68) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 159.62/28.29 (69) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.62/28.29 (70) ~ (e1 = e0)
% 159.62/28.29 (71) all_58_4 = e3
% 159.62/28.29 (72) all_58_3 = e3
% 159.62/28.29 (73) ~ (all_6_2 = e2)
% 159.62/28.29 (74) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.62/28.29 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.62/28.29 e3)
% 159.62/28.29 (75) all_56_14 = all_6_2
% 159.62/28.29 (76) all_54_9 = all_14_0
% 159.62/28.29 (77) all_56_13 = e3
% 159.62/28.29 (78) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.62/28.29 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.62/28.29 (79) ~ (all_52_9 = e2)
% 159.62/28.29 (80) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.62/28.29 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.62/28.29 (81) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.62/28.29 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.62/28.29 (82) op(e0, e2) = all_52_7
% 159.62/28.29 (83) op(e1, e0) = all_52_14
% 159.62/28.29 (84) op(e3, e3) = all_22_1
% 159.62/28.29 (85) all_54_15 = all_4_2
% 159.62/28.29 (86) all_56_1 = e3
% 159.62/28.29 (87) ~ (all_52_6 = e3)
% 159.62/28.29 (88) ~ (all_52_14 = all_6_2)
% 159.62/28.29 (89) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.62/28.29 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.62/28.29 (90) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.62/28.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.62/28.29 (91) all_54_11 = all_52_14
% 159.62/28.29 (92) ~ (all_52_13 = all_52_14)
% 159.62/28.29 (93) ~ (e3 = e2)
% 159.62/28.29 (94) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.62/28.29 (95) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.62/28.29 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.29 (96) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.62/28.29 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.62/28.29 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.62/28.29 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.62/28.29 (97) ~ (all_52_4 = all_14_0)
% 159.62/28.29 (98) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.62/28.29
% 159.62/28.29 Begin of proof
% 159.62/28.29 |
% 159.62/28.29 | BETA: splitting (32) gives:
% 159.62/28.29 |
% 159.62/28.29 | Case 1:
% 159.62/28.29 | |
% 159.62/28.29 | | (99) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 159.62/28.29 | | e2)
% 159.62/28.29 | |
% 159.62/28.29 | | REF_CLOSE: (16), (23), (29), (35), (36), (40), (45), (47), (67), (70), (89),
% 159.62/28.29 | | (90), (93), (99) are inconsistent by sub-proof #744.
% 159.62/28.29 | |
% 159.62/28.29 | Case 2:
% 159.62/28.29 | |
% 159.62/28.29 | | (100) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 159.62/28.29 | | e2)
% 159.62/28.29 | |
% 159.62/28.29 | | BETA: splitting (100) gives:
% 159.62/28.29 | |
% 159.62/28.29 | | Case 1:
% 159.62/28.29 | | |
% 159.62/28.29 | | | (101) all_58_8 = e2 & op(e1, e1) = e2
% 159.62/28.29 | | |
% 159.62/28.29 | | | REF_CLOSE: (27), (35), (40), (47), (49), (65), (67), (70), (71), (101) are
% 159.62/28.29 | | | inconsistent by sub-proof #1338.
% 159.62/28.29 | | |
% 159.62/28.29 | | Case 2:
% 159.62/28.29 | | |
% 159.62/28.29 | | | (102) all_58_11 = e2 & op(e1, e0) = e2
% 159.62/28.29 | | |
% 159.62/28.29 | | | ALPHA: (102) implies:
% 159.62/28.29 | | | (103) all_58_11 = e2
% 159.62/28.29 | | |
% 159.62/28.29 | | | BETA: splitting (2) gives:
% 159.62/28.29 | | |
% 159.62/28.29 | | | Case 1:
% 159.62/28.29 | | | |
% 159.62/28.29 | | | | (104) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 159.62/28.29 | | | | = e1)
% 159.62/28.29 | | | |
% 159.62/28.29 | | | | BETA: splitting (104) gives:
% 159.62/28.29 | | | |
% 159.62/28.29 | | | | Case 1:
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | (105) all_58_6 = e1 & op(e1, e3) = e1
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | ALPHA: (105) implies:
% 159.62/28.29 | | | | | (106) all_58_6 = e1
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (16), (17),
% 159.62/28.29 | | | | | (18), (21), (22), (26), (28), (29), (30), (32), (35), (36),
% 159.62/28.29 | | | | | (37), (39), (40), (41), (43), (44), (45), (46), (47), (49),
% 159.62/28.29 | | | | | (50), (53), (54), (55), (57), (65), (66), (67), (70), (72),
% 159.62/28.29 | | | | | (73), (74), (78), (80), (81), (82), (84), (87), (89), (90),
% 159.62/28.29 | | | | | (93), (95), (96), (106) are inconsistent by sub-proof #685.
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | Case 2:
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | (107) all_58_7 = e1 & op(e1, e2) = e1
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | ALPHA: (107) implies:
% 159.62/28.29 | | | | | (108) all_58_7 = e1
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (14),
% 159.62/28.29 | | | | | (16), (17), (18), (21), (22), (26), (27), (28), (29), (30),
% 159.62/28.29 | | | | | (32), (34), (35), (36), (37), (39), (40), (41), (43), (44),
% 159.62/28.29 | | | | | (45), (46), (47), (49), (50), (53), (54), (55), (57), (60),
% 159.62/28.29 | | | | | (61), (65), (66), (67), (70), (71), (72), (73), (74), (78),
% 159.62/28.29 | | | | | (80), (81), (82), (84), (87), (89), (90), (93), (95), (96),
% 159.62/28.29 | | | | | (108) are inconsistent by sub-proof #722.
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | End of split
% 159.62/28.29 | | | |
% 159.62/28.29 | | | Case 2:
% 159.62/28.29 | | | |
% 159.62/28.29 | | | | (109) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 159.62/28.29 | | | | e0) = e1)
% 159.62/28.29 | | | |
% 159.62/28.29 | | | | BETA: splitting (109) gives:
% 159.62/28.29 | | | |
% 159.62/28.29 | | | | Case 1:
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | (110) all_58_8 = e1 & op(e1, e1) = e1
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | ALPHA: (110) implies:
% 159.62/28.29 | | | | | (111) all_58_8 = e1
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | BETA: splitting (49) gives:
% 159.62/28.29 | | | | |
% 159.62/28.29 | | | | | Case 1:
% 159.62/28.29 | | | | | |
% 159.62/28.29 | | | | | | (112) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 159.62/28.29 | | | | | | e1) = e0)
% 159.62/28.29 | | | | | |
% 159.62/28.29 | | | | | | BETA: splitting (112) gives:
% 159.62/28.29 | | | | | |
% 159.62/28.29 | | | | | | Case 1:
% 159.62/28.29 | | | | | | |
% 159.62/28.29 | | | | | | | (113) all_58_4 = e0 & op(e3, e1) = e0
% 159.62/28.29 | | | | | | |
% 159.62/28.29 | | | | | | | REF_CLOSE: (35), (71), (113) are inconsistent by sub-proof #1344.
% 159.62/28.29 | | | | | | |
% 159.62/28.29 | | | | | | Case 2:
% 159.62/28.29 | | | | | | |
% 159.62/28.29 | | | | | | | (114) all_58_5 = e0 & op(e2, e1) = e0
% 159.62/28.29 | | | | | | |
% 159.62/28.29 | | | | | | | ALPHA: (114) implies:
% 159.62/28.29 | | | | | | | (115) all_58_5 = e0
% 159.62/28.29 | | | | | | |
% 159.62/28.29 | | | | | | | BETA: splitting (33) gives:
% 159.62/28.29 | | | | | | |
% 159.62/28.29 | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | (116) all_54_9 = e2
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | COMBINE_EQS: (76), (116) imply:
% 159.62/28.29 | | | | | | | | (117) all_14_0 = e2
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | SIMP: (117) implies:
% 159.62/28.29 | | | | | | | | (118) all_14_0 = e2
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | REDUCE: (97), (118) imply:
% 159.62/28.29 | | | | | | | | (119) ~ (all_52_4 = e2)
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | REDUCE: (15), (118) imply:
% 159.62/28.29 | | | | | | | | (120) ~ (all_52_14 = e2)
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | REDUCE: (19), (118) imply:
% 159.62/28.29 | | | | | | | | (121) ~ (all_6_2 = e2)
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | REDUCE: (24), (118) imply:
% 159.62/28.29 | | | | | | | | (122) ~ (e3 = e2)
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | BETA: splitting (9) gives:
% 159.62/28.29 | | | | | | | |
% 159.62/28.29 | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | |
% 159.62/28.29 | | | | | | | | | (123) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 159.62/28.29 | | | | | | | | | op(e2, e0) = e3)
% 159.62/28.29 | | | | | | | | |
% 159.62/28.29 | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.62/28.29 | | | | | | | | | (14), (16), (17), (18), (21), (22), (26), (27),
% 159.62/28.29 | | | | | | | | | (28), (29), (30), (32), (35), (36), (37), (39),
% 159.62/28.29 | | | | | | | | | (40), (41), (43), (44), (45), (46), (47), (49),
% 159.62/28.29 | | | | | | | | | (50), (53), (54), (55), (57), (65), (66), (67),
% 159.62/28.29 | | | | | | | | | (70), (71), (72), (73), (74), (78), (80), (81),
% 159.62/28.29 | | | | | | | | | (82), (84), (87), (89), (90), (93), (95), (96),
% 159.62/28.29 | | | | | | | | | (103), (123) are inconsistent by sub-proof #684.
% 159.62/28.29 | | | | | | | | |
% 159.62/28.29 | | | | | | | | Case 2:
% 159.62/28.29 | | | | | | | | |
% 159.62/28.29 | | | | | | | | | (124) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3
% 159.62/28.29 | | | | | | | | | & op(e0, e0) = e3)
% 159.62/28.29 | | | | | | | | |
% 159.62/28.29 | | | | | | | | | BETA: splitting (124) gives:
% 159.62/28.29 | | | | | | | | |
% 159.62/28.29 | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | (125) all_58_11 = e3 & op(e1, e0) = e3
% 159.62/28.29 | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | ALPHA: (125) implies:
% 159.62/28.29 | | | | | | | | | | (126) all_58_11 = e3
% 159.62/28.29 | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | REF_CLOSE: (93), (103), (126) are inconsistent by sub-proof
% 159.62/28.29 | | | | | | | | | | #1049.
% 159.62/28.29 | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | Case 2:
% 159.62/28.29 | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | (127) all_58_15 = e3 & op(e0, e0) = e3
% 159.62/28.29 | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | ALPHA: (127) implies:
% 159.62/28.29 | | | | | | | | | | (128) all_58_15 = e3
% 159.62/28.29 | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | BETA: splitting (96) gives:
% 159.62/28.29 | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | (129) all_58_15 = e0 & op(e0, e0) = e0
% 159.62/28.29 | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | REF_CLOSE: (35), (128), (129) are inconsistent by sub-proof
% 159.62/28.29 | | | | | | | | | | | #1013.
% 159.62/28.29 | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | Case 2:
% 159.62/28.29 | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | (130) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.62/28.29 | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.62/28.29 | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 159.62/28.29 | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.62/28.29 | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.62/28.29 | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | ALPHA: (130) implies:
% 159.62/28.29 | | | | | | | | | | | (131) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.62/28.29 | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 159.62/28.29 | | | | | | | | | | | e0) = e0)
% 159.62/28.29 | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | BETA: splitting (25) gives:
% 159.62/28.29 | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | (132) all_54_1 = e3
% 159.62/28.29 | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | COMBINE_EQS: (20), (132) imply:
% 159.62/28.29 | | | | | | | | | | | | (133) all_52_4 = e3
% 159.62/28.29 | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | REDUCE: (66), (133) imply:
% 159.62/28.29 | | | | | | | | | | | | (134) $false
% 159.62/28.29 | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 159.62/28.29 | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | Case 2:
% 159.62/28.29 | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | (135) ~ (all_54_1 = e3)
% 159.62/28.29 | | | | | | | | | | | | (136) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 159.62/28.29 | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | BETA: splitting (136) gives:
% 159.62/28.29 | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | (137) all_54_1 = e2
% 159.62/28.29 | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | COMBINE_EQS: (20), (137) imply:
% 159.62/28.29 | | | | | | | | | | | | | (138) all_52_4 = e2
% 159.62/28.29 | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | REDUCE: (119), (138) imply:
% 159.62/28.29 | | | | | | | | | | | | | (139) $false
% 159.62/28.29 | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 159.62/28.29 | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | Case 2:
% 159.62/28.29 | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | (140) ~ (all_54_1 = e2)
% 159.62/28.29 | | | | | | | | | | | | | (141) all_54_1 = e1 | all_54_1 = e0
% 159.62/28.29 | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | BETA: splitting (26) gives:
% 159.62/28.29 | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | (142) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 159.62/28.29 | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 159.62/28.29 | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 159.62/28.29 | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | (143) all_58_6 = e3 & op(e1, e3) = e3
% 159.62/28.29 | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 159.62/28.29 | | | | | | | | | | | | | | | (144) all_58_6 = e3
% 159.62/28.29 | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 159.62/28.29 | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | (145) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 159.62/28.29 | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 159.62/28.29 | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 159.62/28.29 | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | (146) all_58_0 = e2 & op(e3, e3) = e2
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 159.62/28.29 | | | | | | | | | | | | | | | | | (147) all_58_0 = e2
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (147) imply:
% 159.62/28.29 | | | | | | | | | | | | | | | | | (148) e2 = e1
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | SIMP: (148) implies:
% 159.62/28.29 | | | | | | | | | | | | | | | | | (149) e2 = e1
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (149) imply:
% 159.62/28.29 | | | | | | | | | | | | | | | | | (150) all_58_11 = e1
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (23), (29), (32), (35), (36), (40),
% 159.62/28.29 | | | | | | | | | | | | | | | | | (45), (47), (67), (70), (73), (89), (90), (93),
% 159.62/28.29 | | | | | | | | | | | | | | | | | (150) are inconsistent by sub-proof #743.
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | (151) all_58_1 = e2 & op(e3, e2) = e2
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 159.62/28.29 | | | | | | | | | | | | | | | | | (152) all_58_1 = e2
% 159.62/28.29 | | | | | | | | | | | | | | | | | (153) op(e3, e2) = e2
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 159.62/28.29 | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | Case 1:
% 159.62/28.29 | | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | | (154) all_54_1 = e1
% 159.62/28.29 | | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (154) imply:
% 159.62/28.29 | | | | | | | | | | | | | | | | | | (155) all_52_4 = e1
% 159.62/28.29 | | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | | REDUCE: (62), (155) imply:
% 159.62/28.29 | | | | | | | | | | | | | | | | | | (156) $false
% 159.62/28.29 | | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 159.62/28.29 | | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | Case 2:
% 159.62/28.29 | | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | | (157) all_54_1 = e0
% 159.62/28.29 | | | | | | | | | | | | | | | | | |
% 159.62/28.29 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (157) imply:
% 159.62/28.29 | | | | | | | | | | | | | | | | | | (158) all_52_4 = e0
% 159.62/28.29 | | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | | REDUCE: (66), (158) imply:
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (159) ~ (e3 = e0)
% 159.69/28.29 | | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | | REDUCE: (119), (158) imply:
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (160) ~ (e2 = e0)
% 159.69/28.29 | | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | | REDUCE: (62), (158) imply:
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (161) ~ (e1 = e0)
% 159.69/28.29 | | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | | REDUCE: (21), (158) imply:
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (162) op(e3, e2) = e0
% 159.69/28.29 | | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (12), (13), (14), (16), (17), (18), (21), (22),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (23), (26), (27), (28), (29), (30), (32), (35),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (36), (37), (38), (39), (40), (41), (42), (43),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (48), (49), (50), (51),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (52), (53), (54), (55), (56), (57), (58), (59),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (60), (61), (63), (64), (65), (66), (67), (68),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (77),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (94), (95), (96), (98), (120), (128), (144),
% 159.69/28.29 | | | | | | | | | | | | | | | | | | (152), (153), (162) are inconsistent by sub-proof
% 159.69/28.29 | | | | | | | | | | | | | | | | | | #678.
% 159.69/28.29 | | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | Case 2:
% 159.69/28.29 | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | (163) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 159.69/28.29 | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 159.69/28.29 | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 159.69/28.29 | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | (164) all_58_4 = e2 & op(e3, e1) = e2
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 159.69/28.29 | | | | | | | | | | | | | | | | | (165) all_58_4 = e2
% 159.69/28.29 | | | | | | | | | | | | | | | | | (166) op(e3, e1) = e2
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.69/28.29 | | | | | | | | | | | | | | | | | (14), (16), (17), (18), (21), (22), (26), (28),
% 159.69/28.29 | | | | | | | | | | | | | | | | | (29), (30), (32), (35), (36), (37), (39), (40),
% 159.69/28.29 | | | | | | | | | | | | | | | | | (41), (43), (44), (45), (46), (47), (49), (50),
% 159.69/28.29 | | | | | | | | | | | | | | | | | (53), (54), (55), (57), (65), (66), (67), (70),
% 159.69/28.29 | | | | | | | | | | | | | | | | | (72), (73), (74), (78), (80), (81), (82), (84),
% 159.69/28.29 | | | | | | | | | | | | | | | | | (87), (89), (90), (93), (95), (96), (165), (166)
% 159.69/28.29 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #751.
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | (167) all_58_9 = e2 & op(e3, e0) = e2
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 159.69/28.29 | | | | | | | | | | | | | | | | | (168) all_58_9 = e2
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (40), (45), (47), (67), (70), (72), (90),
% 159.69/28.29 | | | | | | | | | | | | | | | | | (103), (115), (131), (168) are inconsistent by
% 159.69/28.29 | | | | | | | | | | | | | | | | | sub-proof #677.
% 159.69/28.29 | | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | Case 2:
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | (169) all_58_7 = e3 & op(e1, e2) = e3
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | REF_CLOSE: (50), (87), (90), (169) are inconsistent by
% 159.69/28.29 | | | | | | | | | | | | | | | sub-proof #1184.
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | Case 2:
% 159.69/28.29 | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | (170) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 159.69/28.29 | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 159.69/28.29 | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 159.69/28.29 | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | Case 1:
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | (171) all_58_8 = e3 & op(e1, e1) = e3
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 159.69/28.29 | | | | | | | | | | | | | | | (172) all_58_8 = e3
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | REF_CLOSE: (27), (35), (40), (47), (49), (65), (67), (70),
% 159.69/28.29 | | | | | | | | | | | | | | | (71), (172) are inconsistent by sub-proof #739.
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | Case 2:
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | (173) all_58_11 = e3 & op(e1, e0) = e3
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 159.69/28.29 | | | | | | | | | | | | | | | (174) all_58_11 = e3
% 159.69/28.29 | | | | | | | | | | | | | | | (175) op(e1, e0) = e3
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (17), (18), (35), (40),
% 159.69/28.29 | | | | | | | | | | | | | | | (45), (47), (53), (67), (70), (71), (72), (73),
% 159.69/28.29 | | | | | | | | | | | | | | | (74), (82), (90), (93), (96), (128), (174), (175)
% 159.69/28.29 | | | | | | | | | | | | | | | are inconsistent by sub-proof #833.
% 159.69/28.29 | | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | | |
% 159.69/28.29 | | | | | | | | | End of split
% 159.69/28.29 | | | | | | | | |
% 159.69/28.29 | | | | | | | | End of split
% 159.69/28.29 | | | | | | | |
% 159.69/28.29 | | | | | | | Case 2:
% 159.69/28.29 | | | | | | | |
% 159.69/28.29 | | | | | | | | (176) all_54_9 = e1 | all_54_9 = e0
% 159.69/28.29 | | | | | | | |
% 159.69/28.29 | | | | | | | | REF_CLOSE: (11), (31), (76), (176) are inconsistent by sub-proof
% 159.69/28.29 | | | | | | | | #676.
% 159.69/28.29 | | | | | | | |
% 159.69/28.29 | | | | | | | End of split
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | End of split
% 159.69/28.29 | | | | | |
% 159.69/28.29 | | | | | Case 2:
% 159.69/28.29 | | | | | |
% 159.69/28.29 | | | | | | (177) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 159.69/28.29 | | | | | | op(e0, e1) = e0)
% 159.69/28.29 | | | | | |
% 159.69/28.29 | | | | | | BETA: splitting (177) gives:
% 159.69/28.29 | | | | | |
% 159.69/28.29 | | | | | | Case 1:
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | | (178) all_58_8 = e0 & op(e1, e1) = e0
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | | ALPHA: (178) implies:
% 159.69/28.29 | | | | | | | (179) all_58_8 = e0
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | | REF_CLOSE: (70), (111), (179) are inconsistent by sub-proof #1445.
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | Case 2:
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | | (180) all_58_14 = e0 & op(e0, e1) = e0
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | | ALPHA: (180) implies:
% 159.69/28.29 | | | | | | | (181) op(e0, e1) = e0
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | | REF_CLOSE: (40), (60), (61), (90), (181) are inconsistent by
% 159.69/28.29 | | | | | | | sub-proof #1372.
% 159.69/28.29 | | | | | | |
% 159.69/28.29 | | | | | | End of split
% 159.69/28.29 | | | | | |
% 159.69/28.29 | | | | | End of split
% 159.69/28.29 | | | | |
% 159.69/28.29 | | | | Case 2:
% 159.69/28.29 | | | | |
% 159.69/28.29 | | | | | (182) all_58_11 = e1 & op(e1, e0) = e1
% 159.69/28.29 | | | | |
% 159.69/28.29 | | | | | ALPHA: (182) implies:
% 159.69/28.29 | | | | | (183) all_58_11 = e1
% 159.69/28.29 | | | | |
% 159.69/28.29 | | | | | REF_CLOSE: (6), (16), (23), (29), (32), (35), (36), (40), (45), (47),
% 159.69/28.29 | | | | | (67), (70), (73), (89), (90), (93), (183) are inconsistent
% 159.69/28.29 | | | | | by sub-proof #743.
% 159.69/28.29 | | | | |
% 159.69/28.29 | | | | End of split
% 159.69/28.29 | | | |
% 159.69/28.29 | | | End of split
% 159.69/28.29 | | |
% 159.69/28.29 | | End of split
% 159.69/28.29 | |
% 159.69/28.29 | End of split
% 159.69/28.29 |
% 159.69/28.29 End of proof
% 159.69/28.29
% 159.69/28.29 Sub-proof #676 shows that the following formulas are inconsistent:
% 159.69/28.29 ----------------------------------------------------------------
% 159.69/28.29 (1) all_54_9 = e1 | all_54_9 = e0
% 159.69/28.29 (2) all_54_9 = all_14_0
% 159.69/28.29 (3) ~ (all_14_0 = e1)
% 159.69/28.29 (4) ~ (all_14_0 = e0)
% 159.69/28.29
% 159.69/28.29 Begin of proof
% 159.69/28.29 |
% 159.69/28.29 | BETA: splitting (1) gives:
% 159.69/28.29 |
% 159.69/28.29 | Case 1:
% 159.69/28.29 | |
% 159.69/28.29 | | (5) all_54_9 = e1
% 159.69/28.29 | |
% 159.69/28.29 | | COMBINE_EQS: (2), (5) imply:
% 159.69/28.29 | | (6) all_14_0 = e1
% 159.69/28.29 | |
% 159.69/28.29 | | SIMP: (6) implies:
% 159.69/28.29 | | (7) all_14_0 = e1
% 159.69/28.29 | |
% 159.69/28.29 | | REDUCE: (3), (7) imply:
% 159.69/28.29 | | (8) $false
% 159.69/28.29 | |
% 159.69/28.29 | | CLOSE: (8) is inconsistent.
% 159.69/28.29 | |
% 159.69/28.29 | Case 2:
% 159.69/28.29 | |
% 159.69/28.29 | | (9) all_54_9 = e0
% 159.69/28.29 | |
% 159.69/28.29 | | COMBINE_EQS: (2), (9) imply:
% 159.69/28.29 | | (10) all_14_0 = e0
% 159.69/28.29 | |
% 159.69/28.29 | | SIMP: (10) implies:
% 159.69/28.29 | | (11) all_14_0 = e0
% 159.69/28.29 | |
% 159.69/28.29 | | REDUCE: (4), (11) imply:
% 159.69/28.29 | | (12) $false
% 159.69/28.29 | |
% 159.69/28.29 | | CLOSE: (12) is inconsistent.
% 159.69/28.29 | |
% 159.69/28.29 | End of split
% 159.69/28.29 |
% 159.69/28.29 End of proof
% 159.69/28.29
% 159.69/28.29 Sub-proof #677 shows that the following formulas are inconsistent:
% 159.69/28.29 ----------------------------------------------------------------
% 159.69/28.30 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.30 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.30 (2) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.69/28.30 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.30 (3) ~ (e2 = e0)
% 159.69/28.30 (4) op(e2, e3) = e2
% 159.69/28.30 (5) ~ (e3 = e1)
% 159.69/28.30 (6) all_58_5 = e0
% 159.69/28.30 (7) all_58_11 = e2
% 159.69/28.30 (8) ~ (e2 = e1)
% 159.69/28.30 (9) ~ (e1 = e0)
% 159.69/28.30 (10) all_58_3 = e3
% 159.69/28.30 (11) all_58_9 = e2
% 159.69/28.30 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.30
% 159.69/28.30 Begin of proof
% 159.69/28.30 |
% 159.69/28.30 | BETA: splitting (2) gives:
% 159.69/28.30 |
% 159.69/28.30 | Case 1:
% 159.69/28.30 | |
% 159.69/28.30 | | (13) all_58_9 = e0 & op(e3, e0) = e0
% 159.69/28.30 | |
% 159.69/28.30 | | REF_CLOSE: (3), (11), (13) are inconsistent by sub-proof #1252.
% 159.69/28.30 | |
% 159.69/28.30 | Case 2:
% 159.69/28.30 | |
% 159.69/28.30 | | (14) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.69/28.30 | | e0)
% 159.69/28.30 | |
% 159.69/28.30 | | BETA: splitting (14) gives:
% 159.69/28.30 | |
% 159.69/28.30 | | Case 1:
% 159.69/28.30 | | |
% 159.69/28.30 | | | (15) all_58_10 = e0 & op(e2, e0) = e0
% 159.69/28.30 | | |
% 159.69/28.30 | | | ALPHA: (15) implies:
% 159.69/28.30 | | | (16) all_58_10 = e0
% 159.69/28.30 | | |
% 159.69/28.30 | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (12), (16) are inconsistent
% 159.69/28.30 | | | by sub-proof #839.
% 159.69/28.30 | | |
% 159.69/28.30 | | Case 2:
% 159.69/28.30 | | |
% 159.69/28.30 | | | (17) all_58_11 = e0 & op(e1, e0) = e0
% 159.69/28.30 | | |
% 159.69/28.30 | | | REF_CLOSE: (3), (7), (17) are inconsistent by sub-proof #1470.
% 159.69/28.30 | | |
% 159.69/28.30 | | End of split
% 159.69/28.30 | |
% 159.69/28.30 | End of split
% 159.69/28.30 |
% 159.69/28.30 End of proof
% 159.69/28.30
% 159.69/28.30 Sub-proof #678 shows that the following formulas are inconsistent:
% 159.69/28.30 ----------------------------------------------------------------
% 159.69/28.30 (1) all_58_15 = e3
% 159.69/28.30 (2) op(e3, e2) = e2
% 159.69/28.30 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.30 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.30 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.30 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.69/28.30 (5) ~ (all_52_14 = e2)
% 159.69/28.30 (6) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.69/28.30 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.30 (7) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.30 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.30 (8) op(e1, e1) = all_6_2
% 159.69/28.30 (9) ~ (all_52_7 = e3)
% 159.69/28.30 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.69/28.30 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.69/28.30 e1)
% 159.69/28.30 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.69/28.30 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.69/28.30 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.69/28.30 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.69/28.30 (13) all_54_10 = all_6_2
% 159.69/28.30 (14) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.69/28.30 (15) all_58_0 = e1
% 159.69/28.30 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.30 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.30 (17) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.69/28.30 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.69/28.30 (18) all_58_6 = e3
% 159.69/28.30 (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.69/28.30 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.69/28.30 (20) op(e3, e2) = all_52_4
% 159.69/28.30 (21) ~ (all_4_2 = e2)
% 159.69/28.30 (22) all_58_7 = e0
% 159.69/28.30 (23) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.30 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.30 (24) all_58_14 = e2
% 159.69/28.30 (25) op(e2, e1) = all_52_9
% 159.69/28.30 (26) op(e2, e3) = all_52_1
% 159.69/28.30 (27) ~ (all_52_13 = e3)
% 159.69/28.30 (28) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.30 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.30 (29) ~ (e3 = e0)
% 159.69/28.30 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.30 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.30 (31) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.69/28.30 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.69/28.30 (32) op(e0, e2) = e1
% 159.69/28.30 (33) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.30 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.30 e2)
% 159.69/28.30 (34) ~ (e2 = e0)
% 159.69/28.30 (35) ~ (all_52_9 = e3)
% 159.69/28.30 (36) ~ (all_56_14 = e0) | (all_56_8 = e1 & op(e1, e0) = e1)
% 159.69/28.30 (37) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.30 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.30 (38) op(e2, e0) = all_52_13
% 159.69/28.30 (39) op(e2, e3) = e2
% 159.69/28.30 (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.30 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.30 (41) ~ (e3 = e1)
% 159.69/28.30 (42) all_56_12 = e1
% 159.69/28.30 (43) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.69/28.30 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.69/28.30 (44) op(e1, e2) = all_52_6
% 159.69/28.30 (45) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3, e2) = e3 &
% 159.69/28.30 op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 =
% 159.69/28.30 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 & all_56_6
% 159.69/28.30 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 159.69/28.30 (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3, e1) = e1 &
% 159.69/28.30 op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 =
% 159.69/28.30 e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9
% 159.69/28.30 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 159.69/28.30 (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2, e1) = e2 &
% 159.69/28.30 op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 =
% 159.69/28.30 e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.69/28.30 all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 159.69/28.30 e2) | (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2,
% 159.69/28.30 e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.69/28.30 (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0
% 159.69/28.30 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 159.69/28.30 = e0)
% 159.69/28.30 (46) ~ (all_4_2 = e1)
% 159.69/28.30 (47) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.30 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.30 (48) ~ (all_6_2 = e3)
% 159.69/28.30 (49) op(e0, e0) = all_4_2
% 159.69/28.30 (50) all_54_7 = all_52_13
% 159.69/28.30 (51) op(e3, e2) = e0
% 159.69/28.30 (52) op(e3, e3) = e1
% 159.69/28.30 (53) ~ (all_52_13 = e2)
% 159.69/28.30 (54) all_56_15 = all_4_2
% 159.69/28.30 (55) op(e0, e1) = e2
% 159.69/28.30 (56) op(e0, e1) = all_52_11
% 159.69/28.30 (57) ~ (all_56_15 = e3) | (all_56_9 = e0 & op(e0, e3) = e0)
% 159.69/28.30 (58) ~ (all_52_13 = all_4_2)
% 159.69/28.30 (59) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.30 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.30 (60) ~ (all_52_4 = e3)
% 159.69/28.30 (61) ~ (e2 = e1)
% 159.69/28.30 (62) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 159.69/28.30 (63) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.69/28.30 (64) ~ (e1 = e0)
% 159.69/28.30 (65) all_58_4 = e3
% 159.69/28.30 (66) all_58_3 = e3
% 159.69/28.30 (67) ~ (all_6_2 = e2)
% 159.69/28.30 (68) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.30 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.30 e3)
% 159.69/28.30 (69) all_56_14 = all_6_2
% 159.69/28.30 (70) all_56_13 = e3
% 159.69/28.30 (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.69/28.30 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.69/28.30 (72) ~ (all_52_9 = e2)
% 159.69/28.30 (73) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.30 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.30 (74) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.69/28.30 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.69/28.30 (75) op(e0, e2) = all_52_7
% 159.69/28.30 (76) op(e1, e0) = all_52_14
% 159.69/28.30 (77) op(e3, e3) = all_22_1
% 159.69/28.30 (78) all_54_15 = all_4_2
% 159.69/28.30 (79) all_56_1 = e3
% 159.69/28.30 (80) all_58_1 = e2
% 159.69/28.30 (81) ~ (all_52_6 = e3)
% 159.69/28.30 (82) ~ (all_52_14 = all_6_2)
% 159.69/28.30 (83) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.30 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.30 (84) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.30 (85) all_54_11 = all_52_14
% 159.69/28.30 (86) ~ (all_52_13 = all_52_14)
% 159.69/28.30 (87) ~ (e3 = e2)
% 159.69/28.30 (88) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 159.69/28.30 (89) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.69/28.30 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.30 (90) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.30 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.30 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.30 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.30 (91) all_56_12 = e3 | all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.69/28.30
% 159.69/28.30 Begin of proof
% 159.69/28.30 |
% 159.69/28.30 | BETA: splitting (83) gives:
% 159.69/28.30 |
% 159.69/28.30 | Case 1:
% 159.69/28.30 | |
% 159.69/28.30 | | (92) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 159.69/28.30 | | e0)
% 159.69/28.30 | |
% 159.69/28.30 | | REF_CLOSE: (34), (39), (52), (64), (77), (84), (92) are inconsistent by
% 159.69/28.30 | | sub-proof #761.
% 159.69/28.30 | |
% 159.69/28.30 | Case 2:
% 159.69/28.30 | |
% 159.69/28.30 | | (93) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 159.69/28.30 | | e0)
% 159.69/28.30 | |
% 159.69/28.30 | | BETA: splitting (93) gives:
% 159.69/28.30 | |
% 159.69/28.30 | | Case 1:
% 159.69/28.30 | | |
% 159.69/28.30 | | | (94) all_58_6 = e0 & op(e1, e3) = e0
% 159.69/28.30 | | |
% 159.69/28.30 | | | ALPHA: (94) implies:
% 159.69/28.30 | | | (95) all_58_6 = e0
% 159.69/28.30 | | |
% 159.69/28.30 | | | REF_CLOSE: (18), (29), (95) are inconsistent by sub-proof #1321.
% 159.69/28.30 | | |
% 159.69/28.30 | | Case 2:
% 159.69/28.30 | | |
% 159.69/28.30 | | | (96) all_58_12 = e0 & op(e0, e3) = e0
% 159.69/28.30 | | |
% 159.69/28.30 | | | ALPHA: (96) implies:
% 159.69/28.30 | | | (97) all_58_12 = e0
% 159.69/28.30 | | |
% 159.69/28.30 | | | BETA: splitting (45) gives:
% 159.69/28.30 | | |
% 159.69/28.30 | | | Case 1:
% 159.69/28.30 | | | |
% 159.69/28.30 | | | | (98) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3,
% 159.69/28.30 | | | | e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 = e2
% 159.69/28.30 | | | | & ~ (all_56_12 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 159.69/28.30 | | | | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3,
% 159.69/28.30 | | | | e1) = e3 & op(e1, e3) = e3) | (all_56_1 = e1 & all_56_6 = e1
% 159.69/28.30 | | | | & ~ (all_56_12 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 159.69/28.30 | | | | (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) & op(e3,
% 159.69/28.30 | | | | e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 & all_56_9 = e0
% 159.69/28.30 | | | | & ~ (all_56_12 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.69/28.30 | | | |
% 159.69/28.30 | | | | BETA: splitting (98) gives:
% 159.69/28.30 | | | |
% 159.69/28.30 | | | | Case 1:
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | (99) (all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) & op(e3,
% 159.69/28.30 | | | | | e2) = e3 & op(e2, e3) = e3) | (all_56_0 = e2 & all_56_3 =
% 159.69/28.30 | | | | | e2 & ~ (all_56_12 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 159.69/28.30 | | | | | e2) | (all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) &
% 159.69/28.30 | | | | | op(e3, e1) = e3 & op(e1, e3) = e3)
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | BETA: splitting (99) gives:
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | Case 1:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | (100) all_56_0 = e3 & all_56_3 = e3 & ~ (all_56_13 = e2) &
% 159.69/28.30 | | | | | | op(e3, e2) = e3 & op(e2, e3) = e3
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | ALPHA: (100) implies:
% 159.69/28.30 | | | | | | (101) op(e2, e3) = e3
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | REF_CLOSE: (26), (39), (84), (87), (101) are inconsistent by
% 159.69/28.30 | | | | | | sub-proof #1159.
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | Case 2:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | (102) (all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) &
% 159.69/28.30 | | | | | | op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_1 = e3 &
% 159.69/28.30 | | | | | | all_56_6 = e3 & ~ (all_56_14 = e1) & op(e3, e1) = e3 &
% 159.69/28.30 | | | | | | op(e1, e3) = e3)
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | BETA: splitting (102) gives:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | Case 1:
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | (103) all_56_0 = e2 & all_56_3 = e2 & ~ (all_56_12 = e3) &
% 159.69/28.30 | | | | | | | op(e3, e2) = e2 & op(e2, e3) = e2
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | ALPHA: (103) implies:
% 159.69/28.30 | | | | | | | (104) ~ (all_56_12 = e3)
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | REF_CLOSE: (1), (2), (10), (22), (24), (29), (34), (42), (51),
% 159.69/28.30 | | | | | | | (61), (64), (66), (73), (80), (84), (87), (90), (104)
% 159.69/28.30 | | | | | | | are inconsistent by sub-proof #682.
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | Case 2:
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | (105) all_56_1 = e3 & all_56_6 = e3 & ~ (all_56_14 = e1) &
% 159.69/28.30 | | | | | | | op(e3, e1) = e3 & op(e1, e3) = e3
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | ALPHA: (105) implies:
% 159.69/28.30 | | | | | | | (106) ~ (all_56_14 = e1)
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | REDUCE: (69), (106) imply:
% 159.69/28.30 | | | | | | | (107) ~ (all_6_2 = e1)
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | BETA: splitting (91) gives:
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | Case 1:
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | | (108) all_56_12 = e3
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | | COMBINE_EQS: (42), (108) imply:
% 159.69/28.30 | | | | | | | | (109) e3 = e1
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | | SIMP: (109) implies:
% 159.69/28.30 | | | | | | | | (110) e3 = e1
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (12), (16),
% 159.69/28.30 | | | | | | | | (17), (18), (19), (20), (21), (23), (25), (26), (27),
% 159.69/28.30 | | | | | | | | (28), (29), (30), (31), (33), (34), (35), (37), (38),
% 159.69/28.30 | | | | | | | | (39), (40), (41), (43), (44), (47), (48), (49), (52),
% 159.69/28.30 | | | | | | | | (59), (60), (61), (64), (65), (66), (67), (68), (71),
% 159.69/28.30 | | | | | | | | (73), (74), (75), (77), (81), (83), (84), (87), (89),
% 159.69/28.30 | | | | | | | | (90), (110) are inconsistent by sub-proof #681.
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | Case 2:
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | | (111) ~ (all_56_12 = e3)
% 159.69/28.30 | | | | | | | | (112) all_56_13 = e2 | all_56_14 = e1 | all_56_15 = e0
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | | REDUCE: (42), (111) imply:
% 159.69/28.30 | | | | | | | | (113) ~ (e3 = e1)
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | | BETA: splitting (62) gives:
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | | Case 1:
% 159.69/28.30 | | | | | | | | |
% 159.69/28.30 | | | | | | | | | (114) all_54_10 = e3
% 159.69/28.30 | | | | | | | | |
% 159.69/28.30 | | | | | | | | | REF_CLOSE: (13), (48), (114) are inconsistent by sub-proof
% 159.69/28.30 | | | | | | | | | #1531.
% 159.69/28.30 | | | | | | | | |
% 159.69/28.30 | | | | | | | | Case 2:
% 159.69/28.30 | | | | | | | | |
% 159.69/28.30 | | | | | | | | | (115) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 159.69/28.30 | | | | | | | | |
% 159.69/28.30 | | | | | | | | | BETA: splitting (115) gives:
% 159.69/28.30 | | | | | | | | |
% 159.69/28.30 | | | | | | | | | Case 1:
% 159.69/28.30 | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | (116) all_54_10 = e2
% 159.69/28.30 | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | REF_CLOSE: (13), (67), (116) are inconsistent by sub-proof
% 159.69/28.30 | | | | | | | | | | #1530.
% 159.69/28.30 | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | Case 2:
% 159.69/28.30 | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | (117) all_54_10 = e1 | all_54_10 = e0
% 159.69/28.30 | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | BETA: splitting (112) gives:
% 159.69/28.30 | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | Case 1:
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | (118) all_56_13 = e2
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | COMBINE_EQS: (70), (118) imply:
% 159.69/28.30 | | | | | | | | | | | (119) e3 = e2
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | COMBINE_EQS: (18), (119) imply:
% 159.69/28.30 | | | | | | | | | | | (120) all_58_6 = e2
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | REF_CLOSE: (15), (16), (26), (29), (39), (41), (84), (87),
% 159.69/28.30 | | | | | | | | | | | (97), (120) are inconsistent by sub-proof #1154.
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | Case 2:
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | (121) all_56_14 = e1 | all_56_15 = e0
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | BETA: splitting (121) gives:
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | Case 1:
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | (122) all_56_14 = e1
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | COMBINE_EQS: (69), (122) imply:
% 159.69/28.30 | | | | | | | | | | | | (123) all_6_2 = e1
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | REDUCE: (107), (123) imply:
% 159.69/28.30 | | | | | | | | | | | | (124) $false
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | Case 2:
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | (125) all_56_15 = e0
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | COMBINE_EQS: (54), (125) imply:
% 159.69/28.30 | | | | | | | | | | | | (126) all_4_2 = e0
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | REDUCE: (58), (126) imply:
% 159.69/28.30 | | | | | | | | | | | | (127) ~ (all_52_13 = e0)
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | BETA: splitting (117) gives:
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | Case 1:
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | (128) all_54_10 = e1
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | REF_CLOSE: (13), (107), (128) are inconsistent by sub-proof
% 159.69/28.30 | | | | | | | | | | | | | #1529.
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | Case 2:
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | (129) all_54_10 = e0
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | COMBINE_EQS: (13), (129) imply:
% 159.69/28.30 | | | | | | | | | | | | | (130) all_6_2 = e0
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | SIMP: (130) implies:
% 159.69/28.30 | | | | | | | | | | | | | (131) all_6_2 = e0
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | COMBINE_EQS: (69), (131) imply:
% 159.69/28.30 | | | | | | | | | | | | | (132) all_56_14 = e0
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | REDUCE: (82), (131) imply:
% 159.69/28.30 | | | | | | | | | | | | | (133) ~ (all_52_14 = e0)
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | BETA: splitting (36) gives:
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | Case 1:
% 159.69/28.30 | | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | | (134) ~ (all_56_14 = e0)
% 159.69/28.30 | | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | | REDUCE: (132), (134) imply:
% 159.69/28.30 | | | | | | | | | | | | | | (135) $false
% 159.69/28.30 | | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 159.69/28.30 | | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | Case 2:
% 159.69/28.30 | | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | | (136) all_56_8 = e1 & op(e1, e0) = e1
% 159.69/28.30 | | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | | ALPHA: (136) implies:
% 159.69/28.30 | | | | | | | | | | | | | | (137) op(e1, e0) = e1
% 159.69/28.30 | | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (27), (50), (53), (63), (76), (84),
% 159.69/28.30 | | | | | | | | | | | | | | (85), (86), (127), (133), (137) are inconsistent
% 159.69/28.30 | | | | | | | | | | | | | | by sub-proof #680.
% 159.69/28.30 | | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | | End of split
% 159.69/28.30 | | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | | End of split
% 159.69/28.30 | | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | | End of split
% 159.69/28.30 | | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | | End of split
% 159.69/28.30 | | | | | | | | | |
% 159.69/28.30 | | | | | | | | | End of split
% 159.69/28.30 | | | | | | | | |
% 159.69/28.30 | | | | | | | | End of split
% 159.69/28.30 | | | | | | | |
% 159.69/28.30 | | | | | | | End of split
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | End of split
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | End of split
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | Case 2:
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | (138) (all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) & op(e3,
% 159.69/28.30 | | | | | e1) = e1 & op(e1, e3) = e1) | (all_56_2 = e3 & all_56_9 =
% 159.69/28.30 | | | | | e3 & ~ (all_56_15 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 159.69/28.30 | | | | | e3) | (all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3)
% 159.69/28.30 | | | | | & op(e3, e0) = e0 & op(e0, e3) = e0)
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | BETA: splitting (138) gives:
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | Case 1:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | (139) all_56_1 = e1 & all_56_6 = e1 & ~ (all_56_12 = e3) &
% 159.69/28.30 | | | | | | op(e3, e1) = e1 & op(e1, e3) = e1
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | ALPHA: (139) implies:
% 159.69/28.30 | | | | | | (140) all_56_1 = e1
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | COMBINE_EQS: (79), (140) imply:
% 159.69/28.30 | | | | | | (141) e3 = e1
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (12), (16),
% 159.69/28.30 | | | | | | (17), (18), (19), (20), (21), (23), (25), (26), (27),
% 159.69/28.30 | | | | | | (28), (29), (30), (31), (33), (34), (35), (37), (38),
% 159.69/28.30 | | | | | | (39), (40), (41), (43), (44), (47), (48), (49), (52),
% 159.69/28.30 | | | | | | (59), (60), (61), (64), (65), (66), (67), (68), (71),
% 159.69/28.30 | | | | | | (73), (74), (75), (77), (81), (83), (84), (87), (89),
% 159.69/28.30 | | | | | | (90), (141) are inconsistent by sub-proof #681.
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | Case 2:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | (142) (all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) &
% 159.69/28.30 | | | | | | op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_2 = e0 &
% 159.69/28.30 | | | | | | all_56_9 = e0 & ~ (all_56_12 = e3) & op(e3, e0) = e0 &
% 159.69/28.30 | | | | | | op(e0, e3) = e0)
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | BETA: splitting (142) gives:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | Case 1:
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | (143) all_56_2 = e3 & all_56_9 = e3 & ~ (all_56_15 = e0) &
% 159.69/28.30 | | | | | | | op(e3, e0) = e3 & op(e0, e3) = e3
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | REF_CLOSE: (21), (46), (54), (57), (78), (88), (143) are
% 159.69/28.30 | | | | | | | inconsistent by sub-proof #1294.
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | Case 2:
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | (144) all_56_2 = e0 & all_56_9 = e0 & ~ (all_56_12 = e3) &
% 159.69/28.30 | | | | | | | op(e3, e0) = e0 & op(e0, e3) = e0
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | ALPHA: (144) implies:
% 159.69/28.30 | | | | | | | (145) ~ (all_56_12 = e3)
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | REF_CLOSE: (1), (2), (10), (22), (24), (29), (34), (42), (51),
% 159.69/28.30 | | | | | | | (61), (64), (66), (73), (80), (84), (87), (90), (145)
% 159.69/28.30 | | | | | | | are inconsistent by sub-proof #682.
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | End of split
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | End of split
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | End of split
% 159.69/28.30 | | | |
% 159.69/28.30 | | | Case 2:
% 159.69/28.30 | | | |
% 159.69/28.30 | | | | (146) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2,
% 159.69/28.30 | | | | e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 =
% 159.69/28.30 | | | | e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 159.69/28.30 | | | | | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) &
% 159.69/28.30 | | | | op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_5 = e0 &
% 159.69/28.30 | | | | all_56_10 = e0 & ~ (all_56_13 = e2) & op(e2, e0) = e0 &
% 159.69/28.30 | | | | op(e0, e2) = e0) | (all_56_8 = e1 & all_56_11 = e1 & ~
% 159.69/28.30 | | | | (all_56_15 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 159.69/28.30 | | | | (all_56_8 = e0 & all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1,
% 159.69/28.30 | | | | e0) = e0 & op(e0, e1) = e0)
% 159.69/28.30 | | | |
% 159.69/28.30 | | | | BETA: splitting (146) gives:
% 159.69/28.30 | | | |
% 159.69/28.30 | | | | Case 1:
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | (147) (all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) & op(e2,
% 159.69/28.30 | | | | | e1) = e2 & op(e1, e2) = e2) | (all_56_4 = e1 & all_56_7 =
% 159.69/28.30 | | | | | e1 & ~ (all_56_13 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 159.69/28.30 | | | | | e1) | (all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0)
% 159.69/28.30 | | | | | & op(e2, e0) = e2 & op(e0, e2) = e2)
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | BETA: splitting (147) gives:
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | Case 1:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | (148) all_56_4 = e2 & all_56_7 = e2 & ~ (all_56_14 = e1) &
% 159.69/28.30 | | | | | | op(e2, e1) = e2 & op(e1, e2) = e2
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | ALPHA: (148) implies:
% 159.69/28.30 | | | | | | (149) op(e2, e1) = e2
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | REF_CLOSE: (25), (72), (84), (149) are inconsistent by sub-proof
% 159.69/28.30 | | | | | | #1441.
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | Case 2:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | (150) (all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) &
% 159.69/28.30 | | | | | | op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_5 = e2 &
% 159.69/28.30 | | | | | | all_56_10 = e2 & ~ (all_56_15 = e0) & op(e2, e0) = e2 &
% 159.69/28.30 | | | | | | op(e0, e2) = e2)
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | BETA: splitting (150) gives:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | Case 1:
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | (151) all_56_4 = e1 & all_56_7 = e1 & ~ (all_56_13 = e2) &
% 159.69/28.30 | | | | | | | op(e2, e1) = e1 & op(e1, e2) = e1
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | ALPHA: (151) implies:
% 159.69/28.30 | | | | | | | (152) ~ (all_56_13 = e2)
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | REF_CLOSE: (1), (2), (10), (22), (24), (29), (34), (41), (51),
% 159.69/28.30 | | | | | | | (61), (64), (66), (70), (73), (80), (84), (90), (152)
% 159.69/28.30 | | | | | | | are inconsistent by sub-proof #679.
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | Case 2:
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | (153) all_56_5 = e2 & all_56_10 = e2 & ~ (all_56_15 = e0) &
% 159.69/28.30 | | | | | | | op(e2, e0) = e2 & op(e0, e2) = e2
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | ALPHA: (153) implies:
% 159.69/28.30 | | | | | | | (154) op(e0, e2) = e2
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | | REF_CLOSE: (32), (61), (75), (84), (154) are inconsistent by
% 159.69/28.30 | | | | | | | sub-proof #1319.
% 159.69/28.30 | | | | | | |
% 159.69/28.30 | | | | | | End of split
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | End of split
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | Case 2:
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | (155) (all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) &
% 159.69/28.30 | | | | | op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_8 = e1 &
% 159.69/28.30 | | | | | all_56_11 = e1 & ~ (all_56_15 = e0) & op(e1, e0) = e1 &
% 159.69/28.30 | | | | | op(e0, e1) = e1) | (all_56_8 = e0 & all_56_11 = e0 & ~
% 159.69/28.30 | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | BETA: splitting (155) gives:
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | | Case 1:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | (156) all_56_5 = e0 & all_56_10 = e0 & ~ (all_56_13 = e2) &
% 159.69/28.30 | | | | | | op(e2, e0) = e0 & op(e0, e2) = e0
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | ALPHA: (156) implies:
% 159.69/28.30 | | | | | | (157) ~ (all_56_13 = e2)
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | REF_CLOSE: (1), (2), (10), (22), (24), (29), (34), (41), (51), (61),
% 159.69/28.30 | | | | | | (64), (66), (70), (73), (80), (84), (90), (157) are
% 159.69/28.30 | | | | | | inconsistent by sub-proof #679.
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | Case 2:
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | (158) (all_56_8 = e1 & all_56_11 = e1 & ~ (all_56_15 = e0) &
% 159.69/28.30 | | | | | | op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_8 = e0 &
% 159.69/28.30 | | | | | | all_56_11 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 &
% 159.69/28.30 | | | | | | op(e0, e1) = e0)
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | | REF_CLOSE: (34), (55), (56), (61), (84), (158) are inconsistent by
% 159.69/28.30 | | | | | | sub-proof #1293.
% 159.69/28.30 | | | | | |
% 159.69/28.30 | | | | | End of split
% 159.69/28.30 | | | | |
% 159.69/28.30 | | | | End of split
% 159.69/28.30 | | | |
% 159.69/28.30 | | | End of split
% 159.69/28.30 | | |
% 159.69/28.30 | | End of split
% 159.69/28.30 | |
% 159.69/28.30 | End of split
% 159.69/28.30 |
% 159.69/28.30 End of proof
% 159.69/28.30
% 159.69/28.30 Sub-proof #679 shows that the following formulas are inconsistent:
% 159.69/28.30 ----------------------------------------------------------------
% 159.69/28.30 (1) all_58_15 = e3
% 159.69/28.30 (2) op(e3, e2) = e2
% 159.69/28.30 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.30 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.30 (4) all_58_7 = e0
% 159.69/28.30 (5) all_58_14 = e2
% 159.69/28.30 (6) ~ (e3 = e0)
% 159.69/28.30 (7) ~ (e2 = e0)
% 159.69/28.30 (8) ~ (e3 = e1)
% 159.69/28.30 (9) ~ (all_56_13 = e2)
% 159.69/28.30 (10) op(e3, e2) = e0
% 159.69/28.30 (11) ~ (e2 = e1)
% 159.69/28.30 (12) ~ (e1 = e0)
% 159.69/28.30 (13) all_58_3 = e3
% 159.69/28.30 (14) all_56_13 = e3
% 159.69/28.30 (15) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.30 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.31 (16) all_58_1 = e2
% 159.69/28.31 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.31 (18) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.31 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.31 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.31 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.31
% 159.69/28.31 Begin of proof
% 159.69/28.31 |
% 159.69/28.31 | REDUCE: (9), (14) imply:
% 159.69/28.31 | (19) ~ (e3 = e2)
% 159.69/28.31 |
% 159.69/28.31 | GROUND_INST: instantiating (17) with e0, e2, e2, e3, simplifying with (2),
% 159.69/28.31 | (10) gives:
% 159.69/28.31 | (20) e2 = e0
% 159.69/28.31 |
% 159.69/28.31 | COMBINE_EQS: (16), (20) imply:
% 159.69/28.31 | (21) all_58_1 = e0
% 159.69/28.31 |
% 159.69/28.31 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11), (12), (13), (15), (18),
% 159.69/28.31 | (19), (21) are inconsistent by sub-proof #683.
% 159.69/28.31 |
% 159.69/28.31 End of proof
% 159.69/28.31
% 159.69/28.31 Sub-proof #680 shows that the following formulas are inconsistent:
% 159.69/28.31 ----------------------------------------------------------------
% 159.69/28.31 (1) ~ (all_52_14 = e2)
% 159.69/28.31 (2) ~ (all_52_14 = e0)
% 159.69/28.31 (3) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.69/28.31 (4) ~ (all_52_13 = e3)
% 159.69/28.31 (5) all_54_7 = all_52_13
% 159.69/28.31 (6) op(e1, e0) = e1
% 159.69/28.31 (7) ~ (all_52_13 = e2)
% 159.69/28.31 (8) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 159.69/28.31 (9) ~ (all_52_13 = e0)
% 159.69/28.31 (10) op(e1, e0) = all_52_14
% 159.69/28.31 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.31 (12) all_54_11 = all_52_14
% 159.69/28.31 (13) ~ (all_52_13 = all_52_14)
% 159.69/28.31
% 159.69/28.31 Begin of proof
% 159.69/28.31 |
% 159.69/28.31 | BETA: splitting (3) gives:
% 159.69/28.31 |
% 159.69/28.31 | Case 1:
% 159.69/28.31 | |
% 159.69/28.31 | | (14) all_54_7 = e3
% 159.69/28.31 | |
% 159.69/28.31 | | COMBINE_EQS: (5), (14) imply:
% 159.69/28.31 | | (15) all_52_13 = e3
% 159.69/28.31 | |
% 159.69/28.31 | | REDUCE: (4), (15) imply:
% 159.69/28.31 | | (16) $false
% 159.69/28.31 | |
% 159.69/28.31 | | CLOSE: (16) is inconsistent.
% 159.69/28.31 | |
% 159.69/28.31 | Case 2:
% 159.69/28.31 | |
% 159.69/28.31 | | (17) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 159.69/28.31 | |
% 159.69/28.31 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (17)
% 159.69/28.31 | | are inconsistent by sub-proof #1110.
% 159.69/28.31 | |
% 159.69/28.31 | End of split
% 159.69/28.31 |
% 159.69/28.31 End of proof
% 159.69/28.31
% 159.69/28.31 Sub-proof #681 shows that the following formulas are inconsistent:
% 159.69/28.31 ----------------------------------------------------------------
% 159.69/28.31 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.31 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.31 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.69/28.31 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.69/28.31 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.31 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.31 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.31 (5) op(e1, e1) = all_6_2
% 159.69/28.31 (6) ~ (all_52_7 = e3)
% 159.69/28.31 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.31 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.31 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.69/28.31 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.69/28.31 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.69/28.31 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.69/28.31 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.31 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.31 (11) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.69/28.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.69/28.31 (12) all_58_6 = e3
% 159.69/28.31 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.69/28.31 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.69/28.31 (14) op(e3, e2) = all_52_4
% 159.69/28.31 (15) ~ (all_4_2 = e2)
% 159.69/28.31 (16) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.31 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.31 (17) op(e2, e1) = all_52_9
% 159.69/28.31 (18) op(e2, e3) = all_52_1
% 159.69/28.31 (19) ~ (all_52_13 = e3)
% 159.69/28.31 (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.31 (21) ~ (e3 = e0)
% 159.69/28.31 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.31 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.31 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.69/28.31 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.69/28.31 (24) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.31 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.31 e2)
% 159.69/28.31 (25) ~ (e2 = e0)
% 159.69/28.31 (26) ~ (all_52_9 = e3)
% 159.69/28.31 (27) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.31 (28) op(e2, e0) = all_52_13
% 159.69/28.31 (29) op(e2, e3) = e2
% 159.69/28.31 (30) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.31 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.31 (31) ~ (e3 = e1)
% 159.69/28.31 (32) e3 = e1
% 159.69/28.31 (33) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.69/28.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.69/28.31 (34) op(e1, e2) = all_52_6
% 159.69/28.31 (35) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.31 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.31 (36) ~ (all_6_2 = e3)
% 159.69/28.31 (37) op(e0, e0) = all_4_2
% 159.69/28.31 (38) op(e3, e3) = e1
% 159.69/28.31 (39) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.31 (40) ~ (all_52_4 = e3)
% 159.69/28.31 (41) ~ (e2 = e1)
% 159.69/28.31 (42) ~ (e1 = e0)
% 159.69/28.31 (43) all_58_4 = e3
% 159.69/28.31 (44) all_58_3 = e3
% 159.69/28.31 (45) ~ (all_6_2 = e2)
% 159.69/28.31 (46) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.31 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.31 e3)
% 159.69/28.31 (47) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.69/28.31 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.69/28.31 (48) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.31 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.31 (49) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.69/28.31 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.69/28.31 (50) op(e0, e2) = all_52_7
% 159.69/28.31 (51) op(e3, e3) = all_22_1
% 159.69/28.31 (52) ~ (all_52_6 = e3)
% 159.69/28.31 (53) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.31 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.31 (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.31 (55) ~ (e3 = e2)
% 159.69/28.31 (56) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.69/28.31 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.31 (57) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.31 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.31 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.31 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.31
% 159.69/28.31 Begin of proof
% 159.69/28.31 |
% 159.69/28.31 | COMBINE_EQS: (32), (43) imply:
% 159.69/28.31 | (58) all_58_4 = e1
% 159.69/28.31 |
% 159.69/28.31 | BETA: splitting (9) gives:
% 159.69/28.31 |
% 159.69/28.31 | Case 1:
% 159.69/28.31 | |
% 159.69/28.31 | | (59) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 159.69/28.31 | | e3)
% 159.69/28.31 | |
% 159.69/28.31 | | BETA: splitting (59) gives:
% 159.69/28.31 | |
% 159.69/28.31 | | Case 1:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (60) all_58_4 = e3 & op(e3, e1) = e3
% 159.69/28.31 | | |
% 159.69/28.31 | | | COMBINE_EQS: (12), (32) imply:
% 159.69/28.31 | | | (61) all_58_6 = e1
% 159.69/28.31 | | |
% 159.69/28.31 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 159.69/28.31 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 159.69/28.31 | | | (24), (25), (26), (27), (28), (29), (30), (31), (33), (34),
% 159.69/28.31 | | | (35), (36), (37), (38), (39), (40), (41), (42), (44), (45),
% 159.69/28.31 | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 159.69/28.31 | | | (56), (57), (61) are inconsistent by sub-proof #685.
% 159.69/28.31 | | |
% 159.69/28.31 | | Case 2:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (62) all_58_5 = e3 & op(e2, e1) = e3
% 159.69/28.31 | | |
% 159.69/28.31 | | | ALPHA: (62) implies:
% 159.69/28.31 | | | (63) op(e2, e1) = e3
% 159.69/28.31 | | |
% 159.69/28.31 | | | REF_CLOSE: (17), (26), (54), (63) are inconsistent by sub-proof #1196.
% 159.69/28.31 | | |
% 159.69/28.31 | | End of split
% 159.69/28.31 | |
% 159.69/28.31 | Case 2:
% 159.69/28.31 | |
% 159.69/28.31 | | (64) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 159.69/28.31 | | e3)
% 159.69/28.31 | |
% 159.69/28.31 | | BETA: splitting (64) gives:
% 159.69/28.31 | |
% 159.69/28.31 | | Case 1:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (65) all_58_8 = e3 & op(e1, e1) = e3
% 159.69/28.31 | | |
% 159.69/28.31 | | | REF_CLOSE: (5), (36), (54), (65) are inconsistent by sub-proof #1469.
% 159.69/28.31 | | |
% 159.69/28.31 | | Case 2:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (66) all_58_14 = e3 & op(e0, e1) = e3
% 159.69/28.31 | | |
% 159.69/28.31 | | | ALPHA: (66) implies:
% 159.69/28.31 | | | (67) all_58_14 = e3
% 159.69/28.31 | | |
% 159.69/28.31 | | | REF_CLOSE: (4), (5), (11), (21), (25), (29), (31), (35), (41), (42), (44),
% 159.69/28.31 | | | (45), (54), (55), (58), (67) are inconsistent by sub-proof
% 159.69/28.31 | | | #850.
% 159.69/28.31 | | |
% 159.69/28.31 | | End of split
% 159.69/28.31 | |
% 159.69/28.31 | End of split
% 159.69/28.31 |
% 159.69/28.31 End of proof
% 159.69/28.31
% 159.69/28.31 Sub-proof #682 shows that the following formulas are inconsistent:
% 159.69/28.31 ----------------------------------------------------------------
% 159.69/28.31 (1) all_58_15 = e3
% 159.69/28.31 (2) op(e3, e2) = e2
% 159.69/28.31 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.31 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.31 (4) all_58_7 = e0
% 159.69/28.31 (5) all_58_14 = e2
% 159.69/28.31 (6) ~ (e3 = e0)
% 159.69/28.31 (7) ~ (e2 = e0)
% 159.69/28.31 (8) all_56_12 = e1
% 159.69/28.31 (9) ~ (all_56_12 = e3)
% 159.69/28.31 (10) op(e3, e2) = e0
% 159.69/28.31 (11) ~ (e2 = e1)
% 159.69/28.31 (12) ~ (e1 = e0)
% 159.69/28.31 (13) all_58_3 = e3
% 159.69/28.31 (14) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.31 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.31 (15) all_58_1 = e2
% 159.69/28.31 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.31 (17) ~ (e3 = e2)
% 159.69/28.31 (18) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.31 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.31 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.31 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.31
% 159.69/28.31 Begin of proof
% 159.69/28.31 |
% 159.69/28.31 | REDUCE: (8), (9) imply:
% 159.69/28.31 | (19) ~ (e3 = e1)
% 159.69/28.31 |
% 159.69/28.31 | SIMP: (19) implies:
% 159.69/28.31 | (20) ~ (e3 = e1)
% 159.69/28.31 |
% 159.69/28.31 | GROUND_INST: instantiating (16) with e0, e2, e2, e3, simplifying with (2),
% 159.69/28.31 | (10) gives:
% 159.69/28.31 | (21) e2 = e0
% 159.69/28.31 |
% 159.69/28.31 | COMBINE_EQS: (15), (21) imply:
% 159.69/28.31 | (22) all_58_1 = e0
% 159.69/28.31 |
% 159.69/28.31 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (12), (13), (14), (17), (18),
% 159.69/28.31 | (20), (22) are inconsistent by sub-proof #683.
% 159.69/28.31 |
% 159.69/28.31 End of proof
% 159.69/28.31
% 159.69/28.31 Sub-proof #683 shows that the following formulas are inconsistent:
% 159.69/28.31 ----------------------------------------------------------------
% 159.69/28.31 (1) all_58_15 = e3
% 159.69/28.31 (2) all_58_1 = e0
% 159.69/28.31 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.31 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.31 (4) all_58_7 = e0
% 159.69/28.31 (5) all_58_14 = e2
% 159.69/28.31 (6) ~ (e3 = e0)
% 159.69/28.31 (7) ~ (e2 = e0)
% 159.69/28.31 (8) ~ (e3 = e1)
% 159.69/28.31 (9) ~ (e2 = e1)
% 159.69/28.31 (10) ~ (e1 = e0)
% 159.69/28.31 (11) all_58_3 = e3
% 159.69/28.31 (12) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.31 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.31 (13) ~ (e3 = e2)
% 159.69/28.31 (14) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.31 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.31 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.31 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.31
% 159.69/28.31 Begin of proof
% 159.69/28.31 |
% 159.69/28.31 | BETA: splitting (12) gives:
% 159.69/28.31 |
% 159.69/28.31 | Case 1:
% 159.69/28.31 | |
% 159.69/28.31 | | (15) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 159.69/28.31 | | e2)
% 159.69/28.31 | |
% 159.69/28.31 | | BETA: splitting (15) gives:
% 159.69/28.31 | |
% 159.69/28.31 | | Case 1:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (16) all_58_1 = e2 & op(e3, e2) = e2
% 159.69/28.31 | | |
% 159.69/28.31 | | | REF_CLOSE: (2), (7), (16) are inconsistent by sub-proof #801.
% 159.69/28.31 | | |
% 159.69/28.31 | | Case 2:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (17) all_58_3 = e2 & op(e2, e2) = e2
% 159.69/28.31 | | |
% 159.69/28.31 | | | REF_CLOSE: (11), (13), (17) are inconsistent by sub-proof #719.
% 159.69/28.31 | | |
% 159.69/28.31 | | End of split
% 159.69/28.31 | |
% 159.69/28.31 | Case 2:
% 159.69/28.31 | |
% 159.69/28.31 | | (18) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 159.69/28.31 | | e2)
% 159.69/28.31 | |
% 159.69/28.31 | | BETA: splitting (18) gives:
% 159.69/28.31 | |
% 159.69/28.31 | | Case 1:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (19) all_58_7 = e2 & op(e1, e2) = e2
% 159.69/28.31 | | |
% 159.69/28.31 | | | REF_CLOSE: (4), (7), (19) are inconsistent by sub-proof #746.
% 159.69/28.31 | | |
% 159.69/28.31 | | Case 2:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (20) all_58_13 = e2 & op(e0, e2) = e2
% 159.69/28.31 | | |
% 159.69/28.31 | | | ALPHA: (20) implies:
% 159.69/28.31 | | | (21) all_58_13 = e2
% 159.69/28.31 | | |
% 159.69/28.31 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (14), (21) are
% 159.69/28.31 | | | inconsistent by sub-proof #1204.
% 159.69/28.31 | | |
% 159.69/28.31 | | End of split
% 159.69/28.31 | |
% 159.69/28.31 | End of split
% 159.69/28.31 |
% 159.69/28.31 End of proof
% 159.69/28.31
% 159.69/28.31 Sub-proof #684 shows that the following formulas are inconsistent:
% 159.69/28.31 ----------------------------------------------------------------
% 159.69/28.31 (1) op(e3, e1) = e3
% 159.69/28.31 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.31 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.31 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.69/28.31 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.69/28.31 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.31 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.31 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.31 (6) op(e1, e1) = all_6_2
% 159.69/28.31 (7) ~ (all_52_7 = e3)
% 159.69/28.31 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.31 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.31 (9) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.69/28.31 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.69/28.31 (10) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.69/28.31 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.69/28.31 (11) all_58_0 = e1
% 159.69/28.31 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.31 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.31 (13) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.69/28.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.69/28.31 (14) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.69/28.31 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.69/28.31 (15) op(e3, e2) = all_52_4
% 159.69/28.31 (16) ~ (all_4_2 = e2)
% 159.69/28.31 (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.31 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.31 (18) all_58_14 = e2
% 159.69/28.31 (19) op(e2, e1) = all_52_9
% 159.69/28.31 (20) op(e2, e3) = all_52_1
% 159.69/28.31 (21) ~ (all_52_13 = e3)
% 159.69/28.31 (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.31 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.31 (23) ~ (e3 = e0)
% 159.69/28.31 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.31 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.31 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.69/28.31 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.69/28.31 (26) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.31 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.31 e2)
% 159.69/28.31 (27) ~ (e2 = e0)
% 159.69/28.31 (28) ~ (all_52_9 = e3)
% 159.69/28.31 (29) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.31 (30) op(e2, e0) = all_52_13
% 159.69/28.31 (31) op(e2, e3) = e2
% 159.69/28.31 (32) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.31 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.31 (33) ~ (e3 = e1)
% 159.69/28.31 (34) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.69/28.31 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.69/28.31 (35) op(e1, e2) = all_52_6
% 159.69/28.31 (36) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.31 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.31 (37) ~ (all_6_2 = e3)
% 159.69/28.31 (38) op(e0, e0) = all_4_2
% 159.69/28.31 (39) op(e3, e3) = e1
% 159.69/28.31 (40) all_58_11 = e2
% 159.69/28.31 (41) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.31 (42) ~ (all_52_4 = e3)
% 159.69/28.31 (43) ~ (e2 = e1)
% 159.69/28.31 (44) ~ (e1 = e0)
% 159.69/28.31 (45) all_58_4 = e3
% 159.69/28.31 (46) all_58_3 = e3
% 159.69/28.31 (47) ~ (all_6_2 = e2)
% 159.69/28.31 (48) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 159.69/28.31 (49) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.31 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.31 e3)
% 159.69/28.31 (50) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.69/28.31 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.69/28.31 (51) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.31 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.31 (52) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.69/28.31 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.69/28.31 (53) op(e0, e2) = all_52_7
% 159.69/28.31 (54) op(e3, e3) = all_22_1
% 159.69/28.31 (55) ~ (all_52_6 = e3)
% 159.69/28.31 (56) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.31 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.31 (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.31 (58) ~ (e3 = e2)
% 159.69/28.31 (59) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.69/28.31 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.31 (60) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.31 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.31 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.31 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.31
% 159.69/28.31 Begin of proof
% 159.69/28.31 |
% 159.69/28.31 | BETA: splitting (48) gives:
% 159.69/28.31 |
% 159.69/28.31 | Case 1:
% 159.69/28.31 | |
% 159.69/28.31 | | (61) all_58_9 = e3 & op(e3, e0) = e3
% 159.69/28.31 | |
% 159.69/28.31 | | ALPHA: (61) implies:
% 159.69/28.31 | | (62) all_58_9 = e3
% 159.69/28.31 | |
% 159.69/28.31 | | BETA: splitting (49) gives:
% 159.69/28.31 | |
% 159.69/28.31 | | Case 1:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (63) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2)
% 159.69/28.31 | | | = e3)
% 159.69/28.31 | | |
% 159.69/28.31 | | | BETA: splitting (63) gives:
% 159.69/28.31 | | |
% 159.69/28.31 | | | Case 1:
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | (64) all_58_12 = e3 & op(e0, e3) = e3
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | ALPHA: (64) implies:
% 159.69/28.31 | | | | (65) all_58_12 = e3
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.69/28.31 | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21), (22),
% 159.69/28.31 | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 159.69/28.31 | | | | (33), (34), (35), (36), (37), (38), (39), (41), (42), (43),
% 159.69/28.31 | | | | (44), (45), (46), (47), (49), (50), (51), (52), (53), (54),
% 159.69/28.31 | | | | (55), (56), (57), (58), (59), (60), (62), (65) are
% 159.69/28.31 | | | | inconsistent by sub-proof #737.
% 159.69/28.31 | | | |
% 159.69/28.31 | | | Case 2:
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | (66) all_58_13 = e3 & op(e0, e2) = e3
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | REF_CLOSE: (7), (53), (57), (66) are inconsistent by sub-proof #1449.
% 159.69/28.31 | | | |
% 159.69/28.31 | | | End of split
% 159.69/28.31 | | |
% 159.69/28.31 | | Case 2:
% 159.69/28.31 | | |
% 159.69/28.31 | | | (67) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0)
% 159.69/28.31 | | | = e3)
% 159.69/28.31 | | |
% 159.69/28.31 | | | BETA: splitting (67) gives:
% 159.69/28.31 | | |
% 159.69/28.31 | | | Case 1:
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | (68) all_58_14 = e3 & op(e0, e1) = e3
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | ALPHA: (68) implies:
% 159.69/28.31 | | | | (69) all_58_14 = e3
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | REF_CLOSE: (18), (58), (69) are inconsistent by sub-proof #1405.
% 159.69/28.31 | | | |
% 159.69/28.31 | | | Case 2:
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | (70) all_58_15 = e3 & op(e0, e0) = e3
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | ALPHA: (70) implies:
% 159.69/28.31 | | | | (71) all_58_15 = e3
% 159.69/28.31 | | | |
% 159.69/28.31 | | | | REF_CLOSE: (4), (23), (27), (33), (40), (43), (44), (60), (62), (71) are
% 159.69/28.31 | | | | inconsistent by sub-proof #1316.
% 159.69/28.31 | | | |
% 159.69/28.31 | | | End of split
% 159.69/28.31 | | |
% 159.69/28.31 | | End of split
% 159.69/28.31 | |
% 159.69/28.31 | Case 2:
% 159.69/28.31 | |
% 159.69/28.31 | | (72) all_58_10 = e3 & op(e2, e0) = e3
% 159.69/28.31 | |
% 159.69/28.31 | | ALPHA: (72) implies:
% 159.69/28.31 | | (73) op(e2, e0) = e3
% 159.69/28.31 | |
% 159.69/28.31 | | REF_CLOSE: (21), (30), (57), (73) are inconsistent by sub-proof #1364.
% 159.69/28.31 | |
% 159.69/28.31 | End of split
% 159.69/28.31 |
% 159.69/28.31 End of proof
% 159.69/28.31
% 159.69/28.31 Sub-proof #685 shows that the following formulas are inconsistent:
% 159.69/28.31 ----------------------------------------------------------------
% 159.69/28.31 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.31 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.31 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.31 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.69/28.32 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.69/28.32 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.32 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.32 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.32 (5) op(e1, e1) = all_6_2
% 159.69/28.32 (6) ~ (all_52_7 = e3)
% 159.69/28.32 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.32 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.32 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.69/28.32 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.69/28.32 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.69/28.32 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.69/28.32 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.32 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.32 (11) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.69/28.32 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.69/28.32 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.69/28.32 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.69/28.32 (13) op(e3, e2) = all_52_4
% 159.69/28.32 (14) ~ (all_4_2 = e2)
% 159.69/28.32 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.32 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.32 (16) all_58_6 = e1
% 159.69/28.32 (17) op(e2, e1) = all_52_9
% 159.69/28.32 (18) op(e2, e3) = all_52_1
% 159.69/28.32 (19) ~ (all_52_13 = e3)
% 159.69/28.32 (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.32 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.32 (21) ~ (e3 = e0)
% 159.69/28.32 (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.32 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.32 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.69/28.32 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.69/28.32 (24) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.32 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.32 e2)
% 159.69/28.32 (25) ~ (e2 = e0)
% 159.69/28.32 (26) ~ (all_52_9 = e3)
% 159.69/28.32 (27) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.32 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.32 (28) op(e2, e0) = all_52_13
% 159.69/28.32 (29) op(e2, e3) = e2
% 159.69/28.32 (30) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.32 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.32 (31) ~ (e3 = e1)
% 159.69/28.32 (32) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.69/28.32 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.69/28.32 (33) op(e1, e2) = all_52_6
% 159.69/28.32 (34) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.32 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.32 (35) ~ (all_6_2 = e3)
% 159.69/28.32 (36) op(e0, e0) = all_4_2
% 159.69/28.32 (37) op(e3, e3) = e1
% 159.69/28.32 (38) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.32 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.32 (39) ~ (all_52_4 = e3)
% 159.69/28.32 (40) ~ (e2 = e1)
% 159.69/28.32 (41) ~ (e1 = e0)
% 159.69/28.32 (42) all_58_3 = e3
% 159.69/28.32 (43) ~ (all_6_2 = e2)
% 159.69/28.32 (44) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.32 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.32 e3)
% 159.69/28.32 (45) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 159.69/28.32 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 159.69/28.32 (46) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.32 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.32 (47) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 159.69/28.32 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 159.69/28.32 (48) op(e0, e2) = all_52_7
% 159.69/28.32 (49) op(e3, e3) = all_22_1
% 159.69/28.32 (50) ~ (all_52_6 = e3)
% 159.69/28.32 (51) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.32 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.32 (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.32 (53) ~ (e3 = e2)
% 159.69/28.32 (54) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 159.69/28.32 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.32 (55) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.32 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.32 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.32 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.32
% 159.69/28.32 Begin of proof
% 159.69/28.32 |
% 159.69/28.32 | BETA: splitting (15) gives:
% 159.69/28.32 |
% 159.69/28.32 | Case 1:
% 159.69/28.32 | |
% 159.69/28.32 | | (56) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 159.69/28.32 | | e3)
% 159.69/28.32 | |
% 159.69/28.32 | | REF_CLOSE: (16), (31), (33), (50), (52), (56) are inconsistent by sub-proof
% 159.69/28.32 | | #718.
% 159.69/28.32 | |
% 159.69/28.32 | Case 2:
% 159.69/28.32 | |
% 159.69/28.32 | | (57) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 159.69/28.32 | | e3)
% 159.69/28.32 | |
% 159.69/28.32 | | BETA: splitting (57) gives:
% 159.69/28.32 | |
% 159.69/28.32 | | Case 1:
% 159.69/28.32 | | |
% 159.69/28.32 | | | (58) all_58_8 = e3 & op(e1, e1) = e3
% 159.69/28.32 | | |
% 159.69/28.32 | | | REF_CLOSE: (5), (35), (52), (58) are inconsistent by sub-proof #1469.
% 159.69/28.32 | | |
% 159.69/28.32 | | Case 2:
% 159.69/28.32 | | |
% 159.69/28.32 | | | (59) all_58_11 = e3 & op(e1, e0) = e3
% 159.69/28.32 | | |
% 159.69/28.32 | | | ALPHA: (59) implies:
% 159.69/28.32 | | | (60) all_58_11 = e3
% 159.69/28.32 | | | (61) op(e1, e0) = e3
% 159.69/28.32 | | |
% 159.69/28.32 | | | BETA: splitting (20) gives:
% 159.69/28.32 | | |
% 159.69/28.32 | | | Case 1:
% 159.69/28.32 | | | |
% 159.69/28.32 | | | | (62) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 159.69/28.32 | | | | = e2)
% 159.69/28.32 | | | |
% 159.69/28.32 | | | | BETA: splitting (62) gives:
% 159.69/28.32 | | | |
% 159.69/28.32 | | | | Case 1:
% 159.69/28.32 | | | | |
% 159.69/28.32 | | | | | (63) all_58_6 = e2 & op(e1, e3) = e2
% 159.69/28.32 | | | | |
% 159.69/28.32 | | | | | ALPHA: (63) implies:
% 159.69/28.32 | | | | | (64) all_58_6 = e2
% 159.69/28.32 | | | | |
% 159.69/28.32 | | | | | REF_CLOSE: (10), (18), (21), (22), (25), (29), (31), (40), (41), (51),
% 159.69/28.32 | | | | | (52), (53), (64) are inconsistent by sub-proof #1152.
% 159.69/28.32 | | | | |
% 159.69/28.32 | | | | Case 2:
% 159.69/28.32 | | | | |
% 159.69/28.32 | | | | | (65) all_58_7 = e2 & op(e1, e2) = e2
% 159.69/28.32 | | | | |
% 159.69/28.32 | | | | | ALPHA: (65) implies:
% 159.69/28.32 | | | | | (66) all_58_7 = e2
% 159.69/28.32 | | | | |
% 159.69/28.32 | | | | | BETA: splitting (12) gives:
% 159.69/28.32 | | | | |
% 159.69/28.32 | | | | | Case 1:
% 159.69/28.32 | | | | | |
% 159.69/28.32 | | | | | | (67) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 159.69/28.32 | | | | | | e0) = e2)
% 159.69/28.32 | | | | | |
% 159.69/28.32 | | | | | | BETA: splitting (67) gives:
% 159.69/28.32 | | | | | |
% 159.69/28.32 | | | | | | Case 1:
% 159.69/28.32 | | | | | | |
% 159.69/28.32 | | | | | | | (68) all_58_9 = e2 & op(e3, e0) = e2
% 159.69/28.32 | | | | | | |
% 159.69/28.32 | | | | | | | ALPHA: (68) implies:
% 159.69/28.32 | | | | | | | (69) all_58_9 = e2
% 159.69/28.32 | | | | | | |
% 159.69/28.32 | | | | | | | BETA: splitting (51) gives:
% 159.69/28.32 | | | | | | |
% 159.69/28.32 | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | |
% 159.69/28.32 | | | | | | | | (70) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 159.69/28.32 | | | | | | | | op(e2, e3) = e0)
% 159.69/28.32 | | | | | | | |
% 159.69/28.32 | | | | | | | | BETA: splitting (70) gives:
% 159.69/28.32 | | | | | | | |
% 159.69/28.32 | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | |
% 159.69/28.32 | | | | | | | | | (71) all_58_0 = e0 & op(e3, e3) = e0
% 159.69/28.32 | | | | | | | | |
% 159.69/28.32 | | | | | | | | | ALPHA: (71) implies:
% 159.69/28.32 | | | | | | | | | (72) all_58_0 = e0
% 159.69/28.32 | | | | | | | | | (73) op(e3, e3) = e0
% 159.69/28.32 | | | | | | | | |
% 159.69/28.32 | | | | | | | | | BETA: splitting (2) gives:
% 159.69/28.32 | | | | | | | | |
% 159.69/28.32 | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | (74) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 159.69/28.32 | | | | | | | | | | op(e2, e2) = e1)
% 159.69/28.32 | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | BETA: splitting (74) gives:
% 159.69/28.32 | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | (75) all_58_1 = e1 & op(e3, e2) = e1
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | ALPHA: (75) implies:
% 159.69/28.32 | | | | | | | | | | | (76) all_58_1 = e1
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | BETA: splitting (10) gives:
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | (77) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 159.69/28.32 | | | | | | | | | | | | & op(e2, e3) = e3)
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | REF_CLOSE: (18), (21), (29), (49), (52), (53), (73), (77) are
% 159.69/28.32 | | | | | | | | | | | | inconsistent by sub-proof #717.
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | (78) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 159.69/28.32 | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | BETA: splitting (78) gives:
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | (79) all_58_6 = e3 & op(e1, e3) = e3
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | REF_CLOSE: (16), (31), (79) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | #1335.
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | (80) all_58_12 = e3 & op(e0, e3) = e3
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | ALPHA: (80) implies:
% 159.69/28.32 | | | | | | | | | | | | | (81) all_58_12 = e3
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | BETA: splitting (3) gives:
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | (82) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 159.69/28.32 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | (83) all_58_9 = e1 & op(e3, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | REF_CLOSE: (40), (69), (83) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | #1325.
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | (84) all_58_10 = e1 & op(e2, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | (85) all_58_10 = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (14),
% 159.69/28.32 | | | | | | | | | | | | | | | (15), (17), (18), (20), (21), (22), (24), (25),
% 159.69/28.32 | | | | | | | | | | | | | | | (26), (27), (29), (30), (31), (33), (34), (36),
% 159.69/28.32 | | | | | | | | | | | | | | | (38), (40), (41), (42), (43), (44), (48), (50),
% 159.69/28.32 | | | | | | | | | | | | | | | (51), (52), (53), (55), (60), (61), (66), (72),
% 159.69/28.32 | | | | | | | | | | | | | | | (76), (81), (85) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | #707.
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | (86) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 159.69/28.32 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | (87) all_58_11 = e1 & op(e1, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | (88) op(e1, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | REF_CLOSE: (31), (52), (61), (88) are inconsistent by
% 159.69/28.32 | | | | | | | | | | | | | | | sub-proof #1275.
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | (89) all_58_15 = e1 & op(e0, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | (90) all_58_15 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | (91) op(e0, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | (92) all_58_15 = e0 & op(e0, e0) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (29), (31), (40), (41), (52), (72),
% 159.69/28.32 | | | | | | | | | | | | | | | | (81), (90), (92) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | | #706.
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | (93) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.69/28.32 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.69/28.32 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 159.69/28.32 | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.69/28.32 | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | (94) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.69/28.32 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 159.69/28.32 | | | | | | | | | | | | | | | | e0) = e0)
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | (95) all_58_9 = e0 & op(e3, e0) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (18), (20), (21), (22), (25), (29),
% 159.69/28.32 | | | | | | | | | | | | | | | | | (31), (40), (41), (43), (51), (52), (53), (60),
% 159.69/28.32 | | | | | | | | | | | | | | | | | (66), (69), (81), (95) are inconsistent by
% 159.69/28.32 | | | | | | | | | | | | | | | | | sub-proof #730.
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | (96) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 159.69/28.32 | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | (97) all_58_10 = e0 & op(e2, e0) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | (98) all_58_10 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | (99) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (100) all_58_1 = e0 & op(e3, e2) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (101) all_58_1 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (101) imply:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (102) e1 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (102) imply:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (103) all_58_6 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (29), (31), (40), (41), (52), (72), (81),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (103) are inconsistent by sub-proof #733.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (104) all_58_3 = e0 & op(e2, e2) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (42), (104) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | #910.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | (105) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (106) all_58_7 = e0 & op(e1, e2) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (107) all_58_7 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (18), (20), (21), (22), (25), (29),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (31), (40), (41), (43), (51), (52), (53), (60),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (81), (107) are inconsistent by sub-proof #731.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (108) all_58_13 = e0 & op(e0, e2) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (109) all_58_13 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | (110) op(e0, e2) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | (111) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (31), (40), (42), (52), (111) are
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | (112) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (113) all_58_5 = e1 & op(e2, e1) = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (114) all_58_5 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | (115) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (18), (21), (22), (25), (29), (31), (40),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | (41), (48), (52), (53), (72), (110), (115) are
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | (116) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | (117) all_58_14 = e2 & op(e0, e1) = e2
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | (118) all_58_14 = e2
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | (119) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (120) all_58_4 = e3 & op(e3, e1) = e3
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (121) all_58_4 = e3
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (122) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123) all_58_4 = e1 & op(e3, e1) = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (121), (123) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1345.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e1, all_22_1, e3, e3,
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (37), (49) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (124) all_22_1 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e0, all_22_1, e3, e3,
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (49), (73) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125) all_22_1 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (125) imply:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (126) e1 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (126) imply:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127) all_58_1 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (40), (41), (42), (66), (109), (127)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #857.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (128) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (129) all_58_8 = e1 & op(e1, e1) = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (130) all_58_8 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131) all_58_15 = e0 & op(e0, e0) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (132) all_58_15 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (132) imply:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (133) e1 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (133) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134) e1 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (134) imply:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135) all_58_5 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (29), (31), (40), (41), (42), (52), (98),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135) are inconsistent by sub-proof #839.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (25), (29), (31), (32), (40), (41),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (42), (52), (60), (69), (93), (118), (121), (130)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #704.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136) all_58_14 = e1 & op(e0, e1) = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137) all_58_14 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (18), (21), (22), (25), (29), (31), (40),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (41), (48), (52), (53), (72), (110), (138) are
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (117), (137) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #703.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139) all_58_15 = e2 & op(e0, e0) = e2
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (140) all_58_15 = e2
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141) op(e0, e0) = e2
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (15), (18), (19), (21), (22), (23), (24), (25),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (29), (30), (31), (33), (34), (38), (40),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (41), (42), (43), (44), (46), (48), (50), (51),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (53), (55), (60), (110), (121), (140), (141)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #695.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (142) all_58_5 = e3 & op(e2, e1) = e3
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (143) op(e2, e1) = e3
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (26), (52), (143) are inconsistent by
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1196.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | (144) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (10), (11), (15), (18),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (24), (25), (27), (29), (31),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | (33), (34), (40), (41), (42), (43), (44), (48),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | (50), (51), (52), (53), (55), (60), (61), (66),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | | (81), (144) are inconsistent by sub-proof #709.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | (145) all_58_15 = e2 & op(e0, e0) = e2
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | (146) op(e0, e0) = e2
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (52), (91), (146) are inconsistent by
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1386.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (147) all_58_10 = e1 & op(e2, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (148) all_58_10 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (14),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (15), (17), (18), (20), (21), (22), (24), (25),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (26), (27), (29), (30), (31), (33), (34), (36),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (38), (40), (41), (42), (43), (44), (48), (50),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (51), (52), (53), (55), (60), (61), (66), (72),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | (76), (81), (148) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | | #707.
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | (149) all_58_11 = e0 & op(e1, e0) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (60), (149) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | | | | #1083.
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | (150) all_58_3 = e1 & op(e2, e2) = e1
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | ALPHA: (150) implies:
% 159.69/28.32 | | | | | | | | | | | (151) all_58_3 = e1
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | REF_CLOSE: (31), (42), (151) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | #841.
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | End of split
% 159.69/28.32 | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | (152) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1
% 159.69/28.32 | | | | | | | | | | & op(e0, e2) = e1)
% 159.69/28.32 | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | BETA: splitting (152) gives:
% 159.69/28.32 | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | (153) all_58_7 = e1 & op(e1, e2) = e1
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | ALPHA: (153) implies:
% 159.69/28.32 | | | | | | | | | | | (154) all_58_7 = e1
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | REF_CLOSE: (40), (66), (154) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | #721.
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | (155) all_58_13 = e1 & op(e0, e2) = e1
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | ALPHA: (155) implies:
% 159.69/28.32 | | | | | | | | | | | (156) all_58_13 = e1
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | BETA: splitting (10) gives:
% 159.69/28.32 | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | (157) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 159.69/28.32 | | | | | | | | | | | | & op(e2, e3) = e3)
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | REF_CLOSE: (18), (21), (29), (49), (52), (53), (73), (157)
% 159.69/28.32 | | | | | | | | | | | | are inconsistent by sub-proof #717.
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | (158) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 159.69/28.32 | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | BETA: splitting (158) gives:
% 159.69/28.32 | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | (159) all_58_6 = e3 & op(e1, e3) = e3
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | ALPHA: (159) implies:
% 159.69/28.32 | | | | | | | | | | | | | (160) all_58_6 = e3
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | REF_CLOSE: (16), (31), (160) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | #1073.
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | (161) all_58_12 = e3 & op(e0, e3) = e3
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | ALPHA: (161) implies:
% 159.69/28.32 | | | | | | | | | | | | | (162) all_58_12 = e3
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | BETA: splitting (3) gives:
% 159.69/28.32 | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | (163) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 159.69/28.32 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 159.69/28.32 | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | (164) all_58_9 = e1 & op(e3, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | (165) all_58_9 = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | REF_CLOSE: (40), (69), (165) are inconsistent by sub-proof
% 159.69/28.32 | | | | | | | | | | | | | | | #1324.
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | (166) all_58_10 = e1 & op(e2, e0) = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | (167) all_58_10 = e1
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 159.69/28.32 | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | (168) all_58_15 = e0 & op(e0, e0) = e0
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | (169) all_58_15 = e0
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | (170) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 159.69/28.32 | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | (171) all_58_0 = e1 & op(e3, e3) = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (29), (31), (40), (41), (52), (72),
% 159.69/28.32 | | | | | | | | | | | | | | | | | | (162), (171) are inconsistent by sub-proof #694.
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | (172) all_58_1 = e1 & op(e3, e2) = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.32 | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 159.69/28.32 | | | | | | | | | | | | | | | | | | (173) all_58_1 = e1
% 159.69/28.32 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (14),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (15), (17), (18), (20), (21), (22), (24), (25),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (26), (27), (29), (30), (31), (33), (34), (36),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (38), (40), (41), (42), (43), (44), (48), (50),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (51), (52), (53), (55), (60), (61), (66), (72),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (162), (167), (173) are inconsistent by sub-proof
% 159.69/28.33 | | | | | | | | | | | | | | | | | | #707.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | (174) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (175) all_58_4 = e1 & op(e3, e1) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (176) all_58_4 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | (177) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (178) all_58_4 = e2 & op(e3, e1) = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (179) all_58_4 = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (176), (179) imply:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (180) e2 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | SIMP: (180) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (181) e2 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (181) imply:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (182) all_58_9 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (12), (18), (21), (22), (25), (29),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (31), (34), (40), (41), (42), (52), (53), (60),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (72), (162), (169), (182) are inconsistent by
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | sub-proof #691.
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (183) all_58_5 = e2 & op(e2, e1) = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (184) all_58_5 = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (25), (29), (34), (41), (42), (52), (167),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (184) are inconsistent by sub-proof #899.
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | (185) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (186) all_58_8 = e2 & op(e1, e1) = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (43), (52), (186) are inconsistent by
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | sub-proof #1440.
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (187) all_58_14 = e2 & op(e0, e1) = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (188) all_58_14 = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (15),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (17), (18), (20), (21), (22), (24), (25), (26),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (27), (29), (31), (33), (34), (38), (40), (41),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (42), (43), (44), (48), (50), (51), (52), (53),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (55), (60), (61), (66), (72), (162), (167), (188)
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #708.
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (189) all_58_9 = e1 & op(e3, e0) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (190) all_58_9 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (12), (18), (21), (22), (25), (29),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (31), (34), (40), (41), (42), (52), (53), (60),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (72), (162), (169), (190) are inconsistent by
% 159.69/28.33 | | | | | | | | | | | | | | | | | | sub-proof #691.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | (191) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.69/28.33 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.69/28.33 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 159.69/28.33 | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.69/28.33 | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | (192) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 159.69/28.33 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 159.69/28.33 | | | | | | | | | | | | | | | | e1) = e0)
% 159.69/28.33 | | | | | | | | | | | | | | | | (193) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.69/28.33 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 159.69/28.33 | | | | | | | | | | | | | | | | e0) = e0)
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | (194) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (195) all_58_0 = e1 & op(e3, e3) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (29), (31), (40), (41), (52), (72),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (162), (195) are inconsistent by sub-proof #694.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (196) all_58_1 = e1 & op(e3, e2) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (197) all_58_1 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (16), (18), (20), (21), (22),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (25), (29), (30), (31), (40), (41), (42), (43),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (51), (52), (53), (60), (66), (69), (72), (156),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (162), (193), (197) are inconsistent by sub-proof
% 159.69/28.33 | | | | | | | | | | | | | | | | | | #688.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | (198) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (199) all_58_4 = e1 & op(e3, e1) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (9), (10), (15), (17), (18), (20), (21),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (22), (25), (26), (27), (29), (31), (33), (40),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (41), (43), (50), (51), (52), (53), (60), (61),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (66), (156), (162), (192), (199) are inconsistent
% 159.69/28.33 | | | | | | | | | | | | | | | | | | by sub-proof #687.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (200) all_58_9 = e1 & op(e3, e0) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (201) all_58_9 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (69), (201) are inconsistent by sub-proof
% 159.69/28.33 | | | | | | | | | | | | | | | | | | #1324.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | (202) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 159.69/28.33 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.69/28.33 | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 159.69/28.33 | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | (203) all_58_11 = e1 & op(e1, e0) = e1
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | (204) op(e1, e0) = e1
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | REF_CLOSE: (31), (52), (61), (204) are inconsistent by
% 159.69/28.33 | | | | | | | | | | | | | | | sub-proof #1275.
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | (205) all_58_15 = e1 & op(e0, e0) = e1
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | (206) all_58_15 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | (207) op(e0, e0) = e1
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | (208) all_58_15 = e0 & op(e0, e0) = e0
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (29), (31), (40), (41), (52), (72),
% 159.69/28.33 | | | | | | | | | | | | | | | | (162), (206), (208) are inconsistent by sub-proof
% 159.69/28.33 | | | | | | | | | | | | | | | | #706.
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | (209) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.69/28.33 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 159.69/28.33 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 159.69/28.33 | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.69/28.33 | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | (210) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 159.69/28.33 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 159.69/28.33 | | | | | | | | | | | | | | | | e1) = e0)
% 159.69/28.33 | | | | | | | | | | | | | | | | (211) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 159.69/28.33 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 159.69/28.33 | | | | | | | | | | | | | | | | e0) = e0)
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | (212) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (213) all_58_0 = e1 & op(e3, e3) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (29), (31), (40), (41), (52), (72),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (162), (213) are inconsistent by sub-proof #694.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (214) all_58_1 = e1 & op(e3, e2) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (215) all_58_1 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (16), (18), (20), (21), (22),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (25), (29), (30), (31), (40), (41), (42), (43),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (51), (52), (53), (60), (66), (69), (72), (156),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (162), (211), (215) are inconsistent by sub-proof
% 159.69/28.33 | | | | | | | | | | | | | | | | | | #688.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | (216) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (217) all_58_4 = e1 & op(e3, e1) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (9), (10), (15), (17), (18), (20), (21),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (22), (25), (26), (27), (29), (31), (33), (40),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (41), (43), (50), (51), (52), (53), (60), (61),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (66), (156), (162), (210), (217) are inconsistent
% 159.69/28.33 | | | | | | | | | | | | | | | | | | by sub-proof #687.
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (218) all_58_9 = e1 & op(e3, e0) = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | (219) all_58_9 = e1
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (25), (29), (31), (34), (40), (41),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | (42), (52), (67), (219) are inconsistent by
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | sub-proof #686.
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | (220) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (221) all_58_11 = e2 & op(e1, e0) = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (222) all_58_11 = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (222) imply:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (223) e3 = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (18), (21), (22), (29), (31), (40), (41),
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (52), (53), (72), (162), (223) are inconsistent by
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | sub-proof #777.
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (224) all_58_15 = e2 & op(e0, e0) = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | (225) op(e0, e0) = e2
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (52), (207), (225) are inconsistent by
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | | sub-proof #1386.
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | | |
% 159.69/28.33 | | | | | | | | | End of split
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | (226) all_58_2 = e0 & op(e2, e3) = e0
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | ALPHA: (226) implies:
% 159.69/28.33 | | | | | | | | | (227) op(e2, e3) = e0
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | REF_CLOSE: (25), (29), (52), (227) are inconsistent by
% 159.69/28.33 | | | | | | | | | sub-proof #1156.
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | End of split
% 159.69/28.33 | | | | | | | |
% 159.69/28.33 | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | |
% 159.69/28.33 | | | | | | | | (228) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 159.69/28.33 | | | | | | | | op(e0, e3) = e0)
% 159.69/28.33 | | | | | | | |
% 159.69/28.33 | | | | | | | | BETA: splitting (228) gives:
% 159.69/28.33 | | | | | | | |
% 159.69/28.33 | | | | | | | | Case 1:
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | (229) all_58_6 = e0 & op(e1, e3) = e0
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | ALPHA: (229) implies:
% 159.69/28.33 | | | | | | | | | (230) all_58_6 = e0
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | REF_CLOSE: (16), (41), (230) are inconsistent by sub-proof
% 159.69/28.33 | | | | | | | | | #735.
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | Case 2:
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | (231) all_58_12 = e0 & op(e0, e3) = e0
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | ALPHA: (231) implies:
% 159.69/28.33 | | | | | | | | | (232) all_58_12 = e0
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 159.69/28.33 | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 159.69/28.33 | | | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26),
% 159.69/28.33 | | | | | | | | | (28), (29), (30), (31), (32), (33), (34), (35),
% 159.69/28.33 | | | | | | | | | (36), (38), (39), (40), (41), (42), (43), (44),
% 159.69/28.33 | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 159.69/28.33 | | | | | | | | | (53), (54), (55), (232) are inconsistent by
% 159.69/28.33 | | | | | | | | | sub-proof #757.
% 159.69/28.33 | | | | | | | | |
% 159.69/28.33 | | | | | | | | End of split
% 159.69/28.33 | | | | | | | |
% 159.69/28.33 | | | | | | | End of split
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | Case 2:
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | (233) all_58_10 = e2 & op(e2, e0) = e2
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | ALPHA: (233) implies:
% 159.69/28.33 | | | | | | | (234) all_58_10 = e2
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | REF_CLOSE: (4), (21), (25), (29), (31), (34), (40), (41), (42),
% 159.69/28.33 | | | | | | | (52), (234) are inconsistent by sub-proof #906.
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | End of split
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | Case 2:
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | (235) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 159.69/28.33 | | | | | | op(e0, e0) = e2)
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | BETA: splitting (235) gives:
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | Case 1:
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | (236) all_58_11 = e2 & op(e1, e0) = e2
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | ALPHA: (236) implies:
% 159.69/28.33 | | | | | | | (237) all_58_11 = e2
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | REF_CLOSE: (53), (60), (237) are inconsistent by sub-proof #1049.
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | Case 2:
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | (238) all_58_15 = e2 & op(e0, e0) = e2
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | REF_CLOSE: (14), (36), (52), (238) are inconsistent by sub-proof
% 159.69/28.33 | | | | | | | #1452.
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | End of split
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | End of split
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | End of split
% 159.69/28.33 | | | |
% 159.69/28.33 | | | Case 2:
% 159.69/28.33 | | | |
% 159.69/28.33 | | | | (239) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 159.69/28.33 | | | | e0) = e2)
% 159.69/28.33 | | | |
% 159.69/28.33 | | | | BETA: splitting (239) gives:
% 159.69/28.33 | | | |
% 159.69/28.33 | | | | Case 1:
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | | (240) all_58_8 = e2 & op(e1, e1) = e2
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | | REF_CLOSE: (5), (43), (52), (240) are inconsistent by sub-proof #1440.
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | Case 2:
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | | (241) all_58_11 = e2 & op(e1, e0) = e2
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | | REF_CLOSE: (53), (60), (241) are inconsistent by sub-proof #852.
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | End of split
% 159.69/28.33 | | | |
% 159.69/28.33 | | | End of split
% 159.69/28.33 | | |
% 159.69/28.33 | | End of split
% 159.69/28.33 | |
% 159.69/28.33 | End of split
% 159.69/28.33 |
% 159.69/28.33 End of proof
% 159.69/28.33
% 159.69/28.33 Sub-proof #686 shows that the following formulas are inconsistent:
% 159.69/28.33 ----------------------------------------------------------------
% 159.69/28.33 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.33 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.33 (2) ~ (e3 = e0)
% 159.69/28.33 (3) ~ (e2 = e0)
% 159.69/28.33 (4) op(e2, e3) = e2
% 159.69/28.33 (5) ~ (e3 = e1)
% 159.69/28.33 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.33 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.33 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 159.69/28.33 (8) ~ (e2 = e1)
% 159.69/28.33 (9) ~ (e1 = e0)
% 159.69/28.33 (10) all_58_3 = e3
% 159.69/28.33 (11) all_58_9 = e1
% 159.69/28.33 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.33
% 159.69/28.33 Begin of proof
% 159.69/28.33 |
% 159.69/28.33 | BETA: splitting (7) gives:
% 159.69/28.33 |
% 159.69/28.33 | Case 1:
% 159.69/28.33 | |
% 159.69/28.33 | | (13) all_58_9 = e2 & op(e3, e0) = e2
% 159.69/28.33 | |
% 159.69/28.33 | | ALPHA: (13) implies:
% 159.69/28.33 | | (14) all_58_9 = e2
% 159.69/28.33 | |
% 159.69/28.33 | | REF_CLOSE: (8), (11), (14) are inconsistent by sub-proof #1324.
% 159.69/28.33 | |
% 159.69/28.33 | Case 2:
% 159.69/28.33 | |
% 159.69/28.33 | | (15) all_58_10 = e2 & op(e2, e0) = e2
% 159.69/28.33 | |
% 159.69/28.33 | | ALPHA: (15) implies:
% 159.69/28.33 | | (16) all_58_10 = e2
% 159.69/28.33 | |
% 159.69/28.33 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (16) are
% 159.69/28.33 | | inconsistent by sub-proof #906.
% 159.69/28.33 | |
% 159.69/28.33 | End of split
% 159.69/28.33 |
% 159.69/28.33 End of proof
% 159.69/28.33
% 159.69/28.33 Sub-proof #687 shows that the following formulas are inconsistent:
% 159.69/28.33 ----------------------------------------------------------------
% 159.69/28.33 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.33 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.33 (2) op(e1, e1) = all_6_2
% 159.69/28.33 (3) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.69/28.33 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.69/28.33 (4) all_58_12 = e3
% 159.69/28.33 (5) all_58_7 = e2
% 159.69/28.33 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.33 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.33 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.33 (8) op(e2, e1) = all_52_9
% 159.69/28.33 (9) op(e2, e3) = all_52_1
% 159.69/28.33 (10) all_58_4 = e1 & op(e3, e1) = e1
% 159.69/28.33 (11) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.33 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.33 (12) all_58_13 = e1
% 159.69/28.33 (13) ~ (e3 = e0)
% 159.69/28.33 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.33 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.33 (15) ~ (e2 = e0)
% 159.69/28.33 (16) ~ (all_52_9 = e3)
% 159.69/28.33 (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.33 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.33 (18) op(e2, e3) = e2
% 159.69/28.33 (19) ~ (e3 = e1)
% 159.69/28.33 (20) op(e1, e2) = all_52_6
% 159.69/28.33 (21) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.33 | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.69/28.33 (22) ~ (e2 = e1)
% 159.69/28.33 (23) ~ (e1 = e0)
% 159.69/28.33 (24) ~ (all_6_2 = e2)
% 159.69/28.33 (25) op(e1, e0) = e3
% 159.69/28.33 (26) ~ (all_52_6 = e3)
% 159.69/28.33 (27) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.33 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.33 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.33 (29) ~ (e3 = e2)
% 159.69/28.33 (30) all_58_11 = e3
% 159.69/28.33
% 159.69/28.33 Begin of proof
% 159.69/28.33 |
% 159.69/28.33 | ALPHA: (10) implies:
% 159.69/28.33 | (31) all_58_4 = e1
% 159.69/28.33 |
% 159.69/28.33 | BETA: splitting (3) gives:
% 159.69/28.33 |
% 159.69/28.33 | Case 1:
% 159.69/28.33 | |
% 159.69/28.33 | | (32) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 159.69/28.33 | | e3)
% 159.69/28.33 | |
% 159.69/28.33 | | BETA: splitting (32) gives:
% 159.69/28.33 | |
% 159.69/28.33 | | Case 1:
% 159.69/28.33 | | |
% 159.69/28.33 | | | (33) all_58_4 = e3 & op(e3, e1) = e3
% 159.69/28.33 | | |
% 159.69/28.33 | | | ALPHA: (33) implies:
% 159.69/28.33 | | | (34) all_58_4 = e3
% 159.69/28.33 | | |
% 159.69/28.33 | | | REF_CLOSE: (19), (31), (34) are inconsistent by sub-proof #1282.
% 159.69/28.33 | | |
% 159.69/28.33 | | Case 2:
% 159.69/28.33 | | |
% 159.69/28.33 | | | (35) all_58_5 = e3 & op(e2, e1) = e3
% 159.69/28.33 | | |
% 159.69/28.33 | | | ALPHA: (35) implies:
% 159.69/28.33 | | | (36) op(e2, e1) = e3
% 159.69/28.33 | | |
% 159.69/28.33 | | | REF_CLOSE: (8), (16), (28), (36) are inconsistent by sub-proof #1196.
% 159.69/28.33 | | |
% 159.69/28.33 | | End of split
% 159.69/28.33 | |
% 159.69/28.33 | Case 2:
% 159.69/28.33 | |
% 159.69/28.33 | | (37) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 159.69/28.33 | | e3)
% 159.69/28.33 | |
% 159.69/28.33 | | BETA: splitting (37) gives:
% 159.69/28.33 | |
% 159.69/28.33 | | Case 1:
% 159.69/28.33 | | |
% 159.69/28.33 | | | (38) all_58_8 = e3 & op(e1, e1) = e3
% 159.69/28.33 | | |
% 159.69/28.33 | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (11), (13), (14), (15), (17),
% 159.69/28.33 | | | (18), (19), (20), (22), (23), (24), (25), (26), (27), (28),
% 159.69/28.33 | | | (29), (30), (38) are inconsistent by sub-proof #710.
% 159.69/28.33 | | |
% 159.69/28.33 | | Case 2:
% 159.69/28.33 | | |
% 159.69/28.33 | | | (39) all_58_14 = e3 & op(e0, e1) = e3
% 159.69/28.33 | | |
% 159.69/28.33 | | | ALPHA: (39) implies:
% 159.69/28.33 | | | (40) all_58_14 = e3
% 159.69/28.33 | | |
% 159.69/28.33 | | | REF_CLOSE: (4), (12), (13), (21), (23), (40) are inconsistent by sub-proof
% 159.69/28.33 | | | #881.
% 159.69/28.33 | | |
% 159.69/28.33 | | End of split
% 159.69/28.33 | |
% 159.69/28.33 | End of split
% 159.69/28.33 |
% 159.69/28.33 End of proof
% 159.69/28.33
% 159.69/28.33 Sub-proof #688 shows that the following formulas are inconsistent:
% 159.69/28.33 ----------------------------------------------------------------
% 159.69/28.33 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.33 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.69/28.33 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.33 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.33 (3) op(e1, e1) = all_6_2
% 159.69/28.33 (4) all_58_12 = e3
% 159.69/28.33 (5) all_58_7 = e2
% 159.69/28.33 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.33 (7) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.69/28.33 (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.33 (8) all_58_6 = e1
% 159.69/28.33 (9) op(e2, e3) = all_52_1
% 159.69/28.33 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.33 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.33 (11) all_58_13 = e1
% 159.69/28.33 (12) ~ (e3 = e0)
% 159.69/28.33 (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.33 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.33 (14) ~ (e2 = e0)
% 159.69/28.33 (15) op(e2, e3) = e2
% 159.69/28.33 (16) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.33 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.33 (17) ~ (e3 = e1)
% 159.69/28.33 (18) all_58_1 = e1
% 159.69/28.33 (19) ~ (e2 = e1)
% 159.69/28.33 (20) ~ (e1 = e0)
% 159.69/28.33 (21) all_58_3 = e3
% 159.69/28.33 (22) ~ (all_6_2 = e2)
% 159.69/28.33 (23) all_58_9 = e2
% 159.69/28.33 (24) all_58_0 = e0
% 159.69/28.33 (25) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.33 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.33 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.33 (27) ~ (e3 = e2)
% 159.69/28.33 (28) all_58_11 = e3
% 159.69/28.33
% 159.69/28.33 Begin of proof
% 159.69/28.33 |
% 159.69/28.33 | BETA: splitting (7) gives:
% 159.69/28.33 |
% 159.69/28.33 | Case 1:
% 159.69/28.33 | |
% 159.69/28.33 | | (29) all_58_9 = e0 & op(e3, e0) = e0
% 159.69/28.33 | |
% 159.69/28.33 | | REF_CLOSE: (3), (4), (5), (6), (9), (10), (12), (13), (14), (15), (17),
% 159.69/28.33 | | (19), (20), (22), (23), (25), (26), (27), (28), (29) are
% 159.69/28.33 | | inconsistent by sub-proof #730.
% 159.69/28.33 | |
% 159.69/28.33 | Case 2:
% 159.69/28.33 | |
% 159.69/28.33 | | (30) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.69/28.33 | | e0)
% 159.69/28.33 | |
% 159.69/28.33 | | BETA: splitting (30) gives:
% 159.69/28.33 | |
% 159.69/28.33 | | Case 1:
% 159.69/28.33 | | |
% 159.69/28.33 | | | (31) all_58_10 = e0 & op(e2, e0) = e0
% 159.69/28.33 | | |
% 159.69/28.33 | | | ALPHA: (31) implies:
% 159.69/28.33 | | | (32) all_58_10 = e0
% 159.69/28.33 | | |
% 159.69/28.33 | | | BETA: splitting (2) gives:
% 159.69/28.33 | | |
% 159.69/28.33 | | | Case 1:
% 159.69/28.33 | | | |
% 159.69/28.33 | | | | (33) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 159.69/28.33 | | | | = e1)
% 159.69/28.33 | | | |
% 159.69/28.33 | | | | REF_CLOSE: (15), (17), (19), (21), (26), (33) are inconsistent by
% 159.69/28.33 | | | | sub-proof #911.
% 159.69/28.33 | | | |
% 159.69/28.33 | | | Case 2:
% 159.69/28.33 | | | |
% 159.69/28.33 | | | | (34) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 159.69/28.33 | | | | = e1)
% 159.69/28.33 | | | |
% 159.69/28.33 | | | | BETA: splitting (34) gives:
% 159.69/28.33 | | | |
% 159.69/28.33 | | | | Case 1:
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | | (35) all_58_5 = e1 & op(e2, e1) = e1
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | | ALPHA: (35) implies:
% 159.69/28.33 | | | | | (36) all_58_5 = e1
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | | BETA: splitting (16) gives:
% 159.69/28.33 | | | | |
% 159.69/28.33 | | | | | Case 1:
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | (37) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 159.69/28.33 | | | | | | e2) = e0)
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | BETA: splitting (37) gives:
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | Case 1:
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | (38) all_58_1 = e0 & op(e3, e2) = e0
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | ALPHA: (38) implies:
% 159.69/28.33 | | | | | | | (39) all_58_1 = e0
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | COMBINE_EQS: (18), (39) imply:
% 159.69/28.33 | | | | | | | (40) e1 = e0
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | COMBINE_EQS: (36), (40) imply:
% 159.69/28.33 | | | | | | | (41) all_58_5 = e0
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | REF_CLOSE: (2), (7), (12), (14), (15), (17), (19), (20), (21),
% 159.69/28.33 | | | | | | | (23), (26), (28), (41) are inconsistent by sub-proof
% 159.69/28.33 | | | | | | | #837.
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | Case 2:
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | (42) all_58_3 = e0 & op(e2, e2) = e0
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | | REF_CLOSE: (12), (21), (42) are inconsistent by sub-proof #910.
% 159.69/28.33 | | | | | | |
% 159.69/28.33 | | | | | | End of split
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | Case 2:
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | (43) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 159.69/28.33 | | | | | | e2) = e0)
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | BETA: splitting (43) gives:
% 159.69/28.33 | | | | | |
% 159.69/28.33 | | | | | | Case 1:
% 159.69/28.33 | | | | | | |
% 159.69/28.34 | | | | | | | (44) all_58_7 = e0 & op(e1, e2) = e0
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | ALPHA: (44) implies:
% 159.69/28.34 | | | | | | | (45) all_58_7 = e0
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | REF_CLOSE: (3), (4), (6), (9), (10), (12), (13), (14), (15), (17),
% 159.69/28.34 | | | | | | | (19), (20), (22), (25), (26), (27), (28), (45) are
% 159.69/28.34 | | | | | | | inconsistent by sub-proof #731.
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | Case 2:
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | (46) all_58_13 = e0 & op(e0, e2) = e0
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | ALPHA: (46) implies:
% 159.69/28.34 | | | | | | | (47) all_58_13 = e0
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | REF_CLOSE: (1), (5), (11), (17), (18), (19), (20), (21), (47) are
% 159.69/28.34 | | | | | | | inconsistent by sub-proof #690.
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | End of split
% 159.69/28.34 | | | | | |
% 159.69/28.34 | | | | | End of split
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | Case 2:
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | (48) all_58_10 = e1 & op(e2, e0) = e1
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | REF_CLOSE: (4), (8), (13), (15), (17), (19), (20), (24), (26), (32),
% 159.69/28.34 | | | | | (48) are inconsistent by sub-proof #689.
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | End of split
% 159.69/28.34 | | | |
% 159.69/28.34 | | | End of split
% 159.69/28.34 | | |
% 159.69/28.34 | | Case 2:
% 159.69/28.34 | | |
% 159.69/28.34 | | | (49) all_58_11 = e0 & op(e1, e0) = e0
% 159.69/28.34 | | |
% 159.69/28.34 | | | REF_CLOSE: (12), (28), (49) are inconsistent by sub-proof #1083.
% 159.69/28.34 | | |
% 159.69/28.34 | | End of split
% 159.69/28.34 | |
% 159.69/28.34 | End of split
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #689 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) all_58_12 = e3
% 159.69/28.34 (2) all_58_6 = e1
% 159.69/28.34 (3) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.34 (4) op(e2, e3) = e2
% 159.69/28.34 (5) ~ (e3 = e1)
% 159.69/28.34 (6) all_58_10 = e1 & op(e2, e0) = e1
% 159.69/28.34 (7) ~ (e2 = e1)
% 159.69/28.34 (8) ~ (e1 = e0)
% 159.69/28.34 (9) all_58_10 = e0
% 159.69/28.34 (10) all_58_0 = e0
% 159.69/28.34 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.34
% 159.69/28.34 Begin of proof
% 159.69/28.34 |
% 159.69/28.34 | ALPHA: (6) implies:
% 159.69/28.34 | (12) all_58_10 = e1
% 159.69/28.34 |
% 159.69/28.34 | COMBINE_EQS: (9), (12) imply:
% 159.69/28.34 | (13) e1 = e0
% 159.69/28.34 |
% 159.69/28.34 | SIMP: (13) implies:
% 159.69/28.34 | (14) e1 = e0
% 159.69/28.34 |
% 159.69/28.34 | COMBINE_EQS: (2), (14) imply:
% 159.69/28.34 | (15) all_58_6 = e0
% 159.69/28.34 |
% 159.69/28.34 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (15) are inconsistent by
% 159.69/28.34 | sub-proof #733.
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #690 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) all_58_13 = e0
% 159.69/28.34 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.34 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 159.69/28.34 (3) all_58_7 = e2
% 159.69/28.34 (4) all_58_13 = e1
% 159.69/28.34 (5) ~ (e3 = e1)
% 159.69/28.34 (6) all_58_1 = e1
% 159.69/28.34 (7) ~ (e2 = e1)
% 159.69/28.34 (8) ~ (e1 = e0)
% 159.69/28.34 (9) all_58_3 = e3
% 159.69/28.34
% 159.69/28.34 Begin of proof
% 159.69/28.34 |
% 159.69/28.34 | COMBINE_EQS: (1), (4) imply:
% 159.69/28.34 | (10) e1 = e0
% 159.69/28.34 |
% 159.69/28.34 | SIMP: (10) implies:
% 159.69/28.34 | (11) e1 = e0
% 159.69/28.34 |
% 159.69/28.34 | COMBINE_EQS: (6), (11) imply:
% 159.69/28.34 | (12) all_58_1 = e0
% 159.69/28.34 |
% 159.69/28.34 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (12) are inconsistent by
% 159.69/28.34 | sub-proof #857.
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #691 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) all_58_15 = e0
% 159.69/28.34 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.34 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.34 (3) all_58_12 = e3
% 159.69/28.34 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.34 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.34 (5) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 159.69/28.34 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 159.69/28.34 (6) op(e2, e3) = all_52_1
% 159.69/28.34 (7) ~ (e3 = e0)
% 159.69/28.34 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.34 (9) ~ (e2 = e0)
% 159.69/28.34 (10) op(e2, e3) = e2
% 159.69/28.34 (11) ~ (e3 = e1)
% 159.69/28.34 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.34 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.34 (13) ~ (e2 = e1)
% 159.69/28.34 (14) ~ (e1 = e0)
% 159.69/28.34 (15) all_58_3 = e3
% 159.69/28.34 (16) all_58_9 = e1
% 159.69/28.34 (17) all_58_0 = e0
% 159.69/28.34 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.34 (19) ~ (e3 = e2)
% 159.69/28.34 (20) all_58_11 = e3
% 159.69/28.34
% 159.69/28.34 Begin of proof
% 159.69/28.34 |
% 159.69/28.34 | BETA: splitting (5) gives:
% 159.69/28.34 |
% 159.69/28.34 | Case 1:
% 159.69/28.34 | |
% 159.69/28.34 | | (21) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 159.69/28.34 | | e2)
% 159.69/28.34 | |
% 159.69/28.34 | | REF_CLOSE: (2), (7), (9), (10), (11), (12), (13), (14), (15), (16), (18),
% 159.69/28.34 | | (21) are inconsistent by sub-proof #693.
% 159.69/28.34 | |
% 159.69/28.34 | Case 2:
% 159.69/28.34 | |
% 159.69/28.34 | | (22) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.34 | | e2)
% 159.69/28.34 | |
% 159.69/28.34 | | BETA: splitting (22) gives:
% 159.69/28.34 | |
% 159.69/28.34 | | Case 1:
% 159.69/28.34 | | |
% 159.69/28.34 | | | (23) all_58_11 = e2 & op(e1, e0) = e2
% 159.69/28.34 | | |
% 159.69/28.34 | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (13), (14), (17), (18),
% 159.69/28.34 | | | (19), (20), (23) are inconsistent by sub-proof #692.
% 159.69/28.34 | | |
% 159.69/28.34 | | Case 2:
% 159.69/28.34 | | |
% 159.69/28.34 | | | (24) all_58_15 = e2 & op(e0, e0) = e2
% 159.69/28.34 | | |
% 159.69/28.34 | | | REF_CLOSE: (1), (9), (24) are inconsistent by sub-proof #900.
% 159.69/28.34 | | |
% 159.69/28.34 | | End of split
% 159.69/28.34 | |
% 159.69/28.34 | End of split
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #692 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) all_58_12 = e3
% 159.69/28.34 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.34 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.34 (3) op(e2, e3) = all_52_1
% 159.69/28.34 (4) ~ (e3 = e0)
% 159.69/28.34 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.34 (6) op(e2, e3) = e2
% 159.69/28.34 (7) ~ (e3 = e1)
% 159.69/28.34 (8) ~ (e2 = e1)
% 159.69/28.34 (9) ~ (e1 = e0)
% 159.69/28.34 (10) all_58_0 = e0
% 159.69/28.34 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.34 (12) ~ (e3 = e2)
% 159.69/28.34 (13) all_58_11 = e2 & op(e1, e0) = e2
% 159.69/28.34 (14) all_58_11 = e3
% 159.69/28.34
% 159.69/28.34 Begin of proof
% 159.69/28.34 |
% 159.69/28.34 | ALPHA: (13) implies:
% 159.69/28.34 | (15) all_58_11 = e2
% 159.69/28.34 |
% 159.69/28.34 | COMBINE_EQS: (14), (15) imply:
% 159.69/28.34 | (16) e3 = e2
% 159.69/28.34 |
% 159.69/28.34 | COMBINE_EQS: (1), (16) imply:
% 159.69/28.34 | (17) all_58_12 = e2
% 159.69/28.34 |
% 159.69/28.34 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (17) are
% 159.69/28.34 | inconsistent by sub-proof #1066.
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #693 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.34 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.34 (2) ~ (e3 = e0)
% 159.69/28.34 (3) ~ (e2 = e0)
% 159.69/28.34 (4) op(e2, e3) = e2
% 159.69/28.34 (5) ~ (e3 = e1)
% 159.69/28.34 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.34 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.34 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 159.69/28.34 (8) ~ (e2 = e1)
% 159.69/28.34 (9) ~ (e1 = e0)
% 159.69/28.34 (10) all_58_3 = e3
% 159.69/28.34 (11) all_58_9 = e1
% 159.69/28.34 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.34
% 159.69/28.34 Begin of proof
% 159.69/28.34 |
% 159.69/28.34 | BETA: splitting (7) gives:
% 159.69/28.34 |
% 159.69/28.34 | Case 1:
% 159.69/28.34 | |
% 159.69/28.34 | | (13) all_58_9 = e2 & op(e3, e0) = e2
% 159.69/28.34 | |
% 159.69/28.34 | | REF_CLOSE: (8), (11), (13) are inconsistent by sub-proof #931.
% 159.69/28.34 | |
% 159.69/28.34 | Case 2:
% 159.69/28.34 | |
% 159.69/28.34 | | (14) all_58_10 = e2 & op(e2, e0) = e2
% 159.69/28.34 | |
% 159.69/28.34 | | ALPHA: (14) implies:
% 159.69/28.34 | | (15) all_58_10 = e2
% 159.69/28.34 | |
% 159.69/28.34 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (15) are
% 159.69/28.34 | | inconsistent by sub-proof #906.
% 159.69/28.34 | |
% 159.69/28.34 | End of split
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #694 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) all_58_12 = e3
% 159.69/28.34 (2) all_58_6 = e1
% 159.69/28.34 (3) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.34 (4) all_58_0 = e1 & op(e3, e3) = e1
% 159.69/28.34 (5) op(e2, e3) = e2
% 159.69/28.34 (6) ~ (e3 = e1)
% 159.69/28.34 (7) ~ (e2 = e1)
% 159.69/28.34 (8) ~ (e1 = e0)
% 159.69/28.34 (9) all_58_0 = e0
% 159.69/28.34 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.34
% 159.69/28.34 Begin of proof
% 159.69/28.34 |
% 159.69/28.34 | ALPHA: (4) implies:
% 159.69/28.34 | (11) all_58_0 = e1
% 159.69/28.34 |
% 159.69/28.34 | COMBINE_EQS: (9), (11) imply:
% 159.69/28.34 | (12) e1 = e0
% 159.69/28.34 |
% 159.69/28.34 | SIMP: (12) implies:
% 159.69/28.34 | (13) e1 = e0
% 159.69/28.34 |
% 159.69/28.34 | COMBINE_EQS: (2), (13) imply:
% 159.69/28.34 | (14) all_58_6 = e0
% 159.69/28.34 |
% 159.69/28.34 | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (14) are inconsistent by
% 159.69/28.34 | sub-proof #733.
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #695 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.34 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.34 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.69/28.34 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.34 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.34 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.34 (4) op(e1, e1) = all_6_2
% 159.69/28.34 (5) ~ (all_52_7 = e3)
% 159.69/28.34 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.34 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.34 (7) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.69/28.34 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.69/28.34 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.34 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.34 (9) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.69/28.34 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.69/28.34 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.34 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.34 (11) op(e2, e3) = all_52_1
% 159.69/28.34 (12) ~ (all_52_13 = e3)
% 159.69/28.34 (13) ~ (e3 = e0)
% 159.69/28.34 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.34 (15) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.69/28.34 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.69/28.34 (16) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.34 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.34 e2)
% 159.69/28.34 (17) ~ (e2 = e0)
% 159.69/28.34 (18) op(e2, e0) = all_52_13
% 159.69/28.34 (19) op(e2, e3) = e2
% 159.69/28.34 (20) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.34 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.34 (21) ~ (e3 = e1)
% 159.69/28.34 (22) op(e1, e2) = all_52_6
% 159.69/28.34 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.34 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.34 (24) op(e0, e0) = e2
% 159.69/28.34 (25) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.34 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.34 (26) op(e0, e2) = e0
% 159.69/28.34 (27) all_58_15 = e2
% 159.69/28.34 (28) ~ (e2 = e1)
% 159.69/28.34 (29) ~ (e1 = e0)
% 159.69/28.34 (30) all_58_4 = e3
% 159.69/28.34 (31) all_58_3 = e3
% 159.69/28.34 (32) ~ (all_6_2 = e2)
% 159.69/28.34 (33) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.34 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.34 e3)
% 159.69/28.34 (34) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.34 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.34 (35) op(e0, e2) = all_52_7
% 159.69/28.34 (36) ~ (all_52_6 = e3)
% 159.69/28.34 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.34 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.34 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.34 (39) ~ (e3 = e2)
% 159.69/28.34 (40) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.34 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.34 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.34 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.34 (41) all_58_11 = e3
% 159.69/28.34
% 159.69/28.34 Begin of proof
% 159.69/28.34 |
% 159.69/28.34 | BETA: splitting (9) gives:
% 159.69/28.34 |
% 159.69/28.34 | Case 1:
% 159.69/28.34 | |
% 159.69/28.34 | | (42) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 159.69/28.34 | | e2)
% 159.69/28.34 | |
% 159.69/28.34 | | BETA: splitting (42) gives:
% 159.69/28.34 | |
% 159.69/28.34 | | Case 1:
% 159.69/28.34 | | |
% 159.69/28.34 | | | (43) all_58_4 = e2 & op(e3, e1) = e2
% 159.69/28.34 | | |
% 159.69/28.34 | | | ALPHA: (43) implies:
% 159.69/28.34 | | | (44) all_58_4 = e2
% 159.69/28.34 | | |
% 159.69/28.34 | | | COMBINE_EQS: (30), (44) imply:
% 159.69/28.34 | | | (45) e3 = e2
% 159.69/28.34 | | |
% 159.69/28.34 | | | COMBINE_EQS: (41), (45) imply:
% 159.69/28.34 | | | (46) all_58_11 = e2
% 159.69/28.34 | | |
% 159.69/28.34 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 159.69/28.34 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 159.69/28.34 | | | (25), (26), (28), (29), (31), (33), (34), (35), (36), (37),
% 159.69/28.34 | | | (38), (39), (40), (46) are inconsistent by sub-proof #696.
% 159.69/28.34 | | |
% 159.69/28.34 | | Case 2:
% 159.69/28.34 | | |
% 159.69/28.34 | | | (47) all_58_5 = e2 & op(e2, e1) = e2
% 159.69/28.34 | | |
% 159.69/28.34 | | | ALPHA: (47) implies:
% 159.69/28.34 | | | (48) all_58_5 = e2
% 159.69/28.34 | | |
% 159.69/28.34 | | | REF_CLOSE: (3), (13), (17), (19), (21), (23), (28), (29), (31), (38), (48)
% 159.69/28.34 | | | are inconsistent by sub-proof #898.
% 159.69/28.34 | | |
% 159.69/28.34 | | End of split
% 159.69/28.34 | |
% 159.69/28.34 | Case 2:
% 159.69/28.34 | |
% 159.69/28.34 | | (49) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 159.69/28.34 | | e2)
% 159.69/28.34 | |
% 159.69/28.34 | | REF_CLOSE: (4), (5), (6), (13), (17), (21), (24), (27), (28), (29), (32),
% 159.69/28.34 | | (33), (35), (38), (39), (40), (49) are inconsistent by sub-proof
% 159.69/28.34 | | #891.
% 159.69/28.34 | |
% 159.69/28.34 | End of split
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #696 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.34 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.34 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.69/28.34 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.34 (3) ~ (all_52_7 = e3)
% 159.69/28.34 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.34 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.34 (5) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.69/28.34 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.69/28.34 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.34 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.34 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.34 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.34 (8) op(e2, e3) = all_52_1
% 159.69/28.34 (9) ~ (all_52_13 = e3)
% 159.69/28.34 (10) ~ (e3 = e0)
% 159.69/28.34 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.34 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.34 (12) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.69/28.34 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.69/28.34 (13) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.34 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.34 e2)
% 159.69/28.34 (14) ~ (e2 = e0)
% 159.69/28.34 (15) op(e2, e0) = all_52_13
% 159.69/28.34 (16) op(e2, e3) = e2
% 159.69/28.34 (17) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.34 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.34 (18) ~ (e3 = e1)
% 159.69/28.34 (19) op(e1, e2) = all_52_6
% 159.69/28.34 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.34 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.34 (21) op(e0, e0) = e2
% 159.69/28.34 (22) all_58_11 = e2
% 159.69/28.34 (23) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.34 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.34 (24) op(e0, e2) = e0
% 159.69/28.34 (25) ~ (e2 = e1)
% 159.69/28.34 (26) ~ (e1 = e0)
% 159.69/28.34 (27) all_58_3 = e3
% 159.69/28.34 (28) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.34 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.34 e3)
% 159.69/28.34 (29) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.34 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.34 (30) op(e0, e2) = all_52_7
% 159.69/28.34 (31) ~ (all_52_6 = e3)
% 159.69/28.34 (32) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.34 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.34 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.34 (34) ~ (e3 = e2)
% 159.69/28.34 (35) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.34 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.34 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.34 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.34
% 159.69/28.34 Begin of proof
% 159.69/28.34 |
% 159.69/28.34 | BETA: splitting (5) gives:
% 159.69/28.34 |
% 159.69/28.34 | Case 1:
% 159.69/28.34 | |
% 159.69/28.34 | | (36) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 159.69/28.34 | | e3)
% 159.69/28.34 | |
% 159.69/28.34 | | BETA: splitting (36) gives:
% 159.69/28.34 | |
% 159.69/28.34 | | Case 1:
% 159.69/28.34 | | |
% 159.69/28.34 | | | (37) all_58_9 = e3 & op(e3, e0) = e3
% 159.69/28.34 | | |
% 159.69/28.34 | | | ALPHA: (37) implies:
% 159.69/28.34 | | | (38) all_58_9 = e3
% 159.69/28.34 | | |
% 159.69/28.34 | | | BETA: splitting (13) gives:
% 159.69/28.34 | | |
% 159.69/28.34 | | | Case 1:
% 159.69/28.34 | | | |
% 159.69/28.34 | | | | (39) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 159.69/28.34 | | | | e2) = e2)
% 159.69/28.34 | | | |
% 159.69/28.34 | | | | REF_CLOSE: (6), (8), (10), (11), (14), (16), (18), (24), (25), (26),
% 159.69/28.34 | | | | (30), (32), (33), (34), (39) are inconsistent by sub-proof
% 159.69/28.34 | | | | #1039.
% 159.69/28.34 | | | |
% 159.69/28.34 | | | Case 2:
% 159.69/28.34 | | | |
% 159.69/28.34 | | | | (40) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 159.69/28.34 | | | | e0) = e2)
% 159.69/28.34 | | | |
% 159.69/28.34 | | | | BETA: splitting (40) gives:
% 159.69/28.34 | | | |
% 159.69/28.34 | | | | Case 1:
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | (41) all_58_14 = e2 & op(e0, e1) = e2
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | ALPHA: (41) implies:
% 159.69/28.34 | | | | | (42) all_58_14 = e2
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | BETA: splitting (28) gives:
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | Case 1:
% 159.69/28.34 | | | | | |
% 159.69/28.34 | | | | | | (43) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 159.69/28.34 | | | | | | op(e0, e2) = e3)
% 159.69/28.34 | | | | | |
% 159.69/28.34 | | | | | | BETA: splitting (43) gives:
% 159.69/28.34 | | | | | |
% 159.69/28.34 | | | | | | Case 1:
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | (44) all_58_12 = e3 & op(e0, e3) = e3
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | ALPHA: (44) implies:
% 159.69/28.34 | | | | | | | (45) all_58_12 = e3
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 159.69/28.34 | | | | | | | (12), (14), (15), (16), (17), (18), (19), (20), (21),
% 159.69/28.34 | | | | | | | (22), (23), (24), (25), (26), (27), (29), (30), (31),
% 159.69/28.34 | | | | | | | (32), (33), (34), (42), (45) are inconsistent by
% 159.69/28.34 | | | | | | | sub-proof #697.
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | Case 2:
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | (46) all_58_13 = e3 & op(e0, e2) = e3
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | | REF_CLOSE: (3), (30), (33), (46) are inconsistent by sub-proof
% 159.69/28.34 | | | | | | | #1449.
% 159.69/28.34 | | | | | | |
% 159.69/28.34 | | | | | | End of split
% 159.69/28.34 | | | | | |
% 159.69/28.34 | | | | | Case 2:
% 159.69/28.34 | | | | | |
% 159.69/28.34 | | | | | | (47) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 159.69/28.34 | | | | | | op(e0, e0) = e3)
% 159.69/28.34 | | | | | |
% 159.69/28.34 | | | | | | REF_CLOSE: (21), (33), (34), (42), (47) are inconsistent by
% 159.69/28.34 | | | | | | sub-proof #1381.
% 159.69/28.34 | | | | | |
% 159.69/28.34 | | | | | End of split
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | Case 2:
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | (48) all_58_15 = e2 & op(e0, e0) = e2
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | ALPHA: (48) implies:
% 159.69/28.34 | | | | | (49) all_58_15 = e2
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | | REF_CLOSE: (2), (10), (14), (18), (22), (25), (26), (35), (38), (49)
% 159.69/28.34 | | | | | are inconsistent by sub-proof #1453.
% 159.69/28.34 | | | | |
% 159.69/28.34 | | | | End of split
% 159.69/28.34 | | | |
% 159.69/28.34 | | | End of split
% 159.69/28.34 | | |
% 159.69/28.34 | | Case 2:
% 159.69/28.34 | | |
% 159.69/28.34 | | | (50) all_58_10 = e3 & op(e2, e0) = e3
% 159.69/28.34 | | |
% 159.69/28.34 | | | ALPHA: (50) implies:
% 159.69/28.34 | | | (51) op(e2, e0) = e3
% 159.69/28.34 | | |
% 159.69/28.34 | | | REF_CLOSE: (9), (15), (33), (51) are inconsistent by sub-proof #1364.
% 159.69/28.34 | | |
% 159.69/28.34 | | End of split
% 159.69/28.34 | |
% 159.69/28.34 | Case 2:
% 159.69/28.34 | |
% 159.69/28.34 | | (52) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.34 | | e3)
% 159.69/28.34 | |
% 159.69/28.34 | | REF_CLOSE: (21), (22), (33), (34), (52) are inconsistent by sub-proof #901.
% 159.69/28.34 | |
% 159.69/28.34 | End of split
% 159.69/28.34 |
% 159.69/28.34 End of proof
% 159.69/28.34
% 159.69/28.34 Sub-proof #697 shows that the following formulas are inconsistent:
% 159.69/28.34 ----------------------------------------------------------------
% 159.69/28.34 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.34 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.34 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 159.69/28.34 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.34 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.34 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.35 (4) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 159.69/28.35 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 159.69/28.35 (5) all_58_12 = e3
% 159.69/28.35 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.35 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.35 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.35 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.35 (8) all_58_14 = e2
% 159.69/28.35 (9) op(e2, e3) = all_52_1
% 159.69/28.35 (10) ~ (all_52_13 = e3)
% 159.69/28.35 (11) ~ (e3 = e0)
% 159.69/28.35 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.35 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.35 (13) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 159.69/28.35 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 159.69/28.35 (14) ~ (e2 = e0)
% 159.69/28.35 (15) op(e2, e0) = all_52_13
% 159.69/28.35 (16) op(e2, e3) = e2
% 159.69/28.35 (17) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.35 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.35 (18) ~ (e3 = e1)
% 159.69/28.35 (19) op(e1, e2) = all_52_6
% 159.69/28.35 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.35 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.35 (21) op(e0, e0) = e2
% 159.69/28.35 (22) all_58_11 = e2
% 159.69/28.35 (23) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.35 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.35 (24) op(e0, e2) = e0
% 159.69/28.35 (25) ~ (e2 = e1)
% 159.69/28.35 (26) ~ (e1 = e0)
% 159.69/28.35 (27) all_58_3 = e3
% 159.69/28.35 (28) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.35 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.35 (29) op(e0, e2) = all_52_7
% 159.69/28.35 (30) ~ (all_52_6 = e3)
% 159.69/28.35 (31) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.35 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.35 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.35 (33) ~ (e3 = e2)
% 159.69/28.35
% 159.69/28.35 Begin of proof
% 159.69/28.35 |
% 159.69/28.35 | BETA: splitting (4) gives:
% 159.69/28.35 |
% 159.69/28.35 | Case 1:
% 159.69/28.35 | |
% 159.69/28.35 | | (34) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 159.69/28.35 | | e3)
% 159.69/28.35 | |
% 159.69/28.35 | | BETA: splitting (34) gives:
% 159.69/28.35 | |
% 159.69/28.35 | | Case 1:
% 159.69/28.35 | | |
% 159.69/28.35 | | | (35) all_58_9 = e3 & op(e3, e0) = e3
% 159.69/28.35 | | |
% 159.69/28.35 | | | ALPHA: (35) implies:
% 159.69/28.35 | | | (36) all_58_9 = e3
% 159.69/28.35 | | |
% 159.69/28.35 | | | BETA: splitting (2) gives:
% 159.69/28.35 | | |
% 159.69/28.35 | | | Case 1:
% 159.69/28.35 | | | |
% 159.69/28.35 | | | | (37) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 159.69/28.35 | | | | = e1)
% 159.69/28.35 | | | |
% 159.69/28.35 | | | | BETA: splitting (37) gives:
% 159.69/28.35 | | | |
% 159.69/28.35 | | | | Case 1:
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | | (38) all_58_9 = e1 & op(e3, e0) = e1
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | | ALPHA: (38) implies:
% 159.69/28.35 | | | | | (39) all_58_9 = e1
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | | REF_CLOSE: (18), (36), (39) are inconsistent by sub-proof #1461.
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | Case 2:
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | | (40) all_58_10 = e1 & op(e2, e0) = e1
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | | ALPHA: (40) implies:
% 159.69/28.35 | | | | | (41) all_58_10 = e1
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | | BETA: splitting (31) gives:
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | | Case 1:
% 159.69/28.35 | | | | | |
% 159.69/28.35 | | | | | | (42) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 159.69/28.35 | | | | | | e3) = e0)
% 159.69/28.35 | | | | | |
% 159.69/28.35 | | | | | | BETA: splitting (42) gives:
% 159.69/28.35 | | | | | |
% 159.69/28.35 | | | | | | Case 1:
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | (43) all_58_0 = e0 & op(e3, e3) = e0
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | ALPHA: (43) implies:
% 159.69/28.35 | | | | | | | (44) all_58_0 = e0
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | BETA: splitting (20) gives:
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | (45) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 159.69/28.35 | | | | | | | | op(e2, e2) = e0)
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | REF_CLOSE: (11), (14), (16), (27), (32), (45) are inconsistent
% 159.69/28.35 | | | | | | | | by sub-proof #755.
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | (46) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 159.69/28.35 | | | | | | | | op(e2, e0) = e0)
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | BETA: splitting (46) gives:
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | (47) all_58_5 = e0 & op(e2, e1) = e0
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | ALPHA: (47) implies:
% 159.69/28.35 | | | | | | | | | (48) all_58_5 = e0
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | BETA: splitting (12) gives:
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | (49) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 159.69/28.35 | | | | | | | | | | op(e2, e3) = e1)
% 159.69/28.35 | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | REF_CLOSE: (16), (25), (26), (32), (44), (49) are
% 159.69/28.35 | | | | | | | | | | inconsistent by sub-proof #1160.
% 159.69/28.35 | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | (50) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 159.69/28.35 | | | | | | | | | | & op(e0, e3) = e1)
% 159.69/28.35 | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | BETA: splitting (50) gives:
% 159.69/28.35 | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | (51) all_58_6 = e1 & op(e1, e3) = e1
% 159.69/28.35 | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | ALPHA: (51) implies:
% 159.69/28.35 | | | | | | | | | | | (52) all_58_6 = e1
% 159.69/28.35 | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | BETA: splitting (3) gives:
% 159.69/28.35 | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | (53) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 159.69/28.35 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 159.69/28.35 | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | BETA: splitting (53) gives:
% 159.69/28.35 | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | (54) all_58_12 = e1 & op(e0, e3) = e1
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | REF_CLOSE: (5), (18), (54) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | #1388.
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | (55) all_58_13 = e1 & op(e0, e2) = e1
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | ALPHA: (55) implies:
% 159.69/28.35 | | | | | | | | | | | | | (56) all_58_13 = e1
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | BETA: splitting (7) gives:
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | (57) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 159.69/28.35 | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 159.69/28.35 | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (30), (32), (52), (57) are
% 159.69/28.35 | | | | | | | | | | | | | | inconsistent by sub-proof #718.
% 159.69/28.35 | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | (58) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 159.69/28.35 | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 159.69/28.35 | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 159.69/28.35 | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | (59) all_58_8 = e3 & op(e1, e1) = e3
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | ALPHA: (59) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | (60) all_58_8 = e3
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | (61) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 159.69/28.35 | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | (62) all_58_4 = e1 & op(e3, e1) = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | ALPHA: (62) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | (63) all_58_4 = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | (64) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 159.69/28.35 | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (65) all_58_0 = e2 & op(e3, e3) = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (44), (65) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | #702.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (66) all_58_1 = e2 & op(e3, e2) = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | ALPHA: (66) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (67) all_58_1 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | (68) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (69) all_58_1 = e0 & op(e3, e2) = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (67), (69) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | #796.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (70) all_58_3 = e0 & op(e2, e2) = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (27), (70) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | #910.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | (71) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (72) all_58_7 = e0 & op(e1, e2) = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (72) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (73) all_58_7 = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | (74) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (55) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (75) op(e0, e2) = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_52_7, e0, e2, e0,
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (24), (29) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (76) all_52_7 = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_52_7, e1, e2, e0,
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (29), (75) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (77) all_52_7 = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (77) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (78) e1 = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (78) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (79) all_58_6 = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14),
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (16), (17), (18), (21), (22), (25), (26), (27),
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (28), (32), (33), (60), (79) are inconsistent by
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #700.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (80) all_58_3 = e2 & op(e2, e2) = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (81) all_58_3 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (81) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (82) e3 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (82) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (83) all_58_12 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11), (16), (18), (32), (33), (44),
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (52), (83) are inconsistent by sub-proof #1067.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | (84) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (85) all_58_7 = e2 & op(e1, e2) = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (85) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (86) all_58_7 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (73), (86) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | #1086.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | (87) all_58_13 = e2 & op(e0, e2) = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (56), (87) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | | #727.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (88) all_58_13 = e0 & op(e0, e2) = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (89) all_58_13 = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (89) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (90) e1 = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14),
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (16), (17), (18), (21), (22), (25), (26), (27),
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | (28), (32), (33), (52), (60), (90) are
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #699.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | (91) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 159.69/28.35 | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (92) all_58_4 = e2 & op(e3, e1) = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (93) all_58_4 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (63), (93) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | #1311.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (94) all_58_9 = e2 & op(e3, e0) = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (95) all_58_9 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (95) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (96) e3 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (96) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (97) all_58_12 = e2
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11), (16), (18), (32), (33), (44),
% 159.69/28.35 | | | | | | | | | | | | | | | | | | | (52), (97) are inconsistent by sub-proof #1067.
% 159.69/28.35 | | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | (98) all_58_5 = e1 & op(e2, e1) = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | (99) all_58_5 = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (99) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | | | (100) e1 = e0
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14),
% 159.69/28.35 | | | | | | | | | | | | | | | | | (16), (17), (18), (21), (22), (25), (26), (27),
% 159.69/28.35 | | | | | | | | | | | | | | | | | (28), (32), (33), (52), (60), (100) are
% 159.69/28.35 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #699.
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | (101) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 159.69/28.35 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 159.69/28.35 | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 159.69/28.35 | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | (102) all_58_8 = e1 & op(e1, e1) = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | (103) all_58_8 = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (60), (103) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | | | | | #950.
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | (104) all_58_14 = e1 & op(e0, e1) = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | | | (105) all_58_14 = e1
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (25), (105) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | | | | | #1387.
% 159.69/28.35 | | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | (106) all_58_11 = e3 & op(e1, e0) = e3
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 159.69/28.35 | | | | | | | | | | | | | | | (107) all_58_11 = e3
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | COMBINE_EQS: (22), (107) imply:
% 159.69/28.35 | | | | | | | | | | | | | | | (108) e3 = e2
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (11), (16), (18), (32), (33), (44),
% 159.69/28.35 | | | | | | | | | | | | | | | (52), (108) are inconsistent by sub-proof #698.
% 159.69/28.35 | | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | (109) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 159.69/28.35 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 159.69/28.35 | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | BETA: splitting (109) gives:
% 159.69/28.35 | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | (110) all_58_14 = e1 & op(e0, e1) = e1
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | REF_CLOSE: (8), (25), (110) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | | | #1339.
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | (111) all_58_15 = e1 & op(e0, e0) = e1
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | ALPHA: (111) implies:
% 159.69/28.35 | | | | | | | | | | | | | (112) op(e0, e0) = e1
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | | REF_CLOSE: (21), (25), (32), (112) are inconsistent by
% 159.69/28.35 | | | | | | | | | | | | | sub-proof #1386.
% 159.69/28.35 | | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | (113) all_58_12 = e1 & op(e0, e3) = e1
% 159.69/28.35 | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | | REF_CLOSE: (5), (18), (113) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | | | #1388.
% 159.69/28.35 | | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | | |
% 159.69/28.35 | | | | | | | | | End of split
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | (114) all_58_10 = e0 & op(e2, e0) = e0
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | REF_CLOSE: (26), (41), (114) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | #1459.
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | End of split
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | End of split
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | Case 2:
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | (115) all_58_2 = e0 & op(e2, e3) = e0
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | ALPHA: (115) implies:
% 159.69/28.35 | | | | | | | (116) op(e2, e3) = e0
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | REF_CLOSE: (14), (16), (32), (116) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | #1156.
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | End of split
% 159.69/28.35 | | | | | |
% 159.69/28.35 | | | | | Case 2:
% 159.69/28.35 | | | | | |
% 159.69/28.35 | | | | | | (117) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 159.69/28.35 | | | | | | op(e0, e3) = e0)
% 159.69/28.35 | | | | | |
% 159.69/28.35 | | | | | | BETA: splitting (117) gives:
% 159.69/28.35 | | | | | |
% 159.69/28.35 | | | | | | Case 1:
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | (118) all_58_6 = e0 & op(e1, e3) = e0
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | ALPHA: (118) implies:
% 159.69/28.35 | | | | | | | (119) all_58_6 = e0
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | BETA: splitting (7) gives:
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | (120) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 159.69/28.35 | | | | | | | | op(e1, e2) = e3)
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | BETA: splitting (120) gives:
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | (121) all_58_6 = e3 & op(e1, e3) = e3
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | ALPHA: (121) implies:
% 159.69/28.35 | | | | | | | | | (122) all_58_6 = e3
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | REF_CLOSE: (11), (119), (122) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | #1321.
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | (123) all_58_7 = e3 & op(e1, e2) = e3
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | REF_CLOSE: (19), (30), (32), (123) are inconsistent by
% 159.69/28.35 | | | | | | | | | sub-proof #1184.
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | End of split
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | (124) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 159.69/28.35 | | | | | | | | op(e1, e0) = e3)
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | BETA: splitting (124) gives:
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | | Case 1:
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | (125) all_58_8 = e3 & op(e1, e1) = e3
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | ALPHA: (125) implies:
% 159.69/28.35 | | | | | | | | | (126) all_58_8 = e3
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14),
% 159.69/28.35 | | | | | | | | | (16), (17), (18), (21), (22), (25), (26), (27),
% 159.69/28.35 | | | | | | | | | (28), (32), (33), (119), (126) are inconsistent by
% 159.69/28.35 | | | | | | | | | sub-proof #700.
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | Case 2:
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | (127) all_58_11 = e3 & op(e1, e0) = e3
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | ALPHA: (127) implies:
% 159.69/28.35 | | | | | | | | | (128) all_58_11 = e3
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | COMBINE_EQS: (22), (128) imply:
% 159.69/28.35 | | | | | | | | | (129) e3 = e2
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | COMBINE_EQS: (5), (129) imply:
% 159.69/28.35 | | | | | | | | | (130) all_58_12 = e2
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | | REF_CLOSE: (6), (9), (11), (12), (16), (18), (25), (26), (32),
% 159.69/28.35 | | | | | | | | | (33), (119), (130) are inconsistent by sub-proof
% 159.69/28.35 | | | | | | | | | #1063.
% 159.69/28.35 | | | | | | | | |
% 159.69/28.35 | | | | | | | | End of split
% 159.69/28.35 | | | | | | | |
% 159.69/28.35 | | | | | | | End of split
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | Case 2:
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | (131) all_58_12 = e0 & op(e0, e3) = e0
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | ALPHA: (131) implies:
% 159.69/28.35 | | | | | | | (132) all_58_12 = e0
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | | REF_CLOSE: (5), (11), (132) are inconsistent by sub-proof #1463.
% 159.69/28.35 | | | | | | |
% 159.69/28.35 | | | | | | End of split
% 159.69/28.35 | | | | | |
% 159.69/28.35 | | | | | End of split
% 159.69/28.35 | | | | |
% 159.69/28.35 | | | | End of split
% 159.69/28.35 | | | |
% 159.69/28.35 | | | Case 2:
% 159.69/28.35 | | | |
% 159.69/28.35 | | | | (133) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 159.69/28.35 | | | | e0) = e1)
% 159.69/28.35 | | | |
% 159.69/28.35 | | | | REF_CLOSE: (21), (22), (25), (32), (133) are inconsistent by sub-proof
% 159.69/28.35 | | | | #895.
% 159.69/28.35 | | | |
% 159.69/28.35 | | | End of split
% 159.69/28.35 | | |
% 159.69/28.35 | | Case 2:
% 159.69/28.35 | | |
% 159.69/28.35 | | | (134) all_58_10 = e3 & op(e2, e0) = e3
% 159.69/28.35 | | |
% 159.69/28.35 | | | ALPHA: (134) implies:
% 159.69/28.35 | | | (135) op(e2, e0) = e3
% 159.69/28.35 | | |
% 159.69/28.35 | | | REF_CLOSE: (10), (15), (32), (135) are inconsistent by sub-proof #1364.
% 159.69/28.35 | | |
% 159.69/28.35 | | End of split
% 159.69/28.35 | |
% 159.69/28.35 | Case 2:
% 159.69/28.35 | |
% 159.69/28.35 | | (136) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.35 | | e3)
% 159.69/28.35 | |
% 159.69/28.35 | | BETA: splitting (136) gives:
% 159.69/28.35 | |
% 159.69/28.35 | | Case 1:
% 159.69/28.35 | | |
% 159.69/28.35 | | | (137) all_58_11 = e3 & op(e1, e0) = e3
% 159.69/28.35 | | |
% 159.69/28.35 | | | ALPHA: (137) implies:
% 159.69/28.35 | | | (138) all_58_11 = e3
% 159.69/28.35 | | |
% 159.69/28.35 | | | COMBINE_EQS: (22), (138) imply:
% 159.69/28.35 | | | (139) e3 = e2
% 159.69/28.35 | | |
% 159.69/28.35 | | | COMBINE_EQS: (5), (139) imply:
% 159.69/28.35 | | | (140) all_58_12 = e2
% 159.69/28.35 | | |
% 159.69/28.35 | | | REF_CLOSE: (6), (9), (11), (12), (14), (16), (18), (25), (26), (31), (32),
% 159.69/28.35 | | | (33), (140) are inconsistent by sub-proof #1062.
% 159.69/28.35 | | |
% 159.69/28.35 | | Case 2:
% 159.69/28.35 | | |
% 159.69/28.35 | | | (141) all_58_15 = e3 & op(e0, e0) = e3
% 159.69/28.35 | | |
% 159.69/28.35 | | | ALPHA: (141) implies:
% 159.69/28.35 | | | (142) op(e0, e0) = e3
% 159.69/28.35 | | |
% 159.69/28.35 | | | REF_CLOSE: (21), (32), (33), (142) are inconsistent by sub-proof #1382.
% 159.69/28.35 | | |
% 159.69/28.35 | | End of split
% 159.69/28.35 | |
% 159.69/28.35 | End of split
% 159.69/28.35 |
% 159.69/28.35 End of proof
% 159.69/28.35
% 159.69/28.35 Sub-proof #698 shows that the following formulas are inconsistent:
% 159.69/28.35 ----------------------------------------------------------------
% 159.69/28.35 (1) all_58_12 = e3
% 159.69/28.35 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.35 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.35 (3) all_58_6 = e1
% 159.69/28.35 (4) op(e2, e3) = all_52_1
% 159.69/28.35 (5) ~ (e3 = e0)
% 159.69/28.35 (6) op(e2, e3) = e2
% 159.69/28.35 (7) ~ (e3 = e1)
% 159.69/28.35 (8) e3 = e2
% 159.69/28.35 (9) all_58_0 = e0
% 159.69/28.35 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.35 (11) ~ (e3 = e2)
% 159.69/28.35
% 159.69/28.35 Begin of proof
% 159.69/28.35 |
% 159.69/28.35 | SIMP: (8) implies:
% 159.69/28.35 | (12) e3 = e2
% 159.69/28.35 |
% 159.69/28.35 | COMBINE_EQS: (1), (12) imply:
% 159.69/28.35 | (13) all_58_12 = e2
% 159.69/28.35 |
% 159.69/28.35 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (13) are
% 159.69/28.35 | inconsistent by sub-proof #1067.
% 159.69/28.35 |
% 159.69/28.35 End of proof
% 159.69/28.35
% 159.69/28.35 Sub-proof #699 shows that the following formulas are inconsistent:
% 159.69/28.35 ----------------------------------------------------------------
% 159.69/28.35 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.35 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.35 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.35 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.35 (3) all_58_12 = e3
% 159.69/28.35 (4) all_58_8 = e3
% 159.69/28.35 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.35 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.35 (6) all_58_14 = e2
% 159.69/28.35 (7) all_58_6 = e1
% 159.69/28.35 (8) e1 = e0
% 159.69/28.35 (9) op(e2, e3) = all_52_1
% 159.69/28.35 (10) ~ (e3 = e0)
% 159.69/28.35 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.35 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.35 (12) ~ (e2 = e0)
% 159.69/28.35 (13) op(e2, e3) = e2
% 159.69/28.35 (14) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.35 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.35 (15) ~ (e3 = e1)
% 159.69/28.35 (16) op(e0, e0) = e2
% 159.69/28.35 (17) all_58_11 = e2
% 159.69/28.35 (18) ~ (e2 = e1)
% 159.69/28.35 (19) ~ (e1 = e0)
% 159.69/28.35 (20) all_58_3 = e3
% 159.69/28.35 (21) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.35 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.35 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.35 (23) ~ (e3 = e2)
% 159.69/28.35
% 159.69/28.35 Begin of proof
% 159.69/28.35 |
% 159.69/28.35 | SIMP: (8) implies:
% 159.69/28.35 | (24) e1 = e0
% 159.69/28.35 |
% 159.69/28.35 | COMBINE_EQS: (7), (24) imply:
% 159.69/28.35 | (25) all_58_6 = e0
% 159.69/28.35 |
% 159.69/28.35 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14),
% 159.69/28.35 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (25) are
% 159.69/28.35 | inconsistent by sub-proof #700.
% 159.69/28.35 |
% 159.69/28.35 End of proof
% 159.69/28.35
% 159.69/28.35 Sub-proof #700 shows that the following formulas are inconsistent:
% 159.69/28.35 ----------------------------------------------------------------
% 159.69/28.35 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.35 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.35 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.35 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.35 (3) all_58_12 = e3
% 159.69/28.35 (4) all_58_8 = e3
% 159.69/28.35 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.35 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.35 (6) all_58_14 = e2
% 159.69/28.35 (7) op(e2, e3) = all_52_1
% 159.69/28.35 (8) ~ (e3 = e0)
% 159.69/28.35 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.35 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.35 (10) ~ (e2 = e0)
% 159.69/28.35 (11) all_58_6 = e0
% 159.69/28.35 (12) op(e2, e3) = e2
% 159.69/28.35 (13) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.35 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.35 (14) ~ (e3 = e1)
% 159.69/28.35 (15) op(e0, e0) = e2
% 159.69/28.35 (16) all_58_11 = e2
% 159.69/28.35 (17) ~ (e2 = e1)
% 159.69/28.35 (18) ~ (e1 = e0)
% 159.69/28.35 (19) all_58_3 = e3
% 159.69/28.35 (20) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.35 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.35 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.35 (22) ~ (e3 = e2)
% 159.69/28.35
% 159.69/28.35 Begin of proof
% 159.69/28.35 |
% 159.69/28.35 | BETA: splitting (1) gives:
% 159.69/28.35 |
% 159.69/28.35 | Case 1:
% 159.69/28.35 | |
% 159.69/28.35 | | (23) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 159.69/28.35 | | e1)
% 159.69/28.35 | |
% 159.69/28.35 | | BETA: splitting (23) gives:
% 159.69/28.35 | |
% 159.69/28.35 | | Case 1:
% 159.69/28.35 | | |
% 159.69/28.35 | | | (24) all_58_6 = e1 & op(e1, e3) = e1
% 159.69/28.35 | | |
% 159.69/28.35 | | | ALPHA: (24) implies:
% 159.69/28.35 | | | (25) all_58_6 = e1
% 159.69/28.35 | | |
% 159.69/28.35 | | | REF_CLOSE: (11), (18), (25) are inconsistent by sub-proof #735.
% 159.69/28.35 | | |
% 159.69/28.35 | | Case 2:
% 159.69/28.35 | | |
% 159.69/28.35 | | | (26) all_58_7 = e1 & op(e1, e2) = e1
% 159.69/28.35 | | |
% 159.69/28.35 | | | ALPHA: (26) implies:
% 159.69/28.36 | | | (27) all_58_7 = e1
% 159.69/28.36 | | |
% 159.69/28.36 | | | BETA: splitting (9) gives:
% 159.69/28.36 | | |
% 159.69/28.36 | | | Case 1:
% 159.69/28.36 | | | |
% 159.69/28.36 | | | | (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 159.69/28.36 | | | | = e1)
% 159.69/28.36 | | | |
% 159.69/28.36 | | | | BETA: splitting (28) gives:
% 159.69/28.36 | | | |
% 159.69/28.36 | | | | Case 1:
% 159.69/28.36 | | | | |
% 159.69/28.36 | | | | | (29) all_58_0 = e1 & op(e3, e3) = e1
% 159.69/28.36 | | | | |
% 159.69/28.36 | | | | | ALPHA: (29) implies:
% 159.69/28.36 | | | | | (30) all_58_0 = e1
% 159.69/28.36 | | | | |
% 159.69/28.36 | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.69/28.36 | | | | | (14), (15), (17), (18), (19), (20), (21), (22), (27), (30)
% 159.69/28.36 | | | | | are inconsistent by sub-proof #701.
% 159.69/28.36 | | | | |
% 159.69/28.36 | | | | Case 2:
% 159.69/28.36 | | | | |
% 159.69/28.36 | | | | | (31) all_58_2 = e1 & op(e2, e3) = e1
% 159.69/28.36 | | | | |
% 159.69/28.36 | | | | | ALPHA: (31) implies:
% 159.69/28.36 | | | | | (32) op(e2, e3) = e1
% 159.69/28.36 | | | | |
% 159.69/28.36 | | | | | REF_CLOSE: (12), (17), (21), (32) are inconsistent by sub-proof #1430.
% 159.69/28.36 | | | | |
% 159.69/28.36 | | | | End of split
% 159.69/28.36 | | | |
% 159.69/28.36 | | | Case 2:
% 159.69/28.36 | | | |
% 159.69/28.36 | | | | (33) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 159.69/28.36 | | | | = e1)
% 159.69/28.36 | | | |
% 159.69/28.36 | | | | REF_CLOSE: (3), (11), (14), (18), (33) are inconsistent by sub-proof
% 159.69/28.36 | | | | #734.
% 159.69/28.36 | | | |
% 159.69/28.36 | | | End of split
% 159.69/28.36 | | |
% 159.69/28.36 | | End of split
% 159.69/28.36 | |
% 159.69/28.36 | Case 2:
% 159.69/28.36 | |
% 159.69/28.36 | | (34) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 159.69/28.36 | | e1)
% 159.69/28.36 | |
% 159.69/28.36 | | BETA: splitting (34) gives:
% 159.69/28.36 | |
% 159.69/28.36 | | Case 1:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (35) all_58_8 = e1 & op(e1, e1) = e1
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (4), (14), (35) are inconsistent by sub-proof #959.
% 159.69/28.36 | | |
% 159.69/28.36 | | Case 2:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (36) all_58_11 = e1 & op(e1, e0) = e1
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (16), (17), (36) are inconsistent by sub-proof #1455.
% 159.69/28.36 | | |
% 159.69/28.36 | | End of split
% 159.69/28.36 | |
% 159.69/28.36 | End of split
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #701 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.36 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.36 (2) all_58_12 = e3
% 159.69/28.36 (3) all_58_0 = e1
% 159.69/28.36 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.36 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.36 (5) all_58_14 = e2
% 159.69/28.36 (6) op(e2, e3) = all_52_1
% 159.69/28.36 (7) ~ (e3 = e0)
% 159.69/28.36 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.36 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.36 (9) ~ (e2 = e0)
% 159.69/28.36 (10) all_58_6 = e0
% 159.69/28.36 (11) op(e2, e3) = e2
% 159.69/28.36 (12) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.36 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.36 (13) ~ (e3 = e1)
% 159.69/28.36 (14) all_58_7 = e1
% 159.69/28.36 (15) op(e0, e0) = e2
% 159.69/28.36 (16) ~ (e2 = e1)
% 159.69/28.36 (17) ~ (e1 = e0)
% 159.69/28.36 (18) all_58_3 = e3
% 159.69/28.36 (19) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 159.69/28.36 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.36 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.36 (21) ~ (e3 = e2)
% 159.69/28.36
% 159.69/28.36 Begin of proof
% 159.69/28.36 |
% 159.69/28.36 | BETA: splitting (1) gives:
% 159.69/28.36 |
% 159.69/28.36 | Case 1:
% 159.69/28.36 | |
% 159.69/28.36 | | (22) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 159.69/28.36 | | e1)
% 159.69/28.36 | |
% 159.69/28.36 | | BETA: splitting (22) gives:
% 159.69/28.36 | |
% 159.69/28.36 | | Case 1:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (23) all_58_12 = e1 & op(e0, e3) = e1
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (2), (13), (23) are inconsistent by sub-proof #1388.
% 159.69/28.36 | | |
% 159.69/28.36 | | Case 2:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (24) all_58_13 = e1 & op(e0, e2) = e1
% 159.69/28.36 | | |
% 159.69/28.36 | | | ALPHA: (24) implies:
% 159.69/28.36 | | | (25) all_58_13 = e1
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.69/28.36 | | | (14), (16), (17), (18), (19), (20), (21), (25) are inconsistent
% 159.69/28.36 | | | by sub-proof #726.
% 159.69/28.36 | | |
% 159.69/28.36 | | End of split
% 159.69/28.36 | |
% 159.69/28.36 | Case 2:
% 159.69/28.36 | |
% 159.69/28.36 | | (26) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 159.69/28.36 | | e1)
% 159.69/28.36 | |
% 159.69/28.36 | | REF_CLOSE: (5), (15), (16), (20), (26) are inconsistent by sub-proof #1385.
% 159.69/28.36 | |
% 159.69/28.36 | End of split
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #702 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) all_58_0 = e2 & op(e3, e3) = e2
% 159.69/28.36 (2) all_58_0 = e0
% 159.69/28.36 (3) ~ (e2 = e0)
% 159.69/28.36
% 159.69/28.36 Begin of proof
% 159.69/28.36 |
% 159.69/28.36 | ALPHA: (1) implies:
% 159.69/28.36 | (4) all_58_0 = e2
% 159.69/28.36 |
% 159.69/28.36 | COMBINE_EQS: (2), (4) imply:
% 159.69/28.36 | (5) e2 = e0
% 159.69/28.36 |
% 159.69/28.36 | SIMP: (5) implies:
% 159.69/28.36 | (6) e2 = e0
% 159.69/28.36 |
% 159.69/28.36 | REDUCE: (3), (6) imply:
% 159.69/28.36 | (7) $false
% 159.69/28.36 |
% 159.69/28.36 | CLOSE: (7) is inconsistent.
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #703 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) all_58_14 = e2 & op(e0, e1) = e2
% 159.69/28.36 (2) all_58_14 = e1
% 159.69/28.36 (3) ~ (e2 = e1)
% 159.69/28.36
% 159.69/28.36 Begin of proof
% 159.69/28.36 |
% 159.69/28.36 | ALPHA: (1) implies:
% 159.69/28.36 | (4) all_58_14 = e2
% 159.69/28.36 |
% 159.69/28.36 | COMBINE_EQS: (2), (4) imply:
% 159.69/28.36 | (5) e2 = e1
% 159.69/28.36 |
% 159.69/28.36 | REDUCE: (3), (5) imply:
% 159.69/28.36 | (6) $false
% 159.69/28.36 |
% 159.69/28.36 | CLOSE: (6) is inconsistent.
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #704 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.36 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.36 (2) all_58_14 = e2
% 159.69/28.36 (3) ~ (e3 = e0)
% 159.69/28.36 (4) ~ (e2 = e0)
% 159.69/28.36 (5) op(e2, e3) = e2
% 159.69/28.36 (6) ~ (e3 = e1)
% 159.69/28.36 (7) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 159.69/28.36 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 159.69/28.36 (8) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 159.69/28.36 (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 159.69/28.36 e0) | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 159.69/28.36 e1) = e0))
% 159.69/28.36 (9) ~ (e2 = e1)
% 159.69/28.36 (10) ~ (e1 = e0)
% 159.69/28.36 (11) all_58_4 = e3
% 159.69/28.36 (12) all_58_3 = e3
% 159.69/28.36 (13) all_58_9 = e2
% 159.69/28.36 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.36 (15) all_58_11 = e3
% 159.69/28.36 (16) all_58_8 = e1
% 159.69/28.36
% 159.69/28.36 Begin of proof
% 159.69/28.36 |
% 159.69/28.36 | ALPHA: (8) implies:
% 159.69/28.36 | (17) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.36 | | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.36 |
% 159.69/28.36 | BETA: splitting (7) gives:
% 159.69/28.36 |
% 159.69/28.36 | Case 1:
% 159.69/28.36 | |
% 159.69/28.36 | | (18) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 159.69/28.36 | | e0)
% 159.69/28.36 | |
% 159.69/28.36 | | BETA: splitting (18) gives:
% 159.69/28.36 | |
% 159.69/28.36 | | Case 1:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (19) all_58_4 = e0 & op(e3, e1) = e0
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (3), (11), (19) are inconsistent by sub-proof #1344.
% 159.69/28.36 | | |
% 159.69/28.36 | | Case 2:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (20) all_58_5 = e0 & op(e2, e1) = e0
% 159.69/28.36 | | |
% 159.69/28.36 | | | ALPHA: (20) implies:
% 159.69/28.36 | | | (21) all_58_5 = e0
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (12), (13), (14), (15),
% 159.69/28.36 | | | (17), (21) are inconsistent by sub-proof #837.
% 159.69/28.36 | | |
% 159.69/28.36 | | End of split
% 159.69/28.36 | |
% 159.69/28.36 | Case 2:
% 159.69/28.36 | |
% 159.69/28.36 | | (22) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 159.69/28.36 | | e0)
% 159.69/28.36 | |
% 159.69/28.36 | | BETA: splitting (22) gives:
% 159.69/28.36 | |
% 159.69/28.36 | | Case 1:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (23) all_58_8 = e0 & op(e1, e1) = e0
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (10), (16), (23) are inconsistent by sub-proof #1271.
% 159.69/28.36 | | |
% 159.69/28.36 | | Case 2:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (24) all_58_14 = e0 & op(e0, e1) = e0
% 159.69/28.36 | | |
% 159.69/28.36 | | | ALPHA: (24) implies:
% 159.69/28.36 | | | (25) all_58_14 = e0
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (2), (4), (25) are inconsistent by sub-proof #1408.
% 159.69/28.36 | | |
% 159.69/28.36 | | End of split
% 159.69/28.36 | |
% 159.69/28.36 | End of split
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #705 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.36 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.36 (2) op(e2, e3) = all_52_1
% 159.69/28.36 (3) ~ (e3 = e0)
% 159.69/28.36 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.36 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.36 (5) ~ (e2 = e0)
% 159.69/28.36 (6) op(e2, e3) = e2
% 159.69/28.36 (7) ~ (e3 = e1)
% 159.69/28.36 (8) op(e0, e2) = e0
% 159.69/28.36 (9) ~ (e2 = e1)
% 159.69/28.36 (10) ~ (e1 = e0)
% 159.69/28.36 (11) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.36 (12) op(e0, e2) = all_52_7
% 159.69/28.36 (13) all_58_0 = e0
% 159.69/28.36 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.36 (15) ~ (e3 = e2)
% 159.69/28.36
% 159.69/28.36 Begin of proof
% 159.69/28.36 |
% 159.69/28.36 | BETA: splitting (11) gives:
% 159.69/28.36 |
% 159.69/28.36 | Case 1:
% 159.69/28.36 | |
% 159.69/28.36 | | (16) all_58_12 = e2 & op(e0, e3) = e2
% 159.69/28.36 | |
% 159.69/28.36 | | ALPHA: (16) implies:
% 159.69/28.36 | | (17) all_58_12 = e2
% 159.69/28.36 | |
% 159.69/28.36 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (13), (14), (15), (17)
% 159.69/28.36 | | are inconsistent by sub-proof #1066.
% 159.69/28.36 | |
% 159.69/28.36 | Case 2:
% 159.69/28.36 | |
% 159.69/28.36 | | (18) all_58_13 = e2 & op(e0, e2) = e2
% 159.69/28.36 | |
% 159.69/28.36 | | ALPHA: (18) implies:
% 159.69/28.36 | | (19) op(e0, e2) = e2
% 159.69/28.36 | |
% 159.69/28.36 | | REF_CLOSE: (5), (8), (12), (14), (19) are inconsistent by sub-proof #1040.
% 159.69/28.36 | |
% 159.69/28.36 | End of split
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #706 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) all_58_12 = e3
% 159.69/28.36 (2) all_58_6 = e1
% 159.69/28.36 (3) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.36 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.36 (4) op(e2, e3) = e2
% 159.69/28.36 (5) ~ (e3 = e1)
% 159.69/28.36 (6) all_58_15 = e0 & op(e0, e0) = e0
% 159.69/28.36 (7) all_58_15 = e1
% 159.69/28.36 (8) ~ (e2 = e1)
% 159.69/28.36 (9) ~ (e1 = e0)
% 159.69/28.36 (10) all_58_0 = e0
% 159.69/28.36 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.36
% 159.69/28.36 Begin of proof
% 159.69/28.36 |
% 159.69/28.36 | ALPHA: (6) implies:
% 159.69/28.36 | (12) all_58_15 = e0
% 159.69/28.36 |
% 159.69/28.36 | COMBINE_EQS: (7), (12) imply:
% 159.69/28.36 | (13) e1 = e0
% 159.69/28.36 |
% 159.69/28.36 | SIMP: (13) implies:
% 159.69/28.36 | (14) e1 = e0
% 159.69/28.36 |
% 159.69/28.36 | COMBINE_EQS: (2), (14) imply:
% 159.69/28.36 | (15) all_58_6 = e0
% 159.69/28.36 |
% 159.69/28.36 | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (15) are inconsistent by
% 159.69/28.36 | sub-proof #733.
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #707 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.36 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.36 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.36 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.36 (3) op(e1, e1) = all_6_2
% 159.69/28.36 (4) ~ (all_52_7 = e3)
% 159.69/28.36 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.36 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.36 (6) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.69/28.36 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.69/28.36 (7) all_58_12 = e3
% 159.69/28.36 (8) all_58_7 = e2
% 159.69/28.36 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.36 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.36 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.69/28.36 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.69/28.36 (11) ~ (all_4_2 = e2)
% 159.69/28.36 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.36 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.36 (13) op(e2, e1) = all_52_9
% 159.69/28.36 (14) op(e2, e3) = all_52_1
% 159.69/28.36 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.36 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.36 (16) ~ (e3 = e0)
% 159.69/28.36 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.36 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.36 (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.36 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.36 e2)
% 159.69/28.36 (19) ~ (e2 = e0)
% 159.69/28.36 (20) ~ (all_52_9 = e3)
% 159.69/28.36 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.36 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.36 (22) op(e2, e3) = e2
% 159.69/28.36 (23) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.36 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.69/28.36 (24) ~ (e3 = e1)
% 159.69/28.36 (25) op(e1, e2) = all_52_6
% 159.69/28.36 (26) all_58_1 = e1
% 159.69/28.36 (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.36 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.36 (28) all_58_10 = e1
% 159.69/28.36 (29) op(e0, e0) = all_4_2
% 159.69/28.36 (30) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.36 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.36 (31) ~ (e2 = e1)
% 159.69/28.36 (32) ~ (e1 = e0)
% 159.69/28.36 (33) all_58_3 = e3
% 159.69/28.36 (34) ~ (all_6_2 = e2)
% 159.69/28.36 (35) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.36 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.36 e3)
% 159.69/28.36 (36) op(e1, e0) = e3
% 159.69/28.36 (37) op(e0, e2) = all_52_7
% 159.69/28.36 (38) all_58_0 = e0
% 159.69/28.36 (39) ~ (all_52_6 = e3)
% 159.69/28.36 (40) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.36 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.36 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.36 (42) ~ (e3 = e2)
% 159.69/28.36 (43) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.36 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.36 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.36 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.36 (44) all_58_11 = e3
% 159.69/28.36
% 159.69/28.36 Begin of proof
% 159.69/28.36 |
% 159.69/28.36 | BETA: splitting (18) gives:
% 159.69/28.36 |
% 159.69/28.36 | Case 1:
% 159.69/28.36 | |
% 159.69/28.36 | | (45) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 159.69/28.36 | | e2)
% 159.69/28.36 | |
% 159.69/28.36 | | BETA: splitting (45) gives:
% 159.69/28.36 | |
% 159.69/28.36 | | Case 1:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (46) all_58_12 = e2 & op(e0, e3) = e2
% 159.69/28.36 | | |
% 159.69/28.36 | | | ALPHA: (46) implies:
% 159.69/28.36 | | | (47) all_58_12 = e2
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (9), (14), (16), (17), (22), (24), (31), (32), (38), (41),
% 159.69/28.36 | | | (42), (47) are inconsistent by sub-proof #1066.
% 159.69/28.36 | | |
% 159.69/28.36 | | Case 2:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (48) all_58_13 = e2 & op(e0, e2) = e2
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (3), (7), (9), (14), (15), (16), (17), (19), (22), (23), (24),
% 159.69/28.36 | | | (26), (31), (32), (33), (34), (37), (40), (41), (42), (44),
% 159.69/28.36 | | | (48) are inconsistent by sub-proof #716.
% 159.69/28.36 | | |
% 159.69/28.36 | | End of split
% 159.69/28.36 | |
% 159.69/28.36 | Case 2:
% 159.69/28.36 | |
% 159.69/28.36 | | (49) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.36 | | e2)
% 159.69/28.36 | |
% 159.69/28.36 | | BETA: splitting (49) gives:
% 159.69/28.36 | |
% 159.69/28.36 | | Case 1:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (50) all_58_14 = e2 & op(e0, e1) = e2
% 159.69/28.36 | | |
% 159.69/28.36 | | | ALPHA: (50) implies:
% 159.69/28.36 | | | (51) all_58_14 = e2
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 159.69/28.36 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 159.69/28.36 | | | (25), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 159.69/28.36 | | | (37), (38), (39), (40), (41), (42), (43), (44), (51) are
% 159.69/28.36 | | | inconsistent by sub-proof #708.
% 159.69/28.36 | | |
% 159.69/28.36 | | Case 2:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (52) all_58_15 = e2 & op(e0, e0) = e2
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (11), (29), (41), (52) are inconsistent by sub-proof #1452.
% 159.69/28.36 | | |
% 159.69/28.36 | | End of split
% 159.69/28.36 | |
% 159.69/28.36 | End of split
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #708 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.36 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.36 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.36 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.36 (3) op(e1, e1) = all_6_2
% 159.69/28.36 (4) ~ (all_52_7 = e3)
% 159.69/28.36 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.36 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.36 (6) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 159.69/28.36 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.69/28.36 (7) all_58_12 = e3
% 159.69/28.36 (8) all_58_7 = e2
% 159.69/28.36 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.36 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.36 (10) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.69/28.36 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.69/28.36 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.36 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.36 (12) all_58_14 = e2
% 159.69/28.36 (13) op(e2, e1) = all_52_9
% 159.69/28.36 (14) op(e2, e3) = all_52_1
% 159.69/28.36 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.36 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.36 (16) ~ (e3 = e0)
% 159.69/28.36 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.36 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.36 (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.36 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.36 e2)
% 159.69/28.36 (19) ~ (e2 = e0)
% 159.69/28.36 (20) ~ (all_52_9 = e3)
% 159.69/28.36 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.36 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.36 (22) op(e2, e3) = e2
% 159.69/28.36 (23) ~ (e3 = e1)
% 159.69/28.36 (24) op(e1, e2) = all_52_6
% 159.69/28.36 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.36 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.36 (26) all_58_10 = e1
% 159.69/28.36 (27) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.36 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.36 (28) ~ (e2 = e1)
% 159.69/28.36 (29) ~ (e1 = e0)
% 159.69/28.36 (30) all_58_3 = e3
% 159.69/28.36 (31) ~ (all_6_2 = e2)
% 159.69/28.36 (32) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.36 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.36 e3)
% 159.69/28.36 (33) op(e1, e0) = e3
% 159.69/28.36 (34) op(e0, e2) = all_52_7
% 159.69/28.36 (35) all_58_0 = e0
% 159.69/28.36 (36) ~ (all_52_6 = e3)
% 159.69/28.36 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.36 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.36 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.36 (39) ~ (e3 = e2)
% 159.69/28.36 (40) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.36 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.36 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.36 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.36 (41) all_58_11 = e3
% 159.69/28.36
% 159.69/28.36 Begin of proof
% 159.69/28.36 |
% 159.69/28.36 | BETA: splitting (6) gives:
% 159.69/28.36 |
% 159.69/28.36 | Case 1:
% 159.69/28.36 | |
% 159.69/28.36 | | (42) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 159.69/28.36 | | e3)
% 159.69/28.36 | |
% 159.69/28.36 | | BETA: splitting (42) gives:
% 159.69/28.36 | |
% 159.69/28.36 | | Case 1:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (43) all_58_4 = e3 & op(e3, e1) = e3
% 159.69/28.36 | | |
% 159.69/28.36 | | | ALPHA: (43) implies:
% 159.69/28.36 | | | (44) all_58_4 = e3
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (7), (8), (12), (16), (17), (19), (21), (22), (23), (25), (26),
% 159.69/28.36 | | | (27), (28), (29), (30), (35), (38), (41), (44) are inconsistent
% 159.69/28.36 | | | by sub-proof #712.
% 159.69/28.36 | | |
% 159.69/28.36 | | Case 2:
% 159.69/28.36 | | |
% 159.69/28.36 | | | (45) all_58_5 = e3 & op(e2, e1) = e3
% 159.69/28.36 | | |
% 159.69/28.36 | | | ALPHA: (45) implies:
% 159.69/28.36 | | | (46) op(e2, e1) = e3
% 159.69/28.36 | | |
% 159.69/28.36 | | | REF_CLOSE: (13), (20), (38), (46) are inconsistent by sub-proof #1196.
% 159.69/28.36 | | |
% 159.69/28.36 | | End of split
% 159.69/28.36 | |
% 159.69/28.36 | Case 2:
% 159.69/28.36 | |
% 159.69/28.36 | | (47) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 159.69/28.36 | | e3)
% 159.69/28.36 | |
% 159.69/28.36 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (14), (15),
% 159.69/28.36 | | (16), (17), (18), (19), (21), (22), (23), (24), (25), (28), (29),
% 159.69/28.36 | | (30), (31), (32), (33), (34), (36), (37), (38), (39), (40), (41),
% 159.69/28.36 | | (47) are inconsistent by sub-proof #709.
% 159.69/28.36 | |
% 159.69/28.36 | End of split
% 159.69/28.36 |
% 159.69/28.36 End of proof
% 159.69/28.36
% 159.69/28.36 Sub-proof #709 shows that the following formulas are inconsistent:
% 159.69/28.36 ----------------------------------------------------------------
% 159.69/28.36 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.36 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.36 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.69/28.36 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 159.69/28.36 (3) op(e1, e1) = all_6_2
% 159.69/28.36 (4) ~ (all_52_7 = e3)
% 159.69/28.36 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 159.69/28.36 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 159.69/28.36 (6) all_58_12 = e3
% 159.69/28.36 (7) all_58_7 = e2
% 159.69/28.36 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.36 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.36 (9) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 159.69/28.36 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 159.69/28.36 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.36 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.36 (11) op(e2, e3) = all_52_1
% 159.69/28.36 (12) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.36 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.36 (13) ~ (e3 = e0)
% 159.69/28.37 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.37 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.37 (15) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 159.69/28.37 | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 159.69/28.37 e2)
% 159.69/28.37 (16) ~ (e2 = e0)
% 159.69/28.37 (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.37 (18) op(e2, e3) = e2
% 159.69/28.37 (19) ~ (e3 = e1)
% 159.69/28.37 (20) op(e1, e2) = all_52_6
% 159.69/28.37 (21) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.37 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.37 (22) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 159.69/28.37 (23) ~ (e2 = e1)
% 159.69/28.37 (24) ~ (e1 = e0)
% 159.69/28.37 (25) all_58_3 = e3
% 159.69/28.37 (26) ~ (all_6_2 = e2)
% 159.69/28.37 (27) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 159.69/28.37 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 159.69/28.37 e3)
% 159.69/28.37 (28) op(e1, e0) = e3
% 159.69/28.37 (29) op(e0, e2) = all_52_7
% 159.69/28.37 (30) ~ (all_52_6 = e3)
% 159.69/28.37 (31) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.37 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.37 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.37 (33) ~ (e3 = e2)
% 159.69/28.37 (34) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 159.69/28.37 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 159.69/28.37 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 159.69/28.37 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 159.69/28.37 (35) all_58_11 = e3
% 159.69/28.37
% 159.69/28.37 Begin of proof
% 159.69/28.37 |
% 159.69/28.37 | BETA: splitting (22) gives:
% 159.69/28.37 |
% 159.69/28.37 | Case 1:
% 159.69/28.37 | |
% 159.69/28.37 | | (36) all_58_8 = e3 & op(e1, e1) = e3
% 159.69/28.37 | |
% 159.69/28.37 | | REF_CLOSE: (1), (3), (7), (8), (10), (11), (12), (13), (14), (16), (17),
% 159.69/28.37 | | (18), (19), (20), (23), (24), (26), (28), (30), (31), (32), (33),
% 159.69/28.37 | | (35), (36) are inconsistent by sub-proof #710.
% 159.69/28.37 | |
% 159.69/28.37 | Case 2:
% 159.69/28.37 | |
% 159.69/28.37 | | (37) all_58_14 = e3 & op(e0, e1) = e3
% 159.69/28.37 | |
% 159.69/28.37 | | ALPHA: (37) implies:
% 159.69/28.37 | | (38) all_58_14 = e3
% 159.69/28.37 | |
% 159.69/28.37 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (11), (13), (14), (15), (16),
% 159.69/28.37 | | (18), (19), (21), (23), (24), (25), (26), (27), (29), (31), (32),
% 159.69/28.37 | | (33), (34), (38) are inconsistent by sub-proof #771.
% 159.69/28.37 | |
% 159.69/28.37 | End of split
% 159.69/28.37 |
% 159.69/28.37 End of proof
% 159.69/28.37
% 159.69/28.37 Sub-proof #710 shows that the following formulas are inconsistent:
% 159.69/28.37 ----------------------------------------------------------------
% 159.69/28.37 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.37 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.37 (2) op(e1, e1) = all_6_2
% 159.69/28.37 (3) all_58_7 = e2
% 159.69/28.37 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.69/28.37 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.69/28.37 (5) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.37 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.37 (6) op(e2, e3) = all_52_1
% 159.69/28.37 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.69/28.37 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.69/28.37 (8) ~ (e3 = e0)
% 159.69/28.37 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.37 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.37 (10) ~ (e2 = e0)
% 159.69/28.37 (11) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.37 (12) op(e2, e3) = e2
% 159.69/28.37 (13) ~ (e3 = e1)
% 159.69/28.37 (14) all_58_8 = e3 & op(e1, e1) = e3
% 159.69/28.37 (15) op(e1, e2) = all_52_6
% 159.69/28.37 (16) ~ (e2 = e1)
% 159.69/28.37 (17) ~ (e1 = e0)
% 159.69/28.37 (18) ~ (all_6_2 = e2)
% 159.69/28.37 (19) op(e1, e0) = e3
% 159.69/28.37 (20) ~ (all_52_6 = e3)
% 159.69/28.37 (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.69/28.37 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.69/28.37 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.37 (23) ~ (e3 = e2)
% 159.69/28.37 (24) all_58_11 = e3
% 159.69/28.37
% 159.69/28.37 Begin of proof
% 159.69/28.37 |
% 159.69/28.37 | ALPHA: (14) implies:
% 159.69/28.37 | (25) all_58_8 = e3
% 159.69/28.37 |
% 159.69/28.37 | BETA: splitting (11) gives:
% 159.69/28.37 |
% 159.69/28.37 | Case 1:
% 159.69/28.37 | |
% 159.69/28.37 | | (26) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 159.69/28.37 | | e0)
% 159.69/28.37 | |
% 159.69/28.37 | | BETA: splitting (26) gives:
% 159.69/28.37 | |
% 159.69/28.37 | | Case 1:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (27) all_58_6 = e0 & op(e1, e3) = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | ALPHA: (27) implies:
% 159.69/28.37 | | | (28) all_58_6 = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | BETA: splitting (1) gives:
% 159.69/28.37 | | |
% 159.69/28.37 | | | Case 1:
% 159.69/28.37 | | | |
% 159.69/28.37 | | | | (29) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 159.69/28.37 | | | | = e1)
% 159.69/28.37 | | | |
% 159.69/28.37 | | | | BETA: splitting (29) gives:
% 159.69/28.37 | | | |
% 159.69/28.37 | | | | Case 1:
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | (30) all_58_6 = e1 & op(e1, e3) = e1
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | REF_CLOSE: (17), (28), (30) are inconsistent by sub-proof #1064.
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | Case 2:
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | (31) all_58_7 = e1 & op(e1, e2) = e1
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | ALPHA: (31) implies:
% 159.69/28.37 | | | | | (32) all_58_7 = e1
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | BETA: splitting (7) gives:
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | Case 1:
% 159.69/28.37 | | | | | |
% 159.69/28.37 | | | | | | (33) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 159.69/28.37 | | | | | | e2) = e2)
% 159.69/28.37 | | | | | |
% 159.69/28.37 | | | | | | REF_CLOSE: (4), (6), (8), (9), (10), (12), (13), (16), (17), (21),
% 159.69/28.37 | | | | | | (22), (23), (32), (33) are inconsistent by sub-proof
% 159.69/28.37 | | | | | | #720.
% 159.69/28.37 | | | | | |
% 159.69/28.37 | | | | | Case 2:
% 159.69/28.37 | | | | | |
% 159.69/28.37 | | | | | | (34) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 159.69/28.37 | | | | | | e0) = e2)
% 159.69/28.37 | | | | | |
% 159.69/28.37 | | | | | | BETA: splitting (34) gives:
% 159.69/28.37 | | | | | |
% 159.69/28.37 | | | | | | Case 1:
% 159.69/28.37 | | | | | | |
% 159.69/28.37 | | | | | | | (35) all_58_8 = e2 & op(e1, e1) = e2
% 159.69/28.37 | | | | | | |
% 159.69/28.37 | | | | | | | REF_CLOSE: (2), (18), (22), (35) are inconsistent by sub-proof
% 159.69/28.37 | | | | | | | #1440.
% 159.69/28.37 | | | | | | |
% 159.69/28.37 | | | | | | Case 2:
% 159.69/28.37 | | | | | | |
% 159.69/28.37 | | | | | | | (36) all_58_11 = e2 & op(e1, e0) = e2
% 159.69/28.37 | | | | | | |
% 159.69/28.37 | | | | | | | REF_CLOSE: (1), (5), (8), (10), (11), (13), (15), (16), (17),
% 159.69/28.37 | | | | | | | (20), (22), (23), (24), (25), (36) are inconsistent by
% 159.69/28.37 | | | | | | | sub-proof #711.
% 159.69/28.37 | | | | | | |
% 159.69/28.37 | | | | | | End of split
% 159.69/28.37 | | | | | |
% 159.69/28.37 | | | | | End of split
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | End of split
% 159.69/28.37 | | | |
% 159.69/28.37 | | | Case 2:
% 159.69/28.37 | | | |
% 159.69/28.37 | | | | (37) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 159.69/28.37 | | | | = e1)
% 159.69/28.37 | | | |
% 159.69/28.37 | | | | BETA: splitting (37) gives:
% 159.69/28.37 | | | |
% 159.69/28.37 | | | | Case 1:
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | (38) all_58_8 = e1 & op(e1, e1) = e1
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | ALPHA: (38) implies:
% 159.69/28.37 | | | | | (39) all_58_8 = e1
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | REF_CLOSE: (13), (25), (39) are inconsistent by sub-proof #950.
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | Case 2:
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | (40) all_58_11 = e1 & op(e1, e0) = e1
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | ALPHA: (40) implies:
% 159.69/28.37 | | | | | (41) op(e1, e0) = e1
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | | REF_CLOSE: (13), (19), (22), (41) are inconsistent by sub-proof #1275.
% 159.69/28.37 | | | | |
% 159.69/28.37 | | | | End of split
% 159.69/28.37 | | | |
% 159.69/28.37 | | | End of split
% 159.69/28.37 | | |
% 159.69/28.37 | | Case 2:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (42) all_58_7 = e0 & op(e1, e2) = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | ALPHA: (42) implies:
% 159.69/28.37 | | | (43) all_58_7 = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (3), (10), (43) are inconsistent by sub-proof #1086.
% 159.69/28.37 | | |
% 159.69/28.37 | | End of split
% 159.69/28.37 | |
% 159.69/28.37 | Case 2:
% 159.69/28.37 | |
% 159.69/28.37 | | (44) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.69/28.37 | | e0)
% 159.69/28.37 | |
% 159.69/28.37 | | BETA: splitting (44) gives:
% 159.69/28.37 | |
% 159.69/28.37 | | Case 1:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (45) all_58_8 = e0 & op(e1, e1) = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | ALPHA: (45) implies:
% 159.69/28.37 | | | (46) all_58_8 = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (8), (25), (46) are inconsistent by sub-proof #781.
% 159.69/28.37 | | |
% 159.69/28.37 | | Case 2:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (47) all_58_11 = e0 & op(e1, e0) = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (8), (24), (47) are inconsistent by sub-proof #1083.
% 159.69/28.37 | | |
% 159.69/28.37 | | End of split
% 159.69/28.37 | |
% 159.69/28.37 | End of split
% 159.69/28.37 |
% 159.69/28.37 End of proof
% 159.69/28.37
% 159.69/28.37 Sub-proof #711 shows that the following formulas are inconsistent:
% 159.69/28.37 ----------------------------------------------------------------
% 159.69/28.37 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.69/28.37 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.69/28.37 (2) all_58_8 = e3
% 159.69/28.37 (3) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 159.69/28.37 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 159.69/28.37 (4) ~ (e3 = e0)
% 159.69/28.37 (5) ~ (e2 = e0)
% 159.69/28.37 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.37 (7) ~ (e3 = e1)
% 159.69/28.37 (8) op(e1, e2) = all_52_6
% 159.69/28.37 (9) ~ (e2 = e1)
% 159.69/28.37 (10) ~ (e1 = e0)
% 159.69/28.37 (11) ~ (all_52_6 = e3)
% 159.69/28.37 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.37 (13) ~ (e3 = e2)
% 159.69/28.37 (14) all_58_11 = e2 & op(e1, e0) = e2
% 159.69/28.37 (15) all_58_11 = e3
% 159.69/28.37
% 159.69/28.37 Begin of proof
% 159.69/28.37 |
% 159.69/28.37 | ALPHA: (14) implies:
% 159.69/28.37 | (16) all_58_11 = e2
% 159.69/28.37 |
% 159.69/28.37 | COMBINE_EQS: (15), (16) imply:
% 159.69/28.37 | (17) e3 = e2
% 159.69/28.37 |
% 159.69/28.37 | COMBINE_EQS: (2), (17) imply:
% 159.69/28.37 | (18) all_58_8 = e2
% 159.69/28.37 |
% 159.69/28.37 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 159.69/28.37 | (16), (18) are inconsistent by sub-proof #1068.
% 159.69/28.37 |
% 159.69/28.37 End of proof
% 159.69/28.37
% 159.69/28.37 Sub-proof #712 shows that the following formulas are inconsistent:
% 159.69/28.37 ----------------------------------------------------------------
% 159.69/28.37 (1) all_58_12 = e3
% 159.69/28.37 (2) all_58_7 = e2
% 159.69/28.37 (3) all_58_14 = e2
% 159.69/28.37 (4) ~ (e3 = e0)
% 159.69/28.37 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.37 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.37 (6) ~ (e2 = e0)
% 159.69/28.37 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.37 (8) op(e2, e3) = e2
% 159.69/28.37 (9) ~ (e3 = e1)
% 159.69/28.37 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.69/28.37 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 159.69/28.37 (11) all_58_10 = e1
% 159.69/28.37 (12) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.37 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.37 (13) ~ (e2 = e1)
% 159.69/28.37 (14) ~ (e1 = e0)
% 159.69/28.37 (15) all_58_4 = e3
% 159.69/28.37 (16) all_58_3 = e3
% 159.69/28.37 (17) all_58_0 = e0
% 159.69/28.37 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.37 (19) all_58_11 = e3
% 159.69/28.37
% 159.69/28.37 Begin of proof
% 159.69/28.37 |
% 159.69/28.37 | BETA: splitting (10) gives:
% 159.69/28.37 |
% 159.69/28.37 | Case 1:
% 159.69/28.37 | |
% 159.69/28.37 | | (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 159.69/28.37 | | e0)
% 159.69/28.37 | |
% 159.69/28.37 | | REF_CLOSE: (4), (6), (8), (16), (18), (20) are inconsistent by sub-proof
% 159.69/28.37 | | #909.
% 159.69/28.37 | |
% 159.69/28.37 | Case 2:
% 159.69/28.37 | |
% 159.69/28.37 | | (21) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 159.69/28.37 | | e0)
% 159.69/28.37 | |
% 159.69/28.37 | | BETA: splitting (21) gives:
% 159.69/28.37 | |
% 159.69/28.37 | | Case 1:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (22) all_58_5 = e0 & op(e2, e1) = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | ALPHA: (22) implies:
% 159.69/28.37 | | | (23) all_58_5 = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 159.69/28.37 | | | (15), (17), (18), (19), (23) are inconsistent by sub-proof
% 159.69/28.37 | | | #713.
% 159.69/28.37 | | |
% 159.69/28.37 | | Case 2:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (24) all_58_10 = e0 & op(e2, e0) = e0
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (11), (14), (24) are inconsistent by sub-proof #1459.
% 159.69/28.37 | | |
% 159.69/28.37 | | End of split
% 159.69/28.37 | |
% 159.69/28.37 | End of split
% 159.69/28.37 |
% 159.69/28.37 End of proof
% 159.69/28.37
% 159.69/28.37 Sub-proof #713 shows that the following formulas are inconsistent:
% 159.69/28.37 ----------------------------------------------------------------
% 159.69/28.37 (1) all_58_12 = e3
% 159.69/28.37 (2) all_58_7 = e2
% 159.69/28.37 (3) all_58_14 = e2
% 159.69/28.37 (4) ~ (e3 = e0)
% 159.69/28.37 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.69/28.37 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.69/28.37 (6) ~ (e2 = e0)
% 159.69/28.37 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.69/28.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.69/28.37 (8) op(e2, e3) = e2
% 159.69/28.37 (9) ~ (e3 = e1)
% 159.69/28.37 (10) all_58_5 = e0
% 159.69/28.37 (11) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 159.69/28.37 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 159.69/28.37 (12) ~ (e2 = e1)
% 159.69/28.37 (13) ~ (e1 = e0)
% 159.69/28.37 (14) all_58_4 = e3
% 159.69/28.37 (15) all_58_0 = e0
% 159.69/28.37 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.69/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.69/28.37 (17) all_58_11 = e3
% 159.69/28.37
% 159.69/28.37 Begin of proof
% 159.69/28.37 |
% 159.69/28.37 | BETA: splitting (11) gives:
% 159.69/28.37 |
% 159.69/28.37 | Case 1:
% 159.69/28.37 | |
% 159.69/28.37 | | (18) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 159.69/28.37 | | e1)
% 159.69/28.37 | |
% 159.69/28.37 | | BETA: splitting (18) gives:
% 159.69/28.37 | |
% 159.69/28.37 | | Case 1:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (19) all_58_4 = e1 & op(e3, e1) = e1
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (9), (14), (19) are inconsistent by sub-proof #1345.
% 159.69/28.37 | | |
% 159.69/28.37 | | Case 2:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (20) all_58_5 = e1 & op(e2, e1) = e1
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (10), (13), (20) are inconsistent by sub-proof #1121.
% 159.69/28.37 | | |
% 159.69/28.37 | | End of split
% 159.69/28.37 | |
% 159.69/28.37 | Case 2:
% 159.69/28.37 | |
% 159.69/28.37 | | (21) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 159.69/28.37 | | e1)
% 159.69/28.37 | |
% 159.69/28.37 | | BETA: splitting (21) gives:
% 159.69/28.37 | |
% 159.69/28.37 | | Case 1:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (22) all_58_8 = e1 & op(e1, e1) = e1
% 159.69/28.37 | | |
% 159.69/28.37 | | | ALPHA: (22) implies:
% 159.69/28.37 | | | (23) all_58_8 = e1
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (12), (13), (15), (16),
% 159.69/28.37 | | | (17), (23) are inconsistent by sub-proof #714.
% 159.69/28.37 | | |
% 159.69/28.37 | | Case 2:
% 159.69/28.37 | | |
% 159.69/28.37 | | | (24) all_58_14 = e1 & op(e0, e1) = e1
% 159.69/28.37 | | |
% 159.69/28.37 | | | ALPHA: (24) implies:
% 159.69/28.37 | | | (25) all_58_14 = e1
% 159.69/28.37 | | |
% 159.69/28.37 | | | REF_CLOSE: (3), (12), (25) are inconsistent by sub-proof #1387.
% 159.69/28.37 | | |
% 159.69/28.37 | | End of split
% 159.80/28.37 | |
% 159.80/28.37 | End of split
% 159.80/28.37 |
% 159.80/28.37 End of proof
% 159.80/28.37
% 159.80/28.37 Sub-proof #714 shows that the following formulas are inconsistent:
% 159.80/28.37 ----------------------------------------------------------------
% 159.80/28.37 (1) all_58_12 = e3
% 159.80/28.37 (2) all_58_7 = e2
% 159.80/28.37 (3) ~ (e3 = e0)
% 159.80/28.37 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.80/28.37 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.80/28.37 (5) ~ (e2 = e0)
% 159.80/28.37 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 159.80/28.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 159.80/28.37 (7) op(e2, e3) = e2
% 159.80/28.37 (8) ~ (e3 = e1)
% 159.80/28.37 (9) ~ (e2 = e1)
% 159.80/28.37 (10) ~ (e1 = e0)
% 159.80/28.37 (11) all_58_0 = e0
% 159.80/28.37 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.80/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.80/28.37 (13) all_58_11 = e3
% 159.80/28.37 (14) all_58_8 = e1
% 159.80/28.37
% 159.80/28.37 Begin of proof
% 159.80/28.37 |
% 159.80/28.37 | BETA: splitting (6) gives:
% 159.80/28.37 |
% 159.80/28.37 | Case 1:
% 159.80/28.37 | |
% 159.80/28.37 | | (15) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 159.80/28.37 | | e0)
% 159.80/28.37 | |
% 159.80/28.37 | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (15) are
% 159.80/28.37 | | inconsistent by sub-proof #715.
% 159.80/28.37 | |
% 159.80/28.37 | Case 2:
% 159.80/28.37 | |
% 159.80/28.37 | | (16) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 159.80/28.37 | | e0)
% 159.80/28.37 | |
% 159.80/28.37 | | BETA: splitting (16) gives:
% 159.80/28.37 | |
% 159.80/28.37 | | Case 1:
% 159.80/28.37 | | |
% 159.80/28.37 | | | (17) all_58_8 = e0 & op(e1, e1) = e0
% 159.80/28.37 | | |
% 159.80/28.37 | | | REF_CLOSE: (10), (14), (17) are inconsistent by sub-proof #1271.
% 159.80/28.37 | | |
% 159.80/28.37 | | Case 2:
% 159.80/28.37 | | |
% 159.80/28.37 | | | (18) all_58_11 = e0 & op(e1, e0) = e0
% 159.80/28.37 | | |
% 159.80/28.37 | | | REF_CLOSE: (3), (13), (18) are inconsistent by sub-proof #1083.
% 159.80/28.37 | | |
% 159.80/28.37 | | End of split
% 159.80/28.37 | |
% 159.80/28.37 | End of split
% 159.80/28.37 |
% 159.80/28.37 End of proof
% 159.80/28.37
% 159.80/28.37 Sub-proof #715 shows that the following formulas are inconsistent:
% 159.80/28.37 ----------------------------------------------------------------
% 159.80/28.37 (1) all_58_12 = e3
% 159.80/28.37 (2) all_58_7 = e2
% 159.80/28.37 (3) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.80/28.37 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.80/28.37 (4) ~ (e2 = e0)
% 159.80/28.37 (5) op(e2, e3) = e2
% 159.80/28.37 (6) ~ (e3 = e1)
% 159.80/28.37 (7) ~ (e2 = e1)
% 159.80/28.37 (8) ~ (e1 = e0)
% 159.80/28.37 (9) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 159.80/28.37 (10) all_58_0 = e0
% 159.80/28.37 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.80/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.80/28.37
% 159.80/28.37 Begin of proof
% 159.80/28.37 |
% 159.80/28.37 | BETA: splitting (9) gives:
% 159.80/28.37 |
% 159.80/28.37 | Case 1:
% 159.80/28.37 | |
% 159.80/28.37 | | (12) all_58_6 = e0 & op(e1, e3) = e0
% 159.80/28.37 | |
% 159.80/28.37 | | ALPHA: (12) implies:
% 159.80/28.37 | | (13) all_58_6 = e0
% 159.80/28.37 | |
% 159.80/28.37 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10), (11), (13) are inconsistent
% 159.80/28.37 | | by sub-proof #733.
% 159.80/28.37 | |
% 159.80/28.37 | Case 2:
% 159.80/28.37 | |
% 159.80/28.37 | | (14) all_58_7 = e0 & op(e1, e2) = e0
% 159.80/28.37 | |
% 159.80/28.37 | | ALPHA: (14) implies:
% 159.80/28.37 | | (15) all_58_7 = e0
% 159.80/28.37 | |
% 159.80/28.37 | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #1086.
% 159.80/28.37 | |
% 159.80/28.37 | End of split
% 159.80/28.37 |
% 159.80/28.37 End of proof
% 159.80/28.37
% 159.80/28.37 Sub-proof #716 shows that the following formulas are inconsistent:
% 159.80/28.37 ----------------------------------------------------------------
% 159.80/28.37 (1) op(e1, e1) = all_6_2
% 159.80/28.37 (2) all_58_12 = e3
% 159.80/28.37 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.80/28.37 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.80/28.37 (4) op(e2, e3) = all_52_1
% 159.80/28.37 (5) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 159.80/28.37 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 159.80/28.37 (6) ~ (e3 = e0)
% 159.80/28.37 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.80/28.37 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.80/28.37 (8) ~ (e2 = e0)
% 159.80/28.37 (9) op(e2, e3) = e2
% 159.80/28.37 (10) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 159.80/28.37 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 159.80/28.37 (11) ~ (e3 = e1)
% 159.80/28.37 (12) all_58_1 = e1
% 159.80/28.37 (13) all_58_13 = e2 & op(e0, e2) = e2
% 159.80/28.37 (14) ~ (e2 = e1)
% 159.80/28.37 (15) ~ (e1 = e0)
% 159.80/28.37 (16) all_58_3 = e3
% 159.80/28.37 (17) ~ (all_6_2 = e2)
% 159.80/28.37 (18) op(e0, e2) = all_52_7
% 159.80/28.37 (19) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.80/28.37 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.80/28.37 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.80/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.80/28.37 (21) ~ (e3 = e2)
% 159.80/28.37 (22) all_58_11 = e3
% 159.80/28.37
% 159.80/28.37 Begin of proof
% 159.80/28.37 |
% 159.80/28.37 | ALPHA: (13) implies:
% 159.80/28.37 | (23) op(e0, e2) = e2
% 159.80/28.37 |
% 159.80/28.37 | BETA: splitting (10) gives:
% 159.80/28.37 |
% 159.80/28.37 | Case 1:
% 159.80/28.37 | |
% 159.80/28.37 | | (24) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 159.80/28.37 | | e0)
% 159.80/28.37 | |
% 159.80/28.37 | | BETA: splitting (24) gives:
% 159.80/28.37 | |
% 159.80/28.37 | | Case 1:
% 159.80/28.37 | | |
% 159.80/28.37 | | | (25) all_58_1 = e0 & op(e3, e2) = e0
% 159.80/28.37 | | |
% 159.80/28.37 | | | REF_CLOSE: (12), (15), (25) are inconsistent by sub-proof #1327.
% 159.80/28.37 | | |
% 159.80/28.37 | | Case 2:
% 159.80/28.37 | | |
% 159.80/28.37 | | | (26) all_58_3 = e0 & op(e2, e2) = e0
% 159.80/28.37 | | |
% 159.80/28.37 | | | REF_CLOSE: (6), (16), (26) are inconsistent by sub-proof #756.
% 159.80/28.37 | | |
% 159.80/28.37 | | End of split
% 159.80/28.37 | |
% 159.80/28.37 | Case 2:
% 159.80/28.37 | |
% 159.80/28.37 | | (27) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 159.80/28.37 | | e0)
% 159.80/28.37 | |
% 159.80/28.37 | | BETA: splitting (27) gives:
% 159.80/28.37 | |
% 159.80/28.37 | | Case 1:
% 159.80/28.37 | | |
% 159.80/28.37 | | | (28) all_58_7 = e0 & op(e1, e2) = e0
% 159.80/28.37 | | |
% 159.80/28.37 | | | ALPHA: (28) implies:
% 159.80/28.37 | | | (29) all_58_7 = e0
% 159.80/28.37 | | |
% 159.80/28.37 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (14), (15),
% 159.80/28.37 | | | (17), (19), (20), (21), (22), (29) are inconsistent by
% 159.80/28.37 | | | sub-proof #731.
% 159.80/28.37 | | |
% 159.80/28.37 | | Case 2:
% 159.80/28.37 | | |
% 159.80/28.37 | | | (30) all_58_13 = e0 & op(e0, e2) = e0
% 159.80/28.37 | | |
% 159.80/28.37 | | | ALPHA: (30) implies:
% 159.80/28.37 | | | (31) op(e0, e2) = e0
% 159.80/28.37 | | |
% 159.80/28.37 | | | REF_CLOSE: (8), (18), (20), (23), (31) are inconsistent by sub-proof
% 159.80/28.37 | | | #1040.
% 159.80/28.37 | | |
% 159.80/28.37 | | End of split
% 159.80/28.37 | |
% 159.80/28.37 | End of split
% 159.80/28.37 |
% 159.80/28.37 End of proof
% 159.80/28.37
% 159.80/28.37 Sub-proof #717 shows that the following formulas are inconsistent:
% 159.80/28.37 ----------------------------------------------------------------
% 159.80/28.37 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 159.80/28.37 (2) op(e2, e3) = all_52_1
% 159.80/28.37 (3) ~ (e3 = e0)
% 159.80/28.37 (4) op(e3, e3) = e0
% 159.80/28.37 (5) op(e2, e3) = e2
% 159.80/28.37 (6) op(e3, e3) = all_22_1
% 159.80/28.37 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.80/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.80/28.37 (8) ~ (e3 = e2)
% 159.80/28.37
% 159.80/28.37 Begin of proof
% 159.80/28.37 |
% 159.80/28.37 | BETA: splitting (1) gives:
% 159.80/28.37 |
% 159.80/28.37 | Case 1:
% 159.80/28.37 | |
% 159.80/28.37 | | (9) all_58_0 = e3 & op(e3, e3) = e3
% 159.80/28.37 | |
% 159.80/28.37 | | ALPHA: (9) implies:
% 159.80/28.37 | | (10) op(e3, e3) = e3
% 159.80/28.37 | |
% 159.80/28.37 | | REF_CLOSE: (3), (4), (6), (7), (10) are inconsistent by sub-proof #866.
% 159.80/28.37 | |
% 159.80/28.37 | Case 2:
% 159.80/28.37 | |
% 159.80/28.37 | | (11) all_58_2 = e3 & op(e2, e3) = e3
% 159.80/28.37 | |
% 159.80/28.37 | | ALPHA: (11) implies:
% 159.80/28.37 | | (12) op(e2, e3) = e3
% 159.80/28.37 | |
% 159.80/28.37 | | REF_CLOSE: (2), (5), (7), (8), (12) are inconsistent by sub-proof #1159.
% 159.80/28.37 | |
% 159.80/28.37 | End of split
% 159.80/28.37 |
% 159.80/28.37 End of proof
% 159.80/28.37
% 159.80/28.37 Sub-proof #718 shows that the following formulas are inconsistent:
% 159.80/28.37 ----------------------------------------------------------------
% 159.80/28.37 (1) all_58_6 = e1
% 159.80/28.37 (2) ~ (e3 = e1)
% 159.80/28.37 (3) op(e1, e2) = all_52_6
% 159.80/28.37 (4) ~ (all_52_6 = e3)
% 159.80/28.37 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.80/28.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.80/28.37 (6) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 159.80/28.37
% 159.80/28.37 Begin of proof
% 159.80/28.37 |
% 159.80/28.37 | BETA: splitting (6) gives:
% 159.80/28.37 |
% 159.80/28.37 | Case 1:
% 159.80/28.37 | |
% 159.80/28.37 | | (7) all_58_6 = e3 & op(e1, e3) = e3
% 159.80/28.37 | |
% 159.80/28.37 | | ALPHA: (7) implies:
% 159.80/28.37 | | (8) all_58_6 = e3
% 159.80/28.37 | |
% 159.80/28.37 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #1073.
% 159.80/28.37 | |
% 159.80/28.37 | Case 2:
% 159.80/28.37 | |
% 159.80/28.37 | | (9) all_58_7 = e3 & op(e1, e2) = e3
% 159.80/28.37 | |
% 159.80/28.37 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1184.
% 159.80/28.37 | |
% 159.80/28.37 | End of split
% 159.80/28.37 |
% 159.80/28.37 End of proof
% 159.80/28.37
% 159.80/28.37 Sub-proof #719 shows that the following formulas are inconsistent:
% 159.80/28.37 ----------------------------------------------------------------
% 159.80/28.37 (1) all_58_3 = e2 & op(e2, e2) = e2
% 159.80/28.37 (2) all_58_3 = e3
% 159.80/28.37 (3) ~ (e3 = e2)
% 159.80/28.37
% 159.80/28.37 Begin of proof
% 159.80/28.37 |
% 159.80/28.37 | ALPHA: (1) implies:
% 159.80/28.37 | (4) all_58_3 = e2
% 159.80/28.37 |
% 159.80/28.37 | COMBINE_EQS: (2), (4) imply:
% 159.80/28.37 | (5) e3 = e2
% 159.80/28.37 |
% 159.80/28.37 | REDUCE: (3), (5) imply:
% 159.80/28.37 | (6) $false
% 159.80/28.37 |
% 159.80/28.37 | CLOSE: (6) is inconsistent.
% 159.80/28.37 |
% 159.80/28.37 End of proof
% 159.80/28.37
% 159.80/28.37 Sub-proof #720 shows that the following formulas are inconsistent:
% 159.80/28.37 ----------------------------------------------------------------
% 159.80/28.38 (1) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 159.80/28.38 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 159.80/28.38 (2) op(e2, e3) = all_52_1
% 159.80/28.38 (3) ~ (e3 = e0)
% 159.80/28.38 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 159.80/28.38 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 159.80/28.38 (5) ~ (e2 = e0)
% 159.80/28.38 (6) op(e2, e3) = e2
% 159.80/28.38 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 159.80/28.38 (8) ~ (e3 = e1)
% 159.80/28.38 (9) all_58_7 = e1
% 159.80/28.38 (10) ~ (e2 = e1)
% 159.80/28.38 (11) ~ (e1 = e0)
% 159.80/28.38 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 159.80/28.38 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 159.80/28.38 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.80/28.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 159.80/28.38 (14) ~ (e3 = e2)
% 159.80/28.38
% 159.80/28.38 Begin of proof
% 159.80/28.38 |
% 159.80/28.38 | BETA: splitting (7) gives:
% 159.80/28.38 |
% 159.80/28.38 | Case 1:
% 159.80/28.38 | |
% 159.80/28.38 | | (15) all_58_6 = e2 & op(e1, e3) = e2
% 159.80/28.38 | |
% 159.80/28.38 | | ALPHA: (15) implies:
% 159.80/28.38 | | (16) all_58_6 = e2
% 159.80/28.38 | |
% 159.80/28.38 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 159.80/28.38 | | (16) are inconsistent by sub-proof #1152.
% 159.80/28.38 | |
% 159.80/28.38 | Case 2:
% 159.80/28.38 | |
% 159.80/28.38 | | (17) all_58_7 = e2 & op(e1, e2) = e2
% 159.80/28.38 | |
% 159.80/28.38 | | ALPHA: (17) implies:
% 159.80/28.38 | | (18) all_58_7 = e2
% 159.80/28.38 | |
% 159.80/28.38 | | REF_CLOSE: (9), (10), (18) are inconsistent by sub-proof #721.
% 159.80/28.38 | |
% 159.80/28.38 | End of split
% 159.80/28.38 |
% 159.80/28.38 End of proof
% 159.80/28.38
% 159.80/28.38 Sub-proof #721 shows that the following formulas are inconsistent:
% 159.80/28.38 ----------------------------------------------------------------
% 159.80/28.38 (1) all_58_7 = e2
% 159.80/28.38 (2) all_58_7 = e1
% 159.80/28.38 (3) ~ (e2 = e1)
% 159.80/28.38
% 159.80/28.38 Begin of proof
% 159.80/28.38 |
% 159.80/28.38 | COMBINE_EQS: (1), (2) imply:
% 159.80/28.38 | (4) e2 = e1
% 159.80/28.38 |
% 159.80/28.38 | SIMP: (4) implies:
% 159.80/28.38 | (5) e2 = e1
% 159.80/28.38 |
% 159.80/28.38 | REDUCE: (3), (5) imply:
% 159.80/28.38 | (6) $false
% 159.80/28.38 |
% 159.80/28.38 | CLOSE: (6) is inconsistent.
% 159.80/28.38 |
% 159.80/28.38 End of proof
% 159.80/28.38
% 159.80/28.38 Sub-proof #722 shows that the following formulas are inconsistent:
% 159.80/28.38 ----------------------------------------------------------------
% 159.80/28.38 (1) op(e3, e1) = e3
% 159.80/28.38 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 159.80/28.38 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 159.80/28.38 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 159.80/28.38 (all_58_7 = e1 &